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 expanded first-order arithmetic statement
forall m F o s t n a b. (exists srt_rows_fubini_rows. ((((exists dst_positive_code_fubini_rowsrowssource_table dst_positive_scale_fubini_rowsrowssource_table dst_negative_code_fubini_rowsrowssource_table dst_negative_scale_fubini_rowsrowssource_table. (((F) = (((((dst_positive_code_fubini_rowsrowssource_table) + (dst_positive_scale_fubini_rowsrowssource_table)) * S ((dst_positive_code_fubini_rowsrowssource_table) + (dst_positive_scale_fubini_rowsrowssource_table)) + ((dst_positive_scale_fubini_rowsrowssource_table) + (dst_positive_scale_fubini_rowsrowssource_table))) + (((dst_negative_code_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)) * S ((dst_negative_code_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)) + ((dst_negative_scale_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)))) * S ((((dst_positive_code_fubini_rowsrowssource_table) + (dst_positive_scale_fubini_rowsrowssource_table)) * S ((dst_positive_code_fubini_rowsrowssource_table) + (dst_positive_scale_fubini_rowsrowssource_table)) + ((dst_positive_scale_fubini_rowsrowssource_table) + (dst_positive_scale_fubini_rowsrowssource_table))) + (((dst_negative_code_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)) * S ((dst_negative_code_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)) + ((dst_negative_scale_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)))) + ((((dst_negative_code_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)) * S ((dst_negative_code_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)) + ((dst_negative_scale_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table))) + (((dst_negative_code_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)) * S ((dst_negative_code_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)) + ((dst_negative_scale_fubini_rowsrowssource_table) + (dst_negative_scale_fubini_rowsrowssource_table)))))) /\ (forall dst_index_fubini_rowsrowssource_table. (exists pvs_le_gap_fubini_rowsrowssource_tabledomain. pvs_le_gap_fubini_rowsrowssource_tabledomain + (dst_index_fubini_rowsrowssource_table) = (0)) -> exists dst_positive_fubini_rowsrowssource_table dst_negative_fubini_rowsrowssource_table dst_value_fubini_rowsrowssource_table. ((((exists ff_h_pvs_fubini_rowsrowssource_tableentrypositive. ff_h_pvs_fubini_rowsrowssource_tableentrypositive + S (dst_positive_fubini_rowsrowssource_table) = S ((S (dst_index_fubini_rowsrowssource_table)) * dst_positive_scale_fubini_rowsrowssource_table)) /\ exists ff_q_pvs_fubini_rowsrowssource_tableentrypositive. dst_positive_code_fubini_rowsrowssource_table = ff_q_pvs_fubini_rowsrowssource_tableentrypositive * S ((S (dst_index_fubini_rowsrowssource_table)) * dst_positive_scale_fubini_rowsrowssource_table) + (dst_positive_fubini_rowsrowssource_table))) /\ (((((exists ff_h_pvs_fubini_rowsrowssource_tableentrynegative. ff_h_pvs_fubini_rowsrowssource_tableentrynegative + S (dst_negative_fubini_rowsrowssource_table) = S ((S (dst_index_fubini_rowsrowssource_table)) * dst_negative_scale_fubini_rowsrowssource_table)) /\ exists ff_q_pvs_fubini_rowsrowssource_tableentrynegative. dst_negative_code_fubini_rowsrowssource_table = ff_q_pvs_fubini_rowsrowssource_tableentrynegative * S ((S (dst_index_fubini_rowsrowssource_table)) * dst_negative_scale_fubini_rowsrowssource_table) + (dst_negative_fubini_rowsrowssource_table))) /\ (exists ge_balance_positive_fubini_rowsrowssource_tableentryvalue ge_balance_negative_fubini_rowsrowssource_tableentryvalue. (((((dst_value_fubini_rowsrowssource_table) = 2 * (ge_balance_positive_fubini_rowsrowssource_tableentryvalue) /\ (ge_balance_negative_fubini_rowsrowssource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_rowsrowssource_tableentryvaluedecode. (((dst_value_fubini_rowsrowssource_table) = 2 * ge_signed_half_fubini_rowsrowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_rowsrowssource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_rowsrowssource_tableentryvalue) = S ge_signed_half_fubini_rowsrowssource_tableentryvaluedecode))) /\ ((dst_positive_fubini_rowsrowssource_table) + ge_balance_negative_fubini_rowsrowssource_tableentryvalue = (dst_negative_fubini_rowsrowssource_table) + ge_balance_positive_fubini_rowsrowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_rowsrowsrow_table dst_positive_scale_fubini_rowsrowsrow_table dst_negative_code_fubini_rowsrowsrow_table dst_negative_scale_fubini_rowsrowsrow_table. (((srt_rows_fubini_rows) = (((((dst_positive_code_fubini_rowsrowsrow_table) + (dst_positive_scale_fubini_rowsrowsrow_table)) * S ((dst_positive_code_fubini_rowsrowsrow_table) + (dst_positive_scale_fubini_rowsrowsrow_table)) + ((dst_positive_scale_fubini_rowsrowsrow_table) + (dst_positive_scale_fubini_rowsrowsrow_table))) + (((dst_negative_code_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)) * S ((dst_negative_code_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)) + ((dst_negative_scale_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)))) * S ((((dst_positive_code_fubini_rowsrowsrow_table) + (dst_positive_scale_fubini_rowsrowsrow_table)) * S ((dst_positive_code_fubini_rowsrowsrow_table) + (dst_positive_scale_fubini_rowsrowsrow_table)) + ((dst_positive_scale_fubini_rowsrowsrow_table) + (dst_positive_scale_fubini_rowsrowsrow_table))) + (((dst_negative_code_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)) * S ((dst_negative_code_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)) + ((dst_negative_scale_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)))) + ((((dst_negative_code_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)) * S ((dst_negative_code_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)) + ((dst_negative_scale_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table))) + (((dst_negative_code_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)) * S ((dst_negative_code_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)) + ((dst_negative_scale_fubini_rowsrowsrow_table) + (dst_negative_scale_fubini_rowsrowsrow_table)))))) /\ (forall dst_index_fubini_rowsrowsrow_table. (exists pvs_le_gap_fubini_rowsrowsrow_tabledomain. pvs_le_gap_fubini_rowsrowsrow_tabledomain + (dst_index_fubini_rowsrowsrow_table) = (m)) -> exists dst_positive_fubini_rowsrowsrow_table dst_negative_fubini_rowsrowsrow_table dst_value_fubini_rowsrowsrow_table. ((((exists ff_h_pvs_fubini_rowsrowsrow_tableentrypositive. ff_h_pvs_fubini_rowsrowsrow_tableentrypositive + S (dst_positive_fubini_rowsrowsrow_table) = S ((S (dst_index_fubini_rowsrowsrow_table)) * dst_positive_scale_fubini_rowsrowsrow_table)) /\ exists ff_q_pvs_fubini_rowsrowsrow_tableentrypositive. dst_positive_code_fubini_rowsrowsrow_table = ff_q_pvs_fubini_rowsrowsrow_tableentrypositive * S ((S (dst_index_fubini_rowsrowsrow_table)) * dst_positive_scale_fubini_rowsrowsrow_table) + (dst_positive_fubini_rowsrowsrow_table))) /\ (((((exists ff_h_pvs_fubini_rowsrowsrow_tableentrynegative. ff_h_pvs_fubini_rowsrowsrow_tableentrynegative + S (dst_negative_fubini_rowsrowsrow_table) = S ((S (dst_index_fubini_rowsrowsrow_table)) * dst_negative_scale_fubini_rowsrowsrow_table)) /\ exists ff_q_pvs_fubini_rowsrowsrow_tableentrynegative. dst_negative_code_fubini_rowsrowsrow_table = ff_q_pvs_fubini_rowsrowsrow_tableentrynegative * S ((S (dst_index_fubini_rowsrowsrow_table)) * dst_negative_scale_fubini_rowsrowsrow_table) + (dst_negative_fubini_rowsrowsrow_table))) /\ (exists ge_balance_positive_fubini_rowsrowsrow_tableentryvalue ge_balance_negative_fubini_rowsrowsrow_tableentryvalue. (((((dst_value_fubini_rowsrowsrow_table) = 2 * (ge_balance_positive_fubini_rowsrowsrow_tableentryvalue) /\ (ge_balance_negative_fubini_rowsrowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_rowsrowsrow_tableentryvaluedecode. (((dst_value_fubini_rowsrowsrow_table) = 2 * ge_signed_half_fubini_rowsrowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_rowsrowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_rowsrowsrow_tableentryvalue) = S ge_signed_half_fubini_rowsrowsrow_tableentryvaluedecode))) /\ ((dst_positive_fubini_rowsrowsrow_table) + ge_balance_negative_fubini_rowsrowsrow_tableentryvalue = (dst_negative_fubini_rowsrowsrow_table) + ge_balance_positive_fubini_rowsrowsrow_tableentryvalue))))))))) /\ (forall srt_index_fubini_rowsrows. (exists pvs_gap_fubini_rowsrowsbound. pvs_gap_fubini_rowsrowsbound + S (srt_index_fubini_rowsrows) = (m)) -> exists srt_value_fubini_rowsrows. (((exists dst_positive_code_fubini_rowsrowsrowentry dst_positive_scale_fubini_rowsrowsrowentry dst_negative_code_fubini_rowsrowsrowentry dst_negative_scale_fubini_rowsrowsrowentry dst_positive_fubini_rowsrowsrowentry dst_negative_fubini_rowsrowsrowentry. (((srt_rows_fubini_rows) = (((((dst_positive_code_fubini_rowsrowsrowentry) + (dst_positive_scale_fubini_rowsrowsrowentry)) * S ((dst_positive_code_fubini_rowsrowsrowentry) + (dst_positive_scale_fubini_rowsrowsrowentry)) + ((dst_positive_scale_fubini_rowsrowsrowentry) + (dst_positive_scale_fubini_rowsrowsrowentry))) + (((dst_negative_code_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)) * S ((dst_negative_code_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)) + ((dst_negative_scale_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)))) * S ((((dst_positive_code_fubini_rowsrowsrowentry) + (dst_positive_scale_fubini_rowsrowsrowentry)) * S ((dst_positive_code_fubini_rowsrowsrowentry) + (dst_positive_scale_fubini_rowsrowsrowentry)) + ((dst_positive_scale_fubini_rowsrowsrowentry) + (dst_positive_scale_fubini_rowsrowsrowentry))) + (((dst_negative_code_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)) * S ((dst_negative_code_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)) + ((dst_negative_scale_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)))) + ((((dst_negative_code_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)) * S ((dst_negative_code_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)) + ((dst_negative_scale_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry))) + (((dst_negative_code_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)) * S ((dst_negative_code_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)) + ((dst_negative_scale_fubini_rowsrowsrowentry) + (dst_negative_scale_fubini_rowsrowsrowentry)))))) /\ (((((exists ff_h_pvs_fubini_rowsrowsrowentrypositive. ff_h_pvs_fubini_rowsrowsrowentrypositive + S (dst_positive_fubini_rowsrowsrowentry) = S ((S (srt_index_fubini_rowsrows)) * dst_positive_scale_fubini_rowsrowsrowentry)) /\ exists ff_q_pvs_fubini_rowsrowsrowentrypositive. dst_positive_code_fubini_rowsrowsrowentry = ff_q_pvs_fubini_rowsrowsrowentrypositive * S ((S (srt_index_fubini_rowsrows)) * dst_positive_scale_fubini_rowsrowsrowentry) + (dst_positive_fubini_rowsrowsrowentry))) /\ (((((exists ff_h_pvs_fubini_rowsrowsrowentrynegative. ff_h_pvs_fubini_rowsrowsrowentrynegative + S (dst_negative_fubini_rowsrowsrowentry) = S ((S (srt_index_fubini_rowsrows)) * dst_negative_scale_fubini_rowsrowsrowentry)) /\ exists ff_q_pvs_fubini_rowsrowsrowentrynegative. dst_negative_code_fubini_rowsrowsrowentry = ff_q_pvs_fubini_rowsrowsrowentrynegative * S ((S (srt_index_fubini_rowsrows)) * dst_negative_scale_fubini_rowsrowsrowentry) + (dst_negative_fubini_rowsrowsrowentry))) /\ (exists ge_balance_positive_fubini_rowsrowsrowentryvalue ge_balance_negative_fubini_rowsrowsrowentryvalue. (((((srt_value_fubini_rowsrows) = 2 * (ge_balance_positive_fubini_rowsrowsrowentryvalue) /\ (ge_balance_negative_fubini_rowsrowsrowentryvalue) = 0) \/ exists ge_signed_half_fubini_rowsrowsrowentryvaluedecode. (((srt_value_fubini_rowsrows) = 2 * ge_signed_half_fubini_rowsrowsrowentryvaluedecode + 1 /\ (ge_balance_positive_fubini_rowsrowsrowentryvalue) = 0) /\ (ge_balance_negative_fubini_rowsrowsrowentryvalue) = S ge_signed_half_fubini_rowsrowsrowentryvaluedecode))) /\ ((dst_positive_fubini_rowsrowsrowentry) + ge_balance_negative_fubini_rowsrowsrowentryvalue = (dst_negative_fubini_rowsrowsrowentry) + ge_balance_positive_fubini_rowsrowsrowentryvalue))))))))) /\ (exists srs_slice_fubini_rowsrowsrowrow_sum. ((((exists dst_positive_code_fubini_rowsrowsrowrow_sumslicesource_table dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_fubini_rowsrowsrowrow_sumslicesource_table. (exists pvs_le_gap_fubini_rowsrowsrowrow_sumslicesource_tabledomain. pvs_le_gap_fubini_rowsrowsrowrow_sumslicesource_tabledomain + (dst_index_fubini_rowsrowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_fubini_rowsrowsrowrow_sumslicesource_table dst_negative_fubini_rowsrowsrowrow_sumslicesource_table dst_value_fubini_rowsrowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_fubini_rowsrowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_fubini_rowsrowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_fubini_rowsrowsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_rowsrowsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_rowsrowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_fubini_rowsrowsrowrow_sumslicesource_table = ff_q_pvs_fubini_rowsrowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_fubini_rowsrowsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_positive_fubini_rowsrowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_fubini_rowsrowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_fubini_rowsrowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_fubini_rowsrowsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_rowsrowsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_rowsrowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_fubini_rowsrowsrowrow_sumslicesource_table = ff_q_pvs_fubini_rowsrowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_fubini_rowsrowsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_rowsrowsrowrow_sumslicesource_table) + (dst_negative_fubini_rowsrowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_fubini_rowsrowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_fubini_rowsrowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_fubini_rowsrowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_fubini_rowsrowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_rowsrowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_fubini_rowsrowsrowrow_sumslicesource_table) = 2 * ge_signed_half_fubini_rowsrowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_rowsrowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_fubini_rowsrowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_fubini_rowsrowsrowrow_sumslicesource_table) + ge_balance_negative_fubini_rowsrowsrowrow_sumslicesource_tableentryvalue = (dst_negative_fubini_rowsrowsrowrow_sumslicesource_table) + ge_balance_positive_fubini_rowsrowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_rowsrowsrowrow_sumsliceoutput_table dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table. (((srs_slice_fubini_rowsrowsrowrow_sum) = (((((dst_positive_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_fubini_rowsrowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_fubini_rowsrowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_fubini_rowsrowsrowrow_sumsliceoutput_tabledomain + (dst_index_fubini_rowsrowsrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_fubini_rowsrowsrowrow_sumsliceoutput_table dst_negative_fubini_rowsrowsrowrow_sumsliceoutput_table dst_value_fubini_rowsrowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_fubini_rowsrowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_fubini_rowsrowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_fubini_rowsrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_rowsrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_rowsrowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_fubini_rowsrowsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_rowsrowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_fubini_rowsrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_positive_fubini_rowsrowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_fubini_rowsrowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_fubini_rowsrowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_fubini_rowsrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_rowsrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_rowsrowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_fubini_rowsrowsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_rowsrowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_fubini_rowsrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_rowsrowsrowrow_sumsliceoutput_table) + (dst_negative_fubini_rowsrowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_fubini_rowsrowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_fubini_rowsrowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_fubini_rowsrowsrowrow_sumsliceoutput_table) + ge_balance_negative_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_fubini_rowsrowsrowrow_sumsliceoutput_table) + ge_balance_positive_fubini_rowsrowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_fubini_rowsrowsrowrow_sumslice. (exists pvs_gap_fubini_rowsrowsrowrow_sumslicebound. pvs_gap_fubini_rowsrowsrowrow_sumslicebound + S (srs_index_fubini_rowsrowsrowrow_sumslice) = (n)) -> exists srs_value_fubini_rowsrowsrowrow_sumslice. (((exists dst_positive_code_fubini_rowsrowsrowrow_sumsliceentrysource dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource dst_positive_fubini_rowsrowsrowrow_sumsliceentrysource dst_negative_fubini_rowsrowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_fubini_rowsrowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_fubini_rowsrowsrowrow_sumsliceentrysourcepositive + S (dst_positive_fubini_rowsrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_fubini_rowsrows)))) + ((t) * (srs_index_fubini_rowsrowsrowrow_sumslice))))) * dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_rowsrowsrowrow_sumsliceentrysourcepositive. dst_positive_code_fubini_rowsrowsrowrow_sumsliceentrysource = ff_q_pvs_fubini_rowsrowsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_fubini_rowsrows)))) + ((t) * (srs_index_fubini_rowsrowsrowrow_sumslice))))) * dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_positive_fubini_rowsrowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_fubini_rowsrowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_fubini_rowsrowsrowrow_sumsliceentrysourcenegative + S (dst_negative_fubini_rowsrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_fubini_rowsrows)))) + ((t) * (srs_index_fubini_rowsrowsrowrow_sumslice))))) * dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_rowsrowsrowrow_sumsliceentrysourcenegative. dst_negative_code_fubini_rowsrowsrowrow_sumsliceentrysource = ff_q_pvs_fubini_rowsrowsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_fubini_rowsrows)))) + ((t) * (srs_index_fubini_rowsrowsrowrow_sumslice))))) * dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentrysource) + (dst_negative_fubini_rowsrowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_fubini_rowsrowsrowrow_sumsliceentrysourcevalue ge_balance_negative_fubini_rowsrowsrowrow_sumsliceentrysourcevalue. (((((srs_value_fubini_rowsrowsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_rowsrowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_fubini_rowsrowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_fubini_rowsrowsrowrow_sumslice) = 2 * ge_signed_half_fubini_rowsrowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_fubini_rowsrowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_fubini_rowsrowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_fubini_rowsrowsrowrow_sumsliceentrysource) + ge_balance_negative_fubini_rowsrowsrowrow_sumsliceentrysourcevalue = (dst_negative_fubini_rowsrowsrowrow_sumsliceentrysource) + ge_balance_positive_fubini_rowsrowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_fubini_rowsrowsrowrow_sumsliceentryoutput dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput dst_positive_fubini_rowsrowsrowrow_sumsliceentryoutput dst_negative_fubini_rowsrowsrowrow_sumsliceentryoutput. (((srs_slice_fubini_rowsrowsrowrow_sum) = (((((dst_positive_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_fubini_rowsrowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_fubini_rowsrowsrowrow_sumsliceentryoutputpositive + S (dst_positive_fubini_rowsrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_rowsrowsrowrow_sumslice)) * dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_rowsrowsrowrow_sumsliceentryoutputpositive. dst_positive_code_fubini_rowsrowsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_rowsrowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_fubini_rowsrowsrowrow_sumslice)) * dst_positive_scale_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_positive_fubini_rowsrowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_fubini_rowsrowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_fubini_rowsrowsrowrow_sumsliceentryoutputnegative + S (dst_negative_fubini_rowsrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_rowsrowsrowrow_sumslice)) * dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_rowsrowsrowrow_sumsliceentryoutputnegative. dst_negative_code_fubini_rowsrowsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_rowsrowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_fubini_rowsrowsrowrow_sumslice)) * dst_negative_scale_fubini_rowsrowsrowrow_sumsliceentryoutput) + (dst_negative_fubini_rowsrowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_fubini_rowsrowsrowrow_sumsliceentryoutputvalue ge_balance_negative_fubini_rowsrowsrowrow_sumsliceentryoutputvalue. (((((srs_value_fubini_rowsrowsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_rowsrowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_fubini_rowsrowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_fubini_rowsrowsrowrow_sumslice) = 2 * ge_signed_half_fubini_rowsrowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_fubini_rowsrowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_fubini_rowsrowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_fubini_rowsrowsrowrow_sumsliceentryoutput) + ge_balance_negative_fubini_rowsrowsrowrow_sumsliceentryoutputvalue = (dst_negative_fubini_rowsrowsrowrow_sumsliceentryoutput) + ge_balance_positive_fubini_rowsrowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_fubini_rowsrowsrowrow_sumsum dst_positive_scale_fubini_rowsrowsrowrow_sumsum dst_negative_code_fubini_rowsrowsrowrow_sumsum dst_negative_scale_fubini_rowsrowsrowrow_sumsum dst_positive_sum_fubini_rowsrowsrowrow_sumsum dst_negative_sum_fubini_rowsrowsrowrow_sumsum. (((srs_slice_fubini_rowsrowsrowrow_sum) = (((((dst_positive_code_fubini_rowsrowsrowrow_sumsum) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsum)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumsum) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsum)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumsum) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsum))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)))) * S ((((dst_positive_code_fubini_rowsrowsrowrow_sumsum) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsum)) * S ((dst_positive_code_fubini_rowsrowsrowrow_sumsum) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsum)) + ((dst_positive_scale_fubini_rowsrowsrowrow_sumsum) + (dst_positive_scale_fubini_rowsrowsrowrow_sumsum))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)))) + ((((dst_negative_code_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum))) + (((dst_negative_code_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_rowsrowsrowrow_sumsum) + (dst_negative_scale_fubini_rowsrowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_fubini_rowsrowsrowrow_sumsumpositive fs_v_dst_fubini_rowsrowsrowrow_sumsumpositive. ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_start. fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_start. fs_u_dst_fubini_rowsrowsrowrow_sumsumpositive = fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_terminal. fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_fubini_rowsrowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_terminal. fs_u_dst_fubini_rowsrowsrowrow_sumsumpositive = fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumpositive) + (dst_positive_sum_fubini_rowsrowsrowrow_sumsum))) /\ forall fs_i_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps fs_r_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps fs_s_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_rowsrowsrowrow_sumsum)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_fubini_rowsrowsrowrow_sumsum = fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_rowsrowsrowrow_sumsum) + (fs_a_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_fubini_rowsrowsrowrow_sumsumpositive = fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumpositive) + (fs_r_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_fubini_rowsrowsrowrow_sumsumpositive = fs_q_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumpositive) + (fs_s_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps = fs_r_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps + fs_a_dst_fubini_rowsrowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_rowsrowsrowrow_sumsumnegative fs_v_dst_fubini_rowsrowsrowrow_sumsumnegative. ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_start. fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_start. fs_u_dst_fubini_rowsrowsrowrow_sumsumnegative = fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_terminal. fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_fubini_rowsrowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_terminal. fs_u_dst_fubini_rowsrowsrowrow_sumsumnegative = fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumnegative) + (dst_negative_sum_fubini_rowsrowsrowrow_sumsum))) /\ forall fs_i_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps fs_r_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps fs_s_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_rowsrowsrowrow_sumsum)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_fubini_rowsrowsrowrow_sumsum = fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_rowsrowsrowrow_sumsum) + (fs_a_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_fubini_rowsrowsrowrow_sumsumnegative = fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumnegative) + (fs_r_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_fubini_rowsrowsrowrow_sumsumnegative = fs_q_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_rowsrowsrowrow_sumsumnegative) + (fs_s_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps = fs_r_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps + fs_a_dst_fubini_rowsrowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_rowsrowsrowrow_sumsumresult ge_balance_negative_fubini_rowsrowsrowrow_sumsumresult. (((((srt_value_fubini_rowsrows) = 2 * (ge_balance_positive_fubini_rowsrowsrowrow_sumsumresult) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_fubini_rowsrowsrowrow_sumsumresultdecode. (((srt_value_fubini_rowsrows) = 2 * ge_signed_half_fubini_rowsrowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_fubini_rowsrowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_fubini_rowsrowsrowrow_sumsumresult) = S ge_signed_half_fubini_rowsrowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_fubini_rowsrowsrowrow_sumsum) + ge_balance_negative_fubini_rowsrowsrowrow_sumsumresult = (dst_negative_sum_fubini_rowsrowsrowrow_sumsum) + ge_balance_positive_fubini_rowsrowsrowrow_sumsumresult)))))))))))))))))) /\ (exists dst_positive_code_fubini_rowstotal dst_positive_scale_fubini_rowstotal dst_negative_code_fubini_rowstotal dst_negative_scale_fubini_rowstotal dst_positive_sum_fubini_rowstotal dst_negative_sum_fubini_rowstotal. (((srt_rows_fubini_rows) = (((((dst_positive_code_fubini_rowstotal) + (dst_positive_scale_fubini_rowstotal)) * S ((dst_positive_code_fubini_rowstotal) + (dst_positive_scale_fubini_rowstotal)) + ((dst_positive_scale_fubini_rowstotal) + (dst_positive_scale_fubini_rowstotal))) + (((dst_negative_code_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)) * S ((dst_negative_code_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)) + ((dst_negative_scale_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)))) * S ((((dst_positive_code_fubini_rowstotal) + (dst_positive_scale_fubini_rowstotal)) * S ((dst_positive_code_fubini_rowstotal) + (dst_positive_scale_fubini_rowstotal)) + ((dst_positive_scale_fubini_rowstotal) + (dst_positive_scale_fubini_rowstotal))) + (((dst_negative_code_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)) * S ((dst_negative_code_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)) + ((dst_negative_scale_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)))) + ((((dst_negative_code_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)) * S ((dst_negative_code_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)) + ((dst_negative_scale_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal))) + (((dst_negative_code_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)) * S ((dst_negative_code_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)) + ((dst_negative_scale_fubini_rowstotal) + (dst_negative_scale_fubini_rowstotal)))))) /\ (((exists fs_u_dst_fubini_rowstotalpositive fs_v_dst_fubini_rowstotalpositive. ((((exists fs_h_dst_fubini_rowstotalpositive_body_start. fs_h_dst_fubini_rowstotalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_rowstotalpositive)) /\ exists fs_q_dst_fubini_rowstotalpositive_body_start. fs_u_dst_fubini_rowstotalpositive = fs_q_dst_fubini_rowstotalpositive_body_start * S ((S (0)) * fs_v_dst_fubini_rowstotalpositive) + (0))) /\ ((((exists fs_h_dst_fubini_rowstotalpositive_body_terminal. fs_h_dst_fubini_rowstotalpositive_body_terminal + S (dst_positive_sum_fubini_rowstotal) = S ((S (m)) * fs_v_dst_fubini_rowstotalpositive)) /\ exists fs_q_dst_fubini_rowstotalpositive_body_terminal. fs_u_dst_fubini_rowstotalpositive = fs_q_dst_fubini_rowstotalpositive_body_terminal * S ((S (m)) * fs_v_dst_fubini_rowstotalpositive) + (dst_positive_sum_fubini_rowstotal))) /\ forall fs_i_dst_fubini_rowstotalpositive_body_steps. (exists fs_lt_dst_fubini_rowstotalpositive_body_steps_bound. fs_lt_dst_fubini_rowstotalpositive_body_steps_bound + S fs_i_dst_fubini_rowstotalpositive_body_steps = m) -> exists fs_a_dst_fubini_rowstotalpositive_body_steps fs_r_dst_fubini_rowstotalpositive_body_steps fs_s_dst_fubini_rowstotalpositive_body_steps. ((((exists fs_h_dst_fubini_rowstotalpositive_body_steps_summand. fs_h_dst_fubini_rowstotalpositive_body_steps_summand + S (fs_a_dst_fubini_rowstotalpositive_body_steps) = S ((S (fs_i_dst_fubini_rowstotalpositive_body_steps)) * dst_positive_scale_fubini_rowstotal)) /\ exists fs_q_dst_fubini_rowstotalpositive_body_steps_summand. dst_positive_code_fubini_rowstotal = fs_q_dst_fubini_rowstotalpositive_body_steps_summand * S ((S (fs_i_dst_fubini_rowstotalpositive_body_steps)) * dst_positive_scale_fubini_rowstotal) + (fs_a_dst_fubini_rowstotalpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_rowstotalpositive_body_steps_partial. fs_h_dst_fubini_rowstotalpositive_body_steps_partial + S (fs_r_dst_fubini_rowstotalpositive_body_steps) = S ((S (fs_i_dst_fubini_rowstotalpositive_body_steps)) * fs_v_dst_fubini_rowstotalpositive)) /\ exists fs_q_dst_fubini_rowstotalpositive_body_steps_partial. fs_u_dst_fubini_rowstotalpositive = fs_q_dst_fubini_rowstotalpositive_body_steps_partial * S ((S (fs_i_dst_fubini_rowstotalpositive_body_steps)) * fs_v_dst_fubini_rowstotalpositive) + (fs_r_dst_fubini_rowstotalpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_rowstotalpositive_body_steps_successor. fs_h_dst_fubini_rowstotalpositive_body_steps_successor + S (fs_s_dst_fubini_rowstotalpositive_body_steps) = S ((S (S fs_i_dst_fubini_rowstotalpositive_body_steps)) * fs_v_dst_fubini_rowstotalpositive)) /\ exists fs_q_dst_fubini_rowstotalpositive_body_steps_successor. fs_u_dst_fubini_rowstotalpositive = fs_q_dst_fubini_rowstotalpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_rowstotalpositive_body_steps)) * fs_v_dst_fubini_rowstotalpositive) + (fs_s_dst_fubini_rowstotalpositive_body_steps))) /\ fs_s_dst_fubini_rowstotalpositive_body_steps = fs_r_dst_fubini_rowstotalpositive_body_steps + fs_a_dst_fubini_rowstotalpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_rowstotalnegative fs_v_dst_fubini_rowstotalnegative. ((((exists fs_h_dst_fubini_rowstotalnegative_body_start. fs_h_dst_fubini_rowstotalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_rowstotalnegative)) /\ exists fs_q_dst_fubini_rowstotalnegative_body_start. fs_u_dst_fubini_rowstotalnegative = fs_q_dst_fubini_rowstotalnegative_body_start * S ((S (0)) * fs_v_dst_fubini_rowstotalnegative) + (0))) /\ ((((exists fs_h_dst_fubini_rowstotalnegative_body_terminal. fs_h_dst_fubini_rowstotalnegative_body_terminal + S (dst_negative_sum_fubini_rowstotal) = S ((S (m)) * fs_v_dst_fubini_rowstotalnegative)) /\ exists fs_q_dst_fubini_rowstotalnegative_body_terminal. fs_u_dst_fubini_rowstotalnegative = fs_q_dst_fubini_rowstotalnegative_body_terminal * S ((S (m)) * fs_v_dst_fubini_rowstotalnegative) + (dst_negative_sum_fubini_rowstotal))) /\ forall fs_i_dst_fubini_rowstotalnegative_body_steps. (exists fs_lt_dst_fubini_rowstotalnegative_body_steps_bound. fs_lt_dst_fubini_rowstotalnegative_body_steps_bound + S fs_i_dst_fubini_rowstotalnegative_body_steps = m) -> exists fs_a_dst_fubini_rowstotalnegative_body_steps fs_r_dst_fubini_rowstotalnegative_body_steps fs_s_dst_fubini_rowstotalnegative_body_steps. ((((exists fs_h_dst_fubini_rowstotalnegative_body_steps_summand. fs_h_dst_fubini_rowstotalnegative_body_steps_summand + S (fs_a_dst_fubini_rowstotalnegative_body_steps) = S ((S (fs_i_dst_fubini_rowstotalnegative_body_steps)) * dst_negative_scale_fubini_rowstotal)) /\ exists fs_q_dst_fubini_rowstotalnegative_body_steps_summand. dst_negative_code_fubini_rowstotal = fs_q_dst_fubini_rowstotalnegative_body_steps_summand * S ((S (fs_i_dst_fubini_rowstotalnegative_body_steps)) * dst_negative_scale_fubini_rowstotal) + (fs_a_dst_fubini_rowstotalnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_rowstotalnegative_body_steps_partial. fs_h_dst_fubini_rowstotalnegative_body_steps_partial + S (fs_r_dst_fubini_rowstotalnegative_body_steps) = S ((S (fs_i_dst_fubini_rowstotalnegative_body_steps)) * fs_v_dst_fubini_rowstotalnegative)) /\ exists fs_q_dst_fubini_rowstotalnegative_body_steps_partial. fs_u_dst_fubini_rowstotalnegative = fs_q_dst_fubini_rowstotalnegative_body_steps_partial * S ((S (fs_i_dst_fubini_rowstotalnegative_body_steps)) * fs_v_dst_fubini_rowstotalnegative) + (fs_r_dst_fubini_rowstotalnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_rowstotalnegative_body_steps_successor. fs_h_dst_fubini_rowstotalnegative_body_steps_successor + S (fs_s_dst_fubini_rowstotalnegative_body_steps) = S ((S (S fs_i_dst_fubini_rowstotalnegative_body_steps)) * fs_v_dst_fubini_rowstotalnegative)) /\ exists fs_q_dst_fubini_rowstotalnegative_body_steps_successor. fs_u_dst_fubini_rowstotalnegative = fs_q_dst_fubini_rowstotalnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_rowstotalnegative_body_steps)) * fs_v_dst_fubini_rowstotalnegative) + (fs_s_dst_fubini_rowstotalnegative_body_steps))) /\ fs_s_dst_fubini_rowstotalnegative_body_steps = fs_r_dst_fubini_rowstotalnegative_body_steps + fs_a_dst_fubini_rowstotalnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_rowstotalresult ge_balance_negative_fubini_rowstotalresult. (((((a) = 2 * (ge_balance_positive_fubini_rowstotalresult) /\ (ge_balance_negative_fubini_rowstotalresult) = 0) \/ exists ge_signed_half_fubini_rowstotalresultdecode. (((a) = 2 * ge_signed_half_fubini_rowstotalresultdecode + 1 /\ (ge_balance_positive_fubini_rowstotalresult) = 0) /\ (ge_balance_negative_fubini_rowstotalresult) = S ge_signed_half_fubini_rowstotalresultdecode))) /\ ((dst_positive_sum_fubini_rowstotal) + ge_balance_negative_fubini_rowstotalresult = (dst_negative_sum_fubini_rowstotal) + ge_balance_positive_fubini_rowstotalresult))))))))))) -> (exists srt_rows_fubini_columns. ((((exists dst_positive_code_fubini_columnsrowssource_table dst_positive_scale_fubini_columnsrowssource_table dst_negative_code_fubini_columnsrowssource_table dst_negative_scale_fubini_columnsrowssource_table. (((F) = (((((dst_positive_code_fubini_columnsrowssource_table) + (dst_positive_scale_fubini_columnsrowssource_table)) * S ((dst_positive_code_fubini_columnsrowssource_table) + (dst_positive_scale_fubini_columnsrowssource_table)) + ((dst_positive_scale_fubini_columnsrowssource_table) + (dst_positive_scale_fubini_columnsrowssource_table))) + (((dst_negative_code_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)) * S ((dst_negative_code_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)) + ((dst_negative_scale_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)))) * S ((((dst_positive_code_fubini_columnsrowssource_table) + (dst_positive_scale_fubini_columnsrowssource_table)) * S ((dst_positive_code_fubini_columnsrowssource_table) + (dst_positive_scale_fubini_columnsrowssource_table)) + ((dst_positive_scale_fubini_columnsrowssource_table) + (dst_positive_scale_fubini_columnsrowssource_table))) + (((dst_negative_code_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)) * S ((dst_negative_code_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)) + ((dst_negative_scale_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)))) + ((((dst_negative_code_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)) * S ((dst_negative_code_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)) + ((dst_negative_scale_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table))) + (((dst_negative_code_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)) * S ((dst_negative_code_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)) + ((dst_negative_scale_fubini_columnsrowssource_table) + (dst_negative_scale_fubini_columnsrowssource_table)))))) /\ (forall dst_index_fubini_columnsrowssource_table. (exists pvs_le_gap_fubini_columnsrowssource_tabledomain. pvs_le_gap_fubini_columnsrowssource_tabledomain + (dst_index_fubini_columnsrowssource_table) = (0)) -> exists dst_positive_fubini_columnsrowssource_table dst_negative_fubini_columnsrowssource_table dst_value_fubini_columnsrowssource_table. ((((exists ff_h_pvs_fubini_columnsrowssource_tableentrypositive. ff_h_pvs_fubini_columnsrowssource_tableentrypositive + S (dst_positive_fubini_columnsrowssource_table) = S ((S (dst_index_fubini_columnsrowssource_table)) * dst_positive_scale_fubini_columnsrowssource_table)) /\ exists ff_q_pvs_fubini_columnsrowssource_tableentrypositive. dst_positive_code_fubini_columnsrowssource_table = ff_q_pvs_fubini_columnsrowssource_tableentrypositive * S ((S (dst_index_fubini_columnsrowssource_table)) * dst_positive_scale_fubini_columnsrowssource_table) + (dst_positive_fubini_columnsrowssource_table))) /\ (((((exists ff_h_pvs_fubini_columnsrowssource_tableentrynegative. ff_h_pvs_fubini_columnsrowssource_tableentrynegative + S (dst_negative_fubini_columnsrowssource_table) = S ((S (dst_index_fubini_columnsrowssource_table)) * dst_negative_scale_fubini_columnsrowssource_table)) /\ exists ff_q_pvs_fubini_columnsrowssource_tableentrynegative. dst_negative_code_fubini_columnsrowssource_table = ff_q_pvs_fubini_columnsrowssource_tableentrynegative * S ((S (dst_index_fubini_columnsrowssource_table)) * dst_negative_scale_fubini_columnsrowssource_table) + (dst_negative_fubini_columnsrowssource_table))) /\ (exists ge_balance_positive_fubini_columnsrowssource_tableentryvalue ge_balance_negative_fubini_columnsrowssource_tableentryvalue. (((((dst_value_fubini_columnsrowssource_table) = 2 * (ge_balance_positive_fubini_columnsrowssource_tableentryvalue) /\ (ge_balance_negative_fubini_columnsrowssource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowssource_tableentryvaluedecode. (((dst_value_fubini_columnsrowssource_table) = 2 * ge_signed_half_fubini_columnsrowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowssource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowssource_tableentryvalue) = S ge_signed_half_fubini_columnsrowssource_tableentryvaluedecode))) /\ ((dst_positive_fubini_columnsrowssource_table) + ge_balance_negative_fubini_columnsrowssource_tableentryvalue = (dst_negative_fubini_columnsrowssource_table) + ge_balance_positive_fubini_columnsrowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_columnsrowsrow_table dst_positive_scale_fubini_columnsrowsrow_table dst_negative_code_fubini_columnsrowsrow_table dst_negative_scale_fubini_columnsrowsrow_table. (((srt_rows_fubini_columns) = (((((dst_positive_code_fubini_columnsrowsrow_table) + (dst_positive_scale_fubini_columnsrowsrow_table)) * S ((dst_positive_code_fubini_columnsrowsrow_table) + (dst_positive_scale_fubini_columnsrowsrow_table)) + ((dst_positive_scale_fubini_columnsrowsrow_table) + (dst_positive_scale_fubini_columnsrowsrow_table))) + (((dst_negative_code_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)) * S ((dst_negative_code_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)) + ((dst_negative_scale_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)))) * S ((((dst_positive_code_fubini_columnsrowsrow_table) + (dst_positive_scale_fubini_columnsrowsrow_table)) * S ((dst_positive_code_fubini_columnsrowsrow_table) + (dst_positive_scale_fubini_columnsrowsrow_table)) + ((dst_positive_scale_fubini_columnsrowsrow_table) + (dst_positive_scale_fubini_columnsrowsrow_table))) + (((dst_negative_code_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)) * S ((dst_negative_code_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)) + ((dst_negative_scale_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)))) + ((((dst_negative_code_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)) * S ((dst_negative_code_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)) + ((dst_negative_scale_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table))) + (((dst_negative_code_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)) * S ((dst_negative_code_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)) + ((dst_negative_scale_fubini_columnsrowsrow_table) + (dst_negative_scale_fubini_columnsrowsrow_table)))))) /\ (forall dst_index_fubini_columnsrowsrow_table. (exists pvs_le_gap_fubini_columnsrowsrow_tabledomain. pvs_le_gap_fubini_columnsrowsrow_tabledomain + (dst_index_fubini_columnsrowsrow_table) = (n)) -> exists dst_positive_fubini_columnsrowsrow_table dst_negative_fubini_columnsrowsrow_table dst_value_fubini_columnsrowsrow_table. ((((exists ff_h_pvs_fubini_columnsrowsrow_tableentrypositive. ff_h_pvs_fubini_columnsrowsrow_tableentrypositive + S (dst_positive_fubini_columnsrowsrow_table) = S ((S (dst_index_fubini_columnsrowsrow_table)) * dst_positive_scale_fubini_columnsrowsrow_table)) /\ exists ff_q_pvs_fubini_columnsrowsrow_tableentrypositive. dst_positive_code_fubini_columnsrowsrow_table = ff_q_pvs_fubini_columnsrowsrow_tableentrypositive * S ((S (dst_index_fubini_columnsrowsrow_table)) * dst_positive_scale_fubini_columnsrowsrow_table) + (dst_positive_fubini_columnsrowsrow_table))) /\ (((((exists ff_h_pvs_fubini_columnsrowsrow_tableentrynegative. ff_h_pvs_fubini_columnsrowsrow_tableentrynegative + S (dst_negative_fubini_columnsrowsrow_table) = S ((S (dst_index_fubini_columnsrowsrow_table)) * dst_negative_scale_fubini_columnsrowsrow_table)) /\ exists ff_q_pvs_fubini_columnsrowsrow_tableentrynegative. dst_negative_code_fubini_columnsrowsrow_table = ff_q_pvs_fubini_columnsrowsrow_tableentrynegative * S ((S (dst_index_fubini_columnsrowsrow_table)) * dst_negative_scale_fubini_columnsrowsrow_table) + (dst_negative_fubini_columnsrowsrow_table))) /\ (exists ge_balance_positive_fubini_columnsrowsrow_tableentryvalue ge_balance_negative_fubini_columnsrowsrow_tableentryvalue. (((((dst_value_fubini_columnsrowsrow_table) = 2 * (ge_balance_positive_fubini_columnsrowsrow_tableentryvalue) /\ (ge_balance_negative_fubini_columnsrowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowsrow_tableentryvaluedecode. (((dst_value_fubini_columnsrowsrow_table) = 2 * ge_signed_half_fubini_columnsrowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowsrow_tableentryvalue) = S ge_signed_half_fubini_columnsrowsrow_tableentryvaluedecode))) /\ ((dst_positive_fubini_columnsrowsrow_table) + ge_balance_negative_fubini_columnsrowsrow_tableentryvalue = (dst_negative_fubini_columnsrowsrow_table) + ge_balance_positive_fubini_columnsrowsrow_tableentryvalue))))))))) /\ (forall srt_index_fubini_columnsrows. (exists pvs_gap_fubini_columnsrowsbound. pvs_gap_fubini_columnsrowsbound + S (srt_index_fubini_columnsrows) = (n)) -> exists srt_value_fubini_columnsrows. (((exists dst_positive_code_fubini_columnsrowsrowentry dst_positive_scale_fubini_columnsrowsrowentry dst_negative_code_fubini_columnsrowsrowentry dst_negative_scale_fubini_columnsrowsrowentry dst_positive_fubini_columnsrowsrowentry dst_negative_fubini_columnsrowsrowentry. (((srt_rows_fubini_columns) = (((((dst_positive_code_fubini_columnsrowsrowentry) + (dst_positive_scale_fubini_columnsrowsrowentry)) * S ((dst_positive_code_fubini_columnsrowsrowentry) + (dst_positive_scale_fubini_columnsrowsrowentry)) + ((dst_positive_scale_fubini_columnsrowsrowentry) + (dst_positive_scale_fubini_columnsrowsrowentry))) + (((dst_negative_code_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)) * S ((dst_negative_code_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)) + ((dst_negative_scale_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)))) * S ((((dst_positive_code_fubini_columnsrowsrowentry) + (dst_positive_scale_fubini_columnsrowsrowentry)) * S ((dst_positive_code_fubini_columnsrowsrowentry) + (dst_positive_scale_fubini_columnsrowsrowentry)) + ((dst_positive_scale_fubini_columnsrowsrowentry) + (dst_positive_scale_fubini_columnsrowsrowentry))) + (((dst_negative_code_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)) * S ((dst_negative_code_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)) + ((dst_negative_scale_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)))) + ((((dst_negative_code_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)) * S ((dst_negative_code_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)) + ((dst_negative_scale_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry))) + (((dst_negative_code_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)) * S ((dst_negative_code_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)) + ((dst_negative_scale_fubini_columnsrowsrowentry) + (dst_negative_scale_fubini_columnsrowsrowentry)))))) /\ (((((exists ff_h_pvs_fubini_columnsrowsrowentrypositive. ff_h_pvs_fubini_columnsrowsrowentrypositive + S (dst_positive_fubini_columnsrowsrowentry) = S ((S (srt_index_fubini_columnsrows)) * dst_positive_scale_fubini_columnsrowsrowentry)) /\ exists ff_q_pvs_fubini_columnsrowsrowentrypositive. dst_positive_code_fubini_columnsrowsrowentry = ff_q_pvs_fubini_columnsrowsrowentrypositive * S ((S (srt_index_fubini_columnsrows)) * dst_positive_scale_fubini_columnsrowsrowentry) + (dst_positive_fubini_columnsrowsrowentry))) /\ (((((exists ff_h_pvs_fubini_columnsrowsrowentrynegative. ff_h_pvs_fubini_columnsrowsrowentrynegative + S (dst_negative_fubini_columnsrowsrowentry) = S ((S (srt_index_fubini_columnsrows)) * dst_negative_scale_fubini_columnsrowsrowentry)) /\ exists ff_q_pvs_fubini_columnsrowsrowentrynegative. dst_negative_code_fubini_columnsrowsrowentry = ff_q_pvs_fubini_columnsrowsrowentrynegative * S ((S (srt_index_fubini_columnsrows)) * dst_negative_scale_fubini_columnsrowsrowentry) + (dst_negative_fubini_columnsrowsrowentry))) /\ (exists ge_balance_positive_fubini_columnsrowsrowentryvalue ge_balance_negative_fubini_columnsrowsrowentryvalue. (((((srt_value_fubini_columnsrows) = 2 * (ge_balance_positive_fubini_columnsrowsrowentryvalue) /\ (ge_balance_negative_fubini_columnsrowsrowentryvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowsrowentryvaluedecode. (((srt_value_fubini_columnsrows) = 2 * ge_signed_half_fubini_columnsrowsrowentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowsrowentryvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowsrowentryvalue) = S ge_signed_half_fubini_columnsrowsrowentryvaluedecode))) /\ ((dst_positive_fubini_columnsrowsrowentry) + ge_balance_negative_fubini_columnsrowsrowentryvalue = (dst_negative_fubini_columnsrowsrowentry) + ge_balance_positive_fubini_columnsrowsrowentryvalue))))))))) /\ (exists srs_slice_fubini_columnsrowsrowrow_sum. ((((exists dst_positive_code_fubini_columnsrowsrowrow_sumslicesource_table dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_fubini_columnsrowsrowrow_sumslicesource_table. (exists pvs_le_gap_fubini_columnsrowsrowrow_sumslicesource_tabledomain. pvs_le_gap_fubini_columnsrowsrowrow_sumslicesource_tabledomain + (dst_index_fubini_columnsrowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_fubini_columnsrowsrowrow_sumslicesource_table dst_negative_fubini_columnsrowsrowrow_sumslicesource_table dst_value_fubini_columnsrowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_fubini_columnsrowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_fubini_columnsrowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_fubini_columnsrowsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_columnsrowsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_columnsrowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_fubini_columnsrowsrowrow_sumslicesource_table = ff_q_pvs_fubini_columnsrowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_fubini_columnsrowsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_positive_fubini_columnsrowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_fubini_columnsrowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_fubini_columnsrowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_fubini_columnsrowsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_columnsrowsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_columnsrowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_fubini_columnsrowsrowrow_sumslicesource_table = ff_q_pvs_fubini_columnsrowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_fubini_columnsrowsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_columnsrowsrowrow_sumslicesource_table) + (dst_negative_fubini_columnsrowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_fubini_columnsrowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_fubini_columnsrowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_fubini_columnsrowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_fubini_columnsrowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_fubini_columnsrowsrowrow_sumslicesource_table) = 2 * ge_signed_half_fubini_columnsrowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_fubini_columnsrowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_fubini_columnsrowsrowrow_sumslicesource_table) + ge_balance_negative_fubini_columnsrowsrowrow_sumslicesource_tableentryvalue = (dst_negative_fubini_columnsrowsrowrow_sumslicesource_table) + ge_balance_positive_fubini_columnsrowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_columnsrowsrowrow_sumsliceoutput_table dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table. (((srs_slice_fubini_columnsrowsrowrow_sum) = (((((dst_positive_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_fubini_columnsrowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_fubini_columnsrowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_fubini_columnsrowsrowrow_sumsliceoutput_tabledomain + (dst_index_fubini_columnsrowsrowrow_sumsliceoutput_table) = (m)) -> exists dst_positive_fubini_columnsrowsrowrow_sumsliceoutput_table dst_negative_fubini_columnsrowsrowrow_sumsliceoutput_table dst_value_fubini_columnsrowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_fubini_columnsrowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_fubini_columnsrowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_fubini_columnsrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_columnsrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_columnsrowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_fubini_columnsrowsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_columnsrowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_fubini_columnsrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_positive_fubini_columnsrowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_fubini_columnsrowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_fubini_columnsrowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_fubini_columnsrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_columnsrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_columnsrowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_fubini_columnsrowsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_columnsrowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_fubini_columnsrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_columnsrowsrowrow_sumsliceoutput_table) + (dst_negative_fubini_columnsrowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_fubini_columnsrowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_fubini_columnsrowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_fubini_columnsrowsrowrow_sumsliceoutput_table) + ge_balance_negative_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_fubini_columnsrowsrowrow_sumsliceoutput_table) + ge_balance_positive_fubini_columnsrowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_fubini_columnsrowsrowrow_sumslice. (exists pvs_gap_fubini_columnsrowsrowrow_sumslicebound. pvs_gap_fubini_columnsrowsrowrow_sumslicebound + S (srs_index_fubini_columnsrowsrowrow_sumslice) = (m)) -> exists srs_value_fubini_columnsrowsrowrow_sumslice. (((exists dst_positive_code_fubini_columnsrowsrowrow_sumsliceentrysource dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource dst_positive_fubini_columnsrowsrowrow_sumsliceentrysource dst_negative_fubini_columnsrowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_fubini_columnsrowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_fubini_columnsrowsrowrow_sumsliceentrysourcepositive + S (dst_positive_fubini_columnsrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((t) * (srt_index_fubini_columnsrows)))) + ((s) * (srs_index_fubini_columnsrowsrowrow_sumslice))))) * dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_columnsrowsrowrow_sumsliceentrysourcepositive. dst_positive_code_fubini_columnsrowsrowrow_sumsliceentrysource = ff_q_pvs_fubini_columnsrowsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((t) * (srt_index_fubini_columnsrows)))) + ((s) * (srs_index_fubini_columnsrowsrowrow_sumslice))))) * dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_positive_fubini_columnsrowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_fubini_columnsrowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_fubini_columnsrowsrowrow_sumsliceentrysourcenegative + S (dst_negative_fubini_columnsrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((t) * (srt_index_fubini_columnsrows)))) + ((s) * (srs_index_fubini_columnsrowsrowrow_sumslice))))) * dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_columnsrowsrowrow_sumsliceentrysourcenegative. dst_negative_code_fubini_columnsrowsrowrow_sumsliceentrysource = ff_q_pvs_fubini_columnsrowsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((t) * (srt_index_fubini_columnsrows)))) + ((s) * (srs_index_fubini_columnsrowsrowrow_sumslice))))) * dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentrysource) + (dst_negative_fubini_columnsrowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_fubini_columnsrowsrowrow_sumsliceentrysourcevalue ge_balance_negative_fubini_columnsrowsrowrow_sumsliceentrysourcevalue. (((((srs_value_fubini_columnsrowsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_columnsrowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_fubini_columnsrowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_fubini_columnsrowsrowrow_sumslice) = 2 * ge_signed_half_fubini_columnsrowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_fubini_columnsrowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_fubini_columnsrowsrowrow_sumsliceentrysource) + ge_balance_negative_fubini_columnsrowsrowrow_sumsliceentrysourcevalue = (dst_negative_fubini_columnsrowsrowrow_sumsliceentrysource) + ge_balance_positive_fubini_columnsrowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_fubini_columnsrowsrowrow_sumsliceentryoutput dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput dst_positive_fubini_columnsrowsrowrow_sumsliceentryoutput dst_negative_fubini_columnsrowsrowrow_sumsliceentryoutput. (((srs_slice_fubini_columnsrowsrowrow_sum) = (((((dst_positive_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_fubini_columnsrowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_fubini_columnsrowsrowrow_sumsliceentryoutputpositive + S (dst_positive_fubini_columnsrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_columnsrowsrowrow_sumslice)) * dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_columnsrowsrowrow_sumsliceentryoutputpositive. dst_positive_code_fubini_columnsrowsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_columnsrowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_fubini_columnsrowsrowrow_sumslice)) * dst_positive_scale_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_positive_fubini_columnsrowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_fubini_columnsrowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_fubini_columnsrowsrowrow_sumsliceentryoutputnegative + S (dst_negative_fubini_columnsrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_columnsrowsrowrow_sumslice)) * dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_columnsrowsrowrow_sumsliceentryoutputnegative. dst_negative_code_fubini_columnsrowsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_columnsrowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_fubini_columnsrowsrowrow_sumslice)) * dst_negative_scale_fubini_columnsrowsrowrow_sumsliceentryoutput) + (dst_negative_fubini_columnsrowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_fubini_columnsrowsrowrow_sumsliceentryoutputvalue ge_balance_negative_fubini_columnsrowsrowrow_sumsliceentryoutputvalue. (((((srs_value_fubini_columnsrowsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_columnsrowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_fubini_columnsrowsrowrow_sumslice) = 2 * ge_signed_half_fubini_columnsrowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_fubini_columnsrowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_fubini_columnsrowsrowrow_sumsliceentryoutput) + ge_balance_negative_fubini_columnsrowsrowrow_sumsliceentryoutputvalue = (dst_negative_fubini_columnsrowsrowrow_sumsliceentryoutput) + ge_balance_positive_fubini_columnsrowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_fubini_columnsrowsrowrow_sumsum dst_positive_scale_fubini_columnsrowsrowrow_sumsum dst_negative_code_fubini_columnsrowsrowrow_sumsum dst_negative_scale_fubini_columnsrowsrowrow_sumsum dst_positive_sum_fubini_columnsrowsrowrow_sumsum dst_negative_sum_fubini_columnsrowsrowrow_sumsum. (((srs_slice_fubini_columnsrowsrowrow_sum) = (((((dst_positive_code_fubini_columnsrowsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsum)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsum)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsum))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)))) * S ((((dst_positive_code_fubini_columnsrowsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsum)) * S ((dst_positive_code_fubini_columnsrowsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsum)) + ((dst_positive_scale_fubini_columnsrowsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowsrowrow_sumsum))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)))) + ((((dst_negative_code_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum))) + (((dst_negative_code_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_columnsrowsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_fubini_columnsrowsrowrow_sumsumpositive fs_v_dst_fubini_columnsrowsrowrow_sumsumpositive. ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_start. fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_start. fs_u_dst_fubini_columnsrowsrowrow_sumsumpositive = fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_terminal. fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_fubini_columnsrowsrowrow_sumsum) = S ((S (m)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_terminal. fs_u_dst_fubini_columnsrowsrowrow_sumsumpositive = fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_terminal * S ((S (m)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumpositive) + (dst_positive_sum_fubini_columnsrowsrowrow_sumsum))) /\ forall fs_i_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps = m) -> exists fs_a_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps fs_r_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps fs_s_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_columnsrowsrowrow_sumsum)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_fubini_columnsrowsrowrow_sumsum = fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_columnsrowsrowrow_sumsum) + (fs_a_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_fubini_columnsrowsrowrow_sumsumpositive = fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumpositive) + (fs_r_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_fubini_columnsrowsrowrow_sumsumpositive = fs_q_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumpositive) + (fs_s_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps = fs_r_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps + fs_a_dst_fubini_columnsrowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_columnsrowsrowrow_sumsumnegative fs_v_dst_fubini_columnsrowsrowrow_sumsumnegative. ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_start. fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_start. fs_u_dst_fubini_columnsrowsrowrow_sumsumnegative = fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_terminal. fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_fubini_columnsrowsrowrow_sumsum) = S ((S (m)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_terminal. fs_u_dst_fubini_columnsrowsrowrow_sumsumnegative = fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_terminal * S ((S (m)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumnegative) + (dst_negative_sum_fubini_columnsrowsrowrow_sumsum))) /\ forall fs_i_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps = m) -> exists fs_a_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps fs_r_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps fs_s_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_columnsrowsrowrow_sumsum)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_fubini_columnsrowsrowrow_sumsum = fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_columnsrowsrowrow_sumsum) + (fs_a_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_fubini_columnsrowsrowrow_sumsumnegative = fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumnegative) + (fs_r_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_fubini_columnsrowsrowrow_sumsumnegative = fs_q_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_columnsrowsrowrow_sumsumnegative) + (fs_s_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps = fs_r_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps + fs_a_dst_fubini_columnsrowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_columnsrowsrowrow_sumsumresult ge_balance_negative_fubini_columnsrowsrowrow_sumsumresult. (((((srt_value_fubini_columnsrows) = 2 * (ge_balance_positive_fubini_columnsrowsrowrow_sumsumresult) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_fubini_columnsrowsrowrow_sumsumresultdecode. (((srt_value_fubini_columnsrows) = 2 * ge_signed_half_fubini_columnsrowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_fubini_columnsrowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_fubini_columnsrowsrowrow_sumsumresult) = S ge_signed_half_fubini_columnsrowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_fubini_columnsrowsrowrow_sumsum) + ge_balance_negative_fubini_columnsrowsrowrow_sumsumresult = (dst_negative_sum_fubini_columnsrowsrowrow_sumsum) + ge_balance_positive_fubini_columnsrowsrowrow_sumsumresult)))))))))))))))))) /\ (exists dst_positive_code_fubini_columnstotal dst_positive_scale_fubini_columnstotal dst_negative_code_fubini_columnstotal dst_negative_scale_fubini_columnstotal dst_positive_sum_fubini_columnstotal dst_negative_sum_fubini_columnstotal. (((srt_rows_fubini_columns) = (((((dst_positive_code_fubini_columnstotal) + (dst_positive_scale_fubini_columnstotal)) * S ((dst_positive_code_fubini_columnstotal) + (dst_positive_scale_fubini_columnstotal)) + ((dst_positive_scale_fubini_columnstotal) + (dst_positive_scale_fubini_columnstotal))) + (((dst_negative_code_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)) * S ((dst_negative_code_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)) + ((dst_negative_scale_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)))) * S ((((dst_positive_code_fubini_columnstotal) + (dst_positive_scale_fubini_columnstotal)) * S ((dst_positive_code_fubini_columnstotal) + (dst_positive_scale_fubini_columnstotal)) + ((dst_positive_scale_fubini_columnstotal) + (dst_positive_scale_fubini_columnstotal))) + (((dst_negative_code_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)) * S ((dst_negative_code_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)) + ((dst_negative_scale_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)))) + ((((dst_negative_code_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)) * S ((dst_negative_code_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)) + ((dst_negative_scale_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal))) + (((dst_negative_code_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)) * S ((dst_negative_code_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)) + ((dst_negative_scale_fubini_columnstotal) + (dst_negative_scale_fubini_columnstotal)))))) /\ (((exists fs_u_dst_fubini_columnstotalpositive fs_v_dst_fubini_columnstotalpositive. ((((exists fs_h_dst_fubini_columnstotalpositive_body_start. fs_h_dst_fubini_columnstotalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_columnstotalpositive)) /\ exists fs_q_dst_fubini_columnstotalpositive_body_start. fs_u_dst_fubini_columnstotalpositive = fs_q_dst_fubini_columnstotalpositive_body_start * S ((S (0)) * fs_v_dst_fubini_columnstotalpositive) + (0))) /\ ((((exists fs_h_dst_fubini_columnstotalpositive_body_terminal. fs_h_dst_fubini_columnstotalpositive_body_terminal + S (dst_positive_sum_fubini_columnstotal) = S ((S (n)) * fs_v_dst_fubini_columnstotalpositive)) /\ exists fs_q_dst_fubini_columnstotalpositive_body_terminal. fs_u_dst_fubini_columnstotalpositive = fs_q_dst_fubini_columnstotalpositive_body_terminal * S ((S (n)) * fs_v_dst_fubini_columnstotalpositive) + (dst_positive_sum_fubini_columnstotal))) /\ forall fs_i_dst_fubini_columnstotalpositive_body_steps. (exists fs_lt_dst_fubini_columnstotalpositive_body_steps_bound. fs_lt_dst_fubini_columnstotalpositive_body_steps_bound + S fs_i_dst_fubini_columnstotalpositive_body_steps = n) -> exists fs_a_dst_fubini_columnstotalpositive_body_steps fs_r_dst_fubini_columnstotalpositive_body_steps fs_s_dst_fubini_columnstotalpositive_body_steps. ((((exists fs_h_dst_fubini_columnstotalpositive_body_steps_summand. fs_h_dst_fubini_columnstotalpositive_body_steps_summand + S (fs_a_dst_fubini_columnstotalpositive_body_steps) = S ((S (fs_i_dst_fubini_columnstotalpositive_body_steps)) * dst_positive_scale_fubini_columnstotal)) /\ exists fs_q_dst_fubini_columnstotalpositive_body_steps_summand. dst_positive_code_fubini_columnstotal = fs_q_dst_fubini_columnstotalpositive_body_steps_summand * S ((S (fs_i_dst_fubini_columnstotalpositive_body_steps)) * dst_positive_scale_fubini_columnstotal) + (fs_a_dst_fubini_columnstotalpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_columnstotalpositive_body_steps_partial. fs_h_dst_fubini_columnstotalpositive_body_steps_partial + S (fs_r_dst_fubini_columnstotalpositive_body_steps) = S ((S (fs_i_dst_fubini_columnstotalpositive_body_steps)) * fs_v_dst_fubini_columnstotalpositive)) /\ exists fs_q_dst_fubini_columnstotalpositive_body_steps_partial. fs_u_dst_fubini_columnstotalpositive = fs_q_dst_fubini_columnstotalpositive_body_steps_partial * S ((S (fs_i_dst_fubini_columnstotalpositive_body_steps)) * fs_v_dst_fubini_columnstotalpositive) + (fs_r_dst_fubini_columnstotalpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_columnstotalpositive_body_steps_successor. fs_h_dst_fubini_columnstotalpositive_body_steps_successor + S (fs_s_dst_fubini_columnstotalpositive_body_steps) = S ((S (S fs_i_dst_fubini_columnstotalpositive_body_steps)) * fs_v_dst_fubini_columnstotalpositive)) /\ exists fs_q_dst_fubini_columnstotalpositive_body_steps_successor. fs_u_dst_fubini_columnstotalpositive = fs_q_dst_fubini_columnstotalpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_columnstotalpositive_body_steps)) * fs_v_dst_fubini_columnstotalpositive) + (fs_s_dst_fubini_columnstotalpositive_body_steps))) /\ fs_s_dst_fubini_columnstotalpositive_body_steps = fs_r_dst_fubini_columnstotalpositive_body_steps + fs_a_dst_fubini_columnstotalpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_columnstotalnegative fs_v_dst_fubini_columnstotalnegative. ((((exists fs_h_dst_fubini_columnstotalnegative_body_start. fs_h_dst_fubini_columnstotalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_columnstotalnegative)) /\ exists fs_q_dst_fubini_columnstotalnegative_body_start. fs_u_dst_fubini_columnstotalnegative = fs_q_dst_fubini_columnstotalnegative_body_start * S ((S (0)) * fs_v_dst_fubini_columnstotalnegative) + (0))) /\ ((((exists fs_h_dst_fubini_columnstotalnegative_body_terminal. fs_h_dst_fubini_columnstotalnegative_body_terminal + S (dst_negative_sum_fubini_columnstotal) = S ((S (n)) * fs_v_dst_fubini_columnstotalnegative)) /\ exists fs_q_dst_fubini_columnstotalnegative_body_terminal. fs_u_dst_fubini_columnstotalnegative = fs_q_dst_fubini_columnstotalnegative_body_terminal * S ((S (n)) * fs_v_dst_fubini_columnstotalnegative) + (dst_negative_sum_fubini_columnstotal))) /\ forall fs_i_dst_fubini_columnstotalnegative_body_steps. (exists fs_lt_dst_fubini_columnstotalnegative_body_steps_bound. fs_lt_dst_fubini_columnstotalnegative_body_steps_bound + S fs_i_dst_fubini_columnstotalnegative_body_steps = n) -> exists fs_a_dst_fubini_columnstotalnegative_body_steps fs_r_dst_fubini_columnstotalnegative_body_steps fs_s_dst_fubini_columnstotalnegative_body_steps. ((((exists fs_h_dst_fubini_columnstotalnegative_body_steps_summand. fs_h_dst_fubini_columnstotalnegative_body_steps_summand + S (fs_a_dst_fubini_columnstotalnegative_body_steps) = S ((S (fs_i_dst_fubini_columnstotalnegative_body_steps)) * dst_negative_scale_fubini_columnstotal)) /\ exists fs_q_dst_fubini_columnstotalnegative_body_steps_summand. dst_negative_code_fubini_columnstotal = fs_q_dst_fubini_columnstotalnegative_body_steps_summand * S ((S (fs_i_dst_fubini_columnstotalnegative_body_steps)) * dst_negative_scale_fubini_columnstotal) + (fs_a_dst_fubini_columnstotalnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_columnstotalnegative_body_steps_partial. fs_h_dst_fubini_columnstotalnegative_body_steps_partial + S (fs_r_dst_fubini_columnstotalnegative_body_steps) = S ((S (fs_i_dst_fubini_columnstotalnegative_body_steps)) * fs_v_dst_fubini_columnstotalnegative)) /\ exists fs_q_dst_fubini_columnstotalnegative_body_steps_partial. fs_u_dst_fubini_columnstotalnegative = fs_q_dst_fubini_columnstotalnegative_body_steps_partial * S ((S (fs_i_dst_fubini_columnstotalnegative_body_steps)) * fs_v_dst_fubini_columnstotalnegative) + (fs_r_dst_fubini_columnstotalnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_columnstotalnegative_body_steps_successor. fs_h_dst_fubini_columnstotalnegative_body_steps_successor + S (fs_s_dst_fubini_columnstotalnegative_body_steps) = S ((S (S fs_i_dst_fubini_columnstotalnegative_body_steps)) * fs_v_dst_fubini_columnstotalnegative)) /\ exists fs_q_dst_fubini_columnstotalnegative_body_steps_successor. fs_u_dst_fubini_columnstotalnegative = fs_q_dst_fubini_columnstotalnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_columnstotalnegative_body_steps)) * fs_v_dst_fubini_columnstotalnegative) + (fs_s_dst_fubini_columnstotalnegative_body_steps))) /\ fs_s_dst_fubini_columnstotalnegative_body_steps = fs_r_dst_fubini_columnstotalnegative_body_steps + fs_a_dst_fubini_columnstotalnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_columnstotalresult ge_balance_negative_fubini_columnstotalresult. (((((b) = 2 * (ge_balance_positive_fubini_columnstotalresult) /\ (ge_balance_negative_fubini_columnstotalresult) = 0) \/ exists ge_signed_half_fubini_columnstotalresultdecode. (((b) = 2 * ge_signed_half_fubini_columnstotalresultdecode + 1 /\ (ge_balance_positive_fubini_columnstotalresult) = 0) /\ (ge_balance_negative_fubini_columnstotalresult) = S ge_signed_half_fubini_columnstotalresultdecode))) /\ ((dst_positive_sum_fubini_columnstotal) + ge_balance_negative_fubini_columnstotalresult = (dst_negative_sum_fubini_columnstotal) + ge_balance_positive_fubini_columnstotalresult))))))))))) -> a=bConstructive proof overview
Generated structural guide
Ordinary row-count induction proves finite signed Fubini for arbitrary affine grids, including both zero dimensions, by constructing the missing prefix column table and applying actual signed sum linearity.
The unchanged tactic script uses 11 declared prerequisites and contains 150 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
RS001A signed_rectangular_sum_zero_outer RS001C signed_rectangular_sum_zero_inner divisor_signed_sum_successor_decompose Alpha theorem; checked-use authorized RS0015 signed_rectangular_row_sums_exists arithmetic_signed_sum_exists Alpha theorem; checked-use authorized RS0011 signed_rectangular_row_sums_restrict_outer RS0010 signed_rectangular_row_sums_lookup le_refl Stable theorem; checked-use authorized RS001D signed_rectangular_columns_successor_add signed_prefix_sum_pointwise_add Alpha theorem; checked-use authorized signed_add_functional Alpha theorem; checked-use authorizedDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
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.
Named ingredients (6)
01Induction on mL1–10
02Calculate and transport equalitiesL11–11
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L11
trans 0
03Use earlier factsL12–19
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L12
specialize signed_rectangular_sum_zero_outer (F) - L13
specialize signed_rectangular_sum_zero_outer (o) - L14
specialize signed_rectangular_sum_zero_outer (s) - L15
specialize signed_rectangular_sum_zero_outer (t) - L16
specialize signed_rectangular_sum_zero_outer (n) - L17
specialize signed_rectangular_sum_zero_outer (a) - L18
apply signed_rectangular_sum_zero_outer - L19
exact ha
04Calculate and transport equalitiesL20–20
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L20
symm
05Use earlier factsL21–28
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L21
specialize signed_rectangular_sum_zero_inner (F) - L22
specialize signed_rectangular_sum_zero_inner (o) - L23
specialize signed_rectangular_sum_zero_inner (t) - L24
specialize signed_rectangular_sum_zero_inner (s) - L25
specialize signed_rectangular_sum_zero_inner (n) - L26
specialize signed_rectangular_sum_zero_inner (b) - L27
apply signed_rectangular_sum_zero_inner - L28
exact hb
06Fix variables and assumptionsL29–37
07Separate the logical casesL38–41
08Establish hdL42–47
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply divisor signed sum successor decompose.
- L42
have hd : ∃ u. ∃ v. SignedPrefixSum(x,m,u) ∧ (ArithAt(x,m,v) ∧ SignedAdd(u,v,a))Definitions: SignedAddArithAtSignedPrefixSum - L43
specialize divisor_signed_sum_successor_decompose (x) - L44
specialize divisor_signed_sum_successor_decompose (m) - L45
specialize divisor_signed_sum_successor_decompose (a) - L46
apply divisor_signed_sum_successor_decompose - L47
exact ha_witness_right
09Separate the logical casesL48–51
10Establish hCL52–59
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed rectangular row sums exists.
- L52
have hC : ∃ C. ArithRowSums(F,C,o,t,s,n,m)Definitions: ArithRowSums - L53
specialize signed_rectangular_row_sums_exists (n) - L54
specialize signed_rectangular_row_sums_exists (F) - L55
specialize signed_rectangular_row_sums_exists (o) - L56
specialize signed_rectangular_row_sums_exists (t) - L57
specialize signed_rectangular_row_sums_exists (s) - L58
specialize signed_rectangular_row_sums_exists (m) - L59
apply signed_rectangular_row_sums_exists
11Separate the logical casesL60–61
12Use earlier factsL62–62
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L62
exact ha_witness_left_left
13Separate the logical casesL63–63
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L63
cases hC
14Establish hsumCL64–68
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply arithmetic signed sum exists.
15Separate the logical casesL69–70
16Use earlier factsL71–71
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L71
exact hC_witness_right_left
17Separate the logical casesL72–72
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L72
cases hsumC
18Establish heqL73–81
19Construct an explicit witnessL82–82
Supply the displayed value, then prove that it has the required property.
- L82
exists x
20Separate the logical casesL83–83
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L83
split
21Use earlier factsL84–93
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L84
specialize signed_rectangular_row_sums_restrict_outer (F) - L85
specialize signed_rectangular_row_sums_restrict_outer (x) - L86
specialize signed_rectangular_row_sums_restrict_outer (o) - L87
specialize signed_rectangular_row_sums_restrict_outer (s) - L88
specialize signed_rectangular_row_sums_restrict_outer (t) - L89
specialize signed_rectangular_row_sums_restrict_outer (m) - L90
specialize signed_rectangular_row_sums_restrict_outer (n) - L91
apply signed_rectangular_row_sums_restrict_outer - L92
exact ha_witness_left - L93
exact hd_witness_witness_left
22Construct an explicit witnessL94–94
Supply the displayed value, then prove that it has the required property.
- L94
exists x4
23Separate the logical casesL95–95
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L95
split
24Use earlier factsL96–97
25Establish hlastL98–107
Establish this local claim before using it. It is not an additional assumption.
- L98
have hlast : SignedSliceSum(F,o + s · m,t,n,x3)Definitions: SignedSliceSum - L99
specialize signed_rectangular_row_sums_lookup (F) - L100
specialize signed_rectangular_row_sums_lookup (x) - L101
specialize signed_rectangular_row_sums_lookup (o) - L102
specialize signed_rectangular_row_sums_lookup (s) - L103
specialize signed_rectangular_row_sums_lookup (t) - L104
specialize signed_rectangular_row_sums_lookup (S m) - L105
specialize signed_rectangular_row_sums_lookup (n) - L106
specialize signed_rectangular_row_sums_lookup (m) - L107
specialize signed_rectangular_row_sums_lookup (x3)
26Use earlier factsL108–112
27Separate the logical casesL113–114
28Establish hpointL115–124
Establish this local claim before using it. It is not an additional assumption.
- L115
have hpoint : ArithAdd(x4,x6,x1,n)Definitions: ArithAdd - L116
specialize signed_rectangular_columns_successor_add (F) - L117
specialize signed_rectangular_columns_successor_add (x4) - L118
specialize signed_rectangular_columns_successor_add (x6) - L119
specialize signed_rectangular_columns_successor_add (x1) - L120
specialize signed_rectangular_columns_successor_add (o) - L121
specialize signed_rectangular_columns_successor_add (s) - L122
specialize signed_rectangular_columns_successor_add (t) - L123
specialize signed_rectangular_columns_successor_add (m) - L124
specialize signed_rectangular_columns_successor_add (n)
29Use earlier factsL125–128
30Establish haddL129–138
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed prefix sum pointwise add.
- L129
have hadd : SignedAdd(x5,x3,b)Definitions: SignedAdd - L130
specialize signed_prefix_sum_pointwise_add (n) - L131
specialize signed_prefix_sum_pointwise_add (x4) - L132
specialize signed_prefix_sum_pointwise_add (x6) - L133
specialize signed_prefix_sum_pointwise_add (x1) - L134
specialize signed_prefix_sum_pointwise_add (x5) - L135
specialize signed_prefix_sum_pointwise_add (x3) - L136
specialize signed_prefix_sum_pointwise_add (b) - L137
apply signed_prefix_sum_pointwise_add - L138
exact hpoint
31Use earlier factsL139–141
32Calculate and transport equalitiesL142–143
33Use earlier factsL144–150
Instantiate or apply named facts and discharge the corresponding proof obligations.
Original exact command ledger · 150 lines
- 0001
induction m - 0002
intro F - 0003
intro o - 0004
intro s - 0005
intro t - 0006
intro n - 0007
intro a - 0008
intro b - 0009
intro ha - 0010
intro hb - 0011
trans 0 - 0012
specialize signed_rectangular_sum_zero_outer (F) - 0013
specialize signed_rectangular_sum_zero_outer (o) - 0014
specialize signed_rectangular_sum_zero_outer (s) - 0015
specialize signed_rectangular_sum_zero_outer (t) - 0016
specialize signed_rectangular_sum_zero_outer (n) - 0017
specialize signed_rectangular_sum_zero_outer (a) - 0018
apply signed_rectangular_sum_zero_outer - 0019
exact ha - 0020
symm - 0021
specialize signed_rectangular_sum_zero_inner (F) - 0022
specialize signed_rectangular_sum_zero_inner (o) - 0023
specialize signed_rectangular_sum_zero_inner (t) - 0024
specialize signed_rectangular_sum_zero_inner (s) - 0025
specialize signed_rectangular_sum_zero_inner (n) - 0026
specialize signed_rectangular_sum_zero_inner (b) - 0027
apply signed_rectangular_sum_zero_inner - 0028
exact hb - 0029
intro F - 0030
intro o - 0031
intro s - 0032
intro t - 0033
intro n - 0034
intro a - 0035
intro b - 0036
intro ha - 0037
intro hb - 0038
cases ha - 0039
cases ha_witness - 0040
cases hb - 0041
cases hb_witness - 0042
have hd : exists u v. (((exists dst_positive_code_fubini_prefix dst_positive_scale_fubini_prefix dst_negative_code_fubini_prefix dst_negative_scale_fubini_prefix dst_positive_sum_fubini_prefix dst_negative_sum_fubini_prefix. (((x) = (((((dst_positive_code_fubini_prefix) + (dst_positive_scale_fubini_prefix)) * S ((dst_positive_code_fubini_prefix) + (dst_positive_scale_fubini_prefix)) + ((dst_positive_scale_fubini_prefix) + (dst_positive_scale_fubini_prefix))) + (((dst_negative_code_fubini_prefix) + (dst_negative_scale_fubini_prefix)) * S ((dst_negative_code_fubini_prefix) + (dst_negative_scale_fubini_prefix)) + ((dst_negative_scale_fubini_prefix) + (dst_negative_scale_fubini_prefix)))) * S ((((dst_positive_code_fubini_prefix) + (dst_positive_scale_fubini_prefix)) * S ((dst_positive_code_fubini_prefix) + (dst_positive_scale_fubini_prefix)) + ((dst_positive_scale_fubini_prefix) + (dst_positive_scale_fubini_prefix))) + (((dst_negative_code_fubini_prefix) + (dst_negative_scale_fubini_prefix)) * S ((dst_negative_code_fubini_prefix) + (dst_negative_scale_fubini_prefix)) + ((dst_negative_scale_fubini_prefix) + (dst_negative_scale_fubini_prefix)))) + ((((dst_negative_code_fubini_prefix) + (dst_negative_scale_fubini_prefix)) * S ((dst_negative_code_fubini_prefix) + (dst_negative_scale_fubini_prefix)) + ((dst_negative_scale_fubini_prefix) + (dst_negative_scale_fubini_prefix))) + (((dst_negative_code_fubini_prefix) + (dst_negative_scale_fubini_prefix)) * S ((dst_negative_code_fubini_prefix) + (dst_negative_scale_fubini_prefix)) + ((dst_negative_scale_fubini_prefix) + (dst_negative_scale_fubini_prefix)))))) /\ (((exists fs_u_dst_fubini_prefixpositive fs_v_dst_fubini_prefixpositive. ((((exists fs_h_dst_fubini_prefixpositive_body_start. fs_h_dst_fubini_prefixpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_prefixpositive)) /\ exists fs_q_dst_fubini_prefixpositive_body_start. fs_u_dst_fubini_prefixpositive = fs_q_dst_fubini_prefixpositive_body_start * S ((S (0)) * fs_v_dst_fubini_prefixpositive) + (0))) /\ ((((exists fs_h_dst_fubini_prefixpositive_body_terminal. fs_h_dst_fubini_prefixpositive_body_terminal + S (dst_positive_sum_fubini_prefix) = S ((S (m)) * fs_v_dst_fubini_prefixpositive)) /\ exists fs_q_dst_fubini_prefixpositive_body_terminal. fs_u_dst_fubini_prefixpositive = fs_q_dst_fubini_prefixpositive_body_terminal * S ((S (m)) * fs_v_dst_fubini_prefixpositive) + (dst_positive_sum_fubini_prefix))) /\ forall fs_i_dst_fubini_prefixpositive_body_steps. (exists fs_lt_dst_fubini_prefixpositive_body_steps_bound. fs_lt_dst_fubini_prefixpositive_body_steps_bound + S fs_i_dst_fubini_prefixpositive_body_steps = m) -> exists fs_a_dst_fubini_prefixpositive_body_steps fs_r_dst_fubini_prefixpositive_body_steps fs_s_dst_fubini_prefixpositive_body_steps. ((((exists fs_h_dst_fubini_prefixpositive_body_steps_summand. fs_h_dst_fubini_prefixpositive_body_steps_summand + S (fs_a_dst_fubini_prefixpositive_body_steps) = S ((S (fs_i_dst_fubini_prefixpositive_body_steps)) * dst_positive_scale_fubini_prefix)) /\ exists fs_q_dst_fubini_prefixpositive_body_steps_summand. dst_positive_code_fubini_prefix = fs_q_dst_fubini_prefixpositive_body_steps_summand * S ((S (fs_i_dst_fubini_prefixpositive_body_steps)) * dst_positive_scale_fubini_prefix) + (fs_a_dst_fubini_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_prefixpositive_body_steps_partial. fs_h_dst_fubini_prefixpositive_body_steps_partial + S (fs_r_dst_fubini_prefixpositive_body_steps) = S ((S (fs_i_dst_fubini_prefixpositive_body_steps)) * fs_v_dst_fubini_prefixpositive)) /\ exists fs_q_dst_fubini_prefixpositive_body_steps_partial. fs_u_dst_fubini_prefixpositive = fs_q_dst_fubini_prefixpositive_body_steps_partial * S ((S (fs_i_dst_fubini_prefixpositive_body_steps)) * fs_v_dst_fubini_prefixpositive) + (fs_r_dst_fubini_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_prefixpositive_body_steps_successor. fs_h_dst_fubini_prefixpositive_body_steps_successor + S (fs_s_dst_fubini_prefixpositive_body_steps) = S ((S (S fs_i_dst_fubini_prefixpositive_body_steps)) * fs_v_dst_fubini_prefixpositive)) /\ exists fs_q_dst_fubini_prefixpositive_body_steps_successor. fs_u_dst_fubini_prefixpositive = fs_q_dst_fubini_prefixpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_prefixpositive_body_steps)) * fs_v_dst_fubini_prefixpositive) + (fs_s_dst_fubini_prefixpositive_body_steps))) /\ fs_s_dst_fubini_prefixpositive_body_steps = fs_r_dst_fubini_prefixpositive_body_steps + fs_a_dst_fubini_prefixpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_prefixnegative fs_v_dst_fubini_prefixnegative. ((((exists fs_h_dst_fubini_prefixnegative_body_start. fs_h_dst_fubini_prefixnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_prefixnegative)) /\ exists fs_q_dst_fubini_prefixnegative_body_start. fs_u_dst_fubini_prefixnegative = fs_q_dst_fubini_prefixnegative_body_start * S ((S (0)) * fs_v_dst_fubini_prefixnegative) + (0))) /\ ((((exists fs_h_dst_fubini_prefixnegative_body_terminal. fs_h_dst_fubini_prefixnegative_body_terminal + S (dst_negative_sum_fubini_prefix) = S ((S (m)) * fs_v_dst_fubini_prefixnegative)) /\ exists fs_q_dst_fubini_prefixnegative_body_terminal. fs_u_dst_fubini_prefixnegative = fs_q_dst_fubini_prefixnegative_body_terminal * S ((S (m)) * fs_v_dst_fubini_prefixnegative) + (dst_negative_sum_fubini_prefix))) /\ forall fs_i_dst_fubini_prefixnegative_body_steps. (exists fs_lt_dst_fubini_prefixnegative_body_steps_bound. fs_lt_dst_fubini_prefixnegative_body_steps_bound + S fs_i_dst_fubini_prefixnegative_body_steps = m) -> exists fs_a_dst_fubini_prefixnegative_body_steps fs_r_dst_fubini_prefixnegative_body_steps fs_s_dst_fubini_prefixnegative_body_steps. ((((exists fs_h_dst_fubini_prefixnegative_body_steps_summand. fs_h_dst_fubini_prefixnegative_body_steps_summand + S (fs_a_dst_fubini_prefixnegative_body_steps) = S ((S (fs_i_dst_fubini_prefixnegative_body_steps)) * dst_negative_scale_fubini_prefix)) /\ exists fs_q_dst_fubini_prefixnegative_body_steps_summand. dst_negative_code_fubini_prefix = fs_q_dst_fubini_prefixnegative_body_steps_summand * S ((S (fs_i_dst_fubini_prefixnegative_body_steps)) * dst_negative_scale_fubini_prefix) + (fs_a_dst_fubini_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_prefixnegative_body_steps_partial. fs_h_dst_fubini_prefixnegative_body_steps_partial + S (fs_r_dst_fubini_prefixnegative_body_steps) = S ((S (fs_i_dst_fubini_prefixnegative_body_steps)) * fs_v_dst_fubini_prefixnegative)) /\ exists fs_q_dst_fubini_prefixnegative_body_steps_partial. fs_u_dst_fubini_prefixnegative = fs_q_dst_fubini_prefixnegative_body_steps_partial * S ((S (fs_i_dst_fubini_prefixnegative_body_steps)) * fs_v_dst_fubini_prefixnegative) + (fs_r_dst_fubini_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_prefixnegative_body_steps_successor. fs_h_dst_fubini_prefixnegative_body_steps_successor + S (fs_s_dst_fubini_prefixnegative_body_steps) = S ((S (S fs_i_dst_fubini_prefixnegative_body_steps)) * fs_v_dst_fubini_prefixnegative)) /\ exists fs_q_dst_fubini_prefixnegative_body_steps_successor. fs_u_dst_fubini_prefixnegative = fs_q_dst_fubini_prefixnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_prefixnegative_body_steps)) * fs_v_dst_fubini_prefixnegative) + (fs_s_dst_fubini_prefixnegative_body_steps))) /\ fs_s_dst_fubini_prefixnegative_body_steps = fs_r_dst_fubini_prefixnegative_body_steps + fs_a_dst_fubini_prefixnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_prefixresult ge_balance_negative_fubini_prefixresult. (((((u) = 2 * (ge_balance_positive_fubini_prefixresult) /\ (ge_balance_negative_fubini_prefixresult) = 0) \/ exists ge_signed_half_fubini_prefixresultdecode. (((u) = 2 * ge_signed_half_fubini_prefixresultdecode + 1 /\ (ge_balance_positive_fubini_prefixresult) = 0) /\ (ge_balance_negative_fubini_prefixresult) = S ge_signed_half_fubini_prefixresultdecode))) /\ ((dst_positive_sum_fubini_prefix) + ge_balance_negative_fubini_prefixresult = (dst_negative_sum_fubini_prefix) + ge_balance_positive_fubini_prefixresult))))))))) /\ (((exists dst_positive_code_fubini_last dst_positive_scale_fubini_last dst_negative_code_fubini_last dst_negative_scale_fubini_last dst_positive_fubini_last dst_negative_fubini_last. (((x) = (((((dst_positive_code_fubini_last) + (dst_positive_scale_fubini_last)) * S ((dst_positive_code_fubini_last) + (dst_positive_scale_fubini_last)) + ((dst_positive_scale_fubini_last) + (dst_positive_scale_fubini_last))) + (((dst_negative_code_fubini_last) + (dst_negative_scale_fubini_last)) * S ((dst_negative_code_fubini_last) + (dst_negative_scale_fubini_last)) + ((dst_negative_scale_fubini_last) + (dst_negative_scale_fubini_last)))) * S ((((dst_positive_code_fubini_last) + (dst_positive_scale_fubini_last)) * S ((dst_positive_code_fubini_last) + (dst_positive_scale_fubini_last)) + ((dst_positive_scale_fubini_last) + (dst_positive_scale_fubini_last))) + (((dst_negative_code_fubini_last) + (dst_negative_scale_fubini_last)) * S ((dst_negative_code_fubini_last) + (dst_negative_scale_fubini_last)) + ((dst_negative_scale_fubini_last) + (dst_negative_scale_fubini_last)))) + ((((dst_negative_code_fubini_last) + (dst_negative_scale_fubini_last)) * S ((dst_negative_code_fubini_last) + (dst_negative_scale_fubini_last)) + ((dst_negative_scale_fubini_last) + (dst_negative_scale_fubini_last))) + (((dst_negative_code_fubini_last) + (dst_negative_scale_fubini_last)) * S ((dst_negative_code_fubini_last) + (dst_negative_scale_fubini_last)) + ((dst_negative_scale_fubini_last) + (dst_negative_scale_fubini_last)))))) /\ (((((exists ff_h_pvs_fubini_lastpositive. ff_h_pvs_fubini_lastpositive + S (dst_positive_fubini_last) = S ((S (m)) * dst_positive_scale_fubini_last)) /\ exists ff_q_pvs_fubini_lastpositive. dst_positive_code_fubini_last = ff_q_pvs_fubini_lastpositive * S ((S (m)) * dst_positive_scale_fubini_last) + (dst_positive_fubini_last))) /\ (((((exists ff_h_pvs_fubini_lastnegative. ff_h_pvs_fubini_lastnegative + S (dst_negative_fubini_last) = S ((S (m)) * dst_negative_scale_fubini_last)) /\ exists ff_q_pvs_fubini_lastnegative. dst_negative_code_fubini_last = ff_q_pvs_fubini_lastnegative * S ((S (m)) * dst_negative_scale_fubini_last) + (dst_negative_fubini_last))) /\ (exists ge_balance_positive_fubini_lastvalue ge_balance_negative_fubini_lastvalue. (((((v) = 2 * (ge_balance_positive_fubini_lastvalue) /\ (ge_balance_negative_fubini_lastvalue) = 0) \/ exists ge_signed_half_fubini_lastvaluedecode. (((v) = 2 * ge_signed_half_fubini_lastvaluedecode + 1 /\ (ge_balance_positive_fubini_lastvalue) = 0) /\ (ge_balance_negative_fubini_lastvalue) = S ge_signed_half_fubini_lastvaluedecode))) /\ ((dst_positive_fubini_last) + ge_balance_negative_fubini_lastvalue = (dst_negative_fubini_last) + ge_balance_positive_fubini_lastvalue))))))))) /\ (exists dsa_ap_fubini_add dsa_an_fubini_add dsa_bp_fubini_add dsa_bn_fubini_add dsa_cp_fubini_add dsa_cn_fubini_add. (((((u) = 2 * (dsa_ap_fubini_add) /\ (dsa_an_fubini_add) = 0) \/ exists ge_signed_half_fubini_addleft. (((u) = 2 * ge_signed_half_fubini_addleft + 1 /\ (dsa_ap_fubini_add) = 0) /\ (dsa_an_fubini_add) = S ge_signed_half_fubini_addleft))) /\ ((((((v) = 2 * (dsa_bp_fubini_add) /\ (dsa_bn_fubini_add) = 0) \/ exists ge_signed_half_fubini_addright. (((v) = 2 * ge_signed_half_fubini_addright + 1 /\ (dsa_bp_fubini_add) = 0) /\ (dsa_bn_fubini_add) = S ge_signed_half_fubini_addright))) /\ ((((((a) = 2 * (dsa_cp_fubini_add) /\ (dsa_cn_fubini_add) = 0) \/ exists ge_signed_half_fubini_addoutput. (((a) = 2 * ge_signed_half_fubini_addoutput + 1 /\ (dsa_cp_fubini_add) = 0) /\ (dsa_cn_fubini_add) = S ge_signed_half_fubini_addoutput))) /\ ((dsa_ap_fubini_add + dsa_bp_fubini_add) + dsa_cn_fubini_add = (dsa_an_fubini_add + dsa_bn_fubini_add) + dsa_cp_fubini_add))))))))))) - 0043
specialize divisor_signed_sum_successor_decompose (x) - 0044
specialize divisor_signed_sum_successor_decompose (m) - 0045
specialize divisor_signed_sum_successor_decompose (a) - 0046
apply divisor_signed_sum_successor_decompose - 0047
exact ha_witness_right - 0048
cases hd - 0049
cases hd_witness - 0050
cases hd_witness_witness - 0051
cases hd_witness_witness_right - 0052
have hC : exists C. (((exists dst_positive_code_fubini_columnssource_table dst_positive_scale_fubini_columnssource_table dst_negative_code_fubini_columnssource_table dst_negative_scale_fubini_columnssource_table. (((F) = (((((dst_positive_code_fubini_columnssource_table) + (dst_positive_scale_fubini_columnssource_table)) * S ((dst_positive_code_fubini_columnssource_table) + (dst_positive_scale_fubini_columnssource_table)) + ((dst_positive_scale_fubini_columnssource_table) + (dst_positive_scale_fubini_columnssource_table))) + (((dst_negative_code_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)) * S ((dst_negative_code_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)) + ((dst_negative_scale_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)))) * S ((((dst_positive_code_fubini_columnssource_table) + (dst_positive_scale_fubini_columnssource_table)) * S ((dst_positive_code_fubini_columnssource_table) + (dst_positive_scale_fubini_columnssource_table)) + ((dst_positive_scale_fubini_columnssource_table) + (dst_positive_scale_fubini_columnssource_table))) + (((dst_negative_code_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)) * S ((dst_negative_code_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)) + ((dst_negative_scale_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)))) + ((((dst_negative_code_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)) * S ((dst_negative_code_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)) + ((dst_negative_scale_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table))) + (((dst_negative_code_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)) * S ((dst_negative_code_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)) + ((dst_negative_scale_fubini_columnssource_table) + (dst_negative_scale_fubini_columnssource_table)))))) /\ (forall dst_index_fubini_columnssource_table. (exists pvs_le_gap_fubini_columnssource_tabledomain. pvs_le_gap_fubini_columnssource_tabledomain + (dst_index_fubini_columnssource_table) = (0)) -> exists dst_positive_fubini_columnssource_table dst_negative_fubini_columnssource_table dst_value_fubini_columnssource_table. ((((exists ff_h_pvs_fubini_columnssource_tableentrypositive. ff_h_pvs_fubini_columnssource_tableentrypositive + S (dst_positive_fubini_columnssource_table) = S ((S (dst_index_fubini_columnssource_table)) * dst_positive_scale_fubini_columnssource_table)) /\ exists ff_q_pvs_fubini_columnssource_tableentrypositive. dst_positive_code_fubini_columnssource_table = ff_q_pvs_fubini_columnssource_tableentrypositive * S ((S (dst_index_fubini_columnssource_table)) * dst_positive_scale_fubini_columnssource_table) + (dst_positive_fubini_columnssource_table))) /\ (((((exists ff_h_pvs_fubini_columnssource_tableentrynegative. ff_h_pvs_fubini_columnssource_tableentrynegative + S (dst_negative_fubini_columnssource_table) = S ((S (dst_index_fubini_columnssource_table)) * dst_negative_scale_fubini_columnssource_table)) /\ exists ff_q_pvs_fubini_columnssource_tableentrynegative. dst_negative_code_fubini_columnssource_table = ff_q_pvs_fubini_columnssource_tableentrynegative * S ((S (dst_index_fubini_columnssource_table)) * dst_negative_scale_fubini_columnssource_table) + (dst_negative_fubini_columnssource_table))) /\ (exists ge_balance_positive_fubini_columnssource_tableentryvalue ge_balance_negative_fubini_columnssource_tableentryvalue. (((((dst_value_fubini_columnssource_table) = 2 * (ge_balance_positive_fubini_columnssource_tableentryvalue) /\ (ge_balance_negative_fubini_columnssource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_columnssource_tableentryvaluedecode. (((dst_value_fubini_columnssource_table) = 2 * ge_signed_half_fubini_columnssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnssource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_columnssource_tableentryvalue) = S ge_signed_half_fubini_columnssource_tableentryvaluedecode))) /\ ((dst_positive_fubini_columnssource_table) + ge_balance_negative_fubini_columnssource_tableentryvalue = (dst_negative_fubini_columnssource_table) + ge_balance_positive_fubini_columnssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_columnsrow_table dst_positive_scale_fubini_columnsrow_table dst_negative_code_fubini_columnsrow_table dst_negative_scale_fubini_columnsrow_table. (((C) = (((((dst_positive_code_fubini_columnsrow_table) + (dst_positive_scale_fubini_columnsrow_table)) * S ((dst_positive_code_fubini_columnsrow_table) + (dst_positive_scale_fubini_columnsrow_table)) + ((dst_positive_scale_fubini_columnsrow_table) + (dst_positive_scale_fubini_columnsrow_table))) + (((dst_negative_code_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)) * S ((dst_negative_code_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)) + ((dst_negative_scale_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)))) * S ((((dst_positive_code_fubini_columnsrow_table) + (dst_positive_scale_fubini_columnsrow_table)) * S ((dst_positive_code_fubini_columnsrow_table) + (dst_positive_scale_fubini_columnsrow_table)) + ((dst_positive_scale_fubini_columnsrow_table) + (dst_positive_scale_fubini_columnsrow_table))) + (((dst_negative_code_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)) * S ((dst_negative_code_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)) + ((dst_negative_scale_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)))) + ((((dst_negative_code_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)) * S ((dst_negative_code_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)) + ((dst_negative_scale_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table))) + (((dst_negative_code_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)) * S ((dst_negative_code_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)) + ((dst_negative_scale_fubini_columnsrow_table) + (dst_negative_scale_fubini_columnsrow_table)))))) /\ (forall dst_index_fubini_columnsrow_table. (exists pvs_le_gap_fubini_columnsrow_tabledomain. pvs_le_gap_fubini_columnsrow_tabledomain + (dst_index_fubini_columnsrow_table) = (n)) -> exists dst_positive_fubini_columnsrow_table dst_negative_fubini_columnsrow_table dst_value_fubini_columnsrow_table. ((((exists ff_h_pvs_fubini_columnsrow_tableentrypositive. ff_h_pvs_fubini_columnsrow_tableentrypositive + S (dst_positive_fubini_columnsrow_table) = S ((S (dst_index_fubini_columnsrow_table)) * dst_positive_scale_fubini_columnsrow_table)) /\ exists ff_q_pvs_fubini_columnsrow_tableentrypositive. dst_positive_code_fubini_columnsrow_table = ff_q_pvs_fubini_columnsrow_tableentrypositive * S ((S (dst_index_fubini_columnsrow_table)) * dst_positive_scale_fubini_columnsrow_table) + (dst_positive_fubini_columnsrow_table))) /\ (((((exists ff_h_pvs_fubini_columnsrow_tableentrynegative. ff_h_pvs_fubini_columnsrow_tableentrynegative + S (dst_negative_fubini_columnsrow_table) = S ((S (dst_index_fubini_columnsrow_table)) * dst_negative_scale_fubini_columnsrow_table)) /\ exists ff_q_pvs_fubini_columnsrow_tableentrynegative. dst_negative_code_fubini_columnsrow_table = ff_q_pvs_fubini_columnsrow_tableentrynegative * S ((S (dst_index_fubini_columnsrow_table)) * dst_negative_scale_fubini_columnsrow_table) + (dst_negative_fubini_columnsrow_table))) /\ (exists ge_balance_positive_fubini_columnsrow_tableentryvalue ge_balance_negative_fubini_columnsrow_tableentryvalue. (((((dst_value_fubini_columnsrow_table) = 2 * (ge_balance_positive_fubini_columnsrow_tableentryvalue) /\ (ge_balance_negative_fubini_columnsrow_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_columnsrow_tableentryvaluedecode. (((dst_value_fubini_columnsrow_table) = 2 * ge_signed_half_fubini_columnsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrow_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_columnsrow_tableentryvalue) = S ge_signed_half_fubini_columnsrow_tableentryvaluedecode))) /\ ((dst_positive_fubini_columnsrow_table) + ge_balance_negative_fubini_columnsrow_tableentryvalue = (dst_negative_fubini_columnsrow_table) + ge_balance_positive_fubini_columnsrow_tableentryvalue))))))))) /\ (forall srt_index_fubini_columns. (exists pvs_gap_fubini_columnsbound. pvs_gap_fubini_columnsbound + S (srt_index_fubini_columns) = (n)) -> exists srt_value_fubini_columns. (((exists dst_positive_code_fubini_columnsrowentry dst_positive_scale_fubini_columnsrowentry dst_negative_code_fubini_columnsrowentry dst_negative_scale_fubini_columnsrowentry dst_positive_fubini_columnsrowentry dst_negative_fubini_columnsrowentry. (((C) = (((((dst_positive_code_fubini_columnsrowentry) + (dst_positive_scale_fubini_columnsrowentry)) * S ((dst_positive_code_fubini_columnsrowentry) + (dst_positive_scale_fubini_columnsrowentry)) + ((dst_positive_scale_fubini_columnsrowentry) + (dst_positive_scale_fubini_columnsrowentry))) + (((dst_negative_code_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)) * S ((dst_negative_code_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)) + ((dst_negative_scale_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)))) * S ((((dst_positive_code_fubini_columnsrowentry) + (dst_positive_scale_fubini_columnsrowentry)) * S ((dst_positive_code_fubini_columnsrowentry) + (dst_positive_scale_fubini_columnsrowentry)) + ((dst_positive_scale_fubini_columnsrowentry) + (dst_positive_scale_fubini_columnsrowentry))) + (((dst_negative_code_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)) * S ((dst_negative_code_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)) + ((dst_negative_scale_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)))) + ((((dst_negative_code_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)) * S ((dst_negative_code_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)) + ((dst_negative_scale_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry))) + (((dst_negative_code_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)) * S ((dst_negative_code_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)) + ((dst_negative_scale_fubini_columnsrowentry) + (dst_negative_scale_fubini_columnsrowentry)))))) /\ (((((exists ff_h_pvs_fubini_columnsrowentrypositive. ff_h_pvs_fubini_columnsrowentrypositive + S (dst_positive_fubini_columnsrowentry) = S ((S (srt_index_fubini_columns)) * dst_positive_scale_fubini_columnsrowentry)) /\ exists ff_q_pvs_fubini_columnsrowentrypositive. dst_positive_code_fubini_columnsrowentry = ff_q_pvs_fubini_columnsrowentrypositive * S ((S (srt_index_fubini_columns)) * dst_positive_scale_fubini_columnsrowentry) + (dst_positive_fubini_columnsrowentry))) /\ (((((exists ff_h_pvs_fubini_columnsrowentrynegative. ff_h_pvs_fubini_columnsrowentrynegative + S (dst_negative_fubini_columnsrowentry) = S ((S (srt_index_fubini_columns)) * dst_negative_scale_fubini_columnsrowentry)) /\ exists ff_q_pvs_fubini_columnsrowentrynegative. dst_negative_code_fubini_columnsrowentry = ff_q_pvs_fubini_columnsrowentrynegative * S ((S (srt_index_fubini_columns)) * dst_negative_scale_fubini_columnsrowentry) + (dst_negative_fubini_columnsrowentry))) /\ (exists ge_balance_positive_fubini_columnsrowentryvalue ge_balance_negative_fubini_columnsrowentryvalue. (((((srt_value_fubini_columns) = 2 * (ge_balance_positive_fubini_columnsrowentryvalue) /\ (ge_balance_negative_fubini_columnsrowentryvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowentryvaluedecode. (((srt_value_fubini_columns) = 2 * ge_signed_half_fubini_columnsrowentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowentryvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowentryvalue) = S ge_signed_half_fubini_columnsrowentryvaluedecode))) /\ ((dst_positive_fubini_columnsrowentry) + ge_balance_negative_fubini_columnsrowentryvalue = (dst_negative_fubini_columnsrowentry) + ge_balance_positive_fubini_columnsrowentryvalue))))))))) /\ (exists srs_slice_fubini_columnsrowrow_sum. ((((exists dst_positive_code_fubini_columnsrowrow_sumslicesource_table dst_positive_scale_fubini_columnsrowrow_sumslicesource_table dst_negative_code_fubini_columnsrowrow_sumslicesource_table dst_negative_scale_fubini_columnsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_fubini_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_fubini_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_columnsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)))) + ((((dst_negative_code_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)))))) /\ (forall dst_index_fubini_columnsrowrow_sumslicesource_table. (exists pvs_le_gap_fubini_columnsrowrow_sumslicesource_tabledomain. pvs_le_gap_fubini_columnsrowrow_sumslicesource_tabledomain + (dst_index_fubini_columnsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_fubini_columnsrowrow_sumslicesource_table dst_negative_fubini_columnsrowrow_sumslicesource_table dst_value_fubini_columnsrowrow_sumslicesource_table. ((((exists ff_h_pvs_fubini_columnsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_fubini_columnsrowrow_sumslicesource_tableentrypositive + S (dst_positive_fubini_columnsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_columnsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_columnsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_columnsrowrow_sumslicesource_tableentrypositive. dst_positive_code_fubini_columnsrowrow_sumslicesource_table = ff_q_pvs_fubini_columnsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_fubini_columnsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_columnsrowrow_sumslicesource_table) + (dst_positive_fubini_columnsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_fubini_columnsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_fubini_columnsrowrow_sumslicesource_tableentrynegative + S (dst_negative_fubini_columnsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_columnsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_columnsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_columnsrowrow_sumslicesource_tableentrynegative. dst_negative_code_fubini_columnsrowrow_sumslicesource_table = ff_q_pvs_fubini_columnsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_fubini_columnsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_columnsrowrow_sumslicesource_table) + (dst_negative_fubini_columnsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_fubini_columnsrowrow_sumslicesource_tableentryvalue ge_balance_negative_fubini_columnsrowrow_sumslicesource_tableentryvalue. (((((dst_value_fubini_columnsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_fubini_columnsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_fubini_columnsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_fubini_columnsrowrow_sumslicesource_table) = 2 * ge_signed_half_fubini_columnsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_fubini_columnsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_fubini_columnsrowrow_sumslicesource_table) + ge_balance_negative_fubini_columnsrowrow_sumslicesource_tableentryvalue = (dst_negative_fubini_columnsrowrow_sumslicesource_table) + ge_balance_positive_fubini_columnsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_columnsrowrow_sumsliceoutput_table dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table. (((srs_slice_fubini_columnsrowrow_sum) = (((((dst_positive_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_fubini_columnsrowrow_sumsliceoutput_table. (exists pvs_le_gap_fubini_columnsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_fubini_columnsrowrow_sumsliceoutput_tabledomain + (dst_index_fubini_columnsrowrow_sumsliceoutput_table) = (m)) -> exists dst_positive_fubini_columnsrowrow_sumsliceoutput_table dst_negative_fubini_columnsrowrow_sumsliceoutput_table dst_value_fubini_columnsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_fubini_columnsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_fubini_columnsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_fubini_columnsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_columnsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_columnsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_fubini_columnsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_columnsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_fubini_columnsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_columnsrowrow_sumsliceoutput_table) + (dst_positive_fubini_columnsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_fubini_columnsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_fubini_columnsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_fubini_columnsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_columnsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_columnsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_fubini_columnsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_columnsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_fubini_columnsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_columnsrowrow_sumsliceoutput_table) + (dst_negative_fubini_columnsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_fubini_columnsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_fubini_columnsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_fubini_columnsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_fubini_columnsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_fubini_columnsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_fubini_columnsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_fubini_columnsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_fubini_columnsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_fubini_columnsrowrow_sumsliceoutput_table) + ge_balance_negative_fubini_columnsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_fubini_columnsrowrow_sumsliceoutput_table) + ge_balance_positive_fubini_columnsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_fubini_columnsrowrow_sumslice. (exists pvs_gap_fubini_columnsrowrow_sumslicebound. pvs_gap_fubini_columnsrowrow_sumslicebound + S (srs_index_fubini_columnsrowrow_sumslice) = (m)) -> exists srs_value_fubini_columnsrowrow_sumslice. (((exists dst_positive_code_fubini_columnsrowrow_sumsliceentrysource dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource dst_negative_code_fubini_columnsrowrow_sumsliceentrysource dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource dst_positive_fubini_columnsrowrow_sumsliceentrysource dst_negative_fubini_columnsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_fubini_columnsrowrow_sumsliceentrysourcepositive. ff_h_pvs_fubini_columnsrowrow_sumsliceentrysourcepositive + S (dst_positive_fubini_columnsrowrow_sumsliceentrysource) = S ((S (((((o) + ((t) * (srt_index_fubini_columns)))) + ((s) * (srs_index_fubini_columnsrowrow_sumslice))))) * dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_columnsrowrow_sumsliceentrysourcepositive. dst_positive_code_fubini_columnsrowrow_sumsliceentrysource = ff_q_pvs_fubini_columnsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((t) * (srt_index_fubini_columns)))) + ((s) * (srs_index_fubini_columnsrowrow_sumslice))))) * dst_positive_scale_fubini_columnsrowrow_sumsliceentrysource) + (dst_positive_fubini_columnsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_fubini_columnsrowrow_sumsliceentrysourcenegative. ff_h_pvs_fubini_columnsrowrow_sumsliceentrysourcenegative + S (dst_negative_fubini_columnsrowrow_sumsliceentrysource) = S ((S (((((o) + ((t) * (srt_index_fubini_columns)))) + ((s) * (srs_index_fubini_columnsrowrow_sumslice))))) * dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_columnsrowrow_sumsliceentrysourcenegative. dst_negative_code_fubini_columnsrowrow_sumsliceentrysource = ff_q_pvs_fubini_columnsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((t) * (srt_index_fubini_columns)))) + ((s) * (srs_index_fubini_columnsrowrow_sumslice))))) * dst_negative_scale_fubini_columnsrowrow_sumsliceentrysource) + (dst_negative_fubini_columnsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_fubini_columnsrowrow_sumsliceentrysourcevalue ge_balance_negative_fubini_columnsrowrow_sumsliceentrysourcevalue. (((((srs_value_fubini_columnsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_columnsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_fubini_columnsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_fubini_columnsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_fubini_columnsrowrow_sumslice) = 2 * ge_signed_half_fubini_columnsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_fubini_columnsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_fubini_columnsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_fubini_columnsrowrow_sumsliceentrysource) + ge_balance_negative_fubini_columnsrowrow_sumsliceentrysourcevalue = (dst_negative_fubini_columnsrowrow_sumsliceentrysource) + ge_balance_positive_fubini_columnsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_fubini_columnsrowrow_sumsliceentryoutput dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput dst_positive_fubini_columnsrowrow_sumsliceentryoutput dst_negative_fubini_columnsrowrow_sumsliceentryoutput. (((srs_slice_fubini_columnsrowrow_sum) = (((((dst_positive_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_fubini_columnsrowrow_sumsliceentryoutputpositive. ff_h_pvs_fubini_columnsrowrow_sumsliceentryoutputpositive + S (dst_positive_fubini_columnsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_columnsrowrow_sumslice)) * dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_columnsrowrow_sumsliceentryoutputpositive. dst_positive_code_fubini_columnsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_columnsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_fubini_columnsrowrow_sumslice)) * dst_positive_scale_fubini_columnsrowrow_sumsliceentryoutput) + (dst_positive_fubini_columnsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_fubini_columnsrowrow_sumsliceentryoutputnegative. ff_h_pvs_fubini_columnsrowrow_sumsliceentryoutputnegative + S (dst_negative_fubini_columnsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_columnsrowrow_sumslice)) * dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_columnsrowrow_sumsliceentryoutputnegative. dst_negative_code_fubini_columnsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_columnsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_fubini_columnsrowrow_sumslice)) * dst_negative_scale_fubini_columnsrowrow_sumsliceentryoutput) + (dst_negative_fubini_columnsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_fubini_columnsrowrow_sumsliceentryoutputvalue ge_balance_negative_fubini_columnsrowrow_sumsliceentryoutputvalue. (((((srs_value_fubini_columnsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_columnsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_fubini_columnsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_fubini_columnsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_fubini_columnsrowrow_sumslice) = 2 * ge_signed_half_fubini_columnsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_fubini_columnsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_fubini_columnsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_fubini_columnsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_fubini_columnsrowrow_sumsliceentryoutput) + ge_balance_negative_fubini_columnsrowrow_sumsliceentryoutputvalue = (dst_negative_fubini_columnsrowrow_sumsliceentryoutput) + ge_balance_positive_fubini_columnsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_fubini_columnsrowrow_sumsum dst_positive_scale_fubini_columnsrowrow_sumsum dst_negative_code_fubini_columnsrowrow_sumsum dst_negative_scale_fubini_columnsrowrow_sumsum dst_positive_sum_fubini_columnsrowrow_sumsum dst_negative_sum_fubini_columnsrowrow_sumsum. (((srs_slice_fubini_columnsrowrow_sum) = (((((dst_positive_code_fubini_columnsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowrow_sumsum)) * S ((dst_positive_code_fubini_columnsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowrow_sumsum)) + ((dst_positive_scale_fubini_columnsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowrow_sumsum))) + (((dst_negative_code_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)) * S ((dst_negative_code_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)) + ((dst_negative_scale_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)))) * S ((((dst_positive_code_fubini_columnsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowrow_sumsum)) * S ((dst_positive_code_fubini_columnsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowrow_sumsum)) + ((dst_positive_scale_fubini_columnsrowrow_sumsum) + (dst_positive_scale_fubini_columnsrowrow_sumsum))) + (((dst_negative_code_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)) * S ((dst_negative_code_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)) + ((dst_negative_scale_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)))) + ((((dst_negative_code_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)) * S ((dst_negative_code_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)) + ((dst_negative_scale_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum))) + (((dst_negative_code_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)) * S ((dst_negative_code_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)) + ((dst_negative_scale_fubini_columnsrowrow_sumsum) + (dst_negative_scale_fubini_columnsrowrow_sumsum)))))) /\ (((exists fs_u_dst_fubini_columnsrowrow_sumsumpositive fs_v_dst_fubini_columnsrowrow_sumsumpositive. ((((exists fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_start. fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_columnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_start. fs_u_dst_fubini_columnsrowrow_sumsumpositive = fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_columnsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_terminal. fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_fubini_columnsrowrow_sumsum) = S ((S (m)) * fs_v_dst_fubini_columnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_terminal. fs_u_dst_fubini_columnsrowrow_sumsumpositive = fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_terminal * S ((S (m)) * fs_v_dst_fubini_columnsrowrow_sumsumpositive) + (dst_positive_sum_fubini_columnsrowrow_sumsum))) /\ forall fs_i_dst_fubini_columnsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_fubini_columnsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_fubini_columnsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_fubini_columnsrowrow_sumsumpositive_body_steps = m) -> exists fs_a_dst_fubini_columnsrowrow_sumsumpositive_body_steps fs_r_dst_fubini_columnsrowrow_sumsumpositive_body_steps fs_s_dst_fubini_columnsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_fubini_columnsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_columnsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_columnsrowrow_sumsum)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_fubini_columnsrowrow_sumsum = fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_columnsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_columnsrowrow_sumsum) + (fs_a_dst_fubini_columnsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_fubini_columnsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_columnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_columnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_fubini_columnsrowrow_sumsumpositive = fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_columnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_columnsrowrow_sumsumpositive) + (fs_r_dst_fubini_columnsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_fubini_columnsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_fubini_columnsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_fubini_columnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_columnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_fubini_columnsrowrow_sumsumpositive = fs_q_dst_fubini_columnsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_columnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_columnsrowrow_sumsumpositive) + (fs_s_dst_fubini_columnsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_fubini_columnsrowrow_sumsumpositive_body_steps = fs_r_dst_fubini_columnsrowrow_sumsumpositive_body_steps + fs_a_dst_fubini_columnsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_columnsrowrow_sumsumnegative fs_v_dst_fubini_columnsrowrow_sumsumnegative. ((((exists fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_start. fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_columnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_start. fs_u_dst_fubini_columnsrowrow_sumsumnegative = fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_columnsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_terminal. fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_fubini_columnsrowrow_sumsum) = S ((S (m)) * fs_v_dst_fubini_columnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_terminal. fs_u_dst_fubini_columnsrowrow_sumsumnegative = fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_terminal * S ((S (m)) * fs_v_dst_fubini_columnsrowrow_sumsumnegative) + (dst_negative_sum_fubini_columnsrowrow_sumsum))) /\ forall fs_i_dst_fubini_columnsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_fubini_columnsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_fubini_columnsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_fubini_columnsrowrow_sumsumnegative_body_steps = m) -> exists fs_a_dst_fubini_columnsrowrow_sumsumnegative_body_steps fs_r_dst_fubini_columnsrowrow_sumsumnegative_body_steps fs_s_dst_fubini_columnsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_fubini_columnsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_columnsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_columnsrowrow_sumsum)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_fubini_columnsrowrow_sumsum = fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_columnsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_columnsrowrow_sumsum) + (fs_a_dst_fubini_columnsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_fubini_columnsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_columnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_columnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_fubini_columnsrowrow_sumsumnegative = fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_columnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_columnsrowrow_sumsumnegative) + (fs_r_dst_fubini_columnsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_fubini_columnsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_fubini_columnsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_fubini_columnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_columnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_fubini_columnsrowrow_sumsumnegative = fs_q_dst_fubini_columnsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_columnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_columnsrowrow_sumsumnegative) + (fs_s_dst_fubini_columnsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_fubini_columnsrowrow_sumsumnegative_body_steps = fs_r_dst_fubini_columnsrowrow_sumsumnegative_body_steps + fs_a_dst_fubini_columnsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_columnsrowrow_sumsumresult ge_balance_negative_fubini_columnsrowrow_sumsumresult. (((((srt_value_fubini_columns) = 2 * (ge_balance_positive_fubini_columnsrowrow_sumsumresult) /\ (ge_balance_negative_fubini_columnsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_fubini_columnsrowrow_sumsumresultdecode. (((srt_value_fubini_columns) = 2 * ge_signed_half_fubini_columnsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_fubini_columnsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_fubini_columnsrowrow_sumsumresult) = S ge_signed_half_fubini_columnsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_fubini_columnsrowrow_sumsum) + ge_balance_negative_fubini_columnsrowrow_sumsumresult = (dst_negative_sum_fubini_columnsrowrow_sumsum) + ge_balance_positive_fubini_columnsrowrow_sumsumresult)))))))))))))))))) - 0053
specialize signed_rectangular_row_sums_exists (n) - 0054
specialize signed_rectangular_row_sums_exists (F) - 0055
specialize signed_rectangular_row_sums_exists (o) - 0056
specialize signed_rectangular_row_sums_exists (t) - 0057
specialize signed_rectangular_row_sums_exists (s) - 0058
specialize signed_rectangular_row_sums_exists (m) - 0059
apply signed_rectangular_row_sums_exists - 0060
cases ha_witness_left - 0061
cases ha_witness_left_right - 0062
exact ha_witness_left_left - 0063
cases hC - 0064
have hsumC : exists z. (exists dst_positive_code_fubini_column_sum dst_positive_scale_fubini_column_sum dst_negative_code_fubini_column_sum dst_negative_scale_fubini_column_sum dst_positive_sum_fubini_column_sum dst_negative_sum_fubini_column_sum. (((x4) = (((((dst_positive_code_fubini_column_sum) + (dst_positive_scale_fubini_column_sum)) * S ((dst_positive_code_fubini_column_sum) + (dst_positive_scale_fubini_column_sum)) + ((dst_positive_scale_fubini_column_sum) + (dst_positive_scale_fubini_column_sum))) + (((dst_negative_code_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)) * S ((dst_negative_code_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)) + ((dst_negative_scale_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)))) * S ((((dst_positive_code_fubini_column_sum) + (dst_positive_scale_fubini_column_sum)) * S ((dst_positive_code_fubini_column_sum) + (dst_positive_scale_fubini_column_sum)) + ((dst_positive_scale_fubini_column_sum) + (dst_positive_scale_fubini_column_sum))) + (((dst_negative_code_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)) * S ((dst_negative_code_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)) + ((dst_negative_scale_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)))) + ((((dst_negative_code_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)) * S ((dst_negative_code_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)) + ((dst_negative_scale_fubini_column_sum) + (dst_negative_scale_fubini_column_sum))) + (((dst_negative_code_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)) * S ((dst_negative_code_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)) + ((dst_negative_scale_fubini_column_sum) + (dst_negative_scale_fubini_column_sum)))))) /\ (((exists fs_u_dst_fubini_column_sumpositive fs_v_dst_fubini_column_sumpositive. ((((exists fs_h_dst_fubini_column_sumpositive_body_start. fs_h_dst_fubini_column_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_column_sumpositive)) /\ exists fs_q_dst_fubini_column_sumpositive_body_start. fs_u_dst_fubini_column_sumpositive = fs_q_dst_fubini_column_sumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_column_sumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_column_sumpositive_body_terminal. fs_h_dst_fubini_column_sumpositive_body_terminal + S (dst_positive_sum_fubini_column_sum) = S ((S (n)) * fs_v_dst_fubini_column_sumpositive)) /\ exists fs_q_dst_fubini_column_sumpositive_body_terminal. fs_u_dst_fubini_column_sumpositive = fs_q_dst_fubini_column_sumpositive_body_terminal * S ((S (n)) * fs_v_dst_fubini_column_sumpositive) + (dst_positive_sum_fubini_column_sum))) /\ forall fs_i_dst_fubini_column_sumpositive_body_steps. (exists fs_lt_dst_fubini_column_sumpositive_body_steps_bound. fs_lt_dst_fubini_column_sumpositive_body_steps_bound + S fs_i_dst_fubini_column_sumpositive_body_steps = n) -> exists fs_a_dst_fubini_column_sumpositive_body_steps fs_r_dst_fubini_column_sumpositive_body_steps fs_s_dst_fubini_column_sumpositive_body_steps. ((((exists fs_h_dst_fubini_column_sumpositive_body_steps_summand. fs_h_dst_fubini_column_sumpositive_body_steps_summand + S (fs_a_dst_fubini_column_sumpositive_body_steps) = S ((S (fs_i_dst_fubini_column_sumpositive_body_steps)) * dst_positive_scale_fubini_column_sum)) /\ exists fs_q_dst_fubini_column_sumpositive_body_steps_summand. dst_positive_code_fubini_column_sum = fs_q_dst_fubini_column_sumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_column_sumpositive_body_steps)) * dst_positive_scale_fubini_column_sum) + (fs_a_dst_fubini_column_sumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_column_sumpositive_body_steps_partial. fs_h_dst_fubini_column_sumpositive_body_steps_partial + S (fs_r_dst_fubini_column_sumpositive_body_steps) = S ((S (fs_i_dst_fubini_column_sumpositive_body_steps)) * fs_v_dst_fubini_column_sumpositive)) /\ exists fs_q_dst_fubini_column_sumpositive_body_steps_partial. fs_u_dst_fubini_column_sumpositive = fs_q_dst_fubini_column_sumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_column_sumpositive_body_steps)) * fs_v_dst_fubini_column_sumpositive) + (fs_r_dst_fubini_column_sumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_column_sumpositive_body_steps_successor. fs_h_dst_fubini_column_sumpositive_body_steps_successor + S (fs_s_dst_fubini_column_sumpositive_body_steps) = S ((S (S fs_i_dst_fubini_column_sumpositive_body_steps)) * fs_v_dst_fubini_column_sumpositive)) /\ exists fs_q_dst_fubini_column_sumpositive_body_steps_successor. fs_u_dst_fubini_column_sumpositive = fs_q_dst_fubini_column_sumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_column_sumpositive_body_steps)) * fs_v_dst_fubini_column_sumpositive) + (fs_s_dst_fubini_column_sumpositive_body_steps))) /\ fs_s_dst_fubini_column_sumpositive_body_steps = fs_r_dst_fubini_column_sumpositive_body_steps + fs_a_dst_fubini_column_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_column_sumnegative fs_v_dst_fubini_column_sumnegative. ((((exists fs_h_dst_fubini_column_sumnegative_body_start. fs_h_dst_fubini_column_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_column_sumnegative)) /\ exists fs_q_dst_fubini_column_sumnegative_body_start. fs_u_dst_fubini_column_sumnegative = fs_q_dst_fubini_column_sumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_column_sumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_column_sumnegative_body_terminal. fs_h_dst_fubini_column_sumnegative_body_terminal + S (dst_negative_sum_fubini_column_sum) = S ((S (n)) * fs_v_dst_fubini_column_sumnegative)) /\ exists fs_q_dst_fubini_column_sumnegative_body_terminal. fs_u_dst_fubini_column_sumnegative = fs_q_dst_fubini_column_sumnegative_body_terminal * S ((S (n)) * fs_v_dst_fubini_column_sumnegative) + (dst_negative_sum_fubini_column_sum))) /\ forall fs_i_dst_fubini_column_sumnegative_body_steps. (exists fs_lt_dst_fubini_column_sumnegative_body_steps_bound. fs_lt_dst_fubini_column_sumnegative_body_steps_bound + S fs_i_dst_fubini_column_sumnegative_body_steps = n) -> exists fs_a_dst_fubini_column_sumnegative_body_steps fs_r_dst_fubini_column_sumnegative_body_steps fs_s_dst_fubini_column_sumnegative_body_steps. ((((exists fs_h_dst_fubini_column_sumnegative_body_steps_summand. fs_h_dst_fubini_column_sumnegative_body_steps_summand + S (fs_a_dst_fubini_column_sumnegative_body_steps) = S ((S (fs_i_dst_fubini_column_sumnegative_body_steps)) * dst_negative_scale_fubini_column_sum)) /\ exists fs_q_dst_fubini_column_sumnegative_body_steps_summand. dst_negative_code_fubini_column_sum = fs_q_dst_fubini_column_sumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_column_sumnegative_body_steps)) * dst_negative_scale_fubini_column_sum) + (fs_a_dst_fubini_column_sumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_column_sumnegative_body_steps_partial. fs_h_dst_fubini_column_sumnegative_body_steps_partial + S (fs_r_dst_fubini_column_sumnegative_body_steps) = S ((S (fs_i_dst_fubini_column_sumnegative_body_steps)) * fs_v_dst_fubini_column_sumnegative)) /\ exists fs_q_dst_fubini_column_sumnegative_body_steps_partial. fs_u_dst_fubini_column_sumnegative = fs_q_dst_fubini_column_sumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_column_sumnegative_body_steps)) * fs_v_dst_fubini_column_sumnegative) + (fs_r_dst_fubini_column_sumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_column_sumnegative_body_steps_successor. fs_h_dst_fubini_column_sumnegative_body_steps_successor + S (fs_s_dst_fubini_column_sumnegative_body_steps) = S ((S (S fs_i_dst_fubini_column_sumnegative_body_steps)) * fs_v_dst_fubini_column_sumnegative)) /\ exists fs_q_dst_fubini_column_sumnegative_body_steps_successor. fs_u_dst_fubini_column_sumnegative = fs_q_dst_fubini_column_sumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_column_sumnegative_body_steps)) * fs_v_dst_fubini_column_sumnegative) + (fs_s_dst_fubini_column_sumnegative_body_steps))) /\ fs_s_dst_fubini_column_sumnegative_body_steps = fs_r_dst_fubini_column_sumnegative_body_steps + fs_a_dst_fubini_column_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_column_sumresult ge_balance_negative_fubini_column_sumresult. (((((z) = 2 * (ge_balance_positive_fubini_column_sumresult) /\ (ge_balance_negative_fubini_column_sumresult) = 0) \/ exists ge_signed_half_fubini_column_sumresultdecode. (((z) = 2 * ge_signed_half_fubini_column_sumresultdecode + 1 /\ (ge_balance_positive_fubini_column_sumresult) = 0) /\ (ge_balance_negative_fubini_column_sumresult) = S ge_signed_half_fubini_column_sumresultdecode))) /\ ((dst_positive_sum_fubini_column_sum) + ge_balance_negative_fubini_column_sumresult = (dst_negative_sum_fubini_column_sum) + ge_balance_positive_fubini_column_sumresult))))))))) - 0065
specialize arithmetic_signed_sum_exists (n) - 0066
specialize arithmetic_signed_sum_exists (x4) - 0067
specialize arithmetic_signed_sum_exists (n) - 0068
apply arithmetic_signed_sum_exists - 0069
cases hC_witness - 0070
cases hC_witness_right - 0071
exact hC_witness_right_left - 0072
cases hsumC - 0073
have heq : x2 = x5 - 0074
specialize IH (F) - 0075
specialize IH (o) - 0076
specialize IH (s) - 0077
specialize IH (t) - 0078
specialize IH (n) - 0079
specialize IH (x2) - 0080
specialize IH (x5) - 0081
apply IH - 0082
exists x - 0083
split - 0084
specialize signed_rectangular_row_sums_restrict_outer (F) - 0085
specialize signed_rectangular_row_sums_restrict_outer (x) - 0086
specialize signed_rectangular_row_sums_restrict_outer (o) - 0087
specialize signed_rectangular_row_sums_restrict_outer (s) - 0088
specialize signed_rectangular_row_sums_restrict_outer (t) - 0089
specialize signed_rectangular_row_sums_restrict_outer (m) - 0090
specialize signed_rectangular_row_sums_restrict_outer (n) - 0091
apply signed_rectangular_row_sums_restrict_outer - 0092
exact ha_witness_left - 0093
exact hd_witness_witness_left - 0094
exists x4 - 0095
split - 0096
exact hC_witness - 0097
exact hsumC_witness - 0098
have hlast : exists srs_slice_fubini_last_sum. ((((exists dst_positive_code_fubini_last_sumslicesource_table dst_positive_scale_fubini_last_sumslicesource_table dst_negative_code_fubini_last_sumslicesource_table dst_negative_scale_fubini_last_sumslicesource_table. (((F) = (((((dst_positive_code_fubini_last_sumslicesource_table) + (dst_positive_scale_fubini_last_sumslicesource_table)) * S ((dst_positive_code_fubini_last_sumslicesource_table) + (dst_positive_scale_fubini_last_sumslicesource_table)) + ((dst_positive_scale_fubini_last_sumslicesource_table) + (dst_positive_scale_fubini_last_sumslicesource_table))) + (((dst_negative_code_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)) * S ((dst_negative_code_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)) + ((dst_negative_scale_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)))) * S ((((dst_positive_code_fubini_last_sumslicesource_table) + (dst_positive_scale_fubini_last_sumslicesource_table)) * S ((dst_positive_code_fubini_last_sumslicesource_table) + (dst_positive_scale_fubini_last_sumslicesource_table)) + ((dst_positive_scale_fubini_last_sumslicesource_table) + (dst_positive_scale_fubini_last_sumslicesource_table))) + (((dst_negative_code_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)) * S ((dst_negative_code_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)) + ((dst_negative_scale_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)))) + ((((dst_negative_code_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)) * S ((dst_negative_code_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)) + ((dst_negative_scale_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table))) + (((dst_negative_code_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)) * S ((dst_negative_code_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)) + ((dst_negative_scale_fubini_last_sumslicesource_table) + (dst_negative_scale_fubini_last_sumslicesource_table)))))) /\ (forall dst_index_fubini_last_sumslicesource_table. (exists pvs_le_gap_fubini_last_sumslicesource_tabledomain. pvs_le_gap_fubini_last_sumslicesource_tabledomain + (dst_index_fubini_last_sumslicesource_table) = (0)) -> exists dst_positive_fubini_last_sumslicesource_table dst_negative_fubini_last_sumslicesource_table dst_value_fubini_last_sumslicesource_table. ((((exists ff_h_pvs_fubini_last_sumslicesource_tableentrypositive. ff_h_pvs_fubini_last_sumslicesource_tableentrypositive + S (dst_positive_fubini_last_sumslicesource_table) = S ((S (dst_index_fubini_last_sumslicesource_table)) * dst_positive_scale_fubini_last_sumslicesource_table)) /\ exists ff_q_pvs_fubini_last_sumslicesource_tableentrypositive. dst_positive_code_fubini_last_sumslicesource_table = ff_q_pvs_fubini_last_sumslicesource_tableentrypositive * S ((S (dst_index_fubini_last_sumslicesource_table)) * dst_positive_scale_fubini_last_sumslicesource_table) + (dst_positive_fubini_last_sumslicesource_table))) /\ (((((exists ff_h_pvs_fubini_last_sumslicesource_tableentrynegative. ff_h_pvs_fubini_last_sumslicesource_tableentrynegative + S (dst_negative_fubini_last_sumslicesource_table) = S ((S (dst_index_fubini_last_sumslicesource_table)) * dst_negative_scale_fubini_last_sumslicesource_table)) /\ exists ff_q_pvs_fubini_last_sumslicesource_tableentrynegative. dst_negative_code_fubini_last_sumslicesource_table = ff_q_pvs_fubini_last_sumslicesource_tableentrynegative * S ((S (dst_index_fubini_last_sumslicesource_table)) * dst_negative_scale_fubini_last_sumslicesource_table) + (dst_negative_fubini_last_sumslicesource_table))) /\ (exists ge_balance_positive_fubini_last_sumslicesource_tableentryvalue ge_balance_negative_fubini_last_sumslicesource_tableentryvalue. (((((dst_value_fubini_last_sumslicesource_table) = 2 * (ge_balance_positive_fubini_last_sumslicesource_tableentryvalue) /\ (ge_balance_negative_fubini_last_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_last_sumslicesource_tableentryvaluedecode. (((dst_value_fubini_last_sumslicesource_table) = 2 * ge_signed_half_fubini_last_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_last_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_last_sumslicesource_tableentryvalue) = S ge_signed_half_fubini_last_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_fubini_last_sumslicesource_table) + ge_balance_negative_fubini_last_sumslicesource_tableentryvalue = (dst_negative_fubini_last_sumslicesource_table) + ge_balance_positive_fubini_last_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_last_sumsliceoutput_table dst_positive_scale_fubini_last_sumsliceoutput_table dst_negative_code_fubini_last_sumsliceoutput_table dst_negative_scale_fubini_last_sumsliceoutput_table. (((srs_slice_fubini_last_sum) = (((((dst_positive_code_fubini_last_sumsliceoutput_table) + (dst_positive_scale_fubini_last_sumsliceoutput_table)) * S ((dst_positive_code_fubini_last_sumsliceoutput_table) + (dst_positive_scale_fubini_last_sumsliceoutput_table)) + ((dst_positive_scale_fubini_last_sumsliceoutput_table) + (dst_positive_scale_fubini_last_sumsliceoutput_table))) + (((dst_negative_code_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)) * S ((dst_negative_code_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)) + ((dst_negative_scale_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)))) * S ((((dst_positive_code_fubini_last_sumsliceoutput_table) + (dst_positive_scale_fubini_last_sumsliceoutput_table)) * S ((dst_positive_code_fubini_last_sumsliceoutput_table) + (dst_positive_scale_fubini_last_sumsliceoutput_table)) + ((dst_positive_scale_fubini_last_sumsliceoutput_table) + (dst_positive_scale_fubini_last_sumsliceoutput_table))) + (((dst_negative_code_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)) * S ((dst_negative_code_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)) + ((dst_negative_scale_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)))) + ((((dst_negative_code_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)) * S ((dst_negative_code_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)) + ((dst_negative_scale_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table))) + (((dst_negative_code_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)) * S ((dst_negative_code_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)) + ((dst_negative_scale_fubini_last_sumsliceoutput_table) + (dst_negative_scale_fubini_last_sumsliceoutput_table)))))) /\ (forall dst_index_fubini_last_sumsliceoutput_table. (exists pvs_le_gap_fubini_last_sumsliceoutput_tabledomain. pvs_le_gap_fubini_last_sumsliceoutput_tabledomain + (dst_index_fubini_last_sumsliceoutput_table) = (n)) -> exists dst_positive_fubini_last_sumsliceoutput_table dst_negative_fubini_last_sumsliceoutput_table dst_value_fubini_last_sumsliceoutput_table. ((((exists ff_h_pvs_fubini_last_sumsliceoutput_tableentrypositive. ff_h_pvs_fubini_last_sumsliceoutput_tableentrypositive + S (dst_positive_fubini_last_sumsliceoutput_table) = S ((S (dst_index_fubini_last_sumsliceoutput_table)) * dst_positive_scale_fubini_last_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_last_sumsliceoutput_tableentrypositive. dst_positive_code_fubini_last_sumsliceoutput_table = ff_q_pvs_fubini_last_sumsliceoutput_tableentrypositive * S ((S (dst_index_fubini_last_sumsliceoutput_table)) * dst_positive_scale_fubini_last_sumsliceoutput_table) + (dst_positive_fubini_last_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_fubini_last_sumsliceoutput_tableentrynegative. ff_h_pvs_fubini_last_sumsliceoutput_tableentrynegative + S (dst_negative_fubini_last_sumsliceoutput_table) = S ((S (dst_index_fubini_last_sumsliceoutput_table)) * dst_negative_scale_fubini_last_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_last_sumsliceoutput_tableentrynegative. dst_negative_code_fubini_last_sumsliceoutput_table = ff_q_pvs_fubini_last_sumsliceoutput_tableentrynegative * S ((S (dst_index_fubini_last_sumsliceoutput_table)) * dst_negative_scale_fubini_last_sumsliceoutput_table) + (dst_negative_fubini_last_sumsliceoutput_table))) /\ (exists ge_balance_positive_fubini_last_sumsliceoutput_tableentryvalue ge_balance_negative_fubini_last_sumsliceoutput_tableentryvalue. (((((dst_value_fubini_last_sumsliceoutput_table) = 2 * (ge_balance_positive_fubini_last_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_fubini_last_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_last_sumsliceoutput_tableentryvaluedecode. (((dst_value_fubini_last_sumsliceoutput_table) = 2 * ge_signed_half_fubini_last_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_last_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_last_sumsliceoutput_tableentryvalue) = S ge_signed_half_fubini_last_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_fubini_last_sumsliceoutput_table) + ge_balance_negative_fubini_last_sumsliceoutput_tableentryvalue = (dst_negative_fubini_last_sumsliceoutput_table) + ge_balance_positive_fubini_last_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_fubini_last_sumslice. (exists pvs_gap_fubini_last_sumslicebound. pvs_gap_fubini_last_sumslicebound + S (srs_index_fubini_last_sumslice) = (n)) -> exists srs_value_fubini_last_sumslice. (((exists dst_positive_code_fubini_last_sumsliceentrysource dst_positive_scale_fubini_last_sumsliceentrysource dst_negative_code_fubini_last_sumsliceentrysource dst_negative_scale_fubini_last_sumsliceentrysource dst_positive_fubini_last_sumsliceentrysource dst_negative_fubini_last_sumsliceentrysource. (((F) = (((((dst_positive_code_fubini_last_sumsliceentrysource) + (dst_positive_scale_fubini_last_sumsliceentrysource)) * S ((dst_positive_code_fubini_last_sumsliceentrysource) + (dst_positive_scale_fubini_last_sumsliceentrysource)) + ((dst_positive_scale_fubini_last_sumsliceentrysource) + (dst_positive_scale_fubini_last_sumsliceentrysource))) + (((dst_negative_code_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)) * S ((dst_negative_code_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)) + ((dst_negative_scale_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)))) * S ((((dst_positive_code_fubini_last_sumsliceentrysource) + (dst_positive_scale_fubini_last_sumsliceentrysource)) * S ((dst_positive_code_fubini_last_sumsliceentrysource) + (dst_positive_scale_fubini_last_sumsliceentrysource)) + ((dst_positive_scale_fubini_last_sumsliceentrysource) + (dst_positive_scale_fubini_last_sumsliceentrysource))) + (((dst_negative_code_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)) * S ((dst_negative_code_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)) + ((dst_negative_scale_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)))) + ((((dst_negative_code_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)) * S ((dst_negative_code_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)) + ((dst_negative_scale_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource))) + (((dst_negative_code_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)) * S ((dst_negative_code_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)) + ((dst_negative_scale_fubini_last_sumsliceentrysource) + (dst_negative_scale_fubini_last_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_fubini_last_sumsliceentrysourcepositive. ff_h_pvs_fubini_last_sumsliceentrysourcepositive + S (dst_positive_fubini_last_sumsliceentrysource) = S ((S (((((o) + ((s) * (m)))) + ((t) * (srs_index_fubini_last_sumslice))))) * dst_positive_scale_fubini_last_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_last_sumsliceentrysourcepositive. dst_positive_code_fubini_last_sumsliceentrysource = ff_q_pvs_fubini_last_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (m)))) + ((t) * (srs_index_fubini_last_sumslice))))) * dst_positive_scale_fubini_last_sumsliceentrysource) + (dst_positive_fubini_last_sumsliceentrysource))) /\ (((((exists ff_h_pvs_fubini_last_sumsliceentrysourcenegative. ff_h_pvs_fubini_last_sumsliceentrysourcenegative + S (dst_negative_fubini_last_sumsliceentrysource) = S ((S (((((o) + ((s) * (m)))) + ((t) * (srs_index_fubini_last_sumslice))))) * dst_negative_scale_fubini_last_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_last_sumsliceentrysourcenegative. dst_negative_code_fubini_last_sumsliceentrysource = ff_q_pvs_fubini_last_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (m)))) + ((t) * (srs_index_fubini_last_sumslice))))) * dst_negative_scale_fubini_last_sumsliceentrysource) + (dst_negative_fubini_last_sumsliceentrysource))) /\ (exists ge_balance_positive_fubini_last_sumsliceentrysourcevalue ge_balance_negative_fubini_last_sumsliceentrysourcevalue. (((((srs_value_fubini_last_sumslice) = 2 * (ge_balance_positive_fubini_last_sumsliceentrysourcevalue) /\ (ge_balance_negative_fubini_last_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_fubini_last_sumsliceentrysourcevaluedecode. (((srs_value_fubini_last_sumslice) = 2 * ge_signed_half_fubini_last_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_fubini_last_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_fubini_last_sumsliceentrysourcevalue) = S ge_signed_half_fubini_last_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_fubini_last_sumsliceentrysource) + ge_balance_negative_fubini_last_sumsliceentrysourcevalue = (dst_negative_fubini_last_sumsliceentrysource) + ge_balance_positive_fubini_last_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_fubini_last_sumsliceentryoutput dst_positive_scale_fubini_last_sumsliceentryoutput dst_negative_code_fubini_last_sumsliceentryoutput dst_negative_scale_fubini_last_sumsliceentryoutput dst_positive_fubini_last_sumsliceentryoutput dst_negative_fubini_last_sumsliceentryoutput. (((srs_slice_fubini_last_sum) = (((((dst_positive_code_fubini_last_sumsliceentryoutput) + (dst_positive_scale_fubini_last_sumsliceentryoutput)) * S ((dst_positive_code_fubini_last_sumsliceentryoutput) + (dst_positive_scale_fubini_last_sumsliceentryoutput)) + ((dst_positive_scale_fubini_last_sumsliceentryoutput) + (dst_positive_scale_fubini_last_sumsliceentryoutput))) + (((dst_negative_code_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)) * S ((dst_negative_code_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)) + ((dst_negative_scale_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)))) * S ((((dst_positive_code_fubini_last_sumsliceentryoutput) + (dst_positive_scale_fubini_last_sumsliceentryoutput)) * S ((dst_positive_code_fubini_last_sumsliceentryoutput) + (dst_positive_scale_fubini_last_sumsliceentryoutput)) + ((dst_positive_scale_fubini_last_sumsliceentryoutput) + (dst_positive_scale_fubini_last_sumsliceentryoutput))) + (((dst_negative_code_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)) * S ((dst_negative_code_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)) + ((dst_negative_scale_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)))) + ((((dst_negative_code_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)) * S ((dst_negative_code_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)) + ((dst_negative_scale_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput))) + (((dst_negative_code_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)) * S ((dst_negative_code_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)) + ((dst_negative_scale_fubini_last_sumsliceentryoutput) + (dst_negative_scale_fubini_last_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_fubini_last_sumsliceentryoutputpositive. ff_h_pvs_fubini_last_sumsliceentryoutputpositive + S (dst_positive_fubini_last_sumsliceentryoutput) = S ((S (srs_index_fubini_last_sumslice)) * dst_positive_scale_fubini_last_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_last_sumsliceentryoutputpositive. dst_positive_code_fubini_last_sumsliceentryoutput = ff_q_pvs_fubini_last_sumsliceentryoutputpositive * S ((S (srs_index_fubini_last_sumslice)) * dst_positive_scale_fubini_last_sumsliceentryoutput) + (dst_positive_fubini_last_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_fubini_last_sumsliceentryoutputnegative. ff_h_pvs_fubini_last_sumsliceentryoutputnegative + S (dst_negative_fubini_last_sumsliceentryoutput) = S ((S (srs_index_fubini_last_sumslice)) * dst_negative_scale_fubini_last_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_last_sumsliceentryoutputnegative. dst_negative_code_fubini_last_sumsliceentryoutput = ff_q_pvs_fubini_last_sumsliceentryoutputnegative * S ((S (srs_index_fubini_last_sumslice)) * dst_negative_scale_fubini_last_sumsliceentryoutput) + (dst_negative_fubini_last_sumsliceentryoutput))) /\ (exists ge_balance_positive_fubini_last_sumsliceentryoutputvalue ge_balance_negative_fubini_last_sumsliceentryoutputvalue. (((((srs_value_fubini_last_sumslice) = 2 * (ge_balance_positive_fubini_last_sumsliceentryoutputvalue) /\ (ge_balance_negative_fubini_last_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_fubini_last_sumsliceentryoutputvaluedecode. (((srs_value_fubini_last_sumslice) = 2 * ge_signed_half_fubini_last_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_fubini_last_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_fubini_last_sumsliceentryoutputvalue) = S ge_signed_half_fubini_last_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_fubini_last_sumsliceentryoutput) + ge_balance_negative_fubini_last_sumsliceentryoutputvalue = (dst_negative_fubini_last_sumsliceentryoutput) + ge_balance_positive_fubini_last_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_fubini_last_sumsum dst_positive_scale_fubini_last_sumsum dst_negative_code_fubini_last_sumsum dst_negative_scale_fubini_last_sumsum dst_positive_sum_fubini_last_sumsum dst_negative_sum_fubini_last_sumsum. (((srs_slice_fubini_last_sum) = (((((dst_positive_code_fubini_last_sumsum) + (dst_positive_scale_fubini_last_sumsum)) * S ((dst_positive_code_fubini_last_sumsum) + (dst_positive_scale_fubini_last_sumsum)) + ((dst_positive_scale_fubini_last_sumsum) + (dst_positive_scale_fubini_last_sumsum))) + (((dst_negative_code_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)) * S ((dst_negative_code_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)) + ((dst_negative_scale_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)))) * S ((((dst_positive_code_fubini_last_sumsum) + (dst_positive_scale_fubini_last_sumsum)) * S ((dst_positive_code_fubini_last_sumsum) + (dst_positive_scale_fubini_last_sumsum)) + ((dst_positive_scale_fubini_last_sumsum) + (dst_positive_scale_fubini_last_sumsum))) + (((dst_negative_code_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)) * S ((dst_negative_code_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)) + ((dst_negative_scale_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)))) + ((((dst_negative_code_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)) * S ((dst_negative_code_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)) + ((dst_negative_scale_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum))) + (((dst_negative_code_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)) * S ((dst_negative_code_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)) + ((dst_negative_scale_fubini_last_sumsum) + (dst_negative_scale_fubini_last_sumsum)))))) /\ (((exists fs_u_dst_fubini_last_sumsumpositive fs_v_dst_fubini_last_sumsumpositive. ((((exists fs_h_dst_fubini_last_sumsumpositive_body_start. fs_h_dst_fubini_last_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_last_sumsumpositive)) /\ exists fs_q_dst_fubini_last_sumsumpositive_body_start. fs_u_dst_fubini_last_sumsumpositive = fs_q_dst_fubini_last_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_last_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_last_sumsumpositive_body_terminal. fs_h_dst_fubini_last_sumsumpositive_body_terminal + S (dst_positive_sum_fubini_last_sumsum) = S ((S (n)) * fs_v_dst_fubini_last_sumsumpositive)) /\ exists fs_q_dst_fubini_last_sumsumpositive_body_terminal. fs_u_dst_fubini_last_sumsumpositive = fs_q_dst_fubini_last_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_fubini_last_sumsumpositive) + (dst_positive_sum_fubini_last_sumsum))) /\ forall fs_i_dst_fubini_last_sumsumpositive_body_steps. (exists fs_lt_dst_fubini_last_sumsumpositive_body_steps_bound. fs_lt_dst_fubini_last_sumsumpositive_body_steps_bound + S fs_i_dst_fubini_last_sumsumpositive_body_steps = n) -> exists fs_a_dst_fubini_last_sumsumpositive_body_steps fs_r_dst_fubini_last_sumsumpositive_body_steps fs_s_dst_fubini_last_sumsumpositive_body_steps. ((((exists fs_h_dst_fubini_last_sumsumpositive_body_steps_summand. fs_h_dst_fubini_last_sumsumpositive_body_steps_summand + S (fs_a_dst_fubini_last_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_last_sumsumpositive_body_steps)) * dst_positive_scale_fubini_last_sumsum)) /\ exists fs_q_dst_fubini_last_sumsumpositive_body_steps_summand. dst_positive_code_fubini_last_sumsum = fs_q_dst_fubini_last_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_last_sumsumpositive_body_steps)) * dst_positive_scale_fubini_last_sumsum) + (fs_a_dst_fubini_last_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_last_sumsumpositive_body_steps_partial. fs_h_dst_fubini_last_sumsumpositive_body_steps_partial + S (fs_r_dst_fubini_last_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_last_sumsumpositive_body_steps)) * fs_v_dst_fubini_last_sumsumpositive)) /\ exists fs_q_dst_fubini_last_sumsumpositive_body_steps_partial. fs_u_dst_fubini_last_sumsumpositive = fs_q_dst_fubini_last_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_last_sumsumpositive_body_steps)) * fs_v_dst_fubini_last_sumsumpositive) + (fs_r_dst_fubini_last_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_last_sumsumpositive_body_steps_successor. fs_h_dst_fubini_last_sumsumpositive_body_steps_successor + S (fs_s_dst_fubini_last_sumsumpositive_body_steps) = S ((S (S fs_i_dst_fubini_last_sumsumpositive_body_steps)) * fs_v_dst_fubini_last_sumsumpositive)) /\ exists fs_q_dst_fubini_last_sumsumpositive_body_steps_successor. fs_u_dst_fubini_last_sumsumpositive = fs_q_dst_fubini_last_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_last_sumsumpositive_body_steps)) * fs_v_dst_fubini_last_sumsumpositive) + (fs_s_dst_fubini_last_sumsumpositive_body_steps))) /\ fs_s_dst_fubini_last_sumsumpositive_body_steps = fs_r_dst_fubini_last_sumsumpositive_body_steps + fs_a_dst_fubini_last_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_last_sumsumnegative fs_v_dst_fubini_last_sumsumnegative. ((((exists fs_h_dst_fubini_last_sumsumnegative_body_start. fs_h_dst_fubini_last_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_last_sumsumnegative)) /\ exists fs_q_dst_fubini_last_sumsumnegative_body_start. fs_u_dst_fubini_last_sumsumnegative = fs_q_dst_fubini_last_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_last_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_last_sumsumnegative_body_terminal. fs_h_dst_fubini_last_sumsumnegative_body_terminal + S (dst_negative_sum_fubini_last_sumsum) = S ((S (n)) * fs_v_dst_fubini_last_sumsumnegative)) /\ exists fs_q_dst_fubini_last_sumsumnegative_body_terminal. fs_u_dst_fubini_last_sumsumnegative = fs_q_dst_fubini_last_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_fubini_last_sumsumnegative) + (dst_negative_sum_fubini_last_sumsum))) /\ forall fs_i_dst_fubini_last_sumsumnegative_body_steps. (exists fs_lt_dst_fubini_last_sumsumnegative_body_steps_bound. fs_lt_dst_fubini_last_sumsumnegative_body_steps_bound + S fs_i_dst_fubini_last_sumsumnegative_body_steps = n) -> exists fs_a_dst_fubini_last_sumsumnegative_body_steps fs_r_dst_fubini_last_sumsumnegative_body_steps fs_s_dst_fubini_last_sumsumnegative_body_steps. ((((exists fs_h_dst_fubini_last_sumsumnegative_body_steps_summand. fs_h_dst_fubini_last_sumsumnegative_body_steps_summand + S (fs_a_dst_fubini_last_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_last_sumsumnegative_body_steps)) * dst_negative_scale_fubini_last_sumsum)) /\ exists fs_q_dst_fubini_last_sumsumnegative_body_steps_summand. dst_negative_code_fubini_last_sumsum = fs_q_dst_fubini_last_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_last_sumsumnegative_body_steps)) * dst_negative_scale_fubini_last_sumsum) + (fs_a_dst_fubini_last_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_last_sumsumnegative_body_steps_partial. fs_h_dst_fubini_last_sumsumnegative_body_steps_partial + S (fs_r_dst_fubini_last_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_last_sumsumnegative_body_steps)) * fs_v_dst_fubini_last_sumsumnegative)) /\ exists fs_q_dst_fubini_last_sumsumnegative_body_steps_partial. fs_u_dst_fubini_last_sumsumnegative = fs_q_dst_fubini_last_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_last_sumsumnegative_body_steps)) * fs_v_dst_fubini_last_sumsumnegative) + (fs_r_dst_fubini_last_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_last_sumsumnegative_body_steps_successor. fs_h_dst_fubini_last_sumsumnegative_body_steps_successor + S (fs_s_dst_fubini_last_sumsumnegative_body_steps) = S ((S (S fs_i_dst_fubini_last_sumsumnegative_body_steps)) * fs_v_dst_fubini_last_sumsumnegative)) /\ exists fs_q_dst_fubini_last_sumsumnegative_body_steps_successor. fs_u_dst_fubini_last_sumsumnegative = fs_q_dst_fubini_last_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_last_sumsumnegative_body_steps)) * fs_v_dst_fubini_last_sumsumnegative) + (fs_s_dst_fubini_last_sumsumnegative_body_steps))) /\ fs_s_dst_fubini_last_sumsumnegative_body_steps = fs_r_dst_fubini_last_sumsumnegative_body_steps + fs_a_dst_fubini_last_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_last_sumsumresult ge_balance_negative_fubini_last_sumsumresult. (((((x3) = 2 * (ge_balance_positive_fubini_last_sumsumresult) /\ (ge_balance_negative_fubini_last_sumsumresult) = 0) \/ exists ge_signed_half_fubini_last_sumsumresultdecode. (((x3) = 2 * ge_signed_half_fubini_last_sumsumresultdecode + 1 /\ (ge_balance_positive_fubini_last_sumsumresult) = 0) /\ (ge_balance_negative_fubini_last_sumsumresult) = S ge_signed_half_fubini_last_sumsumresultdecode))) /\ ((dst_positive_sum_fubini_last_sumsum) + ge_balance_negative_fubini_last_sumsumresult = (dst_negative_sum_fubini_last_sumsum) + ge_balance_positive_fubini_last_sumsumresult)))))))))) - 0099
specialize signed_rectangular_row_sums_lookup (F) - 0100
specialize signed_rectangular_row_sums_lookup (x) - 0101
specialize signed_rectangular_row_sums_lookup (o) - 0102
specialize signed_rectangular_row_sums_lookup (s) - 0103
specialize signed_rectangular_row_sums_lookup (t) - 0104
specialize signed_rectangular_row_sums_lookup (S m) - 0105
specialize signed_rectangular_row_sums_lookup (n) - 0106
specialize signed_rectangular_row_sums_lookup (m) - 0107
specialize signed_rectangular_row_sums_lookup (x3) - 0108
apply signed_rectangular_row_sums_lookup - 0109
exact ha_witness_left - 0110
specialize le_refl (S m) - 0111
apply le_refl - 0112
exact hd_witness_witness_right_left - 0113
cases hlast - 0114
cases hlast_witness - 0115
have hpoint : ((exists dst_positive_code_fubini_pointwiseleft_table dst_positive_scale_fubini_pointwiseleft_table dst_negative_code_fubini_pointwiseleft_table dst_negative_scale_fubini_pointwiseleft_table. (((x4) = (((((dst_positive_code_fubini_pointwiseleft_table) + (dst_positive_scale_fubini_pointwiseleft_table)) * S ((dst_positive_code_fubini_pointwiseleft_table) + (dst_positive_scale_fubini_pointwiseleft_table)) + ((dst_positive_scale_fubini_pointwiseleft_table) + (dst_positive_scale_fubini_pointwiseleft_table))) + (((dst_negative_code_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)) * S ((dst_negative_code_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)) + ((dst_negative_scale_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)))) * S ((((dst_positive_code_fubini_pointwiseleft_table) + (dst_positive_scale_fubini_pointwiseleft_table)) * S ((dst_positive_code_fubini_pointwiseleft_table) + (dst_positive_scale_fubini_pointwiseleft_table)) + ((dst_positive_scale_fubini_pointwiseleft_table) + (dst_positive_scale_fubini_pointwiseleft_table))) + (((dst_negative_code_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)) * S ((dst_negative_code_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)) + ((dst_negative_scale_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)))) + ((((dst_negative_code_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)) * S ((dst_negative_code_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)) + ((dst_negative_scale_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table))) + (((dst_negative_code_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)) * S ((dst_negative_code_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)) + ((dst_negative_scale_fubini_pointwiseleft_table) + (dst_negative_scale_fubini_pointwiseleft_table)))))) /\ (forall dst_index_fubini_pointwiseleft_table. (exists pvs_le_gap_fubini_pointwiseleft_tabledomain. pvs_le_gap_fubini_pointwiseleft_tabledomain + (dst_index_fubini_pointwiseleft_table) = (n)) -> exists dst_positive_fubini_pointwiseleft_table dst_negative_fubini_pointwiseleft_table dst_value_fubini_pointwiseleft_table. ((((exists ff_h_pvs_fubini_pointwiseleft_tableentrypositive. ff_h_pvs_fubini_pointwiseleft_tableentrypositive + S (dst_positive_fubini_pointwiseleft_table) = S ((S (dst_index_fubini_pointwiseleft_table)) * dst_positive_scale_fubini_pointwiseleft_table)) /\ exists ff_q_pvs_fubini_pointwiseleft_tableentrypositive. dst_positive_code_fubini_pointwiseleft_table = ff_q_pvs_fubini_pointwiseleft_tableentrypositive * S ((S (dst_index_fubini_pointwiseleft_table)) * dst_positive_scale_fubini_pointwiseleft_table) + (dst_positive_fubini_pointwiseleft_table))) /\ (((((exists ff_h_pvs_fubini_pointwiseleft_tableentrynegative. ff_h_pvs_fubini_pointwiseleft_tableentrynegative + S (dst_negative_fubini_pointwiseleft_table) = S ((S (dst_index_fubini_pointwiseleft_table)) * dst_negative_scale_fubini_pointwiseleft_table)) /\ exists ff_q_pvs_fubini_pointwiseleft_tableentrynegative. dst_negative_code_fubini_pointwiseleft_table = ff_q_pvs_fubini_pointwiseleft_tableentrynegative * S ((S (dst_index_fubini_pointwiseleft_table)) * dst_negative_scale_fubini_pointwiseleft_table) + (dst_negative_fubini_pointwiseleft_table))) /\ (exists ge_balance_positive_fubini_pointwiseleft_tableentryvalue ge_balance_negative_fubini_pointwiseleft_tableentryvalue. (((((dst_value_fubini_pointwiseleft_table) = 2 * (ge_balance_positive_fubini_pointwiseleft_tableentryvalue) /\ (ge_balance_negative_fubini_pointwiseleft_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_pointwiseleft_tableentryvaluedecode. (((dst_value_fubini_pointwiseleft_table) = 2 * ge_signed_half_fubini_pointwiseleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_pointwiseleft_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_pointwiseleft_tableentryvalue) = S ge_signed_half_fubini_pointwiseleft_tableentryvaluedecode))) /\ ((dst_positive_fubini_pointwiseleft_table) + ge_balance_negative_fubini_pointwiseleft_tableentryvalue = (dst_negative_fubini_pointwiseleft_table) + ge_balance_positive_fubini_pointwiseleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_pointwiseright_table dst_positive_scale_fubini_pointwiseright_table dst_negative_code_fubini_pointwiseright_table dst_negative_scale_fubini_pointwiseright_table. (((x6) = (((((dst_positive_code_fubini_pointwiseright_table) + (dst_positive_scale_fubini_pointwiseright_table)) * S ((dst_positive_code_fubini_pointwiseright_table) + (dst_positive_scale_fubini_pointwiseright_table)) + ((dst_positive_scale_fubini_pointwiseright_table) + (dst_positive_scale_fubini_pointwiseright_table))) + (((dst_negative_code_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)) * S ((dst_negative_code_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)) + ((dst_negative_scale_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)))) * S ((((dst_positive_code_fubini_pointwiseright_table) + (dst_positive_scale_fubini_pointwiseright_table)) * S ((dst_positive_code_fubini_pointwiseright_table) + (dst_positive_scale_fubini_pointwiseright_table)) + ((dst_positive_scale_fubini_pointwiseright_table) + (dst_positive_scale_fubini_pointwiseright_table))) + (((dst_negative_code_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)) * S ((dst_negative_code_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)) + ((dst_negative_scale_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)))) + ((((dst_negative_code_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)) * S ((dst_negative_code_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)) + ((dst_negative_scale_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table))) + (((dst_negative_code_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)) * S ((dst_negative_code_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)) + ((dst_negative_scale_fubini_pointwiseright_table) + (dst_negative_scale_fubini_pointwiseright_table)))))) /\ (forall dst_index_fubini_pointwiseright_table. (exists pvs_le_gap_fubini_pointwiseright_tabledomain. pvs_le_gap_fubini_pointwiseright_tabledomain + (dst_index_fubini_pointwiseright_table) = (n)) -> exists dst_positive_fubini_pointwiseright_table dst_negative_fubini_pointwiseright_table dst_value_fubini_pointwiseright_table. ((((exists ff_h_pvs_fubini_pointwiseright_tableentrypositive. ff_h_pvs_fubini_pointwiseright_tableentrypositive + S (dst_positive_fubini_pointwiseright_table) = S ((S (dst_index_fubini_pointwiseright_table)) * dst_positive_scale_fubini_pointwiseright_table)) /\ exists ff_q_pvs_fubini_pointwiseright_tableentrypositive. dst_positive_code_fubini_pointwiseright_table = ff_q_pvs_fubini_pointwiseright_tableentrypositive * S ((S (dst_index_fubini_pointwiseright_table)) * dst_positive_scale_fubini_pointwiseright_table) + (dst_positive_fubini_pointwiseright_table))) /\ (((((exists ff_h_pvs_fubini_pointwiseright_tableentrynegative. ff_h_pvs_fubini_pointwiseright_tableentrynegative + S (dst_negative_fubini_pointwiseright_table) = S ((S (dst_index_fubini_pointwiseright_table)) * dst_negative_scale_fubini_pointwiseright_table)) /\ exists ff_q_pvs_fubini_pointwiseright_tableentrynegative. dst_negative_code_fubini_pointwiseright_table = ff_q_pvs_fubini_pointwiseright_tableentrynegative * S ((S (dst_index_fubini_pointwiseright_table)) * dst_negative_scale_fubini_pointwiseright_table) + (dst_negative_fubini_pointwiseright_table))) /\ (exists ge_balance_positive_fubini_pointwiseright_tableentryvalue ge_balance_negative_fubini_pointwiseright_tableentryvalue. (((((dst_value_fubini_pointwiseright_table) = 2 * (ge_balance_positive_fubini_pointwiseright_tableentryvalue) /\ (ge_balance_negative_fubini_pointwiseright_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_pointwiseright_tableentryvaluedecode. (((dst_value_fubini_pointwiseright_table) = 2 * ge_signed_half_fubini_pointwiseright_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_pointwiseright_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_pointwiseright_tableentryvalue) = S ge_signed_half_fubini_pointwiseright_tableentryvaluedecode))) /\ ((dst_positive_fubini_pointwiseright_table) + ge_balance_negative_fubini_pointwiseright_tableentryvalue = (dst_negative_fubini_pointwiseright_table) + ge_balance_positive_fubini_pointwiseright_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_pointwiseoutput_table dst_positive_scale_fubini_pointwiseoutput_table dst_negative_code_fubini_pointwiseoutput_table dst_negative_scale_fubini_pointwiseoutput_table. (((x1) = (((((dst_positive_code_fubini_pointwiseoutput_table) + (dst_positive_scale_fubini_pointwiseoutput_table)) * S ((dst_positive_code_fubini_pointwiseoutput_table) + (dst_positive_scale_fubini_pointwiseoutput_table)) + ((dst_positive_scale_fubini_pointwiseoutput_table) + (dst_positive_scale_fubini_pointwiseoutput_table))) + (((dst_negative_code_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)) * S ((dst_negative_code_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)) + ((dst_negative_scale_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)))) * S ((((dst_positive_code_fubini_pointwiseoutput_table) + (dst_positive_scale_fubini_pointwiseoutput_table)) * S ((dst_positive_code_fubini_pointwiseoutput_table) + (dst_positive_scale_fubini_pointwiseoutput_table)) + ((dst_positive_scale_fubini_pointwiseoutput_table) + (dst_positive_scale_fubini_pointwiseoutput_table))) + (((dst_negative_code_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)) * S ((dst_negative_code_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)) + ((dst_negative_scale_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)))) + ((((dst_negative_code_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)) * S ((dst_negative_code_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)) + ((dst_negative_scale_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table))) + (((dst_negative_code_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)) * S ((dst_negative_code_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)) + ((dst_negative_scale_fubini_pointwiseoutput_table) + (dst_negative_scale_fubini_pointwiseoutput_table)))))) /\ (forall dst_index_fubini_pointwiseoutput_table. (exists pvs_le_gap_fubini_pointwiseoutput_tabledomain. pvs_le_gap_fubini_pointwiseoutput_tabledomain + (dst_index_fubini_pointwiseoutput_table) = (n)) -> exists dst_positive_fubini_pointwiseoutput_table dst_negative_fubini_pointwiseoutput_table dst_value_fubini_pointwiseoutput_table. ((((exists ff_h_pvs_fubini_pointwiseoutput_tableentrypositive. ff_h_pvs_fubini_pointwiseoutput_tableentrypositive + S (dst_positive_fubini_pointwiseoutput_table) = S ((S (dst_index_fubini_pointwiseoutput_table)) * dst_positive_scale_fubini_pointwiseoutput_table)) /\ exists ff_q_pvs_fubini_pointwiseoutput_tableentrypositive. dst_positive_code_fubini_pointwiseoutput_table = ff_q_pvs_fubini_pointwiseoutput_tableentrypositive * S ((S (dst_index_fubini_pointwiseoutput_table)) * dst_positive_scale_fubini_pointwiseoutput_table) + (dst_positive_fubini_pointwiseoutput_table))) /\ (((((exists ff_h_pvs_fubini_pointwiseoutput_tableentrynegative. ff_h_pvs_fubini_pointwiseoutput_tableentrynegative + S (dst_negative_fubini_pointwiseoutput_table) = S ((S (dst_index_fubini_pointwiseoutput_table)) * dst_negative_scale_fubini_pointwiseoutput_table)) /\ exists ff_q_pvs_fubini_pointwiseoutput_tableentrynegative. dst_negative_code_fubini_pointwiseoutput_table = ff_q_pvs_fubini_pointwiseoutput_tableentrynegative * S ((S (dst_index_fubini_pointwiseoutput_table)) * dst_negative_scale_fubini_pointwiseoutput_table) + (dst_negative_fubini_pointwiseoutput_table))) /\ (exists ge_balance_positive_fubini_pointwiseoutput_tableentryvalue ge_balance_negative_fubini_pointwiseoutput_tableentryvalue. (((((dst_value_fubini_pointwiseoutput_table) = 2 * (ge_balance_positive_fubini_pointwiseoutput_tableentryvalue) /\ (ge_balance_negative_fubini_pointwiseoutput_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_pointwiseoutput_tableentryvaluedecode. (((dst_value_fubini_pointwiseoutput_table) = 2 * ge_signed_half_fubini_pointwiseoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_pointwiseoutput_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_pointwiseoutput_tableentryvalue) = S ge_signed_half_fubini_pointwiseoutput_tableentryvaluedecode))) /\ ((dst_positive_fubini_pointwiseoutput_table) + ge_balance_negative_fubini_pointwiseoutput_tableentryvalue = (dst_negative_fubini_pointwiseoutput_table) + ge_balance_positive_fubini_pointwiseoutput_tableentryvalue))))))))) /\ (forall sto_index_fubini_pointwiseentries. (exists pvs_gap_fubini_pointwiseentriesbound. pvs_gap_fubini_pointwiseentriesbound + S (sto_index_fubini_pointwiseentries) = (n)) -> exists sto_left_fubini_pointwiseentries sto_right_fubini_pointwiseentries sto_output_fubini_pointwiseentries. ((exists dst_positive_code_fubini_pointwiseentriesentryleft dst_positive_scale_fubini_pointwiseentriesentryleft dst_negative_code_fubini_pointwiseentriesentryleft dst_negative_scale_fubini_pointwiseentriesentryleft dst_positive_fubini_pointwiseentriesentryleft dst_negative_fubini_pointwiseentriesentryleft. (((x4) = (((((dst_positive_code_fubini_pointwiseentriesentryleft) + (dst_positive_scale_fubini_pointwiseentriesentryleft)) * S ((dst_positive_code_fubini_pointwiseentriesentryleft) + (dst_positive_scale_fubini_pointwiseentriesentryleft)) + ((dst_positive_scale_fubini_pointwiseentriesentryleft) + (dst_positive_scale_fubini_pointwiseentriesentryleft))) + (((dst_negative_code_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)) * S ((dst_negative_code_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)) + ((dst_negative_scale_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)))) * S ((((dst_positive_code_fubini_pointwiseentriesentryleft) + (dst_positive_scale_fubini_pointwiseentriesentryleft)) * S ((dst_positive_code_fubini_pointwiseentriesentryleft) + (dst_positive_scale_fubini_pointwiseentriesentryleft)) + ((dst_positive_scale_fubini_pointwiseentriesentryleft) + (dst_positive_scale_fubini_pointwiseentriesentryleft))) + (((dst_negative_code_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)) * S ((dst_negative_code_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)) + ((dst_negative_scale_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)))) + ((((dst_negative_code_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)) * S ((dst_negative_code_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)) + ((dst_negative_scale_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft))) + (((dst_negative_code_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)) * S ((dst_negative_code_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)) + ((dst_negative_scale_fubini_pointwiseentriesentryleft) + (dst_negative_scale_fubini_pointwiseentriesentryleft)))))) /\ (((((exists ff_h_pvs_fubini_pointwiseentriesentryleftpositive. ff_h_pvs_fubini_pointwiseentriesentryleftpositive + S (dst_positive_fubini_pointwiseentriesentryleft) = S ((S (sto_index_fubini_pointwiseentries)) * dst_positive_scale_fubini_pointwiseentriesentryleft)) /\ exists ff_q_pvs_fubini_pointwiseentriesentryleftpositive. dst_positive_code_fubini_pointwiseentriesentryleft = ff_q_pvs_fubini_pointwiseentriesentryleftpositive * S ((S (sto_index_fubini_pointwiseentries)) * dst_positive_scale_fubini_pointwiseentriesentryleft) + (dst_positive_fubini_pointwiseentriesentryleft))) /\ (((((exists ff_h_pvs_fubini_pointwiseentriesentryleftnegative. ff_h_pvs_fubini_pointwiseentriesentryleftnegative + S (dst_negative_fubini_pointwiseentriesentryleft) = S ((S (sto_index_fubini_pointwiseentries)) * dst_negative_scale_fubini_pointwiseentriesentryleft)) /\ exists ff_q_pvs_fubini_pointwiseentriesentryleftnegative. dst_negative_code_fubini_pointwiseentriesentryleft = ff_q_pvs_fubini_pointwiseentriesentryleftnegative * S ((S (sto_index_fubini_pointwiseentries)) * dst_negative_scale_fubini_pointwiseentriesentryleft) + (dst_negative_fubini_pointwiseentriesentryleft))) /\ (exists ge_balance_positive_fubini_pointwiseentriesentryleftvalue ge_balance_negative_fubini_pointwiseentriesentryleftvalue. (((((sto_left_fubini_pointwiseentries) = 2 * (ge_balance_positive_fubini_pointwiseentriesentryleftvalue) /\ (ge_balance_negative_fubini_pointwiseentriesentryleftvalue) = 0) \/ exists ge_signed_half_fubini_pointwiseentriesentryleftvaluedecode. (((sto_left_fubini_pointwiseentries) = 2 * ge_signed_half_fubini_pointwiseentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_fubini_pointwiseentriesentryleftvalue) = 0) /\ (ge_balance_negative_fubini_pointwiseentriesentryleftvalue) = S ge_signed_half_fubini_pointwiseentriesentryleftvaluedecode))) /\ ((dst_positive_fubini_pointwiseentriesentryleft) + ge_balance_negative_fubini_pointwiseentriesentryleftvalue = (dst_negative_fubini_pointwiseentriesentryleft) + ge_balance_positive_fubini_pointwiseentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_fubini_pointwiseentriesentryright dst_positive_scale_fubini_pointwiseentriesentryright dst_negative_code_fubini_pointwiseentriesentryright dst_negative_scale_fubini_pointwiseentriesentryright dst_positive_fubini_pointwiseentriesentryright dst_negative_fubini_pointwiseentriesentryright. (((x6) = (((((dst_positive_code_fubini_pointwiseentriesentryright) + (dst_positive_scale_fubini_pointwiseentriesentryright)) * S ((dst_positive_code_fubini_pointwiseentriesentryright) + (dst_positive_scale_fubini_pointwiseentriesentryright)) + ((dst_positive_scale_fubini_pointwiseentriesentryright) + (dst_positive_scale_fubini_pointwiseentriesentryright))) + (((dst_negative_code_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)) * S ((dst_negative_code_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)) + ((dst_negative_scale_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)))) * S ((((dst_positive_code_fubini_pointwiseentriesentryright) + (dst_positive_scale_fubini_pointwiseentriesentryright)) * S ((dst_positive_code_fubini_pointwiseentriesentryright) + (dst_positive_scale_fubini_pointwiseentriesentryright)) + ((dst_positive_scale_fubini_pointwiseentriesentryright) + (dst_positive_scale_fubini_pointwiseentriesentryright))) + (((dst_negative_code_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)) * S ((dst_negative_code_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)) + ((dst_negative_scale_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)))) + ((((dst_negative_code_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)) * S ((dst_negative_code_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)) + ((dst_negative_scale_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright))) + (((dst_negative_code_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)) * S ((dst_negative_code_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)) + ((dst_negative_scale_fubini_pointwiseentriesentryright) + (dst_negative_scale_fubini_pointwiseentriesentryright)))))) /\ (((((exists ff_h_pvs_fubini_pointwiseentriesentryrightpositive. ff_h_pvs_fubini_pointwiseentriesentryrightpositive + S (dst_positive_fubini_pointwiseentriesentryright) = S ((S (sto_index_fubini_pointwiseentries)) * dst_positive_scale_fubini_pointwiseentriesentryright)) /\ exists ff_q_pvs_fubini_pointwiseentriesentryrightpositive. dst_positive_code_fubini_pointwiseentriesentryright = ff_q_pvs_fubini_pointwiseentriesentryrightpositive * S ((S (sto_index_fubini_pointwiseentries)) * dst_positive_scale_fubini_pointwiseentriesentryright) + (dst_positive_fubini_pointwiseentriesentryright))) /\ (((((exists ff_h_pvs_fubini_pointwiseentriesentryrightnegative. ff_h_pvs_fubini_pointwiseentriesentryrightnegative + S (dst_negative_fubini_pointwiseentriesentryright) = S ((S (sto_index_fubini_pointwiseentries)) * dst_negative_scale_fubini_pointwiseentriesentryright)) /\ exists ff_q_pvs_fubini_pointwiseentriesentryrightnegative. dst_negative_code_fubini_pointwiseentriesentryright = ff_q_pvs_fubini_pointwiseentriesentryrightnegative * S ((S (sto_index_fubini_pointwiseentries)) * dst_negative_scale_fubini_pointwiseentriesentryright) + (dst_negative_fubini_pointwiseentriesentryright))) /\ (exists ge_balance_positive_fubini_pointwiseentriesentryrightvalue ge_balance_negative_fubini_pointwiseentriesentryrightvalue. (((((sto_right_fubini_pointwiseentries) = 2 * (ge_balance_positive_fubini_pointwiseentriesentryrightvalue) /\ (ge_balance_negative_fubini_pointwiseentriesentryrightvalue) = 0) \/ exists ge_signed_half_fubini_pointwiseentriesentryrightvaluedecode. (((sto_right_fubini_pointwiseentries) = 2 * ge_signed_half_fubini_pointwiseentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_fubini_pointwiseentriesentryrightvalue) = 0) /\ (ge_balance_negative_fubini_pointwiseentriesentryrightvalue) = S ge_signed_half_fubini_pointwiseentriesentryrightvaluedecode))) /\ ((dst_positive_fubini_pointwiseentriesentryright) + ge_balance_negative_fubini_pointwiseentriesentryrightvalue = (dst_negative_fubini_pointwiseentriesentryright) + ge_balance_positive_fubini_pointwiseentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_fubini_pointwiseentriesentryoutput dst_positive_scale_fubini_pointwiseentriesentryoutput dst_negative_code_fubini_pointwiseentriesentryoutput dst_negative_scale_fubini_pointwiseentriesentryoutput dst_positive_fubini_pointwiseentriesentryoutput dst_negative_fubini_pointwiseentriesentryoutput. (((x1) = (((((dst_positive_code_fubini_pointwiseentriesentryoutput) + (dst_positive_scale_fubini_pointwiseentriesentryoutput)) * S ((dst_positive_code_fubini_pointwiseentriesentryoutput) + (dst_positive_scale_fubini_pointwiseentriesentryoutput)) + ((dst_positive_scale_fubini_pointwiseentriesentryoutput) + (dst_positive_scale_fubini_pointwiseentriesentryoutput))) + (((dst_negative_code_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)) * S ((dst_negative_code_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)) + ((dst_negative_scale_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)))) * S ((((dst_positive_code_fubini_pointwiseentriesentryoutput) + (dst_positive_scale_fubini_pointwiseentriesentryoutput)) * S ((dst_positive_code_fubini_pointwiseentriesentryoutput) + (dst_positive_scale_fubini_pointwiseentriesentryoutput)) + ((dst_positive_scale_fubini_pointwiseentriesentryoutput) + (dst_positive_scale_fubini_pointwiseentriesentryoutput))) + (((dst_negative_code_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)) * S ((dst_negative_code_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)) + ((dst_negative_scale_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)))) + ((((dst_negative_code_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)) * S ((dst_negative_code_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)) + ((dst_negative_scale_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput))) + (((dst_negative_code_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)) * S ((dst_negative_code_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)) + ((dst_negative_scale_fubini_pointwiseentriesentryoutput) + (dst_negative_scale_fubini_pointwiseentriesentryoutput)))))) /\ (((((exists ff_h_pvs_fubini_pointwiseentriesentryoutputpositive. ff_h_pvs_fubini_pointwiseentriesentryoutputpositive + S (dst_positive_fubini_pointwiseentriesentryoutput) = S ((S (sto_index_fubini_pointwiseentries)) * dst_positive_scale_fubini_pointwiseentriesentryoutput)) /\ exists ff_q_pvs_fubini_pointwiseentriesentryoutputpositive. dst_positive_code_fubini_pointwiseentriesentryoutput = ff_q_pvs_fubini_pointwiseentriesentryoutputpositive * S ((S (sto_index_fubini_pointwiseentries)) * dst_positive_scale_fubini_pointwiseentriesentryoutput) + (dst_positive_fubini_pointwiseentriesentryoutput))) /\ (((((exists ff_h_pvs_fubini_pointwiseentriesentryoutputnegative. ff_h_pvs_fubini_pointwiseentriesentryoutputnegative + S (dst_negative_fubini_pointwiseentriesentryoutput) = S ((S (sto_index_fubini_pointwiseentries)) * dst_negative_scale_fubini_pointwiseentriesentryoutput)) /\ exists ff_q_pvs_fubini_pointwiseentriesentryoutputnegative. dst_negative_code_fubini_pointwiseentriesentryoutput = ff_q_pvs_fubini_pointwiseentriesentryoutputnegative * S ((S (sto_index_fubini_pointwiseentries)) * dst_negative_scale_fubini_pointwiseentriesentryoutput) + (dst_negative_fubini_pointwiseentriesentryoutput))) /\ (exists ge_balance_positive_fubini_pointwiseentriesentryoutputvalue ge_balance_negative_fubini_pointwiseentriesentryoutputvalue. (((((sto_output_fubini_pointwiseentries) = 2 * (ge_balance_positive_fubini_pointwiseentriesentryoutputvalue) /\ (ge_balance_negative_fubini_pointwiseentriesentryoutputvalue) = 0) \/ exists ge_signed_half_fubini_pointwiseentriesentryoutputvaluedecode. (((sto_output_fubini_pointwiseentries) = 2 * ge_signed_half_fubini_pointwiseentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_fubini_pointwiseentriesentryoutputvalue) = 0) /\ (ge_balance_negative_fubini_pointwiseentriesentryoutputvalue) = S ge_signed_half_fubini_pointwiseentriesentryoutputvaluedecode))) /\ ((dst_positive_fubini_pointwiseentriesentryoutput) + ge_balance_negative_fubini_pointwiseentriesentryoutputvalue = (dst_negative_fubini_pointwiseentriesentryoutput) + ge_balance_positive_fubini_pointwiseentriesentryoutputvalue))))))))) /\ (exists dsa_ap_fubini_pointwiseentriesentryoperation dsa_an_fubini_pointwiseentriesentryoperation dsa_bp_fubini_pointwiseentriesentryoperation dsa_bn_fubini_pointwiseentriesentryoperation dsa_cp_fubini_pointwiseentriesentryoperation dsa_cn_fubini_pointwiseentriesentryoperation. (((((sto_left_fubini_pointwiseentries) = 2 * (dsa_ap_fubini_pointwiseentriesentryoperation) /\ (dsa_an_fubini_pointwiseentriesentryoperation) = 0) \/ exists ge_signed_half_fubini_pointwiseentriesentryoperationleft. (((sto_left_fubini_pointwiseentries) = 2 * ge_signed_half_fubini_pointwiseentriesentryoperationleft + 1 /\ (dsa_ap_fubini_pointwiseentriesentryoperation) = 0) /\ (dsa_an_fubini_pointwiseentriesentryoperation) = S ge_signed_half_fubini_pointwiseentriesentryoperationleft))) /\ ((((((sto_right_fubini_pointwiseentries) = 2 * (dsa_bp_fubini_pointwiseentriesentryoperation) /\ (dsa_bn_fubini_pointwiseentriesentryoperation) = 0) \/ exists ge_signed_half_fubini_pointwiseentriesentryoperationright. (((sto_right_fubini_pointwiseentries) = 2 * ge_signed_half_fubini_pointwiseentriesentryoperationright + 1 /\ (dsa_bp_fubini_pointwiseentriesentryoperation) = 0) /\ (dsa_bn_fubini_pointwiseentriesentryoperation) = S ge_signed_half_fubini_pointwiseentriesentryoperationright))) /\ ((((((sto_output_fubini_pointwiseentries) = 2 * (dsa_cp_fubini_pointwiseentriesentryoperation) /\ (dsa_cn_fubini_pointwiseentriesentryoperation) = 0) \/ exists ge_signed_half_fubini_pointwiseentriesentryoperationoutput. (((sto_output_fubini_pointwiseentries) = 2 * ge_signed_half_fubini_pointwiseentriesentryoperationoutput + 1 /\ (dsa_cp_fubini_pointwiseentriesentryoperation) = 0) /\ (dsa_cn_fubini_pointwiseentriesentryoperation) = S ge_signed_half_fubini_pointwiseentriesentryoperationoutput))) /\ ((dsa_ap_fubini_pointwiseentriesentryoperation + dsa_bp_fubini_pointwiseentriesentryoperation) + dsa_cn_fubini_pointwiseentriesentryoperation = (dsa_an_fubini_pointwiseentriesentryoperation + dsa_bn_fubini_pointwiseentriesentryoperation) + dsa_cp_fubini_pointwiseentriesentryoperation)))))))))))))))))) - 0116
specialize signed_rectangular_columns_successor_add (F) - 0117
specialize signed_rectangular_columns_successor_add (x4) - 0118
specialize signed_rectangular_columns_successor_add (x6) - 0119
specialize signed_rectangular_columns_successor_add (x1) - 0120
specialize signed_rectangular_columns_successor_add (o) - 0121
specialize signed_rectangular_columns_successor_add (s) - 0122
specialize signed_rectangular_columns_successor_add (t) - 0123
specialize signed_rectangular_columns_successor_add (m) - 0124
specialize signed_rectangular_columns_successor_add (n) - 0125
apply signed_rectangular_columns_successor_add - 0126
exact hC_witness - 0127
exact hlast_witness_left - 0128
exact hb_witness_left - 0129
have hadd : exists dsa_ap_fubini_column_add dsa_an_fubini_column_add dsa_bp_fubini_column_add dsa_bn_fubini_column_add dsa_cp_fubini_column_add dsa_cn_fubini_column_add. (((((x5) = 2 * (dsa_ap_fubini_column_add) /\ (dsa_an_fubini_column_add) = 0) \/ exists ge_signed_half_fubini_column_addleft. (((x5) = 2 * ge_signed_half_fubini_column_addleft + 1 /\ (dsa_ap_fubini_column_add) = 0) /\ (dsa_an_fubini_column_add) = S ge_signed_half_fubini_column_addleft))) /\ ((((((x3) = 2 * (dsa_bp_fubini_column_add) /\ (dsa_bn_fubini_column_add) = 0) \/ exists ge_signed_half_fubini_column_addright. (((x3) = 2 * ge_signed_half_fubini_column_addright + 1 /\ (dsa_bp_fubini_column_add) = 0) /\ (dsa_bn_fubini_column_add) = S ge_signed_half_fubini_column_addright))) /\ ((((((b) = 2 * (dsa_cp_fubini_column_add) /\ (dsa_cn_fubini_column_add) = 0) \/ exists ge_signed_half_fubini_column_addoutput. (((b) = 2 * ge_signed_half_fubini_column_addoutput + 1 /\ (dsa_cp_fubini_column_add) = 0) /\ (dsa_cn_fubini_column_add) = S ge_signed_half_fubini_column_addoutput))) /\ ((dsa_ap_fubini_column_add + dsa_bp_fubini_column_add) + dsa_cn_fubini_column_add = (dsa_an_fubini_column_add + dsa_bn_fubini_column_add) + dsa_cp_fubini_column_add)))))) - 0130
specialize signed_prefix_sum_pointwise_add (n) - 0131
specialize signed_prefix_sum_pointwise_add (x4) - 0132
specialize signed_prefix_sum_pointwise_add (x6) - 0133
specialize signed_prefix_sum_pointwise_add (x1) - 0134
specialize signed_prefix_sum_pointwise_add (x5) - 0135
specialize signed_prefix_sum_pointwise_add (x3) - 0136
specialize signed_prefix_sum_pointwise_add (b) - 0137
apply signed_prefix_sum_pointwise_add - 0138
exact hpoint - 0139
exact hsumC_witness - 0140
exact hlast_witness_right - 0141
exact hb_witness_right - 0142
rewrite heq at hd_witness_witness_right_right - 0143
rewrite heq at hd_witness_witness_right_right - 0144
specialize signed_add_functional (x5) - 0145
specialize signed_add_functional (x3) - 0146
specialize signed_add_functional (a) - 0147
specialize signed_add_functional (b) - 0148
apply signed_add_functional - 0149
exact hd_witness_witness_right_right - 0150
exact hadd