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 F o s t m n. (exists dst_positive_code_fubini_exists_source dst_positive_scale_fubini_exists_source dst_negative_code_fubini_exists_source dst_negative_scale_fubini_exists_source. (((F) = (((((dst_positive_code_fubini_exists_source) + (dst_positive_scale_fubini_exists_source)) * S ((dst_positive_code_fubini_exists_source) + (dst_positive_scale_fubini_exists_source)) + ((dst_positive_scale_fubini_exists_source) + (dst_positive_scale_fubini_exists_source))) + (((dst_negative_code_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)) * S ((dst_negative_code_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)) + ((dst_negative_scale_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)))) * S ((((dst_positive_code_fubini_exists_source) + (dst_positive_scale_fubini_exists_source)) * S ((dst_positive_code_fubini_exists_source) + (dst_positive_scale_fubini_exists_source)) + ((dst_positive_scale_fubini_exists_source) + (dst_positive_scale_fubini_exists_source))) + (((dst_negative_code_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)) * S ((dst_negative_code_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)) + ((dst_negative_scale_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)))) + ((((dst_negative_code_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)) * S ((dst_negative_code_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)) + ((dst_negative_scale_fubini_exists_source) + (dst_negative_scale_fubini_exists_source))) + (((dst_negative_code_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)) * S ((dst_negative_code_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)) + ((dst_negative_scale_fubini_exists_source) + (dst_negative_scale_fubini_exists_source)))))) /\ (forall dst_index_fubini_exists_source. (exists pvs_le_gap_fubini_exists_sourcedomain. pvs_le_gap_fubini_exists_sourcedomain + (dst_index_fubini_exists_source) = (0)) -> exists dst_positive_fubini_exists_source dst_negative_fubini_exists_source dst_value_fubini_exists_source. ((((exists ff_h_pvs_fubini_exists_sourceentrypositive. ff_h_pvs_fubini_exists_sourceentrypositive + S (dst_positive_fubini_exists_source) = S ((S (dst_index_fubini_exists_source)) * dst_positive_scale_fubini_exists_source)) /\ exists ff_q_pvs_fubini_exists_sourceentrypositive. dst_positive_code_fubini_exists_source = ff_q_pvs_fubini_exists_sourceentrypositive * S ((S (dst_index_fubini_exists_source)) * dst_positive_scale_fubini_exists_source) + (dst_positive_fubini_exists_source))) /\ (((((exists ff_h_pvs_fubini_exists_sourceentrynegative. ff_h_pvs_fubini_exists_sourceentrynegative + S (dst_negative_fubini_exists_source) = S ((S (dst_index_fubini_exists_source)) * dst_negative_scale_fubini_exists_source)) /\ exists ff_q_pvs_fubini_exists_sourceentrynegative. dst_negative_code_fubini_exists_source = ff_q_pvs_fubini_exists_sourceentrynegative * S ((S (dst_index_fubini_exists_source)) * dst_negative_scale_fubini_exists_source) + (dst_negative_fubini_exists_source))) /\ (exists ge_balance_positive_fubini_exists_sourceentryvalue ge_balance_negative_fubini_exists_sourceentryvalue. (((((dst_value_fubini_exists_source) = 2 * (ge_balance_positive_fubini_exists_sourceentryvalue) /\ (ge_balance_negative_fubini_exists_sourceentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_sourceentryvaluedecode. (((dst_value_fubini_exists_source) = 2 * ge_signed_half_fubini_exists_sourceentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_sourceentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_sourceentryvalue) = S ge_signed_half_fubini_exists_sourceentryvaluedecode))) /\ ((dst_positive_fubini_exists_source) + ge_balance_negative_fubini_exists_sourceentryvalue = (dst_negative_fubini_exists_source) + ge_balance_positive_fubini_exists_sourceentryvalue))))))))) -> exists R C z. (((((exists dst_positive_code_fubini_exists_resultrowssource_table dst_positive_scale_fubini_exists_resultrowssource_table dst_negative_code_fubini_exists_resultrowssource_table dst_negative_scale_fubini_exists_resultrowssource_table. (((F) = (((((dst_positive_code_fubini_exists_resultrowssource_table) + (dst_positive_scale_fubini_exists_resultrowssource_table)) * S ((dst_positive_code_fubini_exists_resultrowssource_table) + (dst_positive_scale_fubini_exists_resultrowssource_table)) + ((dst_positive_scale_fubini_exists_resultrowssource_table) + (dst_positive_scale_fubini_exists_resultrowssource_table))) + (((dst_negative_code_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)) * S ((dst_negative_code_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)) + ((dst_negative_scale_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)))) * S ((((dst_positive_code_fubini_exists_resultrowssource_table) + (dst_positive_scale_fubini_exists_resultrowssource_table)) * S ((dst_positive_code_fubini_exists_resultrowssource_table) + (dst_positive_scale_fubini_exists_resultrowssource_table)) + ((dst_positive_scale_fubini_exists_resultrowssource_table) + (dst_positive_scale_fubini_exists_resultrowssource_table))) + (((dst_negative_code_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)) * S ((dst_negative_code_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)) + ((dst_negative_scale_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)))) + ((((dst_negative_code_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)) * S ((dst_negative_code_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)) + ((dst_negative_scale_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table))) + (((dst_negative_code_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)) * S ((dst_negative_code_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)) + ((dst_negative_scale_fubini_exists_resultrowssource_table) + (dst_negative_scale_fubini_exists_resultrowssource_table)))))) /\ (forall dst_index_fubini_exists_resultrowssource_table. (exists pvs_le_gap_fubini_exists_resultrowssource_tabledomain. pvs_le_gap_fubini_exists_resultrowssource_tabledomain + (dst_index_fubini_exists_resultrowssource_table) = (0)) -> exists dst_positive_fubini_exists_resultrowssource_table dst_negative_fubini_exists_resultrowssource_table dst_value_fubini_exists_resultrowssource_table. ((((exists ff_h_pvs_fubini_exists_resultrowssource_tableentrypositive. ff_h_pvs_fubini_exists_resultrowssource_tableentrypositive + S (dst_positive_fubini_exists_resultrowssource_table) = S ((S (dst_index_fubini_exists_resultrowssource_table)) * dst_positive_scale_fubini_exists_resultrowssource_table)) /\ exists ff_q_pvs_fubini_exists_resultrowssource_tableentrypositive. dst_positive_code_fubini_exists_resultrowssource_table = ff_q_pvs_fubini_exists_resultrowssource_tableentrypositive * S ((S (dst_index_fubini_exists_resultrowssource_table)) * dst_positive_scale_fubini_exists_resultrowssource_table) + (dst_positive_fubini_exists_resultrowssource_table))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowssource_tableentrynegative. ff_h_pvs_fubini_exists_resultrowssource_tableentrynegative + S (dst_negative_fubini_exists_resultrowssource_table) = S ((S (dst_index_fubini_exists_resultrowssource_table)) * dst_negative_scale_fubini_exists_resultrowssource_table)) /\ exists ff_q_pvs_fubini_exists_resultrowssource_tableentrynegative. dst_negative_code_fubini_exists_resultrowssource_table = ff_q_pvs_fubini_exists_resultrowssource_tableentrynegative * S ((S (dst_index_fubini_exists_resultrowssource_table)) * dst_negative_scale_fubini_exists_resultrowssource_table) + (dst_negative_fubini_exists_resultrowssource_table))) /\ (exists ge_balance_positive_fubini_exists_resultrowssource_tableentryvalue ge_balance_negative_fubini_exists_resultrowssource_tableentryvalue. (((((dst_value_fubini_exists_resultrowssource_table) = 2 * (ge_balance_positive_fubini_exists_resultrowssource_tableentryvalue) /\ (ge_balance_negative_fubini_exists_resultrowssource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultrowssource_tableentryvaluedecode. (((dst_value_fubini_exists_resultrowssource_table) = 2 * ge_signed_half_fubini_exists_resultrowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultrowssource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultrowssource_tableentryvalue) = S ge_signed_half_fubini_exists_resultrowssource_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultrowssource_table) + ge_balance_negative_fubini_exists_resultrowssource_tableentryvalue = (dst_negative_fubini_exists_resultrowssource_table) + ge_balance_positive_fubini_exists_resultrowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_exists_resultrowsrow_table dst_positive_scale_fubini_exists_resultrowsrow_table dst_negative_code_fubini_exists_resultrowsrow_table dst_negative_scale_fubini_exists_resultrowsrow_table. (((R) = (((((dst_positive_code_fubini_exists_resultrowsrow_table) + (dst_positive_scale_fubini_exists_resultrowsrow_table)) * S ((dst_positive_code_fubini_exists_resultrowsrow_table) + (dst_positive_scale_fubini_exists_resultrowsrow_table)) + ((dst_positive_scale_fubini_exists_resultrowsrow_table) + (dst_positive_scale_fubini_exists_resultrowsrow_table))) + (((dst_negative_code_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)) * S ((dst_negative_code_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)) + ((dst_negative_scale_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)))) * S ((((dst_positive_code_fubini_exists_resultrowsrow_table) + (dst_positive_scale_fubini_exists_resultrowsrow_table)) * S ((dst_positive_code_fubini_exists_resultrowsrow_table) + (dst_positive_scale_fubini_exists_resultrowsrow_table)) + ((dst_positive_scale_fubini_exists_resultrowsrow_table) + (dst_positive_scale_fubini_exists_resultrowsrow_table))) + (((dst_negative_code_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)) * S ((dst_negative_code_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)) + ((dst_negative_scale_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)))) + ((((dst_negative_code_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)) * S ((dst_negative_code_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)) + ((dst_negative_scale_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table))) + (((dst_negative_code_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)) * S ((dst_negative_code_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)) + ((dst_negative_scale_fubini_exists_resultrowsrow_table) + (dst_negative_scale_fubini_exists_resultrowsrow_table)))))) /\ (forall dst_index_fubini_exists_resultrowsrow_table. (exists pvs_le_gap_fubini_exists_resultrowsrow_tabledomain. pvs_le_gap_fubini_exists_resultrowsrow_tabledomain + (dst_index_fubini_exists_resultrowsrow_table) = (m)) -> exists dst_positive_fubini_exists_resultrowsrow_table dst_negative_fubini_exists_resultrowsrow_table dst_value_fubini_exists_resultrowsrow_table. ((((exists ff_h_pvs_fubini_exists_resultrowsrow_tableentrypositive. ff_h_pvs_fubini_exists_resultrowsrow_tableentrypositive + S (dst_positive_fubini_exists_resultrowsrow_table) = S ((S (dst_index_fubini_exists_resultrowsrow_table)) * dst_positive_scale_fubini_exists_resultrowsrow_table)) /\ exists ff_q_pvs_fubini_exists_resultrowsrow_tableentrypositive. dst_positive_code_fubini_exists_resultrowsrow_table = ff_q_pvs_fubini_exists_resultrowsrow_tableentrypositive * S ((S (dst_index_fubini_exists_resultrowsrow_table)) * dst_positive_scale_fubini_exists_resultrowsrow_table) + (dst_positive_fubini_exists_resultrowsrow_table))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowsrow_tableentrynegative. ff_h_pvs_fubini_exists_resultrowsrow_tableentrynegative + S (dst_negative_fubini_exists_resultrowsrow_table) = S ((S (dst_index_fubini_exists_resultrowsrow_table)) * dst_negative_scale_fubini_exists_resultrowsrow_table)) /\ exists ff_q_pvs_fubini_exists_resultrowsrow_tableentrynegative. dst_negative_code_fubini_exists_resultrowsrow_table = ff_q_pvs_fubini_exists_resultrowsrow_tableentrynegative * S ((S (dst_index_fubini_exists_resultrowsrow_table)) * dst_negative_scale_fubini_exists_resultrowsrow_table) + (dst_negative_fubini_exists_resultrowsrow_table))) /\ (exists ge_balance_positive_fubini_exists_resultrowsrow_tableentryvalue ge_balance_negative_fubini_exists_resultrowsrow_tableentryvalue. (((((dst_value_fubini_exists_resultrowsrow_table) = 2 * (ge_balance_positive_fubini_exists_resultrowsrow_tableentryvalue) /\ (ge_balance_negative_fubini_exists_resultrowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultrowsrow_tableentryvaluedecode. (((dst_value_fubini_exists_resultrowsrow_table) = 2 * ge_signed_half_fubini_exists_resultrowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultrowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultrowsrow_tableentryvalue) = S ge_signed_half_fubini_exists_resultrowsrow_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultrowsrow_table) + ge_balance_negative_fubini_exists_resultrowsrow_tableentryvalue = (dst_negative_fubini_exists_resultrowsrow_table) + ge_balance_positive_fubini_exists_resultrowsrow_tableentryvalue))))))))) /\ (forall srt_index_fubini_exists_resultrows. (exists pvs_gap_fubini_exists_resultrowsbound. pvs_gap_fubini_exists_resultrowsbound + S (srt_index_fubini_exists_resultrows) = (m)) -> exists srt_value_fubini_exists_resultrows. (((exists dst_positive_code_fubini_exists_resultrowsrowentry dst_positive_scale_fubini_exists_resultrowsrowentry dst_negative_code_fubini_exists_resultrowsrowentry dst_negative_scale_fubini_exists_resultrowsrowentry dst_positive_fubini_exists_resultrowsrowentry dst_negative_fubini_exists_resultrowsrowentry. (((R) = (((((dst_positive_code_fubini_exists_resultrowsrowentry) + (dst_positive_scale_fubini_exists_resultrowsrowentry)) * S ((dst_positive_code_fubini_exists_resultrowsrowentry) + (dst_positive_scale_fubini_exists_resultrowsrowentry)) + ((dst_positive_scale_fubini_exists_resultrowsrowentry) + (dst_positive_scale_fubini_exists_resultrowsrowentry))) + (((dst_negative_code_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)) * S ((dst_negative_code_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)) + ((dst_negative_scale_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)))) * S ((((dst_positive_code_fubini_exists_resultrowsrowentry) + (dst_positive_scale_fubini_exists_resultrowsrowentry)) * S ((dst_positive_code_fubini_exists_resultrowsrowentry) + (dst_positive_scale_fubini_exists_resultrowsrowentry)) + ((dst_positive_scale_fubini_exists_resultrowsrowentry) + (dst_positive_scale_fubini_exists_resultrowsrowentry))) + (((dst_negative_code_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)) * S ((dst_negative_code_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)) + ((dst_negative_scale_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)))) + ((((dst_negative_code_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)) * S ((dst_negative_code_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)) + ((dst_negative_scale_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry))) + (((dst_negative_code_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)) * S ((dst_negative_code_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)) + ((dst_negative_scale_fubini_exists_resultrowsrowentry) + (dst_negative_scale_fubini_exists_resultrowsrowentry)))))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowsrowentrypositive. ff_h_pvs_fubini_exists_resultrowsrowentrypositive + S (dst_positive_fubini_exists_resultrowsrowentry) = S ((S (srt_index_fubini_exists_resultrows)) * dst_positive_scale_fubini_exists_resultrowsrowentry)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowentrypositive. dst_positive_code_fubini_exists_resultrowsrowentry = ff_q_pvs_fubini_exists_resultrowsrowentrypositive * S ((S (srt_index_fubini_exists_resultrows)) * dst_positive_scale_fubini_exists_resultrowsrowentry) + (dst_positive_fubini_exists_resultrowsrowentry))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowsrowentrynegative. ff_h_pvs_fubini_exists_resultrowsrowentrynegative + S (dst_negative_fubini_exists_resultrowsrowentry) = S ((S (srt_index_fubini_exists_resultrows)) * dst_negative_scale_fubini_exists_resultrowsrowentry)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowentrynegative. dst_negative_code_fubini_exists_resultrowsrowentry = ff_q_pvs_fubini_exists_resultrowsrowentrynegative * S ((S (srt_index_fubini_exists_resultrows)) * dst_negative_scale_fubini_exists_resultrowsrowentry) + (dst_negative_fubini_exists_resultrowsrowentry))) /\ (exists ge_balance_positive_fubini_exists_resultrowsrowentryvalue ge_balance_negative_fubini_exists_resultrowsrowentryvalue. (((((srt_value_fubini_exists_resultrows) = 2 * (ge_balance_positive_fubini_exists_resultrowsrowentryvalue) /\ (ge_balance_negative_fubini_exists_resultrowsrowentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultrowsrowentryvaluedecode. (((srt_value_fubini_exists_resultrows) = 2 * ge_signed_half_fubini_exists_resultrowsrowentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultrowsrowentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultrowsrowentryvalue) = S ge_signed_half_fubini_exists_resultrowsrowentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultrowsrowentry) + ge_balance_negative_fubini_exists_resultrowsrowentryvalue = (dst_negative_fubini_exists_resultrowsrowentry) + ge_balance_positive_fubini_exists_resultrowsrowentryvalue))))))))) /\ (exists srs_slice_fubini_exists_resultrowsrowrow_sum. ((((exists dst_positive_code_fubini_exists_resultrowsrowrow_sumslicesource_table dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_fubini_exists_resultrowsrowrow_sumslicesource_table. (exists pvs_le_gap_fubini_exists_resultrowsrowrow_sumslicesource_tabledomain. pvs_le_gap_fubini_exists_resultrowsrowrow_sumslicesource_tabledomain + (dst_index_fubini_exists_resultrowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_fubini_exists_resultrowsrowrow_sumslicesource_table dst_negative_fubini_exists_resultrowsrowrow_sumslicesource_table dst_value_fubini_exists_resultrowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_fubini_exists_resultrowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_fubini_exists_resultrowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_fubini_exists_resultrowsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_exists_resultrowsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_fubini_exists_resultrowsrowrow_sumslicesource_table = ff_q_pvs_fubini_exists_resultrowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_fubini_exists_resultrowsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_positive_fubini_exists_resultrowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_fubini_exists_resultrowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_fubini_exists_resultrowsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_exists_resultrowsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_fubini_exists_resultrowsrowrow_sumslicesource_table = ff_q_pvs_fubini_exists_resultrowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_fubini_exists_resultrowsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumslicesource_table) + (dst_negative_fubini_exists_resultrowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_fubini_exists_resultrowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_fubini_exists_resultrowsrowrow_sumslicesource_table) = 2 * ge_signed_half_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultrowsrowrow_sumslicesource_table) + ge_balance_negative_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvalue = (dst_negative_fubini_exists_resultrowsrowrow_sumslicesource_table) + ge_balance_positive_fubini_exists_resultrowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table. (((srs_slice_fubini_exists_resultrowsrowrow_sum) = (((((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_fubini_exists_resultrowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_fubini_exists_resultrowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_fubini_exists_resultrowsrowrow_sumsliceoutput_tabledomain + (dst_index_fubini_exists_resultrowsrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_fubini_exists_resultrowsrowrow_sumsliceoutput_table dst_negative_fubini_exists_resultrowsrowrow_sumsliceoutput_table dst_value_fubini_exists_resultrowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_fubini_exists_resultrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_fubini_exists_resultrowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_fubini_exists_resultrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_fubini_exists_resultrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_fubini_exists_resultrowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_fubini_exists_resultrowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_fubini_exists_resultrowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_fubini_exists_resultrowsrowrow_sumsliceoutput_table) + ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_fubini_exists_resultrowsrowrow_sumslice. (exists pvs_gap_fubini_exists_resultrowsrowrow_sumslicebound. pvs_gap_fubini_exists_resultrowsrowrow_sumslicebound + S (srs_index_fubini_exists_resultrowsrowrow_sumslice) = (n)) -> exists srs_value_fubini_exists_resultrowsrowrow_sumslice. (((exists dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentrysource dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource dst_positive_fubini_exists_resultrowsrowrow_sumsliceentrysource dst_negative_fubini_exists_resultrowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceentrysourcepositive + S (dst_positive_fubini_exists_resultrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_fubini_exists_resultrows)))) + ((t) * (srs_index_fubini_exists_resultrowsrowrow_sumslice))))) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceentrysourcepositive. dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentrysource = ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_fubini_exists_resultrows)))) + ((t) * (srs_index_fubini_exists_resultrowsrowrow_sumslice))))) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_positive_fubini_exists_resultrowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceentrysourcenegative + S (dst_negative_fubini_exists_resultrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_fubini_exists_resultrows)))) + ((t) * (srs_index_fubini_exists_resultrowsrowrow_sumslice))))) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceentrysourcenegative. dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentrysource = ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_fubini_exists_resultrows)))) + ((t) * (srs_index_fubini_exists_resultrowsrowrow_sumslice))))) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentrysource) + (dst_negative_fubini_exists_resultrowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceentrysourcevalue ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceentrysourcevalue. (((((srs_value_fubini_exists_resultrowsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_fubini_exists_resultrowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_fubini_exists_resultrowsrowrow_sumslice) = 2 * ge_signed_half_fubini_exists_resultrowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_fubini_exists_resultrowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_fubini_exists_resultrowsrowrow_sumsliceentrysource) + ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceentrysourcevalue = (dst_negative_fubini_exists_resultrowsrowrow_sumsliceentrysource) + ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput dst_positive_fubini_exists_resultrowsrowrow_sumsliceentryoutput dst_negative_fubini_exists_resultrowsrowrow_sumsliceentryoutput. (((srs_slice_fubini_exists_resultrowsrowrow_sum) = (((((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceentryoutputpositive + S (dst_positive_fubini_exists_resultrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_exists_resultrowsrowrow_sumslice)) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceentryoutputpositive. dst_positive_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_fubini_exists_resultrowsrowrow_sumslice)) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_fubini_exists_resultrowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_fubini_exists_resultrowsrowrow_sumsliceentryoutputnegative + S (dst_negative_fubini_exists_resultrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_exists_resultrowsrowrow_sumslice)) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceentryoutputnegative. dst_negative_code_fubini_exists_resultrowsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_exists_resultrowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_fubini_exists_resultrowsrowrow_sumslice)) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_fubini_exists_resultrowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceentryoutputvalue ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceentryoutputvalue. (((((srs_value_fubini_exists_resultrowsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultrowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_fubini_exists_resultrowsrowrow_sumslice) = 2 * ge_signed_half_fubini_exists_resultrowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_fubini_exists_resultrowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + ge_balance_negative_fubini_exists_resultrowsrowrow_sumsliceentryoutputvalue = (dst_negative_fubini_exists_resultrowsrowrow_sumsliceentryoutput) + ge_balance_positive_fubini_exists_resultrowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_fubini_exists_resultrowsrowrow_sumsum dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum dst_negative_code_fubini_exists_resultrowsrowrow_sumsum dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum dst_positive_sum_fubini_exists_resultrowsrowrow_sumsum dst_negative_sum_fubini_exists_resultrowsrowrow_sumsum. (((srs_slice_fubini_exists_resultrowsrowrow_sum) = (((((dst_positive_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)))) * S ((((dst_positive_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum)) * S ((dst_positive_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum)) + ((dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)))) + ((((dst_negative_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_fubini_exists_resultrowsrowrow_sumsumpositive fs_v_dst_fubini_exists_resultrowsrowrow_sumsumpositive. ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_start. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_start. fs_u_dst_fubini_exists_resultrowsrowrow_sumsumpositive = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_terminal. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_fubini_exists_resultrowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_terminal. fs_u_dst_fubini_exists_resultrowsrowrow_sumsumpositive = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumpositive) + (dst_positive_sum_fubini_exists_resultrowsrowrow_sumsum))) /\ forall fs_i_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps fs_r_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps fs_s_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_fubini_exists_resultrowsrowrow_sumsum = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_exists_resultrowsrowrow_sumsum) + (fs_a_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_fubini_exists_resultrowsrowrow_sumsumpositive = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumpositive) + (fs_r_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_fubini_exists_resultrowsrowrow_sumsumpositive = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumpositive) + (fs_s_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps = fs_r_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps + fs_a_dst_fubini_exists_resultrowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_exists_resultrowsrowrow_sumsumnegative fs_v_dst_fubini_exists_resultrowsrowrow_sumsumnegative. ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_start. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_start. fs_u_dst_fubini_exists_resultrowsrowrow_sumsumnegative = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_terminal. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_fubini_exists_resultrowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_terminal. fs_u_dst_fubini_exists_resultrowsrowrow_sumsumnegative = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumnegative) + (dst_negative_sum_fubini_exists_resultrowsrowrow_sumsum))) /\ forall fs_i_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps fs_r_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps fs_s_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_fubini_exists_resultrowsrowrow_sumsum = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_exists_resultrowsrowrow_sumsum) + (fs_a_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_fubini_exists_resultrowsrowrow_sumsumnegative = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumnegative) + (fs_r_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_fubini_exists_resultrowsrowrow_sumsumnegative = fs_q_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_resultrowsrowrow_sumsumnegative) + (fs_s_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps = fs_r_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps + fs_a_dst_fubini_exists_resultrowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_exists_resultrowsrowrow_sumsumresult ge_balance_negative_fubini_exists_resultrowsrowrow_sumsumresult. (((((srt_value_fubini_exists_resultrows) = 2 * (ge_balance_positive_fubini_exists_resultrowsrowrow_sumsumresult) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_fubini_exists_resultrowsrowrow_sumsumresultdecode. (((srt_value_fubini_exists_resultrows) = 2 * ge_signed_half_fubini_exists_resultrowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_fubini_exists_resultrowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_fubini_exists_resultrowsrowrow_sumsumresult) = S ge_signed_half_fubini_exists_resultrowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_fubini_exists_resultrowsrowrow_sumsum) + ge_balance_negative_fubini_exists_resultrowsrowrow_sumsumresult = (dst_negative_sum_fubini_exists_resultrowsrowrow_sumsum) + ge_balance_positive_fubini_exists_resultrowsrowrow_sumsumresult)))))))))))))))))) /\ (((((exists dst_positive_code_fubini_exists_resultcolumnssource_table dst_positive_scale_fubini_exists_resultcolumnssource_table dst_negative_code_fubini_exists_resultcolumnssource_table dst_negative_scale_fubini_exists_resultcolumnssource_table. (((F) = (((((dst_positive_code_fubini_exists_resultcolumnssource_table) + (dst_positive_scale_fubini_exists_resultcolumnssource_table)) * S ((dst_positive_code_fubini_exists_resultcolumnssource_table) + (dst_positive_scale_fubini_exists_resultcolumnssource_table)) + ((dst_positive_scale_fubini_exists_resultcolumnssource_table) + (dst_positive_scale_fubini_exists_resultcolumnssource_table))) + (((dst_negative_code_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)) * S ((dst_negative_code_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)) + ((dst_negative_scale_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)))) * S ((((dst_positive_code_fubini_exists_resultcolumnssource_table) + (dst_positive_scale_fubini_exists_resultcolumnssource_table)) * S ((dst_positive_code_fubini_exists_resultcolumnssource_table) + (dst_positive_scale_fubini_exists_resultcolumnssource_table)) + ((dst_positive_scale_fubini_exists_resultcolumnssource_table) + (dst_positive_scale_fubini_exists_resultcolumnssource_table))) + (((dst_negative_code_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)) * S ((dst_negative_code_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)) + ((dst_negative_scale_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)))) + ((((dst_negative_code_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)) * S ((dst_negative_code_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)) + ((dst_negative_scale_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table))) + (((dst_negative_code_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)) * S ((dst_negative_code_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)) + ((dst_negative_scale_fubini_exists_resultcolumnssource_table) + (dst_negative_scale_fubini_exists_resultcolumnssource_table)))))) /\ (forall dst_index_fubini_exists_resultcolumnssource_table. (exists pvs_le_gap_fubini_exists_resultcolumnssource_tabledomain. pvs_le_gap_fubini_exists_resultcolumnssource_tabledomain + (dst_index_fubini_exists_resultcolumnssource_table) = (0)) -> exists dst_positive_fubini_exists_resultcolumnssource_table dst_negative_fubini_exists_resultcolumnssource_table dst_value_fubini_exists_resultcolumnssource_table. ((((exists ff_h_pvs_fubini_exists_resultcolumnssource_tableentrypositive. ff_h_pvs_fubini_exists_resultcolumnssource_tableentrypositive + S (dst_positive_fubini_exists_resultcolumnssource_table) = S ((S (dst_index_fubini_exists_resultcolumnssource_table)) * dst_positive_scale_fubini_exists_resultcolumnssource_table)) /\ exists ff_q_pvs_fubini_exists_resultcolumnssource_tableentrypositive. dst_positive_code_fubini_exists_resultcolumnssource_table = ff_q_pvs_fubini_exists_resultcolumnssource_tableentrypositive * S ((S (dst_index_fubini_exists_resultcolumnssource_table)) * dst_positive_scale_fubini_exists_resultcolumnssource_table) + (dst_positive_fubini_exists_resultcolumnssource_table))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnssource_tableentrynegative. ff_h_pvs_fubini_exists_resultcolumnssource_tableentrynegative + S (dst_negative_fubini_exists_resultcolumnssource_table) = S ((S (dst_index_fubini_exists_resultcolumnssource_table)) * dst_negative_scale_fubini_exists_resultcolumnssource_table)) /\ exists ff_q_pvs_fubini_exists_resultcolumnssource_tableentrynegative. dst_negative_code_fubini_exists_resultcolumnssource_table = ff_q_pvs_fubini_exists_resultcolumnssource_tableentrynegative * S ((S (dst_index_fubini_exists_resultcolumnssource_table)) * dst_negative_scale_fubini_exists_resultcolumnssource_table) + (dst_negative_fubini_exists_resultcolumnssource_table))) /\ (exists ge_balance_positive_fubini_exists_resultcolumnssource_tableentryvalue ge_balance_negative_fubini_exists_resultcolumnssource_tableentryvalue. (((((dst_value_fubini_exists_resultcolumnssource_table) = 2 * (ge_balance_positive_fubini_exists_resultcolumnssource_tableentryvalue) /\ (ge_balance_negative_fubini_exists_resultcolumnssource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultcolumnssource_tableentryvaluedecode. (((dst_value_fubini_exists_resultcolumnssource_table) = 2 * ge_signed_half_fubini_exists_resultcolumnssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultcolumnssource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultcolumnssource_tableentryvalue) = S ge_signed_half_fubini_exists_resultcolumnssource_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultcolumnssource_table) + ge_balance_negative_fubini_exists_resultcolumnssource_tableentryvalue = (dst_negative_fubini_exists_resultcolumnssource_table) + ge_balance_positive_fubini_exists_resultcolumnssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_exists_resultcolumnsrow_table dst_positive_scale_fubini_exists_resultcolumnsrow_table dst_negative_code_fubini_exists_resultcolumnsrow_table dst_negative_scale_fubini_exists_resultcolumnsrow_table. (((C) = (((((dst_positive_code_fubini_exists_resultcolumnsrow_table) + (dst_positive_scale_fubini_exists_resultcolumnsrow_table)) * S ((dst_positive_code_fubini_exists_resultcolumnsrow_table) + (dst_positive_scale_fubini_exists_resultcolumnsrow_table)) + ((dst_positive_scale_fubini_exists_resultcolumnsrow_table) + (dst_positive_scale_fubini_exists_resultcolumnsrow_table))) + (((dst_negative_code_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)))) * S ((((dst_positive_code_fubini_exists_resultcolumnsrow_table) + (dst_positive_scale_fubini_exists_resultcolumnsrow_table)) * S ((dst_positive_code_fubini_exists_resultcolumnsrow_table) + (dst_positive_scale_fubini_exists_resultcolumnsrow_table)) + ((dst_positive_scale_fubini_exists_resultcolumnsrow_table) + (dst_positive_scale_fubini_exists_resultcolumnsrow_table))) + (((dst_negative_code_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)))) + ((((dst_negative_code_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table))) + (((dst_negative_code_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrow_table) + (dst_negative_scale_fubini_exists_resultcolumnsrow_table)))))) /\ (forall dst_index_fubini_exists_resultcolumnsrow_table. (exists pvs_le_gap_fubini_exists_resultcolumnsrow_tabledomain. pvs_le_gap_fubini_exists_resultcolumnsrow_tabledomain + (dst_index_fubini_exists_resultcolumnsrow_table) = (n)) -> exists dst_positive_fubini_exists_resultcolumnsrow_table dst_negative_fubini_exists_resultcolumnsrow_table dst_value_fubini_exists_resultcolumnsrow_table. ((((exists ff_h_pvs_fubini_exists_resultcolumnsrow_tableentrypositive. ff_h_pvs_fubini_exists_resultcolumnsrow_tableentrypositive + S (dst_positive_fubini_exists_resultcolumnsrow_table) = S ((S (dst_index_fubini_exists_resultcolumnsrow_table)) * dst_positive_scale_fubini_exists_resultcolumnsrow_table)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrow_tableentrypositive. dst_positive_code_fubini_exists_resultcolumnsrow_table = ff_q_pvs_fubini_exists_resultcolumnsrow_tableentrypositive * S ((S (dst_index_fubini_exists_resultcolumnsrow_table)) * dst_positive_scale_fubini_exists_resultcolumnsrow_table) + (dst_positive_fubini_exists_resultcolumnsrow_table))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnsrow_tableentrynegative. ff_h_pvs_fubini_exists_resultcolumnsrow_tableentrynegative + S (dst_negative_fubini_exists_resultcolumnsrow_table) = S ((S (dst_index_fubini_exists_resultcolumnsrow_table)) * dst_negative_scale_fubini_exists_resultcolumnsrow_table)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrow_tableentrynegative. dst_negative_code_fubini_exists_resultcolumnsrow_table = ff_q_pvs_fubini_exists_resultcolumnsrow_tableentrynegative * S ((S (dst_index_fubini_exists_resultcolumnsrow_table)) * dst_negative_scale_fubini_exists_resultcolumnsrow_table) + (dst_negative_fubini_exists_resultcolumnsrow_table))) /\ (exists ge_balance_positive_fubini_exists_resultcolumnsrow_tableentryvalue ge_balance_negative_fubini_exists_resultcolumnsrow_tableentryvalue. (((((dst_value_fubini_exists_resultcolumnsrow_table) = 2 * (ge_balance_positive_fubini_exists_resultcolumnsrow_tableentryvalue) /\ (ge_balance_negative_fubini_exists_resultcolumnsrow_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultcolumnsrow_tableentryvaluedecode. (((dst_value_fubini_exists_resultcolumnsrow_table) = 2 * ge_signed_half_fubini_exists_resultcolumnsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultcolumnsrow_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultcolumnsrow_tableentryvalue) = S ge_signed_half_fubini_exists_resultcolumnsrow_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultcolumnsrow_table) + ge_balance_negative_fubini_exists_resultcolumnsrow_tableentryvalue = (dst_negative_fubini_exists_resultcolumnsrow_table) + ge_balance_positive_fubini_exists_resultcolumnsrow_tableentryvalue))))))))) /\ (forall srt_index_fubini_exists_resultcolumns. (exists pvs_gap_fubini_exists_resultcolumnsbound. pvs_gap_fubini_exists_resultcolumnsbound + S (srt_index_fubini_exists_resultcolumns) = (n)) -> exists srt_value_fubini_exists_resultcolumns. (((exists dst_positive_code_fubini_exists_resultcolumnsrowentry dst_positive_scale_fubini_exists_resultcolumnsrowentry dst_negative_code_fubini_exists_resultcolumnsrowentry dst_negative_scale_fubini_exists_resultcolumnsrowentry dst_positive_fubini_exists_resultcolumnsrowentry dst_negative_fubini_exists_resultcolumnsrowentry. (((C) = (((((dst_positive_code_fubini_exists_resultcolumnsrowentry) + (dst_positive_scale_fubini_exists_resultcolumnsrowentry)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowentry) + (dst_positive_scale_fubini_exists_resultcolumnsrowentry)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowentry) + (dst_positive_scale_fubini_exists_resultcolumnsrowentry))) + (((dst_negative_code_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)))) * S ((((dst_positive_code_fubini_exists_resultcolumnsrowentry) + (dst_positive_scale_fubini_exists_resultcolumnsrowentry)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowentry) + (dst_positive_scale_fubini_exists_resultcolumnsrowentry)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowentry) + (dst_positive_scale_fubini_exists_resultcolumnsrowentry))) + (((dst_negative_code_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)))) + ((((dst_negative_code_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry))) + (((dst_negative_code_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowentry) + (dst_negative_scale_fubini_exists_resultcolumnsrowentry)))))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnsrowentrypositive. ff_h_pvs_fubini_exists_resultcolumnsrowentrypositive + S (dst_positive_fubini_exists_resultcolumnsrowentry) = S ((S (srt_index_fubini_exists_resultcolumns)) * dst_positive_scale_fubini_exists_resultcolumnsrowentry)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowentrypositive. dst_positive_code_fubini_exists_resultcolumnsrowentry = ff_q_pvs_fubini_exists_resultcolumnsrowentrypositive * S ((S (srt_index_fubini_exists_resultcolumns)) * dst_positive_scale_fubini_exists_resultcolumnsrowentry) + (dst_positive_fubini_exists_resultcolumnsrowentry))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnsrowentrynegative. ff_h_pvs_fubini_exists_resultcolumnsrowentrynegative + S (dst_negative_fubini_exists_resultcolumnsrowentry) = S ((S (srt_index_fubini_exists_resultcolumns)) * dst_negative_scale_fubini_exists_resultcolumnsrowentry)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowentrynegative. dst_negative_code_fubini_exists_resultcolumnsrowentry = ff_q_pvs_fubini_exists_resultcolumnsrowentrynegative * S ((S (srt_index_fubini_exists_resultcolumns)) * dst_negative_scale_fubini_exists_resultcolumnsrowentry) + (dst_negative_fubini_exists_resultcolumnsrowentry))) /\ (exists ge_balance_positive_fubini_exists_resultcolumnsrowentryvalue ge_balance_negative_fubini_exists_resultcolumnsrowentryvalue. (((((srt_value_fubini_exists_resultcolumns) = 2 * (ge_balance_positive_fubini_exists_resultcolumnsrowentryvalue) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultcolumnsrowentryvaluedecode. (((srt_value_fubini_exists_resultcolumns) = 2 * ge_signed_half_fubini_exists_resultcolumnsrowentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultcolumnsrowentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowentryvalue) = S ge_signed_half_fubini_exists_resultcolumnsrowentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultcolumnsrowentry) + ge_balance_negative_fubini_exists_resultcolumnsrowentryvalue = (dst_negative_fubini_exists_resultcolumnsrowentry) + ge_balance_positive_fubini_exists_resultcolumnsrowentryvalue))))))))) /\ (exists srs_slice_fubini_exists_resultcolumnsrowrow_sum. ((((exists dst_positive_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)))) + ((((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)))))) /\ (forall dst_index_fubini_exists_resultcolumnsrowrow_sumslicesource_table. (exists pvs_le_gap_fubini_exists_resultcolumnsrowrow_sumslicesource_tabledomain. pvs_le_gap_fubini_exists_resultcolumnsrowrow_sumslicesource_tabledomain + (dst_index_fubini_exists_resultcolumnsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_fubini_exists_resultcolumnsrowrow_sumslicesource_table dst_negative_fubini_exists_resultcolumnsrowrow_sumslicesource_table dst_value_fubini_exists_resultcolumnsrowrow_sumslicesource_table. ((((exists ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentrypositive + S (dst_positive_fubini_exists_resultcolumnsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentrypositive. dst_positive_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table = ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_fubini_exists_resultcolumnsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentrynegative + S (dst_negative_fubini_exists_resultcolumnsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentrynegative. dst_negative_code_fubini_exists_resultcolumnsrowrow_sumslicesource_table = ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_fubini_exists_resultcolumnsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_fubini_exists_resultcolumnsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvalue ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvalue. (((((dst_value_fubini_exists_resultcolumnsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_fubini_exists_resultcolumnsrowrow_sumslicesource_table) = 2 * ge_signed_half_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvalue = (dst_negative_fubini_exists_resultcolumnsrowrow_sumslicesource_table) + ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table. (((srs_slice_fubini_exists_resultcolumnsrowrow_sum) = (((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table. (exists pvs_le_gap_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tabledomain + (dst_index_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) = (m)) -> exists dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table dst_value_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceoutput_table) + ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_fubini_exists_resultcolumnsrowrow_sumslice. (exists pvs_gap_fubini_exists_resultcolumnsrowrow_sumslicebound. pvs_gap_fubini_exists_resultcolumnsrowrow_sumslicebound + S (srs_index_fubini_exists_resultcolumnsrowrow_sumslice) = (m)) -> exists srs_value_fubini_exists_resultcolumnsrowrow_sumslice. (((exists dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceentrysource dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcepositive. ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcepositive + S (dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) = S ((S (((((o) + ((t) * (srt_index_fubini_exists_resultcolumns)))) + ((s) * (srs_index_fubini_exists_resultcolumnsrowrow_sumslice))))) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcepositive. dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource = ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((t) * (srt_index_fubini_exists_resultcolumns)))) + ((s) * (srs_index_fubini_exists_resultcolumnsrowrow_sumslice))))) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcenegative. ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcenegative + S (dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) = S ((S (((((o) + ((t) * (srt_index_fubini_exists_resultcolumns)))) + ((s) * (srs_index_fubini_exists_resultcolumnsrowrow_sumslice))))) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcenegative. dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentrysource = ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((t) * (srt_index_fubini_exists_resultcolumns)))) + ((s) * (srs_index_fubini_exists_resultcolumnsrowrow_sumslice))))) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevalue ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevalue. (((((srs_value_fubini_exists_resultcolumnsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_fubini_exists_resultcolumnsrowrow_sumslice) = 2 * ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevalue = (dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceentrysource) + ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput. (((srs_slice_fubini_exists_resultcolumnsrowrow_sum) = (((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputpositive. ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputpositive + S (dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_exists_resultcolumnsrowrow_sumslice)) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputpositive. dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_fubini_exists_resultcolumnsrowrow_sumslice)) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputnegative. ff_h_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputnegative + S (dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_exists_resultcolumnsrowrow_sumslice)) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputnegative. dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_fubini_exists_resultcolumnsrowrow_sumslice)) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvalue ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvalue. (((((srs_value_fubini_exists_resultcolumnsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_fubini_exists_resultcolumnsrowrow_sumslice) = 2 * ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvalue = (dst_negative_fubini_exists_resultcolumnsrowrow_sumsliceentryoutput) + ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsum dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum dst_positive_sum_fubini_exists_resultcolumnsrowrow_sumsum dst_negative_sum_fubini_exists_resultcolumnsrowrow_sumsum. (((srs_slice_fubini_exists_resultcolumnsrowrow_sum) = (((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)))) * S ((((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum)) * S ((dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum)) + ((dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)))) + ((((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)))))) /\ (((exists fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive. ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_start. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_start. fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_terminal. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_fubini_exists_resultcolumnsrowrow_sumsum) = S ((S (m)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_terminal. fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_terminal * S ((S (m)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive) + (dst_positive_sum_fubini_exists_resultcolumnsrowrow_sumsum))) /\ forall fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps = m) -> exists fs_a_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps fs_r_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps fs_s_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_fubini_exists_resultcolumnsrowrow_sumsum = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_exists_resultcolumnsrowrow_sumsum) + (fs_a_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive) + (fs_r_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive) + (fs_s_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps = fs_r_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps + fs_a_dst_fubini_exists_resultcolumnsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative. ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_start. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_start. fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_terminal. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_fubini_exists_resultcolumnsrowrow_sumsum) = S ((S (m)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_terminal. fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_terminal * S ((S (m)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative) + (dst_negative_sum_fubini_exists_resultcolumnsrowrow_sumsum))) /\ forall fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps = m) -> exists fs_a_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps fs_r_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps fs_s_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_fubini_exists_resultcolumnsrowrow_sumsum = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_exists_resultcolumnsrowrow_sumsum) + (fs_a_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative) + (fs_r_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative = fs_q_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative) + (fs_s_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps = fs_r_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps + fs_a_dst_fubini_exists_resultcolumnsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsumresult ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsumresult. (((((srt_value_fubini_exists_resultcolumns) = 2 * (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsumresult) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsumresultdecode. (((srt_value_fubini_exists_resultcolumns) = 2 * ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsumresult) = S ge_signed_half_fubini_exists_resultcolumnsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_fubini_exists_resultcolumnsrowrow_sumsum) + ge_balance_negative_fubini_exists_resultcolumnsrowrow_sumsumresult = (dst_negative_sum_fubini_exists_resultcolumnsrowrow_sumsum) + ge_balance_positive_fubini_exists_resultcolumnsrowrow_sumsumresult)))))))))))))))))) /\ (((exists dst_positive_code_fubini_exists_resultrow_total dst_positive_scale_fubini_exists_resultrow_total dst_negative_code_fubini_exists_resultrow_total dst_negative_scale_fubini_exists_resultrow_total dst_positive_sum_fubini_exists_resultrow_total dst_negative_sum_fubini_exists_resultrow_total. (((R) = (((((dst_positive_code_fubini_exists_resultrow_total) + (dst_positive_scale_fubini_exists_resultrow_total)) * S ((dst_positive_code_fubini_exists_resultrow_total) + (dst_positive_scale_fubini_exists_resultrow_total)) + ((dst_positive_scale_fubini_exists_resultrow_total) + (dst_positive_scale_fubini_exists_resultrow_total))) + (((dst_negative_code_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)) * S ((dst_negative_code_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)) + ((dst_negative_scale_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)))) * S ((((dst_positive_code_fubini_exists_resultrow_total) + (dst_positive_scale_fubini_exists_resultrow_total)) * S ((dst_positive_code_fubini_exists_resultrow_total) + (dst_positive_scale_fubini_exists_resultrow_total)) + ((dst_positive_scale_fubini_exists_resultrow_total) + (dst_positive_scale_fubini_exists_resultrow_total))) + (((dst_negative_code_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)) * S ((dst_negative_code_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)) + ((dst_negative_scale_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)))) + ((((dst_negative_code_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)) * S ((dst_negative_code_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)) + ((dst_negative_scale_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total))) + (((dst_negative_code_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)) * S ((dst_negative_code_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)) + ((dst_negative_scale_fubini_exists_resultrow_total) + (dst_negative_scale_fubini_exists_resultrow_total)))))) /\ (((exists fs_u_dst_fubini_exists_resultrow_totalpositive fs_v_dst_fubini_exists_resultrow_totalpositive. ((((exists fs_h_dst_fubini_exists_resultrow_totalpositive_body_start. fs_h_dst_fubini_exists_resultrow_totalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_resultrow_totalpositive)) /\ exists fs_q_dst_fubini_exists_resultrow_totalpositive_body_start. fs_u_dst_fubini_exists_resultrow_totalpositive = fs_q_dst_fubini_exists_resultrow_totalpositive_body_start * S ((S (0)) * fs_v_dst_fubini_exists_resultrow_totalpositive) + (0))) /\ ((((exists fs_h_dst_fubini_exists_resultrow_totalpositive_body_terminal. fs_h_dst_fubini_exists_resultrow_totalpositive_body_terminal + S (dst_positive_sum_fubini_exists_resultrow_total) = S ((S (m)) * fs_v_dst_fubini_exists_resultrow_totalpositive)) /\ exists fs_q_dst_fubini_exists_resultrow_totalpositive_body_terminal. fs_u_dst_fubini_exists_resultrow_totalpositive = fs_q_dst_fubini_exists_resultrow_totalpositive_body_terminal * S ((S (m)) * fs_v_dst_fubini_exists_resultrow_totalpositive) + (dst_positive_sum_fubini_exists_resultrow_total))) /\ forall fs_i_dst_fubini_exists_resultrow_totalpositive_body_steps. (exists fs_lt_dst_fubini_exists_resultrow_totalpositive_body_steps_bound. fs_lt_dst_fubini_exists_resultrow_totalpositive_body_steps_bound + S fs_i_dst_fubini_exists_resultrow_totalpositive_body_steps = m) -> exists fs_a_dst_fubini_exists_resultrow_totalpositive_body_steps fs_r_dst_fubini_exists_resultrow_totalpositive_body_steps fs_s_dst_fubini_exists_resultrow_totalpositive_body_steps. ((((exists fs_h_dst_fubini_exists_resultrow_totalpositive_body_steps_summand. fs_h_dst_fubini_exists_resultrow_totalpositive_body_steps_summand + S (fs_a_dst_fubini_exists_resultrow_totalpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_resultrow_totalpositive_body_steps)) * dst_positive_scale_fubini_exists_resultrow_total)) /\ exists fs_q_dst_fubini_exists_resultrow_totalpositive_body_steps_summand. dst_positive_code_fubini_exists_resultrow_total = fs_q_dst_fubini_exists_resultrow_totalpositive_body_steps_summand * S ((S (fs_i_dst_fubini_exists_resultrow_totalpositive_body_steps)) * dst_positive_scale_fubini_exists_resultrow_total) + (fs_a_dst_fubini_exists_resultrow_totalpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultrow_totalpositive_body_steps_partial. fs_h_dst_fubini_exists_resultrow_totalpositive_body_steps_partial + S (fs_r_dst_fubini_exists_resultrow_totalpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_resultrow_totalpositive_body_steps)) * fs_v_dst_fubini_exists_resultrow_totalpositive)) /\ exists fs_q_dst_fubini_exists_resultrow_totalpositive_body_steps_partial. fs_u_dst_fubini_exists_resultrow_totalpositive = fs_q_dst_fubini_exists_resultrow_totalpositive_body_steps_partial * S ((S (fs_i_dst_fubini_exists_resultrow_totalpositive_body_steps)) * fs_v_dst_fubini_exists_resultrow_totalpositive) + (fs_r_dst_fubini_exists_resultrow_totalpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultrow_totalpositive_body_steps_successor. fs_h_dst_fubini_exists_resultrow_totalpositive_body_steps_successor + S (fs_s_dst_fubini_exists_resultrow_totalpositive_body_steps) = S ((S (S fs_i_dst_fubini_exists_resultrow_totalpositive_body_steps)) * fs_v_dst_fubini_exists_resultrow_totalpositive)) /\ exists fs_q_dst_fubini_exists_resultrow_totalpositive_body_steps_successor. fs_u_dst_fubini_exists_resultrow_totalpositive = fs_q_dst_fubini_exists_resultrow_totalpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_resultrow_totalpositive_body_steps)) * fs_v_dst_fubini_exists_resultrow_totalpositive) + (fs_s_dst_fubini_exists_resultrow_totalpositive_body_steps))) /\ fs_s_dst_fubini_exists_resultrow_totalpositive_body_steps = fs_r_dst_fubini_exists_resultrow_totalpositive_body_steps + fs_a_dst_fubini_exists_resultrow_totalpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_exists_resultrow_totalnegative fs_v_dst_fubini_exists_resultrow_totalnegative. ((((exists fs_h_dst_fubini_exists_resultrow_totalnegative_body_start. fs_h_dst_fubini_exists_resultrow_totalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_resultrow_totalnegative)) /\ exists fs_q_dst_fubini_exists_resultrow_totalnegative_body_start. fs_u_dst_fubini_exists_resultrow_totalnegative = fs_q_dst_fubini_exists_resultrow_totalnegative_body_start * S ((S (0)) * fs_v_dst_fubini_exists_resultrow_totalnegative) + (0))) /\ ((((exists fs_h_dst_fubini_exists_resultrow_totalnegative_body_terminal. fs_h_dst_fubini_exists_resultrow_totalnegative_body_terminal + S (dst_negative_sum_fubini_exists_resultrow_total) = S ((S (m)) * fs_v_dst_fubini_exists_resultrow_totalnegative)) /\ exists fs_q_dst_fubini_exists_resultrow_totalnegative_body_terminal. fs_u_dst_fubini_exists_resultrow_totalnegative = fs_q_dst_fubini_exists_resultrow_totalnegative_body_terminal * S ((S (m)) * fs_v_dst_fubini_exists_resultrow_totalnegative) + (dst_negative_sum_fubini_exists_resultrow_total))) /\ forall fs_i_dst_fubini_exists_resultrow_totalnegative_body_steps. (exists fs_lt_dst_fubini_exists_resultrow_totalnegative_body_steps_bound. fs_lt_dst_fubini_exists_resultrow_totalnegative_body_steps_bound + S fs_i_dst_fubini_exists_resultrow_totalnegative_body_steps = m) -> exists fs_a_dst_fubini_exists_resultrow_totalnegative_body_steps fs_r_dst_fubini_exists_resultrow_totalnegative_body_steps fs_s_dst_fubini_exists_resultrow_totalnegative_body_steps. ((((exists fs_h_dst_fubini_exists_resultrow_totalnegative_body_steps_summand. fs_h_dst_fubini_exists_resultrow_totalnegative_body_steps_summand + S (fs_a_dst_fubini_exists_resultrow_totalnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_resultrow_totalnegative_body_steps)) * dst_negative_scale_fubini_exists_resultrow_total)) /\ exists fs_q_dst_fubini_exists_resultrow_totalnegative_body_steps_summand. dst_negative_code_fubini_exists_resultrow_total = fs_q_dst_fubini_exists_resultrow_totalnegative_body_steps_summand * S ((S (fs_i_dst_fubini_exists_resultrow_totalnegative_body_steps)) * dst_negative_scale_fubini_exists_resultrow_total) + (fs_a_dst_fubini_exists_resultrow_totalnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultrow_totalnegative_body_steps_partial. fs_h_dst_fubini_exists_resultrow_totalnegative_body_steps_partial + S (fs_r_dst_fubini_exists_resultrow_totalnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_resultrow_totalnegative_body_steps)) * fs_v_dst_fubini_exists_resultrow_totalnegative)) /\ exists fs_q_dst_fubini_exists_resultrow_totalnegative_body_steps_partial. fs_u_dst_fubini_exists_resultrow_totalnegative = fs_q_dst_fubini_exists_resultrow_totalnegative_body_steps_partial * S ((S (fs_i_dst_fubini_exists_resultrow_totalnegative_body_steps)) * fs_v_dst_fubini_exists_resultrow_totalnegative) + (fs_r_dst_fubini_exists_resultrow_totalnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultrow_totalnegative_body_steps_successor. fs_h_dst_fubini_exists_resultrow_totalnegative_body_steps_successor + S (fs_s_dst_fubini_exists_resultrow_totalnegative_body_steps) = S ((S (S fs_i_dst_fubini_exists_resultrow_totalnegative_body_steps)) * fs_v_dst_fubini_exists_resultrow_totalnegative)) /\ exists fs_q_dst_fubini_exists_resultrow_totalnegative_body_steps_successor. fs_u_dst_fubini_exists_resultrow_totalnegative = fs_q_dst_fubini_exists_resultrow_totalnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_resultrow_totalnegative_body_steps)) * fs_v_dst_fubini_exists_resultrow_totalnegative) + (fs_s_dst_fubini_exists_resultrow_totalnegative_body_steps))) /\ fs_s_dst_fubini_exists_resultrow_totalnegative_body_steps = fs_r_dst_fubini_exists_resultrow_totalnegative_body_steps + fs_a_dst_fubini_exists_resultrow_totalnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_exists_resultrow_totalresult ge_balance_negative_fubini_exists_resultrow_totalresult. (((((z) = 2 * (ge_balance_positive_fubini_exists_resultrow_totalresult) /\ (ge_balance_negative_fubini_exists_resultrow_totalresult) = 0) \/ exists ge_signed_half_fubini_exists_resultrow_totalresultdecode. (((z) = 2 * ge_signed_half_fubini_exists_resultrow_totalresultdecode + 1 /\ (ge_balance_positive_fubini_exists_resultrow_totalresult) = 0) /\ (ge_balance_negative_fubini_exists_resultrow_totalresult) = S ge_signed_half_fubini_exists_resultrow_totalresultdecode))) /\ ((dst_positive_sum_fubini_exists_resultrow_total) + ge_balance_negative_fubini_exists_resultrow_totalresult = (dst_negative_sum_fubini_exists_resultrow_total) + ge_balance_positive_fubini_exists_resultrow_totalresult))))))))) /\ (exists dst_positive_code_fubini_exists_resultcolumn_total dst_positive_scale_fubini_exists_resultcolumn_total dst_negative_code_fubini_exists_resultcolumn_total dst_negative_scale_fubini_exists_resultcolumn_total dst_positive_sum_fubini_exists_resultcolumn_total dst_negative_sum_fubini_exists_resultcolumn_total. (((C) = (((((dst_positive_code_fubini_exists_resultcolumn_total) + (dst_positive_scale_fubini_exists_resultcolumn_total)) * S ((dst_positive_code_fubini_exists_resultcolumn_total) + (dst_positive_scale_fubini_exists_resultcolumn_total)) + ((dst_positive_scale_fubini_exists_resultcolumn_total) + (dst_positive_scale_fubini_exists_resultcolumn_total))) + (((dst_negative_code_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)) * S ((dst_negative_code_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)) + ((dst_negative_scale_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)))) * S ((((dst_positive_code_fubini_exists_resultcolumn_total) + (dst_positive_scale_fubini_exists_resultcolumn_total)) * S ((dst_positive_code_fubini_exists_resultcolumn_total) + (dst_positive_scale_fubini_exists_resultcolumn_total)) + ((dst_positive_scale_fubini_exists_resultcolumn_total) + (dst_positive_scale_fubini_exists_resultcolumn_total))) + (((dst_negative_code_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)) * S ((dst_negative_code_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)) + ((dst_negative_scale_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)))) + ((((dst_negative_code_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)) * S ((dst_negative_code_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)) + ((dst_negative_scale_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total))) + (((dst_negative_code_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)) * S ((dst_negative_code_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)) + ((dst_negative_scale_fubini_exists_resultcolumn_total) + (dst_negative_scale_fubini_exists_resultcolumn_total)))))) /\ (((exists fs_u_dst_fubini_exists_resultcolumn_totalpositive fs_v_dst_fubini_exists_resultcolumn_totalpositive. ((((exists fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_start. fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_resultcolumn_totalpositive)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_start. fs_u_dst_fubini_exists_resultcolumn_totalpositive = fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_start * S ((S (0)) * fs_v_dst_fubini_exists_resultcolumn_totalpositive) + (0))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_terminal. fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_terminal + S (dst_positive_sum_fubini_exists_resultcolumn_total) = S ((S (n)) * fs_v_dst_fubini_exists_resultcolumn_totalpositive)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_terminal. fs_u_dst_fubini_exists_resultcolumn_totalpositive = fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_terminal * S ((S (n)) * fs_v_dst_fubini_exists_resultcolumn_totalpositive) + (dst_positive_sum_fubini_exists_resultcolumn_total))) /\ forall fs_i_dst_fubini_exists_resultcolumn_totalpositive_body_steps. (exists fs_lt_dst_fubini_exists_resultcolumn_totalpositive_body_steps_bound. fs_lt_dst_fubini_exists_resultcolumn_totalpositive_body_steps_bound + S fs_i_dst_fubini_exists_resultcolumn_totalpositive_body_steps = n) -> exists fs_a_dst_fubini_exists_resultcolumn_totalpositive_body_steps fs_r_dst_fubini_exists_resultcolumn_totalpositive_body_steps fs_s_dst_fubini_exists_resultcolumn_totalpositive_body_steps. ((((exists fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_steps_summand. fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_steps_summand + S (fs_a_dst_fubini_exists_resultcolumn_totalpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_resultcolumn_totalpositive_body_steps)) * dst_positive_scale_fubini_exists_resultcolumn_total)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_steps_summand. dst_positive_code_fubini_exists_resultcolumn_total = fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_steps_summand * S ((S (fs_i_dst_fubini_exists_resultcolumn_totalpositive_body_steps)) * dst_positive_scale_fubini_exists_resultcolumn_total) + (fs_a_dst_fubini_exists_resultcolumn_totalpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_steps_partial. fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_steps_partial + S (fs_r_dst_fubini_exists_resultcolumn_totalpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_resultcolumn_totalpositive_body_steps)) * fs_v_dst_fubini_exists_resultcolumn_totalpositive)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_steps_partial. fs_u_dst_fubini_exists_resultcolumn_totalpositive = fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_steps_partial * S ((S (fs_i_dst_fubini_exists_resultcolumn_totalpositive_body_steps)) * fs_v_dst_fubini_exists_resultcolumn_totalpositive) + (fs_r_dst_fubini_exists_resultcolumn_totalpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_steps_successor. fs_h_dst_fubini_exists_resultcolumn_totalpositive_body_steps_successor + S (fs_s_dst_fubini_exists_resultcolumn_totalpositive_body_steps) = S ((S (S fs_i_dst_fubini_exists_resultcolumn_totalpositive_body_steps)) * fs_v_dst_fubini_exists_resultcolumn_totalpositive)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_steps_successor. fs_u_dst_fubini_exists_resultcolumn_totalpositive = fs_q_dst_fubini_exists_resultcolumn_totalpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_resultcolumn_totalpositive_body_steps)) * fs_v_dst_fubini_exists_resultcolumn_totalpositive) + (fs_s_dst_fubini_exists_resultcolumn_totalpositive_body_steps))) /\ fs_s_dst_fubini_exists_resultcolumn_totalpositive_body_steps = fs_r_dst_fubini_exists_resultcolumn_totalpositive_body_steps + fs_a_dst_fubini_exists_resultcolumn_totalpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_exists_resultcolumn_totalnegative fs_v_dst_fubini_exists_resultcolumn_totalnegative. ((((exists fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_start. fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_resultcolumn_totalnegative)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_start. fs_u_dst_fubini_exists_resultcolumn_totalnegative = fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_start * S ((S (0)) * fs_v_dst_fubini_exists_resultcolumn_totalnegative) + (0))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_terminal. fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_terminal + S (dst_negative_sum_fubini_exists_resultcolumn_total) = S ((S (n)) * fs_v_dst_fubini_exists_resultcolumn_totalnegative)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_terminal. fs_u_dst_fubini_exists_resultcolumn_totalnegative = fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_terminal * S ((S (n)) * fs_v_dst_fubini_exists_resultcolumn_totalnegative) + (dst_negative_sum_fubini_exists_resultcolumn_total))) /\ forall fs_i_dst_fubini_exists_resultcolumn_totalnegative_body_steps. (exists fs_lt_dst_fubini_exists_resultcolumn_totalnegative_body_steps_bound. fs_lt_dst_fubini_exists_resultcolumn_totalnegative_body_steps_bound + S fs_i_dst_fubini_exists_resultcolumn_totalnegative_body_steps = n) -> exists fs_a_dst_fubini_exists_resultcolumn_totalnegative_body_steps fs_r_dst_fubini_exists_resultcolumn_totalnegative_body_steps fs_s_dst_fubini_exists_resultcolumn_totalnegative_body_steps. ((((exists fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_steps_summand. fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_steps_summand + S (fs_a_dst_fubini_exists_resultcolumn_totalnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_resultcolumn_totalnegative_body_steps)) * dst_negative_scale_fubini_exists_resultcolumn_total)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_steps_summand. dst_negative_code_fubini_exists_resultcolumn_total = fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_steps_summand * S ((S (fs_i_dst_fubini_exists_resultcolumn_totalnegative_body_steps)) * dst_negative_scale_fubini_exists_resultcolumn_total) + (fs_a_dst_fubini_exists_resultcolumn_totalnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_steps_partial. fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_steps_partial + S (fs_r_dst_fubini_exists_resultcolumn_totalnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_resultcolumn_totalnegative_body_steps)) * fs_v_dst_fubini_exists_resultcolumn_totalnegative)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_steps_partial. fs_u_dst_fubini_exists_resultcolumn_totalnegative = fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_steps_partial * S ((S (fs_i_dst_fubini_exists_resultcolumn_totalnegative_body_steps)) * fs_v_dst_fubini_exists_resultcolumn_totalnegative) + (fs_r_dst_fubini_exists_resultcolumn_totalnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_steps_successor. fs_h_dst_fubini_exists_resultcolumn_totalnegative_body_steps_successor + S (fs_s_dst_fubini_exists_resultcolumn_totalnegative_body_steps) = S ((S (S fs_i_dst_fubini_exists_resultcolumn_totalnegative_body_steps)) * fs_v_dst_fubini_exists_resultcolumn_totalnegative)) /\ exists fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_steps_successor. fs_u_dst_fubini_exists_resultcolumn_totalnegative = fs_q_dst_fubini_exists_resultcolumn_totalnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_resultcolumn_totalnegative_body_steps)) * fs_v_dst_fubini_exists_resultcolumn_totalnegative) + (fs_s_dst_fubini_exists_resultcolumn_totalnegative_body_steps))) /\ fs_s_dst_fubini_exists_resultcolumn_totalnegative_body_steps = fs_r_dst_fubini_exists_resultcolumn_totalnegative_body_steps + fs_a_dst_fubini_exists_resultcolumn_totalnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_exists_resultcolumn_totalresult ge_balance_negative_fubini_exists_resultcolumn_totalresult. (((((z) = 2 * (ge_balance_positive_fubini_exists_resultcolumn_totalresult) /\ (ge_balance_negative_fubini_exists_resultcolumn_totalresult) = 0) \/ exists ge_signed_half_fubini_exists_resultcolumn_totalresultdecode. (((z) = 2 * ge_signed_half_fubini_exists_resultcolumn_totalresultdecode + 1 /\ (ge_balance_positive_fubini_exists_resultcolumn_totalresult) = 0) /\ (ge_balance_negative_fubini_exists_resultcolumn_totalresult) = S ge_signed_half_fubini_exists_resultcolumn_totalresultdecode))) /\ ((dst_positive_sum_fubini_exists_resultcolumn_total) + ge_balance_negative_fubini_exists_resultcolumn_totalresult = (dst_negative_sum_fubini_exists_resultcolumn_total) + ge_balance_positive_fubini_exists_resultcolumn_totalresult)))))))))))))))Constructive proof overview
Generated structural guide
Construct actual row and column sum tables and actual signed sum traces sharing one canonical value; no supplied slice, table, sum, or permutation witness is required.
The unchanged tactic script uses 3 declared prerequisites and contains 76 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
RS0015 signed_rectangular_row_sums_exists arithmetic_signed_sum_exists Alpha theorem; checked-use authorized RS001E signed_rectangular_fubiniDirect 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 (2)
01Fix variables and assumptionsL1–7
02Establish hRL8–16
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed rectangular row sums exists.
- L8
have hR : ∃ R. ArithRowSums(F,R,o,s,t,m,n)Definitions: ArithRowSums - L9
specialize signed_rectangular_row_sums_exists (m) - L10
specialize signed_rectangular_row_sums_exists (F) - L11
specialize signed_rectangular_row_sums_exists (o) - L12
specialize signed_rectangular_row_sums_exists (s) - L13
specialize signed_rectangular_row_sums_exists (t) - L14
specialize signed_rectangular_row_sums_exists (n) - L15
apply signed_rectangular_row_sums_exists - L16
exact hF
03Separate the logical casesL17–17
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L17
cases hR
04Establish hzL18–22
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply arithmetic signed sum exists.
05Separate the logical casesL23–24
06Use earlier factsL25–25
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L25
exact hR_witness_right_left
07Separate the logical casesL26–26
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L26
cases hz
08Establish hCL27–35
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed rectangular row sums exists.
- L27
have hC : ∃ C. ArithRowSums(F,C,o,t,s,n,m)Definitions: ArithRowSums - L28
specialize signed_rectangular_row_sums_exists (n) - L29
specialize signed_rectangular_row_sums_exists (F) - L30
specialize signed_rectangular_row_sums_exists (o) - L31
specialize signed_rectangular_row_sums_exists (t) - L32
specialize signed_rectangular_row_sums_exists (s) - L33
specialize signed_rectangular_row_sums_exists (m) - L34
apply signed_rectangular_row_sums_exists - L35
exact hF
09Separate the logical casesL36–36
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L36
cases hC
10Establish hwL37–41
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply arithmetic signed sum exists.
11Separate the logical casesL42–43
12Use earlier factsL44–44
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L44
exact hC_witness_right_left
13Separate the logical casesL45–45
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L45
cases hw
14Establish heqL46–55
Establish this local claim before using it. It is not an additional assumption.
- L46
have heq : x3 = x1 - L47
symm - L48
specialize signed_rectangular_fubini (m) - L49
specialize signed_rectangular_fubini (F) - L50
specialize signed_rectangular_fubini (o) - L51
specialize signed_rectangular_fubini (s) - L52
specialize signed_rectangular_fubini (t) - L53
specialize signed_rectangular_fubini (n) - L54
specialize signed_rectangular_fubini (x1) - L55
specialize signed_rectangular_fubini (x3)
15Use earlier factsL56–56
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L56
apply signed_rectangular_fubini
16Construct an explicit witnessL57–57
Supply the displayed value, then prove that it has the required property.
- L57
exists x
17Separate the logical casesL58–58
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L58
split
18Use earlier factsL59–60
19Construct an explicit witnessL61–61
Supply the displayed value, then prove that it has the required property.
- L61
exists x2
20Separate the logical casesL62–62
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L62
split
21Use earlier factsL63–64
22Calculate and transport equalitiesL65–66
23Construct an explicit witnessL67–69
24Separate the logical casesL70–70
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L70
split
25Use earlier factsL71–71
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L71
exact hR_witness
26Separate the logical casesL72–72
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L72
split
27Use earlier factsL73–73
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L73
exact hC_witness
28Separate the logical casesL74–74
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L74
split
Original exact command ledger · 76 lines
- 0001
intro F - 0002
intro o - 0003
intro s - 0004
intro t - 0005
intro m - 0006
intro n - 0007
intro hF - 0008
have hR : exists R. (((exists dst_positive_code_fubini_exists_rowssource_table dst_positive_scale_fubini_exists_rowssource_table dst_negative_code_fubini_exists_rowssource_table dst_negative_scale_fubini_exists_rowssource_table. (((F) = (((((dst_positive_code_fubini_exists_rowssource_table) + (dst_positive_scale_fubini_exists_rowssource_table)) * S ((dst_positive_code_fubini_exists_rowssource_table) + (dst_positive_scale_fubini_exists_rowssource_table)) + ((dst_positive_scale_fubini_exists_rowssource_table) + (dst_positive_scale_fubini_exists_rowssource_table))) + (((dst_negative_code_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)) * S ((dst_negative_code_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)) + ((dst_negative_scale_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)))) * S ((((dst_positive_code_fubini_exists_rowssource_table) + (dst_positive_scale_fubini_exists_rowssource_table)) * S ((dst_positive_code_fubini_exists_rowssource_table) + (dst_positive_scale_fubini_exists_rowssource_table)) + ((dst_positive_scale_fubini_exists_rowssource_table) + (dst_positive_scale_fubini_exists_rowssource_table))) + (((dst_negative_code_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)) * S ((dst_negative_code_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)) + ((dst_negative_scale_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)))) + ((((dst_negative_code_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)) * S ((dst_negative_code_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)) + ((dst_negative_scale_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table))) + (((dst_negative_code_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)) * S ((dst_negative_code_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)) + ((dst_negative_scale_fubini_exists_rowssource_table) + (dst_negative_scale_fubini_exists_rowssource_table)))))) /\ (forall dst_index_fubini_exists_rowssource_table. (exists pvs_le_gap_fubini_exists_rowssource_tabledomain. pvs_le_gap_fubini_exists_rowssource_tabledomain + (dst_index_fubini_exists_rowssource_table) = (0)) -> exists dst_positive_fubini_exists_rowssource_table dst_negative_fubini_exists_rowssource_table dst_value_fubini_exists_rowssource_table. ((((exists ff_h_pvs_fubini_exists_rowssource_tableentrypositive. ff_h_pvs_fubini_exists_rowssource_tableentrypositive + S (dst_positive_fubini_exists_rowssource_table) = S ((S (dst_index_fubini_exists_rowssource_table)) * dst_positive_scale_fubini_exists_rowssource_table)) /\ exists ff_q_pvs_fubini_exists_rowssource_tableentrypositive. dst_positive_code_fubini_exists_rowssource_table = ff_q_pvs_fubini_exists_rowssource_tableentrypositive * S ((S (dst_index_fubini_exists_rowssource_table)) * dst_positive_scale_fubini_exists_rowssource_table) + (dst_positive_fubini_exists_rowssource_table))) /\ (((((exists ff_h_pvs_fubini_exists_rowssource_tableentrynegative. ff_h_pvs_fubini_exists_rowssource_tableentrynegative + S (dst_negative_fubini_exists_rowssource_table) = S ((S (dst_index_fubini_exists_rowssource_table)) * dst_negative_scale_fubini_exists_rowssource_table)) /\ exists ff_q_pvs_fubini_exists_rowssource_tableentrynegative. dst_negative_code_fubini_exists_rowssource_table = ff_q_pvs_fubini_exists_rowssource_tableentrynegative * S ((S (dst_index_fubini_exists_rowssource_table)) * dst_negative_scale_fubini_exists_rowssource_table) + (dst_negative_fubini_exists_rowssource_table))) /\ (exists ge_balance_positive_fubini_exists_rowssource_tableentryvalue ge_balance_negative_fubini_exists_rowssource_tableentryvalue. (((((dst_value_fubini_exists_rowssource_table) = 2 * (ge_balance_positive_fubini_exists_rowssource_tableentryvalue) /\ (ge_balance_negative_fubini_exists_rowssource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_rowssource_tableentryvaluedecode. (((dst_value_fubini_exists_rowssource_table) = 2 * ge_signed_half_fubini_exists_rowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_rowssource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_rowssource_tableentryvalue) = S ge_signed_half_fubini_exists_rowssource_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_rowssource_table) + ge_balance_negative_fubini_exists_rowssource_tableentryvalue = (dst_negative_fubini_exists_rowssource_table) + ge_balance_positive_fubini_exists_rowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_exists_rowsrow_table dst_positive_scale_fubini_exists_rowsrow_table dst_negative_code_fubini_exists_rowsrow_table dst_negative_scale_fubini_exists_rowsrow_table. (((R) = (((((dst_positive_code_fubini_exists_rowsrow_table) + (dst_positive_scale_fubini_exists_rowsrow_table)) * S ((dst_positive_code_fubini_exists_rowsrow_table) + (dst_positive_scale_fubini_exists_rowsrow_table)) + ((dst_positive_scale_fubini_exists_rowsrow_table) + (dst_positive_scale_fubini_exists_rowsrow_table))) + (((dst_negative_code_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)) * S ((dst_negative_code_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)) + ((dst_negative_scale_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)))) * S ((((dst_positive_code_fubini_exists_rowsrow_table) + (dst_positive_scale_fubini_exists_rowsrow_table)) * S ((dst_positive_code_fubini_exists_rowsrow_table) + (dst_positive_scale_fubini_exists_rowsrow_table)) + ((dst_positive_scale_fubini_exists_rowsrow_table) + (dst_positive_scale_fubini_exists_rowsrow_table))) + (((dst_negative_code_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)) * S ((dst_negative_code_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)) + ((dst_negative_scale_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)))) + ((((dst_negative_code_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)) * S ((dst_negative_code_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)) + ((dst_negative_scale_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table))) + (((dst_negative_code_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)) * S ((dst_negative_code_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)) + ((dst_negative_scale_fubini_exists_rowsrow_table) + (dst_negative_scale_fubini_exists_rowsrow_table)))))) /\ (forall dst_index_fubini_exists_rowsrow_table. (exists pvs_le_gap_fubini_exists_rowsrow_tabledomain. pvs_le_gap_fubini_exists_rowsrow_tabledomain + (dst_index_fubini_exists_rowsrow_table) = (m)) -> exists dst_positive_fubini_exists_rowsrow_table dst_negative_fubini_exists_rowsrow_table dst_value_fubini_exists_rowsrow_table. ((((exists ff_h_pvs_fubini_exists_rowsrow_tableentrypositive. ff_h_pvs_fubini_exists_rowsrow_tableentrypositive + S (dst_positive_fubini_exists_rowsrow_table) = S ((S (dst_index_fubini_exists_rowsrow_table)) * dst_positive_scale_fubini_exists_rowsrow_table)) /\ exists ff_q_pvs_fubini_exists_rowsrow_tableentrypositive. dst_positive_code_fubini_exists_rowsrow_table = ff_q_pvs_fubini_exists_rowsrow_tableentrypositive * S ((S (dst_index_fubini_exists_rowsrow_table)) * dst_positive_scale_fubini_exists_rowsrow_table) + (dst_positive_fubini_exists_rowsrow_table))) /\ (((((exists ff_h_pvs_fubini_exists_rowsrow_tableentrynegative. ff_h_pvs_fubini_exists_rowsrow_tableentrynegative + S (dst_negative_fubini_exists_rowsrow_table) = S ((S (dst_index_fubini_exists_rowsrow_table)) * dst_negative_scale_fubini_exists_rowsrow_table)) /\ exists ff_q_pvs_fubini_exists_rowsrow_tableentrynegative. dst_negative_code_fubini_exists_rowsrow_table = ff_q_pvs_fubini_exists_rowsrow_tableentrynegative * S ((S (dst_index_fubini_exists_rowsrow_table)) * dst_negative_scale_fubini_exists_rowsrow_table) + (dst_negative_fubini_exists_rowsrow_table))) /\ (exists ge_balance_positive_fubini_exists_rowsrow_tableentryvalue ge_balance_negative_fubini_exists_rowsrow_tableentryvalue. (((((dst_value_fubini_exists_rowsrow_table) = 2 * (ge_balance_positive_fubini_exists_rowsrow_tableentryvalue) /\ (ge_balance_negative_fubini_exists_rowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_rowsrow_tableentryvaluedecode. (((dst_value_fubini_exists_rowsrow_table) = 2 * ge_signed_half_fubini_exists_rowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_rowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_rowsrow_tableentryvalue) = S ge_signed_half_fubini_exists_rowsrow_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_rowsrow_table) + ge_balance_negative_fubini_exists_rowsrow_tableentryvalue = (dst_negative_fubini_exists_rowsrow_table) + ge_balance_positive_fubini_exists_rowsrow_tableentryvalue))))))))) /\ (forall srt_index_fubini_exists_rows. (exists pvs_gap_fubini_exists_rowsbound. pvs_gap_fubini_exists_rowsbound + S (srt_index_fubini_exists_rows) = (m)) -> exists srt_value_fubini_exists_rows. (((exists dst_positive_code_fubini_exists_rowsrowentry dst_positive_scale_fubini_exists_rowsrowentry dst_negative_code_fubini_exists_rowsrowentry dst_negative_scale_fubini_exists_rowsrowentry dst_positive_fubini_exists_rowsrowentry dst_negative_fubini_exists_rowsrowentry. (((R) = (((((dst_positive_code_fubini_exists_rowsrowentry) + (dst_positive_scale_fubini_exists_rowsrowentry)) * S ((dst_positive_code_fubini_exists_rowsrowentry) + (dst_positive_scale_fubini_exists_rowsrowentry)) + ((dst_positive_scale_fubini_exists_rowsrowentry) + (dst_positive_scale_fubini_exists_rowsrowentry))) + (((dst_negative_code_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)) * S ((dst_negative_code_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)) + ((dst_negative_scale_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)))) * S ((((dst_positive_code_fubini_exists_rowsrowentry) + (dst_positive_scale_fubini_exists_rowsrowentry)) * S ((dst_positive_code_fubini_exists_rowsrowentry) + (dst_positive_scale_fubini_exists_rowsrowentry)) + ((dst_positive_scale_fubini_exists_rowsrowentry) + (dst_positive_scale_fubini_exists_rowsrowentry))) + (((dst_negative_code_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)) * S ((dst_negative_code_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)) + ((dst_negative_scale_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)))) + ((((dst_negative_code_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)) * S ((dst_negative_code_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)) + ((dst_negative_scale_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry))) + (((dst_negative_code_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)) * S ((dst_negative_code_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)) + ((dst_negative_scale_fubini_exists_rowsrowentry) + (dst_negative_scale_fubini_exists_rowsrowentry)))))) /\ (((((exists ff_h_pvs_fubini_exists_rowsrowentrypositive. ff_h_pvs_fubini_exists_rowsrowentrypositive + S (dst_positive_fubini_exists_rowsrowentry) = S ((S (srt_index_fubini_exists_rows)) * dst_positive_scale_fubini_exists_rowsrowentry)) /\ exists ff_q_pvs_fubini_exists_rowsrowentrypositive. dst_positive_code_fubini_exists_rowsrowentry = ff_q_pvs_fubini_exists_rowsrowentrypositive * S ((S (srt_index_fubini_exists_rows)) * dst_positive_scale_fubini_exists_rowsrowentry) + (dst_positive_fubini_exists_rowsrowentry))) /\ (((((exists ff_h_pvs_fubini_exists_rowsrowentrynegative. ff_h_pvs_fubini_exists_rowsrowentrynegative + S (dst_negative_fubini_exists_rowsrowentry) = S ((S (srt_index_fubini_exists_rows)) * dst_negative_scale_fubini_exists_rowsrowentry)) /\ exists ff_q_pvs_fubini_exists_rowsrowentrynegative. dst_negative_code_fubini_exists_rowsrowentry = ff_q_pvs_fubini_exists_rowsrowentrynegative * S ((S (srt_index_fubini_exists_rows)) * dst_negative_scale_fubini_exists_rowsrowentry) + (dst_negative_fubini_exists_rowsrowentry))) /\ (exists ge_balance_positive_fubini_exists_rowsrowentryvalue ge_balance_negative_fubini_exists_rowsrowentryvalue. (((((srt_value_fubini_exists_rows) = 2 * (ge_balance_positive_fubini_exists_rowsrowentryvalue) /\ (ge_balance_negative_fubini_exists_rowsrowentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_rowsrowentryvaluedecode. (((srt_value_fubini_exists_rows) = 2 * ge_signed_half_fubini_exists_rowsrowentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_rowsrowentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_rowsrowentryvalue) = S ge_signed_half_fubini_exists_rowsrowentryvaluedecode))) /\ ((dst_positive_fubini_exists_rowsrowentry) + ge_balance_negative_fubini_exists_rowsrowentryvalue = (dst_negative_fubini_exists_rowsrowentry) + ge_balance_positive_fubini_exists_rowsrowentryvalue))))))))) /\ (exists srs_slice_fubini_exists_rowsrowrow_sum. ((((exists dst_positive_code_fubini_exists_rowsrowrow_sumslicesource_table dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_fubini_exists_rowsrowrow_sumslicesource_table. (exists pvs_le_gap_fubini_exists_rowsrowrow_sumslicesource_tabledomain. pvs_le_gap_fubini_exists_rowsrowrow_sumslicesource_tabledomain + (dst_index_fubini_exists_rowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_fubini_exists_rowsrowrow_sumslicesource_table dst_negative_fubini_exists_rowsrowrow_sumslicesource_table dst_value_fubini_exists_rowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_fubini_exists_rowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_fubini_exists_rowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_fubini_exists_rowsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_exists_rowsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_exists_rowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_fubini_exists_rowsrowrow_sumslicesource_table = ff_q_pvs_fubini_exists_rowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_fubini_exists_rowsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_positive_fubini_exists_rowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_fubini_exists_rowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_fubini_exists_rowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_fubini_exists_rowsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_exists_rowsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_exists_rowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_fubini_exists_rowsrowrow_sumslicesource_table = ff_q_pvs_fubini_exists_rowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_fubini_exists_rowsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_exists_rowsrowrow_sumslicesource_table) + (dst_negative_fubini_exists_rowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_fubini_exists_rowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_fubini_exists_rowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_fubini_exists_rowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_fubini_exists_rowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_rowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_fubini_exists_rowsrowrow_sumslicesource_table) = 2 * ge_signed_half_fubini_exists_rowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_rowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_fubini_exists_rowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_rowsrowrow_sumslicesource_table) + ge_balance_negative_fubini_exists_rowsrowrow_sumslicesource_tableentryvalue = (dst_negative_fubini_exists_rowsrowrow_sumslicesource_table) + ge_balance_positive_fubini_exists_rowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_exists_rowsrowrow_sumsliceoutput_table dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table. (((srs_slice_fubini_exists_rowsrowrow_sum) = (((((dst_positive_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_fubini_exists_rowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_fubini_exists_rowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_fubini_exists_rowsrowrow_sumsliceoutput_tabledomain + (dst_index_fubini_exists_rowsrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_fubini_exists_rowsrowrow_sumsliceoutput_table dst_negative_fubini_exists_rowsrowrow_sumsliceoutput_table dst_value_fubini_exists_rowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_fubini_exists_rowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_fubini_exists_rowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_fubini_exists_rowsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_exists_rowsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_exists_rowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_fubini_exists_rowsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_exists_rowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_fubini_exists_rowsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_positive_fubini_exists_rowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_fubini_exists_rowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_fubini_exists_rowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_fubini_exists_rowsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_exists_rowsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_exists_rowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_fubini_exists_rowsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_exists_rowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_fubini_exists_rowsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_exists_rowsrowrow_sumsliceoutput_table) + (dst_negative_fubini_exists_rowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_fubini_exists_rowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_fubini_exists_rowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_rowsrowrow_sumsliceoutput_table) + ge_balance_negative_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_fubini_exists_rowsrowrow_sumsliceoutput_table) + ge_balance_positive_fubini_exists_rowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_fubini_exists_rowsrowrow_sumslice. (exists pvs_gap_fubini_exists_rowsrowrow_sumslicebound. pvs_gap_fubini_exists_rowsrowrow_sumslicebound + S (srs_index_fubini_exists_rowsrowrow_sumslice) = (n)) -> exists srs_value_fubini_exists_rowsrowrow_sumslice. (((exists dst_positive_code_fubini_exists_rowsrowrow_sumsliceentrysource dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource dst_positive_fubini_exists_rowsrowrow_sumsliceentrysource dst_negative_fubini_exists_rowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_fubini_exists_rowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_fubini_exists_rowsrowrow_sumsliceentrysourcepositive + S (dst_positive_fubini_exists_rowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_fubini_exists_rows)))) + ((t) * (srs_index_fubini_exists_rowsrowrow_sumslice))))) * dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_exists_rowsrowrow_sumsliceentrysourcepositive. dst_positive_code_fubini_exists_rowsrowrow_sumsliceentrysource = ff_q_pvs_fubini_exists_rowsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_fubini_exists_rows)))) + ((t) * (srs_index_fubini_exists_rowsrowrow_sumslice))))) * dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_positive_fubini_exists_rowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_fubini_exists_rowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_fubini_exists_rowsrowrow_sumsliceentrysourcenegative + S (dst_negative_fubini_exists_rowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_fubini_exists_rows)))) + ((t) * (srs_index_fubini_exists_rowsrowrow_sumslice))))) * dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_exists_rowsrowrow_sumsliceentrysourcenegative. dst_negative_code_fubini_exists_rowsrowrow_sumsliceentrysource = ff_q_pvs_fubini_exists_rowsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_fubini_exists_rows)))) + ((t) * (srs_index_fubini_exists_rowsrowrow_sumslice))))) * dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentrysource) + (dst_negative_fubini_exists_rowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_fubini_exists_rowsrowrow_sumsliceentrysourcevalue ge_balance_negative_fubini_exists_rowsrowrow_sumsliceentrysourcevalue. (((((srs_value_fubini_exists_rowsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_exists_rowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_fubini_exists_rowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_fubini_exists_rowsrowrow_sumslice) = 2 * ge_signed_half_fubini_exists_rowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_fubini_exists_rowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_fubini_exists_rowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_fubini_exists_rowsrowrow_sumsliceentrysource) + ge_balance_negative_fubini_exists_rowsrowrow_sumsliceentrysourcevalue = (dst_negative_fubini_exists_rowsrowrow_sumsliceentrysource) + ge_balance_positive_fubini_exists_rowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_fubini_exists_rowsrowrow_sumsliceentryoutput dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput dst_positive_fubini_exists_rowsrowrow_sumsliceentryoutput dst_negative_fubini_exists_rowsrowrow_sumsliceentryoutput. (((srs_slice_fubini_exists_rowsrowrow_sum) = (((((dst_positive_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_fubini_exists_rowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_fubini_exists_rowsrowrow_sumsliceentryoutputpositive + S (dst_positive_fubini_exists_rowsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_exists_rowsrowrow_sumslice)) * dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_exists_rowsrowrow_sumsliceentryoutputpositive. dst_positive_code_fubini_exists_rowsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_exists_rowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_fubini_exists_rowsrowrow_sumslice)) * dst_positive_scale_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_positive_fubini_exists_rowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_fubini_exists_rowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_fubini_exists_rowsrowrow_sumsliceentryoutputnegative + S (dst_negative_fubini_exists_rowsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_exists_rowsrowrow_sumslice)) * dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_exists_rowsrowrow_sumsliceentryoutputnegative. dst_negative_code_fubini_exists_rowsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_exists_rowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_fubini_exists_rowsrowrow_sumslice)) * dst_negative_scale_fubini_exists_rowsrowrow_sumsliceentryoutput) + (dst_negative_fubini_exists_rowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_fubini_exists_rowsrowrow_sumsliceentryoutputvalue ge_balance_negative_fubini_exists_rowsrowrow_sumsliceentryoutputvalue. (((((srs_value_fubini_exists_rowsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_exists_rowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_fubini_exists_rowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_fubini_exists_rowsrowrow_sumslice) = 2 * ge_signed_half_fubini_exists_rowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_rowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_fubini_exists_rowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_fubini_exists_rowsrowrow_sumsliceentryoutput) + ge_balance_negative_fubini_exists_rowsrowrow_sumsliceentryoutputvalue = (dst_negative_fubini_exists_rowsrowrow_sumsliceentryoutput) + ge_balance_positive_fubini_exists_rowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_fubini_exists_rowsrowrow_sumsum dst_positive_scale_fubini_exists_rowsrowrow_sumsum dst_negative_code_fubini_exists_rowsrowrow_sumsum dst_negative_scale_fubini_exists_rowsrowrow_sumsum dst_positive_sum_fubini_exists_rowsrowrow_sumsum dst_negative_sum_fubini_exists_rowsrowrow_sumsum. (((srs_slice_fubini_exists_rowsrowrow_sum) = (((((dst_positive_code_fubini_exists_rowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsum)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsum)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)))) * S ((((dst_positive_code_fubini_exists_rowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsum)) * S ((dst_positive_code_fubini_exists_rowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsum)) + ((dst_positive_scale_fubini_exists_rowsrowrow_sumsum) + (dst_positive_scale_fubini_exists_rowsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)))) + ((((dst_negative_code_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_rowsrowrow_sumsum) + (dst_negative_scale_fubini_exists_rowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_fubini_exists_rowsrowrow_sumsumpositive fs_v_dst_fubini_exists_rowsrowrow_sumsumpositive. ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_start. fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_start. fs_u_dst_fubini_exists_rowsrowrow_sumsumpositive = fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_terminal. fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_fubini_exists_rowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_terminal. fs_u_dst_fubini_exists_rowsrowrow_sumsumpositive = fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumpositive) + (dst_positive_sum_fubini_exists_rowsrowrow_sumsum))) /\ forall fs_i_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps fs_r_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps fs_s_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_exists_rowsrowrow_sumsum)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_fubini_exists_rowsrowrow_sumsum = fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_exists_rowsrowrow_sumsum) + (fs_a_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_fubini_exists_rowsrowrow_sumsumpositive = fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumpositive) + (fs_r_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_fubini_exists_rowsrowrow_sumsumpositive = fs_q_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumpositive) + (fs_s_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps = fs_r_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps + fs_a_dst_fubini_exists_rowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_exists_rowsrowrow_sumsumnegative fs_v_dst_fubini_exists_rowsrowrow_sumsumnegative. ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_start. fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_start. fs_u_dst_fubini_exists_rowsrowrow_sumsumnegative = fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_terminal. fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_fubini_exists_rowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_terminal. fs_u_dst_fubini_exists_rowsrowrow_sumsumnegative = fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumnegative) + (dst_negative_sum_fubini_exists_rowsrowrow_sumsum))) /\ forall fs_i_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps fs_r_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps fs_s_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_exists_rowsrowrow_sumsum)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_fubini_exists_rowsrowrow_sumsum = fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_exists_rowsrowrow_sumsum) + (fs_a_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_fubini_exists_rowsrowrow_sumsumnegative = fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumnegative) + (fs_r_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_fubini_exists_rowsrowrow_sumsumnegative = fs_q_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_rowsrowrow_sumsumnegative) + (fs_s_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps = fs_r_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps + fs_a_dst_fubini_exists_rowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_exists_rowsrowrow_sumsumresult ge_balance_negative_fubini_exists_rowsrowrow_sumsumresult. (((((srt_value_fubini_exists_rows) = 2 * (ge_balance_positive_fubini_exists_rowsrowrow_sumsumresult) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_fubini_exists_rowsrowrow_sumsumresultdecode. (((srt_value_fubini_exists_rows) = 2 * ge_signed_half_fubini_exists_rowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_fubini_exists_rowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_fubini_exists_rowsrowrow_sumsumresult) = S ge_signed_half_fubini_exists_rowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_fubini_exists_rowsrowrow_sumsum) + ge_balance_negative_fubini_exists_rowsrowrow_sumsumresult = (dst_negative_sum_fubini_exists_rowsrowrow_sumsum) + ge_balance_positive_fubini_exists_rowsrowrow_sumsumresult)))))))))))))))))) - 0009
specialize signed_rectangular_row_sums_exists (m) - 0010
specialize signed_rectangular_row_sums_exists (F) - 0011
specialize signed_rectangular_row_sums_exists (o) - 0012
specialize signed_rectangular_row_sums_exists (s) - 0013
specialize signed_rectangular_row_sums_exists (t) - 0014
specialize signed_rectangular_row_sums_exists (n) - 0015
apply signed_rectangular_row_sums_exists - 0016
exact hF - 0017
cases hR - 0018
have hz : exists z. (exists dst_positive_code_fubini_exists_row_sum dst_positive_scale_fubini_exists_row_sum dst_negative_code_fubini_exists_row_sum dst_negative_scale_fubini_exists_row_sum dst_positive_sum_fubini_exists_row_sum dst_negative_sum_fubini_exists_row_sum. (((x) = (((((dst_positive_code_fubini_exists_row_sum) + (dst_positive_scale_fubini_exists_row_sum)) * S ((dst_positive_code_fubini_exists_row_sum) + (dst_positive_scale_fubini_exists_row_sum)) + ((dst_positive_scale_fubini_exists_row_sum) + (dst_positive_scale_fubini_exists_row_sum))) + (((dst_negative_code_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)) * S ((dst_negative_code_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)) + ((dst_negative_scale_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)))) * S ((((dst_positive_code_fubini_exists_row_sum) + (dst_positive_scale_fubini_exists_row_sum)) * S ((dst_positive_code_fubini_exists_row_sum) + (dst_positive_scale_fubini_exists_row_sum)) + ((dst_positive_scale_fubini_exists_row_sum) + (dst_positive_scale_fubini_exists_row_sum))) + (((dst_negative_code_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)) * S ((dst_negative_code_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)) + ((dst_negative_scale_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)))) + ((((dst_negative_code_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)) * S ((dst_negative_code_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)) + ((dst_negative_scale_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum))) + (((dst_negative_code_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)) * S ((dst_negative_code_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)) + ((dst_negative_scale_fubini_exists_row_sum) + (dst_negative_scale_fubini_exists_row_sum)))))) /\ (((exists fs_u_dst_fubini_exists_row_sumpositive fs_v_dst_fubini_exists_row_sumpositive. ((((exists fs_h_dst_fubini_exists_row_sumpositive_body_start. fs_h_dst_fubini_exists_row_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_row_sumpositive)) /\ exists fs_q_dst_fubini_exists_row_sumpositive_body_start. fs_u_dst_fubini_exists_row_sumpositive = fs_q_dst_fubini_exists_row_sumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_exists_row_sumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_exists_row_sumpositive_body_terminal. fs_h_dst_fubini_exists_row_sumpositive_body_terminal + S (dst_positive_sum_fubini_exists_row_sum) = S ((S (m)) * fs_v_dst_fubini_exists_row_sumpositive)) /\ exists fs_q_dst_fubini_exists_row_sumpositive_body_terminal. fs_u_dst_fubini_exists_row_sumpositive = fs_q_dst_fubini_exists_row_sumpositive_body_terminal * S ((S (m)) * fs_v_dst_fubini_exists_row_sumpositive) + (dst_positive_sum_fubini_exists_row_sum))) /\ forall fs_i_dst_fubini_exists_row_sumpositive_body_steps. (exists fs_lt_dst_fubini_exists_row_sumpositive_body_steps_bound. fs_lt_dst_fubini_exists_row_sumpositive_body_steps_bound + S fs_i_dst_fubini_exists_row_sumpositive_body_steps = m) -> exists fs_a_dst_fubini_exists_row_sumpositive_body_steps fs_r_dst_fubini_exists_row_sumpositive_body_steps fs_s_dst_fubini_exists_row_sumpositive_body_steps. ((((exists fs_h_dst_fubini_exists_row_sumpositive_body_steps_summand. fs_h_dst_fubini_exists_row_sumpositive_body_steps_summand + S (fs_a_dst_fubini_exists_row_sumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_row_sumpositive_body_steps)) * dst_positive_scale_fubini_exists_row_sum)) /\ exists fs_q_dst_fubini_exists_row_sumpositive_body_steps_summand. dst_positive_code_fubini_exists_row_sum = fs_q_dst_fubini_exists_row_sumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_exists_row_sumpositive_body_steps)) * dst_positive_scale_fubini_exists_row_sum) + (fs_a_dst_fubini_exists_row_sumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_row_sumpositive_body_steps_partial. fs_h_dst_fubini_exists_row_sumpositive_body_steps_partial + S (fs_r_dst_fubini_exists_row_sumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_row_sumpositive_body_steps)) * fs_v_dst_fubini_exists_row_sumpositive)) /\ exists fs_q_dst_fubini_exists_row_sumpositive_body_steps_partial. fs_u_dst_fubini_exists_row_sumpositive = fs_q_dst_fubini_exists_row_sumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_exists_row_sumpositive_body_steps)) * fs_v_dst_fubini_exists_row_sumpositive) + (fs_r_dst_fubini_exists_row_sumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_row_sumpositive_body_steps_successor. fs_h_dst_fubini_exists_row_sumpositive_body_steps_successor + S (fs_s_dst_fubini_exists_row_sumpositive_body_steps) = S ((S (S fs_i_dst_fubini_exists_row_sumpositive_body_steps)) * fs_v_dst_fubini_exists_row_sumpositive)) /\ exists fs_q_dst_fubini_exists_row_sumpositive_body_steps_successor. fs_u_dst_fubini_exists_row_sumpositive = fs_q_dst_fubini_exists_row_sumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_row_sumpositive_body_steps)) * fs_v_dst_fubini_exists_row_sumpositive) + (fs_s_dst_fubini_exists_row_sumpositive_body_steps))) /\ fs_s_dst_fubini_exists_row_sumpositive_body_steps = fs_r_dst_fubini_exists_row_sumpositive_body_steps + fs_a_dst_fubini_exists_row_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_exists_row_sumnegative fs_v_dst_fubini_exists_row_sumnegative. ((((exists fs_h_dst_fubini_exists_row_sumnegative_body_start. fs_h_dst_fubini_exists_row_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_row_sumnegative)) /\ exists fs_q_dst_fubini_exists_row_sumnegative_body_start. fs_u_dst_fubini_exists_row_sumnegative = fs_q_dst_fubini_exists_row_sumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_exists_row_sumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_exists_row_sumnegative_body_terminal. fs_h_dst_fubini_exists_row_sumnegative_body_terminal + S (dst_negative_sum_fubini_exists_row_sum) = S ((S (m)) * fs_v_dst_fubini_exists_row_sumnegative)) /\ exists fs_q_dst_fubini_exists_row_sumnegative_body_terminal. fs_u_dst_fubini_exists_row_sumnegative = fs_q_dst_fubini_exists_row_sumnegative_body_terminal * S ((S (m)) * fs_v_dst_fubini_exists_row_sumnegative) + (dst_negative_sum_fubini_exists_row_sum))) /\ forall fs_i_dst_fubini_exists_row_sumnegative_body_steps. (exists fs_lt_dst_fubini_exists_row_sumnegative_body_steps_bound. fs_lt_dst_fubini_exists_row_sumnegative_body_steps_bound + S fs_i_dst_fubini_exists_row_sumnegative_body_steps = m) -> exists fs_a_dst_fubini_exists_row_sumnegative_body_steps fs_r_dst_fubini_exists_row_sumnegative_body_steps fs_s_dst_fubini_exists_row_sumnegative_body_steps. ((((exists fs_h_dst_fubini_exists_row_sumnegative_body_steps_summand. fs_h_dst_fubini_exists_row_sumnegative_body_steps_summand + S (fs_a_dst_fubini_exists_row_sumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_row_sumnegative_body_steps)) * dst_negative_scale_fubini_exists_row_sum)) /\ exists fs_q_dst_fubini_exists_row_sumnegative_body_steps_summand. dst_negative_code_fubini_exists_row_sum = fs_q_dst_fubini_exists_row_sumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_exists_row_sumnegative_body_steps)) * dst_negative_scale_fubini_exists_row_sum) + (fs_a_dst_fubini_exists_row_sumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_row_sumnegative_body_steps_partial. fs_h_dst_fubini_exists_row_sumnegative_body_steps_partial + S (fs_r_dst_fubini_exists_row_sumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_row_sumnegative_body_steps)) * fs_v_dst_fubini_exists_row_sumnegative)) /\ exists fs_q_dst_fubini_exists_row_sumnegative_body_steps_partial. fs_u_dst_fubini_exists_row_sumnegative = fs_q_dst_fubini_exists_row_sumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_exists_row_sumnegative_body_steps)) * fs_v_dst_fubini_exists_row_sumnegative) + (fs_r_dst_fubini_exists_row_sumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_row_sumnegative_body_steps_successor. fs_h_dst_fubini_exists_row_sumnegative_body_steps_successor + S (fs_s_dst_fubini_exists_row_sumnegative_body_steps) = S ((S (S fs_i_dst_fubini_exists_row_sumnegative_body_steps)) * fs_v_dst_fubini_exists_row_sumnegative)) /\ exists fs_q_dst_fubini_exists_row_sumnegative_body_steps_successor. fs_u_dst_fubini_exists_row_sumnegative = fs_q_dst_fubini_exists_row_sumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_row_sumnegative_body_steps)) * fs_v_dst_fubini_exists_row_sumnegative) + (fs_s_dst_fubini_exists_row_sumnegative_body_steps))) /\ fs_s_dst_fubini_exists_row_sumnegative_body_steps = fs_r_dst_fubini_exists_row_sumnegative_body_steps + fs_a_dst_fubini_exists_row_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_exists_row_sumresult ge_balance_negative_fubini_exists_row_sumresult. (((((z) = 2 * (ge_balance_positive_fubini_exists_row_sumresult) /\ (ge_balance_negative_fubini_exists_row_sumresult) = 0) \/ exists ge_signed_half_fubini_exists_row_sumresultdecode. (((z) = 2 * ge_signed_half_fubini_exists_row_sumresultdecode + 1 /\ (ge_balance_positive_fubini_exists_row_sumresult) = 0) /\ (ge_balance_negative_fubini_exists_row_sumresult) = S ge_signed_half_fubini_exists_row_sumresultdecode))) /\ ((dst_positive_sum_fubini_exists_row_sum) + ge_balance_negative_fubini_exists_row_sumresult = (dst_negative_sum_fubini_exists_row_sum) + ge_balance_positive_fubini_exists_row_sumresult))))))))) - 0019
specialize arithmetic_signed_sum_exists (m) - 0020
specialize arithmetic_signed_sum_exists (x) - 0021
specialize arithmetic_signed_sum_exists (m) - 0022
apply arithmetic_signed_sum_exists - 0023
cases hR_witness - 0024
cases hR_witness_right - 0025
exact hR_witness_right_left - 0026
cases hz - 0027
have hC : exists C. (((exists dst_positive_code_fubini_exists_columnssource_table dst_positive_scale_fubini_exists_columnssource_table dst_negative_code_fubini_exists_columnssource_table dst_negative_scale_fubini_exists_columnssource_table. (((F) = (((((dst_positive_code_fubini_exists_columnssource_table) + (dst_positive_scale_fubini_exists_columnssource_table)) * S ((dst_positive_code_fubini_exists_columnssource_table) + (dst_positive_scale_fubini_exists_columnssource_table)) + ((dst_positive_scale_fubini_exists_columnssource_table) + (dst_positive_scale_fubini_exists_columnssource_table))) + (((dst_negative_code_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)) * S ((dst_negative_code_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)) + ((dst_negative_scale_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)))) * S ((((dst_positive_code_fubini_exists_columnssource_table) + (dst_positive_scale_fubini_exists_columnssource_table)) * S ((dst_positive_code_fubini_exists_columnssource_table) + (dst_positive_scale_fubini_exists_columnssource_table)) + ((dst_positive_scale_fubini_exists_columnssource_table) + (dst_positive_scale_fubini_exists_columnssource_table))) + (((dst_negative_code_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)) * S ((dst_negative_code_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)) + ((dst_negative_scale_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)))) + ((((dst_negative_code_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)) * S ((dst_negative_code_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)) + ((dst_negative_scale_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table))) + (((dst_negative_code_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)) * S ((dst_negative_code_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)) + ((dst_negative_scale_fubini_exists_columnssource_table) + (dst_negative_scale_fubini_exists_columnssource_table)))))) /\ (forall dst_index_fubini_exists_columnssource_table. (exists pvs_le_gap_fubini_exists_columnssource_tabledomain. pvs_le_gap_fubini_exists_columnssource_tabledomain + (dst_index_fubini_exists_columnssource_table) = (0)) -> exists dst_positive_fubini_exists_columnssource_table dst_negative_fubini_exists_columnssource_table dst_value_fubini_exists_columnssource_table. ((((exists ff_h_pvs_fubini_exists_columnssource_tableentrypositive. ff_h_pvs_fubini_exists_columnssource_tableentrypositive + S (dst_positive_fubini_exists_columnssource_table) = S ((S (dst_index_fubini_exists_columnssource_table)) * dst_positive_scale_fubini_exists_columnssource_table)) /\ exists ff_q_pvs_fubini_exists_columnssource_tableentrypositive. dst_positive_code_fubini_exists_columnssource_table = ff_q_pvs_fubini_exists_columnssource_tableentrypositive * S ((S (dst_index_fubini_exists_columnssource_table)) * dst_positive_scale_fubini_exists_columnssource_table) + (dst_positive_fubini_exists_columnssource_table))) /\ (((((exists ff_h_pvs_fubini_exists_columnssource_tableentrynegative. ff_h_pvs_fubini_exists_columnssource_tableentrynegative + S (dst_negative_fubini_exists_columnssource_table) = S ((S (dst_index_fubini_exists_columnssource_table)) * dst_negative_scale_fubini_exists_columnssource_table)) /\ exists ff_q_pvs_fubini_exists_columnssource_tableentrynegative. dst_negative_code_fubini_exists_columnssource_table = ff_q_pvs_fubini_exists_columnssource_tableentrynegative * S ((S (dst_index_fubini_exists_columnssource_table)) * dst_negative_scale_fubini_exists_columnssource_table) + (dst_negative_fubini_exists_columnssource_table))) /\ (exists ge_balance_positive_fubini_exists_columnssource_tableentryvalue ge_balance_negative_fubini_exists_columnssource_tableentryvalue. (((((dst_value_fubini_exists_columnssource_table) = 2 * (ge_balance_positive_fubini_exists_columnssource_tableentryvalue) /\ (ge_balance_negative_fubini_exists_columnssource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_columnssource_tableentryvaluedecode. (((dst_value_fubini_exists_columnssource_table) = 2 * ge_signed_half_fubini_exists_columnssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_columnssource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_columnssource_tableentryvalue) = S ge_signed_half_fubini_exists_columnssource_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_columnssource_table) + ge_balance_negative_fubini_exists_columnssource_tableentryvalue = (dst_negative_fubini_exists_columnssource_table) + ge_balance_positive_fubini_exists_columnssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_exists_columnsrow_table dst_positive_scale_fubini_exists_columnsrow_table dst_negative_code_fubini_exists_columnsrow_table dst_negative_scale_fubini_exists_columnsrow_table. (((C) = (((((dst_positive_code_fubini_exists_columnsrow_table) + (dst_positive_scale_fubini_exists_columnsrow_table)) * S ((dst_positive_code_fubini_exists_columnsrow_table) + (dst_positive_scale_fubini_exists_columnsrow_table)) + ((dst_positive_scale_fubini_exists_columnsrow_table) + (dst_positive_scale_fubini_exists_columnsrow_table))) + (((dst_negative_code_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)) * S ((dst_negative_code_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)) + ((dst_negative_scale_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)))) * S ((((dst_positive_code_fubini_exists_columnsrow_table) + (dst_positive_scale_fubini_exists_columnsrow_table)) * S ((dst_positive_code_fubini_exists_columnsrow_table) + (dst_positive_scale_fubini_exists_columnsrow_table)) + ((dst_positive_scale_fubini_exists_columnsrow_table) + (dst_positive_scale_fubini_exists_columnsrow_table))) + (((dst_negative_code_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)) * S ((dst_negative_code_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)) + ((dst_negative_scale_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)))) + ((((dst_negative_code_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)) * S ((dst_negative_code_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)) + ((dst_negative_scale_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table))) + (((dst_negative_code_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)) * S ((dst_negative_code_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)) + ((dst_negative_scale_fubini_exists_columnsrow_table) + (dst_negative_scale_fubini_exists_columnsrow_table)))))) /\ (forall dst_index_fubini_exists_columnsrow_table. (exists pvs_le_gap_fubini_exists_columnsrow_tabledomain. pvs_le_gap_fubini_exists_columnsrow_tabledomain + (dst_index_fubini_exists_columnsrow_table) = (n)) -> exists dst_positive_fubini_exists_columnsrow_table dst_negative_fubini_exists_columnsrow_table dst_value_fubini_exists_columnsrow_table. ((((exists ff_h_pvs_fubini_exists_columnsrow_tableentrypositive. ff_h_pvs_fubini_exists_columnsrow_tableentrypositive + S (dst_positive_fubini_exists_columnsrow_table) = S ((S (dst_index_fubini_exists_columnsrow_table)) * dst_positive_scale_fubini_exists_columnsrow_table)) /\ exists ff_q_pvs_fubini_exists_columnsrow_tableentrypositive. dst_positive_code_fubini_exists_columnsrow_table = ff_q_pvs_fubini_exists_columnsrow_tableentrypositive * S ((S (dst_index_fubini_exists_columnsrow_table)) * dst_positive_scale_fubini_exists_columnsrow_table) + (dst_positive_fubini_exists_columnsrow_table))) /\ (((((exists ff_h_pvs_fubini_exists_columnsrow_tableentrynegative. ff_h_pvs_fubini_exists_columnsrow_tableentrynegative + S (dst_negative_fubini_exists_columnsrow_table) = S ((S (dst_index_fubini_exists_columnsrow_table)) * dst_negative_scale_fubini_exists_columnsrow_table)) /\ exists ff_q_pvs_fubini_exists_columnsrow_tableentrynegative. dst_negative_code_fubini_exists_columnsrow_table = ff_q_pvs_fubini_exists_columnsrow_tableentrynegative * S ((S (dst_index_fubini_exists_columnsrow_table)) * dst_negative_scale_fubini_exists_columnsrow_table) + (dst_negative_fubini_exists_columnsrow_table))) /\ (exists ge_balance_positive_fubini_exists_columnsrow_tableentryvalue ge_balance_negative_fubini_exists_columnsrow_tableentryvalue. (((((dst_value_fubini_exists_columnsrow_table) = 2 * (ge_balance_positive_fubini_exists_columnsrow_tableentryvalue) /\ (ge_balance_negative_fubini_exists_columnsrow_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_columnsrow_tableentryvaluedecode. (((dst_value_fubini_exists_columnsrow_table) = 2 * ge_signed_half_fubini_exists_columnsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_columnsrow_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_columnsrow_tableentryvalue) = S ge_signed_half_fubini_exists_columnsrow_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_columnsrow_table) + ge_balance_negative_fubini_exists_columnsrow_tableentryvalue = (dst_negative_fubini_exists_columnsrow_table) + ge_balance_positive_fubini_exists_columnsrow_tableentryvalue))))))))) /\ (forall srt_index_fubini_exists_columns. (exists pvs_gap_fubini_exists_columnsbound. pvs_gap_fubini_exists_columnsbound + S (srt_index_fubini_exists_columns) = (n)) -> exists srt_value_fubini_exists_columns. (((exists dst_positive_code_fubini_exists_columnsrowentry dst_positive_scale_fubini_exists_columnsrowentry dst_negative_code_fubini_exists_columnsrowentry dst_negative_scale_fubini_exists_columnsrowentry dst_positive_fubini_exists_columnsrowentry dst_negative_fubini_exists_columnsrowentry. (((C) = (((((dst_positive_code_fubini_exists_columnsrowentry) + (dst_positive_scale_fubini_exists_columnsrowentry)) * S ((dst_positive_code_fubini_exists_columnsrowentry) + (dst_positive_scale_fubini_exists_columnsrowentry)) + ((dst_positive_scale_fubini_exists_columnsrowentry) + (dst_positive_scale_fubini_exists_columnsrowentry))) + (((dst_negative_code_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)) * S ((dst_negative_code_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)) + ((dst_negative_scale_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)))) * S ((((dst_positive_code_fubini_exists_columnsrowentry) + (dst_positive_scale_fubini_exists_columnsrowentry)) * S ((dst_positive_code_fubini_exists_columnsrowentry) + (dst_positive_scale_fubini_exists_columnsrowentry)) + ((dst_positive_scale_fubini_exists_columnsrowentry) + (dst_positive_scale_fubini_exists_columnsrowentry))) + (((dst_negative_code_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)) * S ((dst_negative_code_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)) + ((dst_negative_scale_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)))) + ((((dst_negative_code_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)) * S ((dst_negative_code_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)) + ((dst_negative_scale_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry))) + (((dst_negative_code_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)) * S ((dst_negative_code_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)) + ((dst_negative_scale_fubini_exists_columnsrowentry) + (dst_negative_scale_fubini_exists_columnsrowentry)))))) /\ (((((exists ff_h_pvs_fubini_exists_columnsrowentrypositive. ff_h_pvs_fubini_exists_columnsrowentrypositive + S (dst_positive_fubini_exists_columnsrowentry) = S ((S (srt_index_fubini_exists_columns)) * dst_positive_scale_fubini_exists_columnsrowentry)) /\ exists ff_q_pvs_fubini_exists_columnsrowentrypositive. dst_positive_code_fubini_exists_columnsrowentry = ff_q_pvs_fubini_exists_columnsrowentrypositive * S ((S (srt_index_fubini_exists_columns)) * dst_positive_scale_fubini_exists_columnsrowentry) + (dst_positive_fubini_exists_columnsrowentry))) /\ (((((exists ff_h_pvs_fubini_exists_columnsrowentrynegative. ff_h_pvs_fubini_exists_columnsrowentrynegative + S (dst_negative_fubini_exists_columnsrowentry) = S ((S (srt_index_fubini_exists_columns)) * dst_negative_scale_fubini_exists_columnsrowentry)) /\ exists ff_q_pvs_fubini_exists_columnsrowentrynegative. dst_negative_code_fubini_exists_columnsrowentry = ff_q_pvs_fubini_exists_columnsrowentrynegative * S ((S (srt_index_fubini_exists_columns)) * dst_negative_scale_fubini_exists_columnsrowentry) + (dst_negative_fubini_exists_columnsrowentry))) /\ (exists ge_balance_positive_fubini_exists_columnsrowentryvalue ge_balance_negative_fubini_exists_columnsrowentryvalue. (((((srt_value_fubini_exists_columns) = 2 * (ge_balance_positive_fubini_exists_columnsrowentryvalue) /\ (ge_balance_negative_fubini_exists_columnsrowentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_columnsrowentryvaluedecode. (((srt_value_fubini_exists_columns) = 2 * ge_signed_half_fubini_exists_columnsrowentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_columnsrowentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_columnsrowentryvalue) = S ge_signed_half_fubini_exists_columnsrowentryvaluedecode))) /\ ((dst_positive_fubini_exists_columnsrowentry) + ge_balance_negative_fubini_exists_columnsrowentryvalue = (dst_negative_fubini_exists_columnsrowentry) + ge_balance_positive_fubini_exists_columnsrowentryvalue))))))))) /\ (exists srs_slice_fubini_exists_columnsrowrow_sum. ((((exists dst_positive_code_fubini_exists_columnsrowrow_sumslicesource_table dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)))) + ((((dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)))))) /\ (forall dst_index_fubini_exists_columnsrowrow_sumslicesource_table. (exists pvs_le_gap_fubini_exists_columnsrowrow_sumslicesource_tabledomain. pvs_le_gap_fubini_exists_columnsrowrow_sumslicesource_tabledomain + (dst_index_fubini_exists_columnsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_fubini_exists_columnsrowrow_sumslicesource_table dst_negative_fubini_exists_columnsrowrow_sumslicesource_table dst_value_fubini_exists_columnsrowrow_sumslicesource_table. ((((exists ff_h_pvs_fubini_exists_columnsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_fubini_exists_columnsrowrow_sumslicesource_tableentrypositive + S (dst_positive_fubini_exists_columnsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_exists_columnsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_exists_columnsrowrow_sumslicesource_tableentrypositive. dst_positive_code_fubini_exists_columnsrowrow_sumslicesource_table = ff_q_pvs_fubini_exists_columnsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_fubini_exists_columnsrowrow_sumslicesource_table)) * dst_positive_scale_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_positive_fubini_exists_columnsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_fubini_exists_columnsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_fubini_exists_columnsrowrow_sumslicesource_tableentrynegative + S (dst_negative_fubini_exists_columnsrowrow_sumslicesource_table) = S ((S (dst_index_fubini_exists_columnsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_fubini_exists_columnsrowrow_sumslicesource_tableentrynegative. dst_negative_code_fubini_exists_columnsrowrow_sumslicesource_table = ff_q_pvs_fubini_exists_columnsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_fubini_exists_columnsrowrow_sumslicesource_table)) * dst_negative_scale_fubini_exists_columnsrowrow_sumslicesource_table) + (dst_negative_fubini_exists_columnsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_fubini_exists_columnsrowrow_sumslicesource_tableentryvalue ge_balance_negative_fubini_exists_columnsrowrow_sumslicesource_tableentryvalue. (((((dst_value_fubini_exists_columnsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_fubini_exists_columnsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_columnsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_fubini_exists_columnsrowrow_sumslicesource_table) = 2 * ge_signed_half_fubini_exists_columnsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_columnsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_fubini_exists_columnsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_columnsrowrow_sumslicesource_table) + ge_balance_negative_fubini_exists_columnsrowrow_sumslicesource_tableentryvalue = (dst_negative_fubini_exists_columnsrowrow_sumslicesource_table) + ge_balance_positive_fubini_exists_columnsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_fubini_exists_columnsrowrow_sumsliceoutput_table dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table. (((srs_slice_fubini_exists_columnsrowrow_sum) = (((((dst_positive_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_fubini_exists_columnsrowrow_sumsliceoutput_table. (exists pvs_le_gap_fubini_exists_columnsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_fubini_exists_columnsrowrow_sumsliceoutput_tabledomain + (dst_index_fubini_exists_columnsrowrow_sumsliceoutput_table) = (m)) -> exists dst_positive_fubini_exists_columnsrowrow_sumsliceoutput_table dst_negative_fubini_exists_columnsrowrow_sumsliceoutput_table dst_value_fubini_exists_columnsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_fubini_exists_columnsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_fubini_exists_columnsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_fubini_exists_columnsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_exists_columnsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_exists_columnsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_fubini_exists_columnsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_exists_columnsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_fubini_exists_columnsrowrow_sumsliceoutput_table)) * dst_positive_scale_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_positive_fubini_exists_columnsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_fubini_exists_columnsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_fubini_exists_columnsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_fubini_exists_columnsrowrow_sumsliceoutput_table) = S ((S (dst_index_fubini_exists_columnsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_fubini_exists_columnsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_fubini_exists_columnsrowrow_sumsliceoutput_table = ff_q_pvs_fubini_exists_columnsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_fubini_exists_columnsrowrow_sumsliceoutput_table)) * dst_negative_scale_fubini_exists_columnsrowrow_sumsliceoutput_table) + (dst_negative_fubini_exists_columnsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_fubini_exists_columnsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_fubini_exists_columnsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_fubini_exists_columnsrowrow_sumsliceoutput_table) + ge_balance_negative_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_fubini_exists_columnsrowrow_sumsliceoutput_table) + ge_balance_positive_fubini_exists_columnsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_fubini_exists_columnsrowrow_sumslice. (exists pvs_gap_fubini_exists_columnsrowrow_sumslicebound. pvs_gap_fubini_exists_columnsrowrow_sumslicebound + S (srs_index_fubini_exists_columnsrowrow_sumslice) = (m)) -> exists srs_value_fubini_exists_columnsrowrow_sumslice. (((exists dst_positive_code_fubini_exists_columnsrowrow_sumsliceentrysource dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource dst_positive_fubini_exists_columnsrowrow_sumsliceentrysource dst_negative_fubini_exists_columnsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_fubini_exists_columnsrowrow_sumsliceentrysourcepositive. ff_h_pvs_fubini_exists_columnsrowrow_sumsliceentrysourcepositive + S (dst_positive_fubini_exists_columnsrowrow_sumsliceentrysource) = S ((S (((((o) + ((t) * (srt_index_fubini_exists_columns)))) + ((s) * (srs_index_fubini_exists_columnsrowrow_sumslice))))) * dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_exists_columnsrowrow_sumsliceentrysourcepositive. dst_positive_code_fubini_exists_columnsrowrow_sumsliceentrysource = ff_q_pvs_fubini_exists_columnsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((t) * (srt_index_fubini_exists_columns)))) + ((s) * (srs_index_fubini_exists_columnsrowrow_sumslice))))) * dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_positive_fubini_exists_columnsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_fubini_exists_columnsrowrow_sumsliceentrysourcenegative. ff_h_pvs_fubini_exists_columnsrowrow_sumsliceentrysourcenegative + S (dst_negative_fubini_exists_columnsrowrow_sumsliceentrysource) = S ((S (((((o) + ((t) * (srt_index_fubini_exists_columns)))) + ((s) * (srs_index_fubini_exists_columnsrowrow_sumslice))))) * dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_fubini_exists_columnsrowrow_sumsliceentrysourcenegative. dst_negative_code_fubini_exists_columnsrowrow_sumsliceentrysource = ff_q_pvs_fubini_exists_columnsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((t) * (srt_index_fubini_exists_columns)))) + ((s) * (srs_index_fubini_exists_columnsrowrow_sumslice))))) * dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentrysource) + (dst_negative_fubini_exists_columnsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_fubini_exists_columnsrowrow_sumsliceentrysourcevalue ge_balance_negative_fubini_exists_columnsrowrow_sumsliceentrysourcevalue. (((((srs_value_fubini_exists_columnsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_exists_columnsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_fubini_exists_columnsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_fubini_exists_columnsrowrow_sumslice) = 2 * ge_signed_half_fubini_exists_columnsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_fubini_exists_columnsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_fubini_exists_columnsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_fubini_exists_columnsrowrow_sumsliceentrysource) + ge_balance_negative_fubini_exists_columnsrowrow_sumsliceentrysourcevalue = (dst_negative_fubini_exists_columnsrowrow_sumsliceentrysource) + ge_balance_positive_fubini_exists_columnsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_fubini_exists_columnsrowrow_sumsliceentryoutput dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput dst_positive_fubini_exists_columnsrowrow_sumsliceentryoutput dst_negative_fubini_exists_columnsrowrow_sumsliceentryoutput. (((srs_slice_fubini_exists_columnsrowrow_sum) = (((((dst_positive_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_fubini_exists_columnsrowrow_sumsliceentryoutputpositive. ff_h_pvs_fubini_exists_columnsrowrow_sumsliceentryoutputpositive + S (dst_positive_fubini_exists_columnsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_exists_columnsrowrow_sumslice)) * dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_exists_columnsrowrow_sumsliceentryoutputpositive. dst_positive_code_fubini_exists_columnsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_exists_columnsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_fubini_exists_columnsrowrow_sumslice)) * dst_positive_scale_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_positive_fubini_exists_columnsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_fubini_exists_columnsrowrow_sumsliceentryoutputnegative. ff_h_pvs_fubini_exists_columnsrowrow_sumsliceentryoutputnegative + S (dst_negative_fubini_exists_columnsrowrow_sumsliceentryoutput) = S ((S (srs_index_fubini_exists_columnsrowrow_sumslice)) * dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_fubini_exists_columnsrowrow_sumsliceentryoutputnegative. dst_negative_code_fubini_exists_columnsrowrow_sumsliceentryoutput = ff_q_pvs_fubini_exists_columnsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_fubini_exists_columnsrowrow_sumslice)) * dst_negative_scale_fubini_exists_columnsrowrow_sumsliceentryoutput) + (dst_negative_fubini_exists_columnsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_fubini_exists_columnsrowrow_sumsliceentryoutputvalue ge_balance_negative_fubini_exists_columnsrowrow_sumsliceentryoutputvalue. (((((srs_value_fubini_exists_columnsrowrow_sumslice) = 2 * (ge_balance_positive_fubini_exists_columnsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_fubini_exists_columnsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_fubini_exists_columnsrowrow_sumslice) = 2 * ge_signed_half_fubini_exists_columnsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_fubini_exists_columnsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_fubini_exists_columnsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_fubini_exists_columnsrowrow_sumsliceentryoutput) + ge_balance_negative_fubini_exists_columnsrowrow_sumsliceentryoutputvalue = (dst_negative_fubini_exists_columnsrowrow_sumsliceentryoutput) + ge_balance_positive_fubini_exists_columnsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_fubini_exists_columnsrowrow_sumsum dst_positive_scale_fubini_exists_columnsrowrow_sumsum dst_negative_code_fubini_exists_columnsrowrow_sumsum dst_negative_scale_fubini_exists_columnsrowrow_sumsum dst_positive_sum_fubini_exists_columnsrowrow_sumsum dst_negative_sum_fubini_exists_columnsrowrow_sumsum. (((srs_slice_fubini_exists_columnsrowrow_sum) = (((((dst_positive_code_fubini_exists_columnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsum)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsum)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)))) * S ((((dst_positive_code_fubini_exists_columnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsum)) * S ((dst_positive_code_fubini_exists_columnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsum)) + ((dst_positive_scale_fubini_exists_columnsrowrow_sumsum) + (dst_positive_scale_fubini_exists_columnsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)))) + ((((dst_negative_code_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum))) + (((dst_negative_code_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)) * S ((dst_negative_code_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)) + ((dst_negative_scale_fubini_exists_columnsrowrow_sumsum) + (dst_negative_scale_fubini_exists_columnsrowrow_sumsum)))))) /\ (((exists fs_u_dst_fubini_exists_columnsrowrow_sumsumpositive fs_v_dst_fubini_exists_columnsrowrow_sumsumpositive. ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_start. fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_start. fs_u_dst_fubini_exists_columnsrowrow_sumsumpositive = fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_terminal. fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_fubini_exists_columnsrowrow_sumsum) = S ((S (m)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_terminal. fs_u_dst_fubini_exists_columnsrowrow_sumsumpositive = fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_terminal * S ((S (m)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumpositive) + (dst_positive_sum_fubini_exists_columnsrowrow_sumsum))) /\ forall fs_i_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps = m) -> exists fs_a_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps fs_r_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps fs_s_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_exists_columnsrowrow_sumsum)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_fubini_exists_columnsrowrow_sumsum = fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_fubini_exists_columnsrowrow_sumsum) + (fs_a_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_fubini_exists_columnsrowrow_sumsumpositive = fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumpositive) + (fs_r_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumpositive)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_fubini_exists_columnsrowrow_sumsumpositive = fs_q_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumpositive) + (fs_s_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps = fs_r_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps + fs_a_dst_fubini_exists_columnsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_exists_columnsrowrow_sumsumnegative fs_v_dst_fubini_exists_columnsrowrow_sumsumnegative. ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_start. fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_start. fs_u_dst_fubini_exists_columnsrowrow_sumsumnegative = fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_terminal. fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_fubini_exists_columnsrowrow_sumsum) = S ((S (m)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_terminal. fs_u_dst_fubini_exists_columnsrowrow_sumsumnegative = fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_terminal * S ((S (m)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumnegative) + (dst_negative_sum_fubini_exists_columnsrowrow_sumsum))) /\ forall fs_i_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps = m) -> exists fs_a_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps fs_r_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps fs_s_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_exists_columnsrowrow_sumsum)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_fubini_exists_columnsrowrow_sumsum = fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_fubini_exists_columnsrowrow_sumsum) + (fs_a_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_fubini_exists_columnsrowrow_sumsumnegative = fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumnegative) + (fs_r_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumnegative)) /\ exists fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_fubini_exists_columnsrowrow_sumsumnegative = fs_q_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_fubini_exists_columnsrowrow_sumsumnegative) + (fs_s_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps = fs_r_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps + fs_a_dst_fubini_exists_columnsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_exists_columnsrowrow_sumsumresult ge_balance_negative_fubini_exists_columnsrowrow_sumsumresult. (((((srt_value_fubini_exists_columns) = 2 * (ge_balance_positive_fubini_exists_columnsrowrow_sumsumresult) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_fubini_exists_columnsrowrow_sumsumresultdecode. (((srt_value_fubini_exists_columns) = 2 * ge_signed_half_fubini_exists_columnsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_fubini_exists_columnsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_fubini_exists_columnsrowrow_sumsumresult) = S ge_signed_half_fubini_exists_columnsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_fubini_exists_columnsrowrow_sumsum) + ge_balance_negative_fubini_exists_columnsrowrow_sumsumresult = (dst_negative_sum_fubini_exists_columnsrowrow_sumsum) + ge_balance_positive_fubini_exists_columnsrowrow_sumsumresult)))))))))))))))))) - 0028
specialize signed_rectangular_row_sums_exists (n) - 0029
specialize signed_rectangular_row_sums_exists (F) - 0030
specialize signed_rectangular_row_sums_exists (o) - 0031
specialize signed_rectangular_row_sums_exists (t) - 0032
specialize signed_rectangular_row_sums_exists (s) - 0033
specialize signed_rectangular_row_sums_exists (m) - 0034
apply signed_rectangular_row_sums_exists - 0035
exact hF - 0036
cases hC - 0037
have hw : exists w. (exists dst_positive_code_fubini_exists_column_sum dst_positive_scale_fubini_exists_column_sum dst_negative_code_fubini_exists_column_sum dst_negative_scale_fubini_exists_column_sum dst_positive_sum_fubini_exists_column_sum dst_negative_sum_fubini_exists_column_sum. (((x2) = (((((dst_positive_code_fubini_exists_column_sum) + (dst_positive_scale_fubini_exists_column_sum)) * S ((dst_positive_code_fubini_exists_column_sum) + (dst_positive_scale_fubini_exists_column_sum)) + ((dst_positive_scale_fubini_exists_column_sum) + (dst_positive_scale_fubini_exists_column_sum))) + (((dst_negative_code_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)) * S ((dst_negative_code_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)) + ((dst_negative_scale_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)))) * S ((((dst_positive_code_fubini_exists_column_sum) + (dst_positive_scale_fubini_exists_column_sum)) * S ((dst_positive_code_fubini_exists_column_sum) + (dst_positive_scale_fubini_exists_column_sum)) + ((dst_positive_scale_fubini_exists_column_sum) + (dst_positive_scale_fubini_exists_column_sum))) + (((dst_negative_code_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)) * S ((dst_negative_code_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)) + ((dst_negative_scale_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)))) + ((((dst_negative_code_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)) * S ((dst_negative_code_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)) + ((dst_negative_scale_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum))) + (((dst_negative_code_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)) * S ((dst_negative_code_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)) + ((dst_negative_scale_fubini_exists_column_sum) + (dst_negative_scale_fubini_exists_column_sum)))))) /\ (((exists fs_u_dst_fubini_exists_column_sumpositive fs_v_dst_fubini_exists_column_sumpositive. ((((exists fs_h_dst_fubini_exists_column_sumpositive_body_start. fs_h_dst_fubini_exists_column_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_column_sumpositive)) /\ exists fs_q_dst_fubini_exists_column_sumpositive_body_start. fs_u_dst_fubini_exists_column_sumpositive = fs_q_dst_fubini_exists_column_sumpositive_body_start * S ((S (0)) * fs_v_dst_fubini_exists_column_sumpositive) + (0))) /\ ((((exists fs_h_dst_fubini_exists_column_sumpositive_body_terminal. fs_h_dst_fubini_exists_column_sumpositive_body_terminal + S (dst_positive_sum_fubini_exists_column_sum) = S ((S (n)) * fs_v_dst_fubini_exists_column_sumpositive)) /\ exists fs_q_dst_fubini_exists_column_sumpositive_body_terminal. fs_u_dst_fubini_exists_column_sumpositive = fs_q_dst_fubini_exists_column_sumpositive_body_terminal * S ((S (n)) * fs_v_dst_fubini_exists_column_sumpositive) + (dst_positive_sum_fubini_exists_column_sum))) /\ forall fs_i_dst_fubini_exists_column_sumpositive_body_steps. (exists fs_lt_dst_fubini_exists_column_sumpositive_body_steps_bound. fs_lt_dst_fubini_exists_column_sumpositive_body_steps_bound + S fs_i_dst_fubini_exists_column_sumpositive_body_steps = n) -> exists fs_a_dst_fubini_exists_column_sumpositive_body_steps fs_r_dst_fubini_exists_column_sumpositive_body_steps fs_s_dst_fubini_exists_column_sumpositive_body_steps. ((((exists fs_h_dst_fubini_exists_column_sumpositive_body_steps_summand. fs_h_dst_fubini_exists_column_sumpositive_body_steps_summand + S (fs_a_dst_fubini_exists_column_sumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_column_sumpositive_body_steps)) * dst_positive_scale_fubini_exists_column_sum)) /\ exists fs_q_dst_fubini_exists_column_sumpositive_body_steps_summand. dst_positive_code_fubini_exists_column_sum = fs_q_dst_fubini_exists_column_sumpositive_body_steps_summand * S ((S (fs_i_dst_fubini_exists_column_sumpositive_body_steps)) * dst_positive_scale_fubini_exists_column_sum) + (fs_a_dst_fubini_exists_column_sumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_column_sumpositive_body_steps_partial. fs_h_dst_fubini_exists_column_sumpositive_body_steps_partial + S (fs_r_dst_fubini_exists_column_sumpositive_body_steps) = S ((S (fs_i_dst_fubini_exists_column_sumpositive_body_steps)) * fs_v_dst_fubini_exists_column_sumpositive)) /\ exists fs_q_dst_fubini_exists_column_sumpositive_body_steps_partial. fs_u_dst_fubini_exists_column_sumpositive = fs_q_dst_fubini_exists_column_sumpositive_body_steps_partial * S ((S (fs_i_dst_fubini_exists_column_sumpositive_body_steps)) * fs_v_dst_fubini_exists_column_sumpositive) + (fs_r_dst_fubini_exists_column_sumpositive_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_column_sumpositive_body_steps_successor. fs_h_dst_fubini_exists_column_sumpositive_body_steps_successor + S (fs_s_dst_fubini_exists_column_sumpositive_body_steps) = S ((S (S fs_i_dst_fubini_exists_column_sumpositive_body_steps)) * fs_v_dst_fubini_exists_column_sumpositive)) /\ exists fs_q_dst_fubini_exists_column_sumpositive_body_steps_successor. fs_u_dst_fubini_exists_column_sumpositive = fs_q_dst_fubini_exists_column_sumpositive_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_column_sumpositive_body_steps)) * fs_v_dst_fubini_exists_column_sumpositive) + (fs_s_dst_fubini_exists_column_sumpositive_body_steps))) /\ fs_s_dst_fubini_exists_column_sumpositive_body_steps = fs_r_dst_fubini_exists_column_sumpositive_body_steps + fs_a_dst_fubini_exists_column_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_fubini_exists_column_sumnegative fs_v_dst_fubini_exists_column_sumnegative. ((((exists fs_h_dst_fubini_exists_column_sumnegative_body_start. fs_h_dst_fubini_exists_column_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_fubini_exists_column_sumnegative)) /\ exists fs_q_dst_fubini_exists_column_sumnegative_body_start. fs_u_dst_fubini_exists_column_sumnegative = fs_q_dst_fubini_exists_column_sumnegative_body_start * S ((S (0)) * fs_v_dst_fubini_exists_column_sumnegative) + (0))) /\ ((((exists fs_h_dst_fubini_exists_column_sumnegative_body_terminal. fs_h_dst_fubini_exists_column_sumnegative_body_terminal + S (dst_negative_sum_fubini_exists_column_sum) = S ((S (n)) * fs_v_dst_fubini_exists_column_sumnegative)) /\ exists fs_q_dst_fubini_exists_column_sumnegative_body_terminal. fs_u_dst_fubini_exists_column_sumnegative = fs_q_dst_fubini_exists_column_sumnegative_body_terminal * S ((S (n)) * fs_v_dst_fubini_exists_column_sumnegative) + (dst_negative_sum_fubini_exists_column_sum))) /\ forall fs_i_dst_fubini_exists_column_sumnegative_body_steps. (exists fs_lt_dst_fubini_exists_column_sumnegative_body_steps_bound. fs_lt_dst_fubini_exists_column_sumnegative_body_steps_bound + S fs_i_dst_fubini_exists_column_sumnegative_body_steps = n) -> exists fs_a_dst_fubini_exists_column_sumnegative_body_steps fs_r_dst_fubini_exists_column_sumnegative_body_steps fs_s_dst_fubini_exists_column_sumnegative_body_steps. ((((exists fs_h_dst_fubini_exists_column_sumnegative_body_steps_summand. fs_h_dst_fubini_exists_column_sumnegative_body_steps_summand + S (fs_a_dst_fubini_exists_column_sumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_column_sumnegative_body_steps)) * dst_negative_scale_fubini_exists_column_sum)) /\ exists fs_q_dst_fubini_exists_column_sumnegative_body_steps_summand. dst_negative_code_fubini_exists_column_sum = fs_q_dst_fubini_exists_column_sumnegative_body_steps_summand * S ((S (fs_i_dst_fubini_exists_column_sumnegative_body_steps)) * dst_negative_scale_fubini_exists_column_sum) + (fs_a_dst_fubini_exists_column_sumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_column_sumnegative_body_steps_partial. fs_h_dst_fubini_exists_column_sumnegative_body_steps_partial + S (fs_r_dst_fubini_exists_column_sumnegative_body_steps) = S ((S (fs_i_dst_fubini_exists_column_sumnegative_body_steps)) * fs_v_dst_fubini_exists_column_sumnegative)) /\ exists fs_q_dst_fubini_exists_column_sumnegative_body_steps_partial. fs_u_dst_fubini_exists_column_sumnegative = fs_q_dst_fubini_exists_column_sumnegative_body_steps_partial * S ((S (fs_i_dst_fubini_exists_column_sumnegative_body_steps)) * fs_v_dst_fubini_exists_column_sumnegative) + (fs_r_dst_fubini_exists_column_sumnegative_body_steps))) /\ ((((exists fs_h_dst_fubini_exists_column_sumnegative_body_steps_successor. fs_h_dst_fubini_exists_column_sumnegative_body_steps_successor + S (fs_s_dst_fubini_exists_column_sumnegative_body_steps) = S ((S (S fs_i_dst_fubini_exists_column_sumnegative_body_steps)) * fs_v_dst_fubini_exists_column_sumnegative)) /\ exists fs_q_dst_fubini_exists_column_sumnegative_body_steps_successor. fs_u_dst_fubini_exists_column_sumnegative = fs_q_dst_fubini_exists_column_sumnegative_body_steps_successor * S ((S (S fs_i_dst_fubini_exists_column_sumnegative_body_steps)) * fs_v_dst_fubini_exists_column_sumnegative) + (fs_s_dst_fubini_exists_column_sumnegative_body_steps))) /\ fs_s_dst_fubini_exists_column_sumnegative_body_steps = fs_r_dst_fubini_exists_column_sumnegative_body_steps + fs_a_dst_fubini_exists_column_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_fubini_exists_column_sumresult ge_balance_negative_fubini_exists_column_sumresult. (((((w) = 2 * (ge_balance_positive_fubini_exists_column_sumresult) /\ (ge_balance_negative_fubini_exists_column_sumresult) = 0) \/ exists ge_signed_half_fubini_exists_column_sumresultdecode. (((w) = 2 * ge_signed_half_fubini_exists_column_sumresultdecode + 1 /\ (ge_balance_positive_fubini_exists_column_sumresult) = 0) /\ (ge_balance_negative_fubini_exists_column_sumresult) = S ge_signed_half_fubini_exists_column_sumresultdecode))) /\ ((dst_positive_sum_fubini_exists_column_sum) + ge_balance_negative_fubini_exists_column_sumresult = (dst_negative_sum_fubini_exists_column_sum) + ge_balance_positive_fubini_exists_column_sumresult))))))))) - 0038
specialize arithmetic_signed_sum_exists (n) - 0039
specialize arithmetic_signed_sum_exists (x2) - 0040
specialize arithmetic_signed_sum_exists (n) - 0041
apply arithmetic_signed_sum_exists - 0042
cases hC_witness - 0043
cases hC_witness_right - 0044
exact hC_witness_right_left - 0045
cases hw - 0046
have heq : x3 = x1 - 0047
symm - 0048
specialize signed_rectangular_fubini (m) - 0049
specialize signed_rectangular_fubini (F) - 0050
specialize signed_rectangular_fubini (o) - 0051
specialize signed_rectangular_fubini (s) - 0052
specialize signed_rectangular_fubini (t) - 0053
specialize signed_rectangular_fubini (n) - 0054
specialize signed_rectangular_fubini (x1) - 0055
specialize signed_rectangular_fubini (x3) - 0056
apply signed_rectangular_fubini - 0057
exists x - 0058
split - 0059
exact hR_witness - 0060
exact hz_witness - 0061
exists x2 - 0062
split - 0063
exact hC_witness - 0064
exact hw_witness - 0065
rewrite heq at hw_witness - 0066
rewrite heq at hw_witness - 0067
exists x - 0068
exists x2 - 0069
exists x1 - 0070
split - 0071
exact hR_witness - 0072
split - 0073
exact hC_witness - 0074
split - 0075
exact hz_witness - 0076
exact hw_witness