Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
This branch proves the finite determinant/rank/span substrate. It does not claim Smith or Hermite normal form, lattice index equals determinant, determinant multiplicativity, lattice reduction, or geometry-of-numbers theorems.
Exact theorem in conservative defined notation
∀ ab. ∀ ac. ∀ bb. ∀ bc. ∀ d. ∀ D. ∀ E. PositiveDeterminantMatrixData(ab,ac,bb,bc,d,D) → PositiveDeterminantMatrixData(ab,ac,bb,bc,d,E) → D = EEvery linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Original expanded first-order statement
forall ab ac bb bc d D E. (((~(d = 0)) /\ ((~(D = 0)) /\ (exists mdr_p_first_positive_dataabsolute mdr_n_first_positive_dataabsolute. ((exists mdr_b_first_positive_dataabsoluteevaluation mdr_c_first_positive_dataabsoluteevaluation mdr_l_first_positive_dataabsoluteevaluation mdr_i_first_positive_dataabsoluteevaluation. ((forall mdr_i_first_positive_dataabsoluteevaluationh. (exists mdr_gap_first_positive_dataabsoluteevaluationhi. mdr_gap_first_positive_dataabsoluteevaluationhi + S (mdr_i_first_positive_dataabsoluteevaluationh) = (mdr_l_first_positive_dataabsoluteevaluation)) -> exists mdr_d_first_positive_dataabsoluteevaluationh mdr_pb_first_positive_dataabsoluteevaluationh mdr_pc_first_positive_dataabsoluteevaluationh mdr_nb_first_positive_dataabsoluteevaluationh mdr_nc_first_positive_dataabsoluteevaluationh mdr_p_first_positive_dataabsoluteevaluationh mdr_n_first_positive_dataabsoluteevaluationh. ((exists mdr_z_first_positive_dataabsoluteevaluationhr. ((exists mdr_a_first_positive_dataabsoluteevaluationhrc mdr_b_first_positive_dataabsoluteevaluationhrc mdr_c_first_positive_dataabsoluteevaluationhrc mdr_e_first_positive_dataabsoluteevaluationhrc mdr_f_first_positive_dataabsoluteevaluationhrc. ((mdr_a_first_positive_dataabsoluteevaluationhrc = ((mdr_d_first_positive_dataabsoluteevaluationh) + (mdr_pb_first_positive_dataabsoluteevaluationh)) * S ((mdr_d_first_positive_dataabsoluteevaluationh) + (mdr_pb_first_positive_dataabsoluteevaluationh)) + ((mdr_pb_first_positive_dataabsoluteevaluationh) + (mdr_pb_first_positive_dataabsoluteevaluationh))) /\ ((mdr_b_first_positive_dataabsoluteevaluationhrc = ((mdr_pc_first_positive_dataabsoluteevaluationh) + (mdr_nb_first_positive_dataabsoluteevaluationh)) * S ((mdr_pc_first_positive_dataabsoluteevaluationh) + (mdr_nb_first_positive_dataabsoluteevaluationh)) + ((mdr_nb_first_positive_dataabsoluteevaluationh) + (mdr_nb_first_positive_dataabsoluteevaluationh))) /\ ((mdr_c_first_positive_dataabsoluteevaluationhrc = ((mdr_a_first_positive_dataabsoluteevaluationhrc) + (mdr_b_first_positive_dataabsoluteevaluationhrc)) * S ((mdr_a_first_positive_dataabsoluteevaluationhrc) + (mdr_b_first_positive_dataabsoluteevaluationhrc)) + ((mdr_b_first_positive_dataabsoluteevaluationhrc) + (mdr_b_first_positive_dataabsoluteevaluationhrc))) /\ ((mdr_e_first_positive_dataabsoluteevaluationhrc = ((mdr_p_first_positive_dataabsoluteevaluationh) + (mdr_n_first_positive_dataabsoluteevaluationh)) * S ((mdr_p_first_positive_dataabsoluteevaluationh) + (mdr_n_first_positive_dataabsoluteevaluationh)) + ((mdr_n_first_positive_dataabsoluteevaluationh) + (mdr_n_first_positive_dataabsoluteevaluationh))) /\ ((mdr_f_first_positive_dataabsoluteevaluationhrc = ((mdr_nc_first_positive_dataabsoluteevaluationh) + (mdr_e_first_positive_dataabsoluteevaluationhrc)) * S ((mdr_nc_first_positive_dataabsoluteevaluationh) + (mdr_e_first_positive_dataabsoluteevaluationhrc)) + ((mdr_e_first_positive_dataabsoluteevaluationhrc) + (mdr_e_first_positive_dataabsoluteevaluationhrc))) /\ ((mdr_z_first_positive_dataabsoluteevaluationhr) = ((mdr_c_first_positive_dataabsoluteevaluationhrc) + (mdr_f_first_positive_dataabsoluteevaluationhrc)) * S ((mdr_c_first_positive_dataabsoluteevaluationhrc) + (mdr_f_first_positive_dataabsoluteevaluationhrc)) + ((mdr_f_first_positive_dataabsoluteevaluationhrc) + (mdr_f_first_positive_dataabsoluteevaluationhrc))))))))) /\ (((exists ff_h_mdr_first_positive_dataabsoluteevaluationhrb. ff_h_mdr_first_positive_dataabsoluteevaluationhrb + S (mdr_z_first_positive_dataabsoluteevaluationhr) = S ((S (mdr_i_first_positive_dataabsoluteevaluationh)) * mdr_c_first_positive_dataabsoluteevaluation)) /\ exists ff_q_mdr_first_positive_dataabsoluteevaluationhrb. mdr_b_first_positive_dataabsoluteevaluation = ff_q_mdr_first_positive_dataabsoluteevaluationhrb * S ((S (mdr_i_first_positive_dataabsoluteevaluationh)) * mdr_c_first_positive_dataabsoluteevaluation) + (mdr_z_first_positive_dataabsoluteevaluationhr))))) /\ (((((mdr_d_first_positive_dataabsoluteevaluationh) = 0) /\ (((mdr_p_first_positive_dataabsoluteevaluationh) = 1) /\ ((mdr_n_first_positive_dataabsoluteevaluationh) = 0))) \/ exists mdr_q_first_positive_dataabsoluteevaluationhs mdr_eb_first_positive_dataabsoluteevaluationhs mdr_ec_first_positive_dataabsoluteevaluationhs mdr_fb_first_positive_dataabsoluteevaluationhs mdr_fc_first_positive_dataabsoluteevaluationhs. (((mdr_d_first_positive_dataabsoluteevaluationh) = S (mdr_q_first_positive_dataabsoluteevaluationhs)) /\ ((forall mdr_j_first_positive_dataabsoluteevaluationhsc. (exists mdr_gap_first_positive_dataabsoluteevaluationhscj. mdr_gap_first_positive_dataabsoluteevaluationhscj + S (mdr_j_first_positive_dataabsoluteevaluationhsc) = (S (mdr_q_first_positive_dataabsoluteevaluationhs))) -> exists mdr_i_first_positive_dataabsoluteevaluationhsc mdr_up_first_positive_dataabsoluteevaluationhsc mdr_us_first_positive_dataabsoluteevaluationhsc mdr_un_first_positive_dataabsoluteevaluationhsc mdr_ut_first_positive_dataabsoluteevaluationhsc mdr_p_first_positive_dataabsoluteevaluationhsc mdr_n_first_positive_dataabsoluteevaluationhsc. ((exists mdr_gap_first_positive_dataabsoluteevaluationhsci. mdr_gap_first_positive_dataabsoluteevaluationhsci + S (mdr_i_first_positive_dataabsoluteevaluationhsc) = (mdr_i_first_positive_dataabsoluteevaluationh)) /\ ((exists mdr_z_first_positive_dataabsoluteevaluationhscr. ((exists mdr_a_first_positive_dataabsoluteevaluationhscrc mdr_b_first_positive_dataabsoluteevaluationhscrc mdr_c_first_positive_dataabsoluteevaluationhscrc mdr_e_first_positive_dataabsoluteevaluationhscrc mdr_f_first_positive_dataabsoluteevaluationhscrc. ((mdr_a_first_positive_dataabsoluteevaluationhscrc = ((mdr_q_first_positive_dataabsoluteevaluationhs) + (mdr_up_first_positive_dataabsoluteevaluationhsc)) * S ((mdr_q_first_positive_dataabsoluteevaluationhs) + (mdr_up_first_positive_dataabsoluteevaluationhsc)) + ((mdr_up_first_positive_dataabsoluteevaluationhsc) + (mdr_up_first_positive_dataabsoluteevaluationhsc))) /\ ((mdr_b_first_positive_dataabsoluteevaluationhscrc = ((mdr_us_first_positive_dataabsoluteevaluationhsc) + (mdr_un_first_positive_dataabsoluteevaluationhsc)) * S ((mdr_us_first_positive_dataabsoluteevaluationhsc) + (mdr_un_first_positive_dataabsoluteevaluationhsc)) + ((mdr_un_first_positive_dataabsoluteevaluationhsc) + (mdr_un_first_positive_dataabsoluteevaluationhsc))) /\ ((mdr_c_first_positive_dataabsoluteevaluationhscrc = ((mdr_a_first_positive_dataabsoluteevaluationhscrc) + (mdr_b_first_positive_dataabsoluteevaluationhscrc)) * S ((mdr_a_first_positive_dataabsoluteevaluationhscrc) + (mdr_b_first_positive_dataabsoluteevaluationhscrc)) + ((mdr_b_first_positive_dataabsoluteevaluationhscrc) + (mdr_b_first_positive_dataabsoluteevaluationhscrc))) /\ ((mdr_e_first_positive_dataabsoluteevaluationhscrc = ((mdr_p_first_positive_dataabsoluteevaluationhsc) + (mdr_n_first_positive_dataabsoluteevaluationhsc)) * S ((mdr_p_first_positive_dataabsoluteevaluationhsc) + (mdr_n_first_positive_dataabsoluteevaluationhsc)) + ((mdr_n_first_positive_dataabsoluteevaluationhsc) + (mdr_n_first_positive_dataabsoluteevaluationhsc))) /\ ((mdr_f_first_positive_dataabsoluteevaluationhscrc = ((mdr_ut_first_positive_dataabsoluteevaluationhsc) + (mdr_e_first_positive_dataabsoluteevaluationhscrc)) * S ((mdr_ut_first_positive_dataabsoluteevaluationhsc) + (mdr_e_first_positive_dataabsoluteevaluationhscrc)) + ((mdr_e_first_positive_dataabsoluteevaluationhscrc) + (mdr_e_first_positive_dataabsoluteevaluationhscrc))) /\ ((mdr_z_first_positive_dataabsoluteevaluationhscr) = ((mdr_c_first_positive_dataabsoluteevaluationhscrc) + (mdr_f_first_positive_dataabsoluteevaluationhscrc)) * S ((mdr_c_first_positive_dataabsoluteevaluationhscrc) + (mdr_f_first_positive_dataabsoluteevaluationhscrc)) + ((mdr_f_first_positive_dataabsoluteevaluationhscrc) + (mdr_f_first_positive_dataabsoluteevaluationhscrc))))))))) /\ (((exists ff_h_mdr_first_positive_dataabsoluteevaluationhscrb. ff_h_mdr_first_positive_dataabsoluteevaluationhscrb + S (mdr_z_first_positive_dataabsoluteevaluationhscr) = S ((S (mdr_i_first_positive_dataabsoluteevaluationhsc)) * mdr_c_first_positive_dataabsoluteevaluation)) /\ exists ff_q_mdr_first_positive_dataabsoluteevaluationhscrb. mdr_b_first_positive_dataabsoluteevaluation = ff_q_mdr_first_positive_dataabsoluteevaluationhscrb * S ((S (mdr_i_first_positive_dataabsoluteevaluationhsc)) * mdr_c_first_positive_dataabsoluteevaluation) + (mdr_z_first_positive_dataabsoluteevaluationhscr))))) /\ ((((forall ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive. (exists ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_positive_index_bound. ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_positive_index_bound + S (ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive) = ((mdr_q_first_positive_dataabsoluteevaluationhs) * (mdr_q_first_positive_dataabsoluteevaluationhs))) -> exists ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive. (ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive = (mdr_q_first_positive_dataabsoluteevaluationhs) * ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive + ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive /\ ((exists ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_positive_column_bound. ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_positive_column_bound + S (ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive) = (mdr_q_first_positive_dataabsoluteevaluationhs)) /\ ((exists ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell. (((((exists ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_row_before. ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_row_before + S (ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive) = (0)) /\ ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell = ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive) \/ ((exists ff_gap_mdm_le_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_row_after. ff_gap_mdm_le_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_row_after + (0) = (ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive)) /\ ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell = S ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive))) /\ (((((exists ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_column_before. ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_column_before + S (ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive) = (mdr_j_first_positive_dataabsoluteevaluationhsc)) /\ ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell = ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive) \/ ((exists ff_gap_mdm_le_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_column_after. ff_gap_mdm_le_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_column_after + (mdr_j_first_positive_dataabsoluteevaluationhsc) = (ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive)) /\ ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell = S ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive))) /\ (((exists ff_h_mdm_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_source. ff_h_mdm_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_source + S (ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive) = S ((S ((ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell) * (S (mdr_q_first_positive_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell))) * mdr_pc_first_positive_dataabsoluteevaluationh)) /\ exists ff_q_mdm_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_source. mdr_pb_first_positive_dataabsoluteevaluationh = ff_q_mdm_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell_source * S ((S ((ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell) * (S (mdr_q_first_positive_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_positive_cell))) * mdr_pc_first_positive_dataabsoluteevaluationh) + (ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive)))))) /\ (((exists ff_h_mdm_mdr_first_positive_dataabsoluteevaluationhscm_positive_target. ff_h_mdm_mdr_first_positive_dataabsoluteevaluationhscm_positive_target + S (ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive) = S ((S (ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive)) * mdr_us_first_positive_dataabsoluteevaluationhsc)) /\ exists ff_q_mdm_mdr_first_positive_dataabsoluteevaluationhscm_positive_target. mdr_up_first_positive_dataabsoluteevaluationhsc = ff_q_mdm_mdr_first_positive_dataabsoluteevaluationhscm_positive_target * S ((S (ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive)) * mdr_us_first_positive_dataabsoluteevaluationhsc) + (ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_positive))))))) /\ (forall ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative. (exists ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_negative_index_bound. ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_negative_index_bound + S (ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative) = ((mdr_q_first_positive_dataabsoluteevaluationhs) * (mdr_q_first_positive_dataabsoluteevaluationhs))) -> exists ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative. (ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative = (mdr_q_first_positive_dataabsoluteevaluationhs) * ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative + ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative /\ ((exists ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_negative_column_bound. ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_negative_column_bound + S (ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative) = (mdr_q_first_positive_dataabsoluteevaluationhs)) /\ ((exists ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell. (((((exists ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_row_before. ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_row_before + S (ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative) = (0)) /\ ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell = ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative) \/ ((exists ff_gap_mdm_le_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_row_after. ff_gap_mdm_le_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_row_after + (0) = (ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative)) /\ ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell = S ff_row_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative))) /\ (((((exists ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_column_before. ff_gap_mdm_lt_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_column_before + S (ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative) = (mdr_j_first_positive_dataabsoluteevaluationhsc)) /\ ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell = ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative) \/ ((exists ff_gap_mdm_le_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_column_after. ff_gap_mdm_le_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_column_after + (mdr_j_first_positive_dataabsoluteevaluationhsc) = (ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative)) /\ ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell = S ff_column_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative))) /\ (((exists ff_h_mdm_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_source. ff_h_mdm_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_source + S (ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative) = S ((S ((ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell) * (S (mdr_q_first_positive_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell))) * mdr_nc_first_positive_dataabsoluteevaluationh)) /\ exists ff_q_mdm_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_source. mdr_nb_first_positive_dataabsoluteevaluationh = ff_q_mdm_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell_source * S ((S ((ff_row_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell) * (S (mdr_q_first_positive_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_first_positive_dataabsoluteevaluationhscm_negative_cell))) * mdr_nc_first_positive_dataabsoluteevaluationh) + (ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative)))))) /\ (((exists ff_h_mdm_mdr_first_positive_dataabsoluteevaluationhscm_negative_target. ff_h_mdm_mdr_first_positive_dataabsoluteevaluationhscm_negative_target + S (ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative) = S ((S (ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative)) * mdr_ut_first_positive_dataabsoluteevaluationhsc)) /\ exists ff_q_mdm_mdr_first_positive_dataabsoluteevaluationhscm_negative_target. mdr_un_first_positive_dataabsoluteevaluationhsc = ff_q_mdm_mdr_first_positive_dataabsoluteevaluationhscm_negative_target * S ((S (ff_index_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative)) * mdr_ut_first_positive_dataabsoluteevaluationhsc) + (ff_value_mdm_prefix_mdr_first_positive_dataabsoluteevaluationhscm_negative))))))))) /\ ((((exists ff_h_mdr_first_positive_dataabsoluteevaluationhscp. ff_h_mdr_first_positive_dataabsoluteevaluationhscp + S (mdr_p_first_positive_dataabsoluteevaluationhsc) = S ((S (mdr_j_first_positive_dataabsoluteevaluationhsc)) * mdr_ec_first_positive_dataabsoluteevaluationhs)) /\ exists ff_q_mdr_first_positive_dataabsoluteevaluationhscp. mdr_eb_first_positive_dataabsoluteevaluationhs = ff_q_mdr_first_positive_dataabsoluteevaluationhscp * S ((S (mdr_j_first_positive_dataabsoluteevaluationhsc)) * mdr_ec_first_positive_dataabsoluteevaluationhs) + (mdr_p_first_positive_dataabsoluteevaluationhsc))) /\ (((exists ff_h_mdr_first_positive_dataabsoluteevaluationhscn. ff_h_mdr_first_positive_dataabsoluteevaluationhscn + S (mdr_n_first_positive_dataabsoluteevaluationhsc) = S ((S (mdr_j_first_positive_dataabsoluteevaluationhsc)) * mdr_fc_first_positive_dataabsoluteevaluationhs)) /\ exists ff_q_mdr_first_positive_dataabsoluteevaluationhscn. mdr_fb_first_positive_dataabsoluteevaluationhs = ff_q_mdr_first_positive_dataabsoluteevaluationhscn * S ((S (mdr_j_first_positive_dataabsoluteevaluationhsc)) * mdr_fc_first_positive_dataabsoluteevaluationhs) + (mdr_n_first_positive_dataabsoluteevaluationhsc)))))))) /\ (exists ff_ub_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf ff_uc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf ff_vb_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf ff_vc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf. ((forall ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix. (exists ff_gap_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_index. ff_gap_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_index + S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) = (S (mdr_q_first_positive_dataabsoluteevaluationhs))) -> exists ff_ap_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix ff_an_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix ff_bp_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix ff_bn_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix ff_p_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix ff_n_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix. ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_ap. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_ap + S (ff_ap_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * mdr_pc_first_positive_dataabsoluteevaluationh)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_ap. mdr_pb_first_positive_dataabsoluteevaluationh = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_ap * S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * mdr_pc_first_positive_dataabsoluteevaluationh) + (ff_ap_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_an. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_an + S (ff_an_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * mdr_nc_first_positive_dataabsoluteevaluationh)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_an. mdr_nb_first_positive_dataabsoluteevaluationh = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_an * S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * mdr_nc_first_positive_dataabsoluteevaluationh) + (ff_an_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_bp. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_bp + S (ff_bp_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * mdr_ec_first_positive_dataabsoluteevaluationhs)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_bp. mdr_eb_first_positive_dataabsoluteevaluationhs = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_bp * S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * mdr_ec_first_positive_dataabsoluteevaluationhs) + (ff_bp_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_bn. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_bn + S (ff_bn_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * mdr_fc_first_positive_dataabsoluteevaluationhs)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_bn. mdr_fb_first_positive_dataabsoluteevaluationhs = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_bn * S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * mdr_fc_first_positive_dataabsoluteevaluationhs) + (ff_bn_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_positive. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_positive + S (ff_p_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * ff_uc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_positive. ff_ub_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_positive * S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * ff_uc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf) + (ff_p_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_negative. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_negative + S (ff_n_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * ff_vc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_negative. ff_vb_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_prefix_negative * S ((S (ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix)) * ff_vc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf) + (ff_n_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix))) /\ (((exists ff_even_mce_term_mdr_first_positive_dataabsoluteevaluationhsf_prefix_term. ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix = 2 * ff_even_mce_term_mdr_first_positive_dataabsoluteevaluationhsf_prefix_term) /\ (ff_p_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) /\ ff_n_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix))) \/ ((exists ff_odd_mce_term_mdr_first_positive_dataabsoluteevaluationhsf_prefix_term. ff_index_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix = 2 * ff_odd_mce_term_mdr_first_positive_dataabsoluteevaluationhsf_prefix_term + 1) /\ (ff_p_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) /\ ff_n_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_first_positive_dataabsoluteevaluationhsf_prefix))))))))))) /\ ((exists ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive. ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_start. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_start + S (0) = S ((S (0)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_start. ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_start * S ((S (0)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive) + (0))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_terminal. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_terminal + S (mdr_p_first_positive_dataabsoluteevaluationh) = S ((S ((S (mdr_q_first_positive_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_terminal. ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_terminal * S ((S ((S (mdr_q_first_positive_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive) + (mdr_p_first_positive_dataabsoluteevaluationh))) /\ forall ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive. (exists ff_lt_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_bound. ff_lt_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_bound + S ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive = (S (mdr_q_first_positive_dataabsoluteevaluationhs))) -> exists ff_a_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive ff_r_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive ff_s_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive. ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_summand. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_summand + S (ff_a_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive) = S ((S (ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) * ff_uc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_summand. ff_ub_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_summand * S ((S (ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) * ff_uc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf) + (ff_a_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_partial. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_partial + S (ff_r_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive) = S ((S (ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_partial. ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_partial * S ((S (ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive) + (ff_r_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_successor. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_successor + S (ff_s_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive) = S ((S (S ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_successor. ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive_successor * S ((S (S ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive) + (ff_s_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive))) /\ ff_s_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive = ff_r_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive + ff_a_mce_mdr_first_positive_dataabsoluteevaluationhsf_positive)))))) /\ (exists ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative. ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_start. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_start + S (0) = S ((S (0)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_start. ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_start * S ((S (0)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative) + (0))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_terminal. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_terminal + S (mdr_n_first_positive_dataabsoluteevaluationh) = S ((S ((S (mdr_q_first_positive_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_terminal. ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_terminal * S ((S ((S (mdr_q_first_positive_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative) + (mdr_n_first_positive_dataabsoluteevaluationh))) /\ forall ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative. (exists ff_lt_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_bound. ff_lt_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_bound + S ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative = (S (mdr_q_first_positive_dataabsoluteevaluationhs))) -> exists ff_a_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative ff_r_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative ff_s_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative. ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_summand. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_summand + S (ff_a_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative) = S ((S (ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) * ff_vc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_summand. ff_vb_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_summand * S ((S (ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) * ff_vc_mce_fold_mdr_first_positive_dataabsoluteevaluationhsf) + (ff_a_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_partial. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_partial + S (ff_r_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative) = S ((S (ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_partial. ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_partial * S ((S (ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative) + (ff_r_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative))) /\ ((((exists ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_successor. ff_h_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_successor + S (ff_s_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative) = S ((S (S ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_successor. ff_u_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative_successor * S ((S (S ff_i_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative) + (ff_s_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative))) /\ ff_s_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative = ff_r_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative + ff_a_mce_mdr_first_positive_dataabsoluteevaluationhsf_negative))))))))))))))) /\ ((exists mdr_gap_first_positive_dataabsoluteevaluationi. mdr_gap_first_positive_dataabsoluteevaluationi + S (mdr_i_first_positive_dataabsoluteevaluation) = (mdr_l_first_positive_dataabsoluteevaluation)) /\ (exists mdr_z_first_positive_dataabsoluteevaluationr. ((exists mdr_a_first_positive_dataabsoluteevaluationrc mdr_b_first_positive_dataabsoluteevaluationrc mdr_c_first_positive_dataabsoluteevaluationrc mdr_e_first_positive_dataabsoluteevaluationrc mdr_f_first_positive_dataabsoluteevaluationrc. ((mdr_a_first_positive_dataabsoluteevaluationrc = ((d) + (ab)) * S ((d) + (ab)) + ((ab) + (ab))) /\ ((mdr_b_first_positive_dataabsoluteevaluationrc = ((ac) + (bb)) * S ((ac) + (bb)) + ((bb) + (bb))) /\ ((mdr_c_first_positive_dataabsoluteevaluationrc = ((mdr_a_first_positive_dataabsoluteevaluationrc) + (mdr_b_first_positive_dataabsoluteevaluationrc)) * S ((mdr_a_first_positive_dataabsoluteevaluationrc) + (mdr_b_first_positive_dataabsoluteevaluationrc)) + ((mdr_b_first_positive_dataabsoluteevaluationrc) + (mdr_b_first_positive_dataabsoluteevaluationrc))) /\ ((mdr_e_first_positive_dataabsoluteevaluationrc = ((mdr_p_first_positive_dataabsolute) + (mdr_n_first_positive_dataabsolute)) * S ((mdr_p_first_positive_dataabsolute) + (mdr_n_first_positive_dataabsolute)) + ((mdr_n_first_positive_dataabsolute) + (mdr_n_first_positive_dataabsolute))) /\ ((mdr_f_first_positive_dataabsoluteevaluationrc = ((bc) + (mdr_e_first_positive_dataabsoluteevaluationrc)) * S ((bc) + (mdr_e_first_positive_dataabsoluteevaluationrc)) + ((mdr_e_first_positive_dataabsoluteevaluationrc) + (mdr_e_first_positive_dataabsoluteevaluationrc))) /\ ((mdr_z_first_positive_dataabsoluteevaluationr) = ((mdr_c_first_positive_dataabsoluteevaluationrc) + (mdr_f_first_positive_dataabsoluteevaluationrc)) * S ((mdr_c_first_positive_dataabsoluteevaluationrc) + (mdr_f_first_positive_dataabsoluteevaluationrc)) + ((mdr_f_first_positive_dataabsoluteevaluationrc) + (mdr_f_first_positive_dataabsoluteevaluationrc))))))))) /\ (((exists ff_h_mdr_first_positive_dataabsoluteevaluationrb. ff_h_mdr_first_positive_dataabsoluteevaluationrb + S (mdr_z_first_positive_dataabsoluteevaluationr) = S ((S (mdr_i_first_positive_dataabsoluteevaluation)) * mdr_c_first_positive_dataabsoluteevaluation)) /\ exists ff_q_mdr_first_positive_dataabsoluteevaluationrb. mdr_b_first_positive_dataabsoluteevaluation = ff_q_mdr_first_positive_dataabsoluteevaluationrb * S ((S (mdr_i_first_positive_dataabsoluteevaluation)) * mdr_c_first_positive_dataabsoluteevaluation) + (mdr_z_first_positive_dataabsoluteevaluationr)))))))) /\ (((mdr_p_first_positive_dataabsolute) = (mdr_n_first_positive_dataabsolute) + (D)) \/ ((mdr_n_first_positive_dataabsolute) = (mdr_p_first_positive_dataabsolute) + (D)))))))) -> (((~(d = 0)) /\ ((~(E = 0)) /\ (exists mdr_p_second_positive_dataabsolute mdr_n_second_positive_dataabsolute. ((exists mdr_b_second_positive_dataabsoluteevaluation mdr_c_second_positive_dataabsoluteevaluation mdr_l_second_positive_dataabsoluteevaluation mdr_i_second_positive_dataabsoluteevaluation. ((forall mdr_i_second_positive_dataabsoluteevaluationh. (exists mdr_gap_second_positive_dataabsoluteevaluationhi. mdr_gap_second_positive_dataabsoluteevaluationhi + S (mdr_i_second_positive_dataabsoluteevaluationh) = (mdr_l_second_positive_dataabsoluteevaluation)) -> exists mdr_d_second_positive_dataabsoluteevaluationh mdr_pb_second_positive_dataabsoluteevaluationh mdr_pc_second_positive_dataabsoluteevaluationh mdr_nb_second_positive_dataabsoluteevaluationh mdr_nc_second_positive_dataabsoluteevaluationh mdr_p_second_positive_dataabsoluteevaluationh mdr_n_second_positive_dataabsoluteevaluationh. ((exists mdr_z_second_positive_dataabsoluteevaluationhr. ((exists mdr_a_second_positive_dataabsoluteevaluationhrc mdr_b_second_positive_dataabsoluteevaluationhrc mdr_c_second_positive_dataabsoluteevaluationhrc mdr_e_second_positive_dataabsoluteevaluationhrc mdr_f_second_positive_dataabsoluteevaluationhrc. ((mdr_a_second_positive_dataabsoluteevaluationhrc = ((mdr_d_second_positive_dataabsoluteevaluationh) + (mdr_pb_second_positive_dataabsoluteevaluationh)) * S ((mdr_d_second_positive_dataabsoluteevaluationh) + (mdr_pb_second_positive_dataabsoluteevaluationh)) + ((mdr_pb_second_positive_dataabsoluteevaluationh) + (mdr_pb_second_positive_dataabsoluteevaluationh))) /\ ((mdr_b_second_positive_dataabsoluteevaluationhrc = ((mdr_pc_second_positive_dataabsoluteevaluationh) + (mdr_nb_second_positive_dataabsoluteevaluationh)) * S ((mdr_pc_second_positive_dataabsoluteevaluationh) + (mdr_nb_second_positive_dataabsoluteevaluationh)) + ((mdr_nb_second_positive_dataabsoluteevaluationh) + (mdr_nb_second_positive_dataabsoluteevaluationh))) /\ ((mdr_c_second_positive_dataabsoluteevaluationhrc = ((mdr_a_second_positive_dataabsoluteevaluationhrc) + (mdr_b_second_positive_dataabsoluteevaluationhrc)) * S ((mdr_a_second_positive_dataabsoluteevaluationhrc) + (mdr_b_second_positive_dataabsoluteevaluationhrc)) + ((mdr_b_second_positive_dataabsoluteevaluationhrc) + (mdr_b_second_positive_dataabsoluteevaluationhrc))) /\ ((mdr_e_second_positive_dataabsoluteevaluationhrc = ((mdr_p_second_positive_dataabsoluteevaluationh) + (mdr_n_second_positive_dataabsoluteevaluationh)) * S ((mdr_p_second_positive_dataabsoluteevaluationh) + (mdr_n_second_positive_dataabsoluteevaluationh)) + ((mdr_n_second_positive_dataabsoluteevaluationh) + (mdr_n_second_positive_dataabsoluteevaluationh))) /\ ((mdr_f_second_positive_dataabsoluteevaluationhrc = ((mdr_nc_second_positive_dataabsoluteevaluationh) + (mdr_e_second_positive_dataabsoluteevaluationhrc)) * S ((mdr_nc_second_positive_dataabsoluteevaluationh) + (mdr_e_second_positive_dataabsoluteevaluationhrc)) + ((mdr_e_second_positive_dataabsoluteevaluationhrc) + (mdr_e_second_positive_dataabsoluteevaluationhrc))) /\ ((mdr_z_second_positive_dataabsoluteevaluationhr) = ((mdr_c_second_positive_dataabsoluteevaluationhrc) + (mdr_f_second_positive_dataabsoluteevaluationhrc)) * S ((mdr_c_second_positive_dataabsoluteevaluationhrc) + (mdr_f_second_positive_dataabsoluteevaluationhrc)) + ((mdr_f_second_positive_dataabsoluteevaluationhrc) + (mdr_f_second_positive_dataabsoluteevaluationhrc))))))))) /\ (((exists ff_h_mdr_second_positive_dataabsoluteevaluationhrb. ff_h_mdr_second_positive_dataabsoluteevaluationhrb + S (mdr_z_second_positive_dataabsoluteevaluationhr) = S ((S (mdr_i_second_positive_dataabsoluteevaluationh)) * mdr_c_second_positive_dataabsoluteevaluation)) /\ exists ff_q_mdr_second_positive_dataabsoluteevaluationhrb. mdr_b_second_positive_dataabsoluteevaluation = ff_q_mdr_second_positive_dataabsoluteevaluationhrb * S ((S (mdr_i_second_positive_dataabsoluteevaluationh)) * mdr_c_second_positive_dataabsoluteevaluation) + (mdr_z_second_positive_dataabsoluteevaluationhr))))) /\ (((((mdr_d_second_positive_dataabsoluteevaluationh) = 0) /\ (((mdr_p_second_positive_dataabsoluteevaluationh) = 1) /\ ((mdr_n_second_positive_dataabsoluteevaluationh) = 0))) \/ exists mdr_q_second_positive_dataabsoluteevaluationhs mdr_eb_second_positive_dataabsoluteevaluationhs mdr_ec_second_positive_dataabsoluteevaluationhs mdr_fb_second_positive_dataabsoluteevaluationhs mdr_fc_second_positive_dataabsoluteevaluationhs. (((mdr_d_second_positive_dataabsoluteevaluationh) = S (mdr_q_second_positive_dataabsoluteevaluationhs)) /\ ((forall mdr_j_second_positive_dataabsoluteevaluationhsc. (exists mdr_gap_second_positive_dataabsoluteevaluationhscj. mdr_gap_second_positive_dataabsoluteevaluationhscj + S (mdr_j_second_positive_dataabsoluteevaluationhsc) = (S (mdr_q_second_positive_dataabsoluteevaluationhs))) -> exists mdr_i_second_positive_dataabsoluteevaluationhsc mdr_up_second_positive_dataabsoluteevaluationhsc mdr_us_second_positive_dataabsoluteevaluationhsc mdr_un_second_positive_dataabsoluteevaluationhsc mdr_ut_second_positive_dataabsoluteevaluationhsc mdr_p_second_positive_dataabsoluteevaluationhsc mdr_n_second_positive_dataabsoluteevaluationhsc. ((exists mdr_gap_second_positive_dataabsoluteevaluationhsci. mdr_gap_second_positive_dataabsoluteevaluationhsci + S (mdr_i_second_positive_dataabsoluteevaluationhsc) = (mdr_i_second_positive_dataabsoluteevaluationh)) /\ ((exists mdr_z_second_positive_dataabsoluteevaluationhscr. ((exists mdr_a_second_positive_dataabsoluteevaluationhscrc mdr_b_second_positive_dataabsoluteevaluationhscrc mdr_c_second_positive_dataabsoluteevaluationhscrc mdr_e_second_positive_dataabsoluteevaluationhscrc mdr_f_second_positive_dataabsoluteevaluationhscrc. ((mdr_a_second_positive_dataabsoluteevaluationhscrc = ((mdr_q_second_positive_dataabsoluteevaluationhs) + (mdr_up_second_positive_dataabsoluteevaluationhsc)) * S ((mdr_q_second_positive_dataabsoluteevaluationhs) + (mdr_up_second_positive_dataabsoluteevaluationhsc)) + ((mdr_up_second_positive_dataabsoluteevaluationhsc) + (mdr_up_second_positive_dataabsoluteevaluationhsc))) /\ ((mdr_b_second_positive_dataabsoluteevaluationhscrc = ((mdr_us_second_positive_dataabsoluteevaluationhsc) + (mdr_un_second_positive_dataabsoluteevaluationhsc)) * S ((mdr_us_second_positive_dataabsoluteevaluationhsc) + (mdr_un_second_positive_dataabsoluteevaluationhsc)) + ((mdr_un_second_positive_dataabsoluteevaluationhsc) + (mdr_un_second_positive_dataabsoluteevaluationhsc))) /\ ((mdr_c_second_positive_dataabsoluteevaluationhscrc = ((mdr_a_second_positive_dataabsoluteevaluationhscrc) + (mdr_b_second_positive_dataabsoluteevaluationhscrc)) * S ((mdr_a_second_positive_dataabsoluteevaluationhscrc) + (mdr_b_second_positive_dataabsoluteevaluationhscrc)) + ((mdr_b_second_positive_dataabsoluteevaluationhscrc) + (mdr_b_second_positive_dataabsoluteevaluationhscrc))) /\ ((mdr_e_second_positive_dataabsoluteevaluationhscrc = ((mdr_p_second_positive_dataabsoluteevaluationhsc) + (mdr_n_second_positive_dataabsoluteevaluationhsc)) * S ((mdr_p_second_positive_dataabsoluteevaluationhsc) + (mdr_n_second_positive_dataabsoluteevaluationhsc)) + ((mdr_n_second_positive_dataabsoluteevaluationhsc) + (mdr_n_second_positive_dataabsoluteevaluationhsc))) /\ ((mdr_f_second_positive_dataabsoluteevaluationhscrc = ((mdr_ut_second_positive_dataabsoluteevaluationhsc) + (mdr_e_second_positive_dataabsoluteevaluationhscrc)) * S ((mdr_ut_second_positive_dataabsoluteevaluationhsc) + (mdr_e_second_positive_dataabsoluteevaluationhscrc)) + ((mdr_e_second_positive_dataabsoluteevaluationhscrc) + (mdr_e_second_positive_dataabsoluteevaluationhscrc))) /\ ((mdr_z_second_positive_dataabsoluteevaluationhscr) = ((mdr_c_second_positive_dataabsoluteevaluationhscrc) + (mdr_f_second_positive_dataabsoluteevaluationhscrc)) * S ((mdr_c_second_positive_dataabsoluteevaluationhscrc) + (mdr_f_second_positive_dataabsoluteevaluationhscrc)) + ((mdr_f_second_positive_dataabsoluteevaluationhscrc) + (mdr_f_second_positive_dataabsoluteevaluationhscrc))))))))) /\ (((exists ff_h_mdr_second_positive_dataabsoluteevaluationhscrb. ff_h_mdr_second_positive_dataabsoluteevaluationhscrb + S (mdr_z_second_positive_dataabsoluteevaluationhscr) = S ((S (mdr_i_second_positive_dataabsoluteevaluationhsc)) * mdr_c_second_positive_dataabsoluteevaluation)) /\ exists ff_q_mdr_second_positive_dataabsoluteevaluationhscrb. mdr_b_second_positive_dataabsoluteevaluation = ff_q_mdr_second_positive_dataabsoluteevaluationhscrb * S ((S (mdr_i_second_positive_dataabsoluteevaluationhsc)) * mdr_c_second_positive_dataabsoluteevaluation) + (mdr_z_second_positive_dataabsoluteevaluationhscr))))) /\ ((((forall ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive. (exists ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_positive_index_bound. ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_positive_index_bound + S (ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive) = ((mdr_q_second_positive_dataabsoluteevaluationhs) * (mdr_q_second_positive_dataabsoluteevaluationhs))) -> exists ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive. (ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive = (mdr_q_second_positive_dataabsoluteevaluationhs) * ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive + ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive /\ ((exists ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_positive_column_bound. ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_positive_column_bound + S (ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive) = (mdr_q_second_positive_dataabsoluteevaluationhs)) /\ ((exists ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell. (((((exists ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_row_before. ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_row_before + S (ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive) = (0)) /\ ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell = ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive) \/ ((exists ff_gap_mdm_le_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_row_after. ff_gap_mdm_le_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_row_after + (0) = (ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive)) /\ ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell = S ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive))) /\ (((((exists ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_column_before. ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_column_before + S (ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive) = (mdr_j_second_positive_dataabsoluteevaluationhsc)) /\ ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell = ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive) \/ ((exists ff_gap_mdm_le_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_column_after. ff_gap_mdm_le_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_column_after + (mdr_j_second_positive_dataabsoluteevaluationhsc) = (ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive)) /\ ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell = S ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive))) /\ (((exists ff_h_mdm_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_source. ff_h_mdm_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_source + S (ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive) = S ((S ((ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell) * (S (mdr_q_second_positive_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell))) * mdr_pc_second_positive_dataabsoluteevaluationh)) /\ exists ff_q_mdm_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_source. mdr_pb_second_positive_dataabsoluteevaluationh = ff_q_mdm_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell_source * S ((S ((ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell) * (S (mdr_q_second_positive_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_positive_cell))) * mdr_pc_second_positive_dataabsoluteevaluationh) + (ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive)))))) /\ (((exists ff_h_mdm_mdr_second_positive_dataabsoluteevaluationhscm_positive_target. ff_h_mdm_mdr_second_positive_dataabsoluteevaluationhscm_positive_target + S (ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive) = S ((S (ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive)) * mdr_us_second_positive_dataabsoluteevaluationhsc)) /\ exists ff_q_mdm_mdr_second_positive_dataabsoluteevaluationhscm_positive_target. mdr_up_second_positive_dataabsoluteevaluationhsc = ff_q_mdm_mdr_second_positive_dataabsoluteevaluationhscm_positive_target * S ((S (ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive)) * mdr_us_second_positive_dataabsoluteevaluationhsc) + (ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_positive))))))) /\ (forall ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative. (exists ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_negative_index_bound. ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_negative_index_bound + S (ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative) = ((mdr_q_second_positive_dataabsoluteevaluationhs) * (mdr_q_second_positive_dataabsoluteevaluationhs))) -> exists ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative. (ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative = (mdr_q_second_positive_dataabsoluteevaluationhs) * ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative + ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative /\ ((exists ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_negative_column_bound. ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_negative_column_bound + S (ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative) = (mdr_q_second_positive_dataabsoluteevaluationhs)) /\ ((exists ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell. (((((exists ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_row_before. ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_row_before + S (ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative) = (0)) /\ ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell = ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative) \/ ((exists ff_gap_mdm_le_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_row_after. ff_gap_mdm_le_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_row_after + (0) = (ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative)) /\ ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell = S ff_row_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative))) /\ (((((exists ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_column_before. ff_gap_mdm_lt_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_column_before + S (ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative) = (mdr_j_second_positive_dataabsoluteevaluationhsc)) /\ ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell = ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative) \/ ((exists ff_gap_mdm_le_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_column_after. ff_gap_mdm_le_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_column_after + (mdr_j_second_positive_dataabsoluteevaluationhsc) = (ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative)) /\ ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell = S ff_column_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative))) /\ (((exists ff_h_mdm_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_source. ff_h_mdm_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_source + S (ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative) = S ((S ((ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell) * (S (mdr_q_second_positive_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell))) * mdr_nc_second_positive_dataabsoluteevaluationh)) /\ exists ff_q_mdm_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_source. mdr_nb_second_positive_dataabsoluteevaluationh = ff_q_mdm_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell_source * S ((S ((ff_row_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell) * (S (mdr_q_second_positive_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_second_positive_dataabsoluteevaluationhscm_negative_cell))) * mdr_nc_second_positive_dataabsoluteevaluationh) + (ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative)))))) /\ (((exists ff_h_mdm_mdr_second_positive_dataabsoluteevaluationhscm_negative_target. ff_h_mdm_mdr_second_positive_dataabsoluteevaluationhscm_negative_target + S (ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative) = S ((S (ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative)) * mdr_ut_second_positive_dataabsoluteevaluationhsc)) /\ exists ff_q_mdm_mdr_second_positive_dataabsoluteevaluationhscm_negative_target. mdr_un_second_positive_dataabsoluteevaluationhsc = ff_q_mdm_mdr_second_positive_dataabsoluteevaluationhscm_negative_target * S ((S (ff_index_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative)) * mdr_ut_second_positive_dataabsoluteevaluationhsc) + (ff_value_mdm_prefix_mdr_second_positive_dataabsoluteevaluationhscm_negative))))))))) /\ ((((exists ff_h_mdr_second_positive_dataabsoluteevaluationhscp. ff_h_mdr_second_positive_dataabsoluteevaluationhscp + S (mdr_p_second_positive_dataabsoluteevaluationhsc) = S ((S (mdr_j_second_positive_dataabsoluteevaluationhsc)) * mdr_ec_second_positive_dataabsoluteevaluationhs)) /\ exists ff_q_mdr_second_positive_dataabsoluteevaluationhscp. mdr_eb_second_positive_dataabsoluteevaluationhs = ff_q_mdr_second_positive_dataabsoluteevaluationhscp * S ((S (mdr_j_second_positive_dataabsoluteevaluationhsc)) * mdr_ec_second_positive_dataabsoluteevaluationhs) + (mdr_p_second_positive_dataabsoluteevaluationhsc))) /\ (((exists ff_h_mdr_second_positive_dataabsoluteevaluationhscn. ff_h_mdr_second_positive_dataabsoluteevaluationhscn + S (mdr_n_second_positive_dataabsoluteevaluationhsc) = S ((S (mdr_j_second_positive_dataabsoluteevaluationhsc)) * mdr_fc_second_positive_dataabsoluteevaluationhs)) /\ exists ff_q_mdr_second_positive_dataabsoluteevaluationhscn. mdr_fb_second_positive_dataabsoluteevaluationhs = ff_q_mdr_second_positive_dataabsoluteevaluationhscn * S ((S (mdr_j_second_positive_dataabsoluteevaluationhsc)) * mdr_fc_second_positive_dataabsoluteevaluationhs) + (mdr_n_second_positive_dataabsoluteevaluationhsc)))))))) /\ (exists ff_ub_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf ff_uc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf ff_vb_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf ff_vc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf. ((forall ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix. (exists ff_gap_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_index. ff_gap_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_index + S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) = (S (mdr_q_second_positive_dataabsoluteevaluationhs))) -> exists ff_ap_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix ff_an_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix ff_bp_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix ff_bn_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix ff_p_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix ff_n_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix. ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_ap. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_ap + S (ff_ap_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * mdr_pc_second_positive_dataabsoluteevaluationh)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_ap. mdr_pb_second_positive_dataabsoluteevaluationh = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_ap * S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * mdr_pc_second_positive_dataabsoluteevaluationh) + (ff_ap_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_an. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_an + S (ff_an_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * mdr_nc_second_positive_dataabsoluteevaluationh)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_an. mdr_nb_second_positive_dataabsoluteevaluationh = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_an * S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * mdr_nc_second_positive_dataabsoluteevaluationh) + (ff_an_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_bp. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_bp + S (ff_bp_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * mdr_ec_second_positive_dataabsoluteevaluationhs)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_bp. mdr_eb_second_positive_dataabsoluteevaluationhs = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_bp * S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * mdr_ec_second_positive_dataabsoluteevaluationhs) + (ff_bp_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_bn. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_bn + S (ff_bn_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * mdr_fc_second_positive_dataabsoluteevaluationhs)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_bn. mdr_fb_second_positive_dataabsoluteevaluationhs = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_bn * S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * mdr_fc_second_positive_dataabsoluteevaluationhs) + (ff_bn_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_positive. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_positive + S (ff_p_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * ff_uc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_positive. ff_ub_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_positive * S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * ff_uc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf) + (ff_p_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_negative. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_negative + S (ff_n_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * ff_vc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_negative. ff_vb_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_prefix_negative * S ((S (ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix)) * ff_vc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf) + (ff_n_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix))) /\ (((exists ff_even_mce_term_mdr_second_positive_dataabsoluteevaluationhsf_prefix_term. ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix = 2 * ff_even_mce_term_mdr_second_positive_dataabsoluteevaluationhsf_prefix_term) /\ (ff_p_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) /\ ff_n_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix))) \/ ((exists ff_odd_mce_term_mdr_second_positive_dataabsoluteevaluationhsf_prefix_term. ff_index_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix = 2 * ff_odd_mce_term_mdr_second_positive_dataabsoluteevaluationhsf_prefix_term + 1) /\ (ff_p_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) /\ ff_n_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_second_positive_dataabsoluteevaluationhsf_prefix))))))))))) /\ ((exists ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive. ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_start. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_start + S (0) = S ((S (0)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_start. ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_start * S ((S (0)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive) + (0))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_terminal. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_terminal + S (mdr_p_second_positive_dataabsoluteevaluationh) = S ((S ((S (mdr_q_second_positive_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_terminal. ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_terminal * S ((S ((S (mdr_q_second_positive_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive) + (mdr_p_second_positive_dataabsoluteevaluationh))) /\ forall ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive. (exists ff_lt_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_bound. ff_lt_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_bound + S ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive = (S (mdr_q_second_positive_dataabsoluteevaluationhs))) -> exists ff_a_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive ff_r_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive ff_s_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive. ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_summand. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_summand + S (ff_a_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive) = S ((S (ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) * ff_uc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_summand. ff_ub_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_summand * S ((S (ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) * ff_uc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf) + (ff_a_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_partial. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_partial + S (ff_r_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive) = S ((S (ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_partial. ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_partial * S ((S (ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive) + (ff_r_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_successor. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_successor + S (ff_s_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive) = S ((S (S ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_successor. ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive_successor * S ((S (S ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive) + (ff_s_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive))) /\ ff_s_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive = ff_r_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive + ff_a_mce_mdr_second_positive_dataabsoluteevaluationhsf_positive)))))) /\ (exists ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative. ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_start. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_start + S (0) = S ((S (0)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_start. ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_start * S ((S (0)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative) + (0))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_terminal. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_terminal + S (mdr_n_second_positive_dataabsoluteevaluationh) = S ((S ((S (mdr_q_second_positive_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_terminal. ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_terminal * S ((S ((S (mdr_q_second_positive_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative) + (mdr_n_second_positive_dataabsoluteevaluationh))) /\ forall ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative. (exists ff_lt_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_bound. ff_lt_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_bound + S ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative = (S (mdr_q_second_positive_dataabsoluteevaluationhs))) -> exists ff_a_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative ff_r_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative ff_s_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative. ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_summand. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_summand + S (ff_a_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative) = S ((S (ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) * ff_vc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_summand. ff_vb_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_summand * S ((S (ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) * ff_vc_mce_fold_mdr_second_positive_dataabsoluteevaluationhsf) + (ff_a_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_partial. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_partial + S (ff_r_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative) = S ((S (ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_partial. ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_partial * S ((S (ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative) + (ff_r_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative))) /\ ((((exists ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_successor. ff_h_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_successor + S (ff_s_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative) = S ((S (S ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_successor. ff_u_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative_successor * S ((S (S ff_i_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative) + (ff_s_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative))) /\ ff_s_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative = ff_r_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative + ff_a_mce_mdr_second_positive_dataabsoluteevaluationhsf_negative))))))))))))))) /\ ((exists mdr_gap_second_positive_dataabsoluteevaluationi. mdr_gap_second_positive_dataabsoluteevaluationi + S (mdr_i_second_positive_dataabsoluteevaluation) = (mdr_l_second_positive_dataabsoluteevaluation)) /\ (exists mdr_z_second_positive_dataabsoluteevaluationr. ((exists mdr_a_second_positive_dataabsoluteevaluationrc mdr_b_second_positive_dataabsoluteevaluationrc mdr_c_second_positive_dataabsoluteevaluationrc mdr_e_second_positive_dataabsoluteevaluationrc mdr_f_second_positive_dataabsoluteevaluationrc. ((mdr_a_second_positive_dataabsoluteevaluationrc = ((d) + (ab)) * S ((d) + (ab)) + ((ab) + (ab))) /\ ((mdr_b_second_positive_dataabsoluteevaluationrc = ((ac) + (bb)) * S ((ac) + (bb)) + ((bb) + (bb))) /\ ((mdr_c_second_positive_dataabsoluteevaluationrc = ((mdr_a_second_positive_dataabsoluteevaluationrc) + (mdr_b_second_positive_dataabsoluteevaluationrc)) * S ((mdr_a_second_positive_dataabsoluteevaluationrc) + (mdr_b_second_positive_dataabsoluteevaluationrc)) + ((mdr_b_second_positive_dataabsoluteevaluationrc) + (mdr_b_second_positive_dataabsoluteevaluationrc))) /\ ((mdr_e_second_positive_dataabsoluteevaluationrc = ((mdr_p_second_positive_dataabsolute) + (mdr_n_second_positive_dataabsolute)) * S ((mdr_p_second_positive_dataabsolute) + (mdr_n_second_positive_dataabsolute)) + ((mdr_n_second_positive_dataabsolute) + (mdr_n_second_positive_dataabsolute))) /\ ((mdr_f_second_positive_dataabsoluteevaluationrc = ((bc) + (mdr_e_second_positive_dataabsoluteevaluationrc)) * S ((bc) + (mdr_e_second_positive_dataabsoluteevaluationrc)) + ((mdr_e_second_positive_dataabsoluteevaluationrc) + (mdr_e_second_positive_dataabsoluteevaluationrc))) /\ ((mdr_z_second_positive_dataabsoluteevaluationr) = ((mdr_c_second_positive_dataabsoluteevaluationrc) + (mdr_f_second_positive_dataabsoluteevaluationrc)) * S ((mdr_c_second_positive_dataabsoluteevaluationrc) + (mdr_f_second_positive_dataabsoluteevaluationrc)) + ((mdr_f_second_positive_dataabsoluteevaluationrc) + (mdr_f_second_positive_dataabsoluteevaluationrc))))))))) /\ (((exists ff_h_mdr_second_positive_dataabsoluteevaluationrb. ff_h_mdr_second_positive_dataabsoluteevaluationrb + S (mdr_z_second_positive_dataabsoluteevaluationr) = S ((S (mdr_i_second_positive_dataabsoluteevaluation)) * mdr_c_second_positive_dataabsoluteevaluation)) /\ exists ff_q_mdr_second_positive_dataabsoluteevaluationrb. mdr_b_second_positive_dataabsoluteevaluation = ff_q_mdr_second_positive_dataabsoluteevaluationrb * S ((S (mdr_i_second_positive_dataabsoluteevaluation)) * mdr_c_second_positive_dataabsoluteevaluation) + (mdr_z_second_positive_dataabsoluteevaluationr)))))))) /\ (((mdr_p_second_positive_dataabsolute) = (mdr_n_second_positive_dataabsolute) + (E)) \/ ((mdr_n_second_positive_dataabsolute) = (mdr_p_second_positive_dataabsolute) + (E)))))))) -> D = EComplete tactic proof in conservative notation
All 23 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay script.
Read the argument
Proof checkpoints
23 script commands · 3 reading checkpoints · 0 local claims
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.
Named ingredients (1)
01Fix variables and assumptionsL1–9
02Separate the logical casesL10–13
03Use earlier factsL14–23
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L14
specialize absolute_recursive_determinant_functional (ab) - L15
specialize absolute_recursive_determinant_functional (ac) - L16
specialize absolute_recursive_determinant_functional (bb) - L17
specialize absolute_recursive_determinant_functional (bc) - L18
specialize absolute_recursive_determinant_functional (d) - L19
specialize absolute_recursive_determinant_functional (D) - L20
specialize absolute_recursive_determinant_functional (E) - L21
apply absolute_recursive_determinant_functional - L22
exact hfirst_right_right - L23
exact hsecond_right_right
Original defined command ledger · 23 lines
- 0001
intro ab - 0002
intro ac - 0003
intro bb - 0004
intro bc - 0005
intro d - 0006
intro D - 0007
intro E - 0008
intro hfirst - 0009
intro hsecond - 0010
cases hfirst - 0011
cases hfirst_right - 0012
cases hsecond - 0013
cases hsecond_right - 0014
specialize absolute_recursive_determinant_functional (ab) - 0015
specialize absolute_recursive_determinant_functional (ac) - 0016
specialize absolute_recursive_determinant_functional (bb) - 0017
specialize absolute_recursive_determinant_functional (bc) - 0018
specialize absolute_recursive_determinant_functional (d) - 0019
specialize absolute_recursive_determinant_functional (D) - 0020
specialize absolute_recursive_determinant_functional (E) - 0021
apply absolute_recursive_determinant_functional - 0022
exact hfirst_right_right - 0023
exact hsecond_right_right