RS001C

signed_rectangular_sum_zero_inner

Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

A rectangle with zero columns has actual signed total zero for every row count.

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 z. (exists srt_rows_zero_inner_input. ((((exists dst_positive_code_zero_inner_inputrowssource_table dst_positive_scale_zero_inner_inputrowssource_table dst_negative_code_zero_inner_inputrowssource_table dst_negative_scale_zero_inner_inputrowssource_table. (((F) = (((((dst_positive_code_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table)) * S ((dst_positive_code_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table)) + ((dst_positive_scale_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table))) + (((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) * S ((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) + ((dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)))) * S ((((dst_positive_code_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table)) * S ((dst_positive_code_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table)) + ((dst_positive_scale_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table))) + (((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) * S ((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) + ((dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)))) + ((((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) * S ((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) + ((dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table))) + (((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) * S ((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) + ((dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)))))) /\ (forall dst_index_zero_inner_inputrowssource_table. (exists pvs_le_gap_zero_inner_inputrowssource_tabledomain. pvs_le_gap_zero_inner_inputrowssource_tabledomain + (dst_index_zero_inner_inputrowssource_table) = (0)) -> exists dst_positive_zero_inner_inputrowssource_table dst_negative_zero_inner_inputrowssource_table dst_value_zero_inner_inputrowssource_table. ((((exists ff_h_pvs_zero_inner_inputrowssource_tableentrypositive. ff_h_pvs_zero_inner_inputrowssource_tableentrypositive + S (dst_positive_zero_inner_inputrowssource_table) = S ((S (dst_index_zero_inner_inputrowssource_table)) * dst_positive_scale_zero_inner_inputrowssource_table)) /\ exists ff_q_pvs_zero_inner_inputrowssource_tableentrypositive. dst_positive_code_zero_inner_inputrowssource_table = ff_q_pvs_zero_inner_inputrowssource_tableentrypositive * S ((S (dst_index_zero_inner_inputrowssource_table)) * dst_positive_scale_zero_inner_inputrowssource_table) + (dst_positive_zero_inner_inputrowssource_table))) /\ (((((exists ff_h_pvs_zero_inner_inputrowssource_tableentrynegative. ff_h_pvs_zero_inner_inputrowssource_tableentrynegative + S (dst_negative_zero_inner_inputrowssource_table) = S ((S (dst_index_zero_inner_inputrowssource_table)) * dst_negative_scale_zero_inner_inputrowssource_table)) /\ exists ff_q_pvs_zero_inner_inputrowssource_tableentrynegative. dst_negative_code_zero_inner_inputrowssource_table = ff_q_pvs_zero_inner_inputrowssource_tableentrynegative * S ((S (dst_index_zero_inner_inputrowssource_table)) * dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_zero_inner_inputrowssource_table))) /\ (exists ge_balance_positive_zero_inner_inputrowssource_tableentryvalue ge_balance_negative_zero_inner_inputrowssource_tableentryvalue. (((((dst_value_zero_inner_inputrowssource_table) = 2 * (ge_balance_positive_zero_inner_inputrowssource_tableentryvalue) /\ (ge_balance_negative_zero_inner_inputrowssource_tableentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowssource_tableentryvaluedecode. (((dst_value_zero_inner_inputrowssource_table) = 2 * ge_signed_half_zero_inner_inputrowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowssource_tableentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowssource_tableentryvalue) = S ge_signed_half_zero_inner_inputrowssource_tableentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowssource_table) + ge_balance_negative_zero_inner_inputrowssource_tableentryvalue = (dst_negative_zero_inner_inputrowssource_table) + ge_balance_positive_zero_inner_inputrowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_zero_inner_inputrowsrow_table dst_positive_scale_zero_inner_inputrowsrow_table dst_negative_code_zero_inner_inputrowsrow_table dst_negative_scale_zero_inner_inputrowsrow_table. (((srt_rows_zero_inner_input) = (((((dst_positive_code_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table)) * S ((dst_positive_code_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table)) + ((dst_positive_scale_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table))) + (((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) * S ((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) + ((dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)))) * S ((((dst_positive_code_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table)) * S ((dst_positive_code_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table)) + ((dst_positive_scale_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table))) + (((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) * S ((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) + ((dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)))) + ((((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) * S ((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) + ((dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table))) + (((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) * S ((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) + ((dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)))))) /\ (forall dst_index_zero_inner_inputrowsrow_table. (exists pvs_le_gap_zero_inner_inputrowsrow_tabledomain. pvs_le_gap_zero_inner_inputrowsrow_tabledomain + (dst_index_zero_inner_inputrowsrow_table) = (m)) -> exists dst_positive_zero_inner_inputrowsrow_table dst_negative_zero_inner_inputrowsrow_table dst_value_zero_inner_inputrowsrow_table. ((((exists ff_h_pvs_zero_inner_inputrowsrow_tableentrypositive. ff_h_pvs_zero_inner_inputrowsrow_tableentrypositive + S (dst_positive_zero_inner_inputrowsrow_table) = S ((S (dst_index_zero_inner_inputrowsrow_table)) * dst_positive_scale_zero_inner_inputrowsrow_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrow_tableentrypositive. dst_positive_code_zero_inner_inputrowsrow_table = ff_q_pvs_zero_inner_inputrowsrow_tableentrypositive * S ((S (dst_index_zero_inner_inputrowsrow_table)) * dst_positive_scale_zero_inner_inputrowsrow_table) + (dst_positive_zero_inner_inputrowsrow_table))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrow_tableentrynegative. ff_h_pvs_zero_inner_inputrowsrow_tableentrynegative + S (dst_negative_zero_inner_inputrowsrow_table) = S ((S (dst_index_zero_inner_inputrowsrow_table)) * dst_negative_scale_zero_inner_inputrowsrow_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrow_tableentrynegative. dst_negative_code_zero_inner_inputrowsrow_table = ff_q_pvs_zero_inner_inputrowsrow_tableentrynegative * S ((S (dst_index_zero_inner_inputrowsrow_table)) * dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_zero_inner_inputrowsrow_table))) /\ (exists ge_balance_positive_zero_inner_inputrowsrow_tableentryvalue ge_balance_negative_zero_inner_inputrowsrow_tableentryvalue. (((((dst_value_zero_inner_inputrowsrow_table) = 2 * (ge_balance_positive_zero_inner_inputrowsrow_tableentryvalue) /\ (ge_balance_negative_zero_inner_inputrowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrow_tableentryvaluedecode. (((dst_value_zero_inner_inputrowsrow_table) = 2 * ge_signed_half_zero_inner_inputrowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrow_tableentryvalue) = S ge_signed_half_zero_inner_inputrowsrow_tableentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrow_table) + ge_balance_negative_zero_inner_inputrowsrow_tableentryvalue = (dst_negative_zero_inner_inputrowsrow_table) + ge_balance_positive_zero_inner_inputrowsrow_tableentryvalue))))))))) /\ (forall srt_index_zero_inner_inputrows. (exists pvs_gap_zero_inner_inputrowsbound. pvs_gap_zero_inner_inputrowsbound + S (srt_index_zero_inner_inputrows) = (m)) -> exists srt_value_zero_inner_inputrows. (((exists dst_positive_code_zero_inner_inputrowsrowentry dst_positive_scale_zero_inner_inputrowsrowentry dst_negative_code_zero_inner_inputrowsrowentry dst_negative_scale_zero_inner_inputrowsrowentry dst_positive_zero_inner_inputrowsrowentry dst_negative_zero_inner_inputrowsrowentry. (((srt_rows_zero_inner_input) = (((((dst_positive_code_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry)) * S ((dst_positive_code_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry)) + ((dst_positive_scale_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry))) + (((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) * S ((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) + ((dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)))) * S ((((dst_positive_code_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry)) * S ((dst_positive_code_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry)) + ((dst_positive_scale_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry))) + (((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) * S ((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) + ((dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)))) + ((((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) * S ((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) + ((dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry))) + (((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) * S ((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) + ((dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)))))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowentrypositive. ff_h_pvs_zero_inner_inputrowsrowentrypositive + S (dst_positive_zero_inner_inputrowsrowentry) = S ((S (srt_index_zero_inner_inputrows)) * dst_positive_scale_zero_inner_inputrowsrowentry)) /\ exists ff_q_pvs_zero_inner_inputrowsrowentrypositive. dst_positive_code_zero_inner_inputrowsrowentry = ff_q_pvs_zero_inner_inputrowsrowentrypositive * S ((S (srt_index_zero_inner_inputrows)) * dst_positive_scale_zero_inner_inputrowsrowentry) + (dst_positive_zero_inner_inputrowsrowentry))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowentrynegative. ff_h_pvs_zero_inner_inputrowsrowentrynegative + S (dst_negative_zero_inner_inputrowsrowentry) = S ((S (srt_index_zero_inner_inputrows)) * dst_negative_scale_zero_inner_inputrowsrowentry)) /\ exists ff_q_pvs_zero_inner_inputrowsrowentrynegative. dst_negative_code_zero_inner_inputrowsrowentry = ff_q_pvs_zero_inner_inputrowsrowentrynegative * S ((S (srt_index_zero_inner_inputrows)) * dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_zero_inner_inputrowsrowentry))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowentryvalue ge_balance_negative_zero_inner_inputrowsrowentryvalue. (((((srt_value_zero_inner_inputrows) = 2 * (ge_balance_positive_zero_inner_inputrowsrowentryvalue) /\ (ge_balance_negative_zero_inner_inputrowsrowentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowentryvaluedecode. (((srt_value_zero_inner_inputrows) = 2 * ge_signed_half_zero_inner_inputrowsrowentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowentryvalue) = S ge_signed_half_zero_inner_inputrowsrowentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowentry) + ge_balance_negative_zero_inner_inputrowsrowentryvalue = (dst_negative_zero_inner_inputrowsrowentry) + ge_balance_positive_zero_inner_inputrowsrowentryvalue))))))))) /\ (exists srs_slice_zero_inner_inputrowsrowrow_sum. ((((exists dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_zero_inner_inputrowsrowrow_sumslicesource_table. (exists pvs_le_gap_zero_inner_inputrowsrowrow_sumslicesource_tabledomain. pvs_le_gap_zero_inner_inputrowsrowrow_sumslicesource_tabledomain + (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_zero_inner_inputrowsrowrow_sumslicesource_table dst_negative_zero_inner_inputrowsrowrow_sumslicesource_table dst_value_zero_inner_inputrowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_zero_inner_inputrowsrowrow_sumslicesource_table) = S ((S (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table = ff_q_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_zero_inner_inputrowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_zero_inner_inputrowsrowrow_sumslicesource_table) = S ((S (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table = ff_q_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_zero_inner_inputrowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_zero_inner_inputrowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_zero_inner_inputrowsrowrow_sumslicesource_table) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_zero_inner_inputrowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowrow_sumslicesource_table) + ge_balance_negative_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue = (dst_negative_zero_inner_inputrowsrowrow_sumslicesource_table) + ge_balance_positive_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table. (((srs_slice_zero_inner_inputrowsrowrow_sum) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_zero_inner_inputrowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_zero_inner_inputrowsrowrow_sumsliceoutput_tabledomain + (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table) = (0)) -> exists dst_positive_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_negative_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_value_zero_inner_inputrowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_zero_inner_inputrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_zero_inner_inputrowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_zero_inner_inputrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_zero_inner_inputrowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_zero_inner_inputrowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_zero_inner_inputrowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowrow_sumsliceoutput_table) + ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_zero_inner_inputrowsrowrow_sumsliceoutput_table) + ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_zero_inner_inputrowsrowrow_sumslice. (exists pvs_gap_zero_inner_inputrowsrowrow_sumslicebound. pvs_gap_zero_inner_inputrowsrowrow_sumslicebound + S (srs_index_zero_inner_inputrowsrowrow_sumslice) = (0)) -> exists srs_value_zero_inner_inputrowsrowrow_sumslice. (((exists dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource dst_positive_zero_inner_inputrowsrowrow_sumsliceentrysource dst_negative_zero_inner_inputrowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcepositive + S (dst_positive_zero_inner_inputrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_zero_inner_inputrows)))) + ((t) * (srs_index_zero_inner_inputrowsrowrow_sumslice))))) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcepositive. dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_zero_inner_inputrows)))) + ((t) * (srs_index_zero_inner_inputrowsrowrow_sumslice))))) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_zero_inner_inputrowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcenegative + S (dst_negative_zero_inner_inputrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_zero_inner_inputrows)))) + ((t) * (srs_index_zero_inner_inputrowsrowrow_sumslice))))) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcenegative. dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_zero_inner_inputrows)))) + ((t) * (srs_index_zero_inner_inputrowsrowrow_sumslice))))) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_zero_inner_inputrowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue. (((((srs_value_zero_inner_inputrowsrowrow_sumslice) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_zero_inner_inputrowsrowrow_sumslice) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowrow_sumsliceentrysource) + ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue = (dst_negative_zero_inner_inputrowsrowrow_sumsliceentrysource) + ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_positive_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_negative_zero_inner_inputrowsrowrow_sumsliceentryoutput. (((srs_slice_zero_inner_inputrowsrowrow_sum) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputpositive + S (dst_positive_zero_inner_inputrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_zero_inner_inputrowsrowrow_sumslice)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputpositive. dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_zero_inner_inputrowsrowrow_sumslice)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_zero_inner_inputrowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputnegative + S (dst_negative_zero_inner_inputrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_zero_inner_inputrowsrowrow_sumslice)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputnegative. dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_zero_inner_inputrowsrowrow_sumslice)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_zero_inner_inputrowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue. (((((srs_value_zero_inner_inputrowsrowrow_sumslice) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_zero_inner_inputrowsrowrow_sumslice) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowrow_sumsliceentryoutput) + ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue = (dst_negative_zero_inner_inputrowsrowrow_sumsliceentryoutput) + ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_zero_inner_inputrowsrowrow_sumsum dst_positive_scale_zero_inner_inputrowsrowrow_sumsum dst_negative_code_zero_inner_inputrowsrowrow_sumsum dst_negative_scale_zero_inner_inputrowsrowrow_sumsum dst_positive_sum_zero_inner_inputrowsrowrow_sumsum dst_negative_sum_zero_inner_inputrowsrowrow_sumsum. (((srs_slice_zero_inner_inputrowsrowrow_sum) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive. ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_start. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_start. fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_terminal. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_zero_inner_inputrowsrowrow_sumsum) = S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_terminal. fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_terminal * S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive) + (dst_positive_sum_zero_inner_inputrowsrowrow_sumsum))) /\ forall fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps = 0) -> exists fs_a_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps fs_r_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps fs_s_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_zero_inner_inputrowsrowrow_sumsum = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsum) + (fs_a_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive) + (fs_r_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive) + (fs_s_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps = fs_r_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps + fs_a_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative. ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_start. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_start. fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_terminal. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_zero_inner_inputrowsrowrow_sumsum) = S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_terminal. fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_terminal * S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative) + (dst_negative_sum_zero_inner_inputrowsrowrow_sumsum))) /\ forall fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps = 0) -> exists fs_a_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps fs_r_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps fs_s_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_zero_inner_inputrowsrowrow_sumsum = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (fs_a_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative) + (fs_r_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative) + (fs_s_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps = fs_r_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps + fs_a_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumsumresult ge_balance_negative_zero_inner_inputrowsrowrow_sumsumresult. (((((srt_value_zero_inner_inputrows) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumsumresult) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumsumresultdecode. (((srt_value_zero_inner_inputrows) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsumresult) = S ge_signed_half_zero_inner_inputrowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_zero_inner_inputrowsrowrow_sumsum) + ge_balance_negative_zero_inner_inputrowsrowrow_sumsumresult = (dst_negative_sum_zero_inner_inputrowsrowrow_sumsum) + ge_balance_positive_zero_inner_inputrowsrowrow_sumsumresult)))))))))))))))))) /\ (exists dst_positive_code_zero_inner_inputtotal dst_positive_scale_zero_inner_inputtotal dst_negative_code_zero_inner_inputtotal dst_negative_scale_zero_inner_inputtotal dst_positive_sum_zero_inner_inputtotal dst_negative_sum_zero_inner_inputtotal. (((srt_rows_zero_inner_input) = (((((dst_positive_code_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal)) * S ((dst_positive_code_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal)) + ((dst_positive_scale_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal))) + (((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) * S ((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) + ((dst_negative_scale_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)))) * S ((((dst_positive_code_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal)) * S ((dst_positive_code_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal)) + ((dst_positive_scale_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal))) + (((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) * S ((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) + ((dst_negative_scale_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)))) + ((((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) * S ((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) + ((dst_negative_scale_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal))) + (((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) * S ((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) + ((dst_negative_scale_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)))))) /\ (((exists fs_u_dst_zero_inner_inputtotalpositive fs_v_dst_zero_inner_inputtotalpositive. ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_start. fs_h_dst_zero_inner_inputtotalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_inner_inputtotalpositive)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_start. fs_u_dst_zero_inner_inputtotalpositive = fs_q_dst_zero_inner_inputtotalpositive_body_start * S ((S (0)) * fs_v_dst_zero_inner_inputtotalpositive) + (0))) /\ ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_terminal. fs_h_dst_zero_inner_inputtotalpositive_body_terminal + S (dst_positive_sum_zero_inner_inputtotal) = S ((S (m)) * fs_v_dst_zero_inner_inputtotalpositive)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_terminal. fs_u_dst_zero_inner_inputtotalpositive = fs_q_dst_zero_inner_inputtotalpositive_body_terminal * S ((S (m)) * fs_v_dst_zero_inner_inputtotalpositive) + (dst_positive_sum_zero_inner_inputtotal))) /\ forall fs_i_dst_zero_inner_inputtotalpositive_body_steps. (exists fs_lt_dst_zero_inner_inputtotalpositive_body_steps_bound. fs_lt_dst_zero_inner_inputtotalpositive_body_steps_bound + S fs_i_dst_zero_inner_inputtotalpositive_body_steps = m) -> exists fs_a_dst_zero_inner_inputtotalpositive_body_steps fs_r_dst_zero_inner_inputtotalpositive_body_steps fs_s_dst_zero_inner_inputtotalpositive_body_steps. ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_steps_summand. fs_h_dst_zero_inner_inputtotalpositive_body_steps_summand + S (fs_a_dst_zero_inner_inputtotalpositive_body_steps) = S ((S (fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * dst_positive_scale_zero_inner_inputtotal)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_steps_summand. dst_positive_code_zero_inner_inputtotal = fs_q_dst_zero_inner_inputtotalpositive_body_steps_summand * S ((S (fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * dst_positive_scale_zero_inner_inputtotal) + (fs_a_dst_zero_inner_inputtotalpositive_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_steps_partial. fs_h_dst_zero_inner_inputtotalpositive_body_steps_partial + S (fs_r_dst_zero_inner_inputtotalpositive_body_steps) = S ((S (fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * fs_v_dst_zero_inner_inputtotalpositive)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_steps_partial. fs_u_dst_zero_inner_inputtotalpositive = fs_q_dst_zero_inner_inputtotalpositive_body_steps_partial * S ((S (fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * fs_v_dst_zero_inner_inputtotalpositive) + (fs_r_dst_zero_inner_inputtotalpositive_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_steps_successor. fs_h_dst_zero_inner_inputtotalpositive_body_steps_successor + S (fs_s_dst_zero_inner_inputtotalpositive_body_steps) = S ((S (S fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * fs_v_dst_zero_inner_inputtotalpositive)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_steps_successor. fs_u_dst_zero_inner_inputtotalpositive = fs_q_dst_zero_inner_inputtotalpositive_body_steps_successor * S ((S (S fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * fs_v_dst_zero_inner_inputtotalpositive) + (fs_s_dst_zero_inner_inputtotalpositive_body_steps))) /\ fs_s_dst_zero_inner_inputtotalpositive_body_steps = fs_r_dst_zero_inner_inputtotalpositive_body_steps + fs_a_dst_zero_inner_inputtotalpositive_body_steps)))))) /\ (((exists fs_u_dst_zero_inner_inputtotalnegative fs_v_dst_zero_inner_inputtotalnegative. ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_start. fs_h_dst_zero_inner_inputtotalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_inner_inputtotalnegative)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_start. fs_u_dst_zero_inner_inputtotalnegative = fs_q_dst_zero_inner_inputtotalnegative_body_start * S ((S (0)) * fs_v_dst_zero_inner_inputtotalnegative) + (0))) /\ ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_terminal. fs_h_dst_zero_inner_inputtotalnegative_body_terminal + S (dst_negative_sum_zero_inner_inputtotal) = S ((S (m)) * fs_v_dst_zero_inner_inputtotalnegative)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_terminal. fs_u_dst_zero_inner_inputtotalnegative = fs_q_dst_zero_inner_inputtotalnegative_body_terminal * S ((S (m)) * fs_v_dst_zero_inner_inputtotalnegative) + (dst_negative_sum_zero_inner_inputtotal))) /\ forall fs_i_dst_zero_inner_inputtotalnegative_body_steps. (exists fs_lt_dst_zero_inner_inputtotalnegative_body_steps_bound. fs_lt_dst_zero_inner_inputtotalnegative_body_steps_bound + S fs_i_dst_zero_inner_inputtotalnegative_body_steps = m) -> exists fs_a_dst_zero_inner_inputtotalnegative_body_steps fs_r_dst_zero_inner_inputtotalnegative_body_steps fs_s_dst_zero_inner_inputtotalnegative_body_steps. ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_steps_summand. fs_h_dst_zero_inner_inputtotalnegative_body_steps_summand + S (fs_a_dst_zero_inner_inputtotalnegative_body_steps) = S ((S (fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * dst_negative_scale_zero_inner_inputtotal)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_steps_summand. dst_negative_code_zero_inner_inputtotal = fs_q_dst_zero_inner_inputtotalnegative_body_steps_summand * S ((S (fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * dst_negative_scale_zero_inner_inputtotal) + (fs_a_dst_zero_inner_inputtotalnegative_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_steps_partial. fs_h_dst_zero_inner_inputtotalnegative_body_steps_partial + S (fs_r_dst_zero_inner_inputtotalnegative_body_steps) = S ((S (fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * fs_v_dst_zero_inner_inputtotalnegative)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_steps_partial. fs_u_dst_zero_inner_inputtotalnegative = fs_q_dst_zero_inner_inputtotalnegative_body_steps_partial * S ((S (fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * fs_v_dst_zero_inner_inputtotalnegative) + (fs_r_dst_zero_inner_inputtotalnegative_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_steps_successor. fs_h_dst_zero_inner_inputtotalnegative_body_steps_successor + S (fs_s_dst_zero_inner_inputtotalnegative_body_steps) = S ((S (S fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * fs_v_dst_zero_inner_inputtotalnegative)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_steps_successor. fs_u_dst_zero_inner_inputtotalnegative = fs_q_dst_zero_inner_inputtotalnegative_body_steps_successor * S ((S (S fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * fs_v_dst_zero_inner_inputtotalnegative) + (fs_s_dst_zero_inner_inputtotalnegative_body_steps))) /\ fs_s_dst_zero_inner_inputtotalnegative_body_steps = fs_r_dst_zero_inner_inputtotalnegative_body_steps + fs_a_dst_zero_inner_inputtotalnegative_body_steps)))))) /\ (exists ge_balance_positive_zero_inner_inputtotalresult ge_balance_negative_zero_inner_inputtotalresult. (((((z) = 2 * (ge_balance_positive_zero_inner_inputtotalresult) /\ (ge_balance_negative_zero_inner_inputtotalresult) = 0) \/ exists ge_signed_half_zero_inner_inputtotalresultdecode. (((z) = 2 * ge_signed_half_zero_inner_inputtotalresultdecode + 1 /\ (ge_balance_positive_zero_inner_inputtotalresult) = 0) /\ (ge_balance_negative_zero_inner_inputtotalresult) = S ge_signed_half_zero_inner_inputtotalresultdecode))) /\ ((dst_positive_sum_zero_inner_inputtotal) + ge_balance_negative_zero_inner_inputtotalresult = (dst_negative_sum_zero_inner_inputtotal) + ge_balance_positive_zero_inner_inputtotalresult))))))))))) -> z=0

Constructive proof overview

Generated structural guide

A rectangle with zero columns has actual signed total zero for every row count.

The unchanged tactic script uses 1 declared prerequisite and contains 19 exact native proof lines.

Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

Direct 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

19 script commands · 3 reading checkpoints · 0 local claims

This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.

Named ingredients (1)
01Fix variables and assumptionsL1–7

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro F
  2. L2
    intro o
  3. L3
    intro s
  4. L4
    intro t
  5. L5
    intro m
  6. L6
    intro z
  7. L7
    intro hz
02Separate the logical casesL8–9

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L8
    cases hz
  2. L9
    cases hz_witness
03Use earlier factsL10–19

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L10
    specialize signed_rectangular_row_sums_zero_inner (m)
  2. L11
    specialize signed_rectangular_row_sums_zero_inner (F)
  3. L12
    specialize signed_rectangular_row_sums_zero_inner (x)
  4. L13
    specialize signed_rectangular_row_sums_zero_inner (o)
  5. L14
    specialize signed_rectangular_row_sums_zero_inner (s)
  6. L15
    specialize signed_rectangular_row_sums_zero_inner (t)
  7. L16
    specialize signed_rectangular_row_sums_zero_inner (z)
  8. L17
    apply signed_rectangular_row_sums_zero_inner
  9. L18
    exact hz_witness_left
  10. L19
    exact hz_witness_right

Library-wide reading audit

Original exact command ledger · 19 lines
  1. 0001intro F
  2. 0002intro o
  3. 0003intro s
  4. 0004intro t
  5. 0005intro m
  6. 0006intro z
  7. 0007intro hz
  8. 0008cases hz
  9. 0009cases hz_witness
  10. 0010specialize signed_rectangular_row_sums_zero_inner (m)
  11. 0011specialize signed_rectangular_row_sums_zero_inner (F)
  12. 0012specialize signed_rectangular_row_sums_zero_inner (x)
  13. 0013specialize signed_rectangular_row_sums_zero_inner (o)
  14. 0014specialize signed_rectangular_row_sums_zero_inner (s)
  15. 0015specialize signed_rectangular_row_sums_zero_inner (t)
  16. 0016specialize signed_rectangular_row_sums_zero_inner (z)
  17. 0017apply signed_rectangular_row_sums_zero_inner
  18. 0018exact hz_witness_left
  19. 0019exact hz_witness_right