RS0016

signed_rectangular_row_sums_exists_extensionally_unique

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

Construct a genuine row-sum table and prove its precise extensional uniqueness at every i<m.

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_unique_source dst_positive_scale_unique_source dst_negative_code_unique_source dst_negative_scale_unique_source. (((F) = (((((dst_positive_code_unique_source) + (dst_positive_scale_unique_source)) * S ((dst_positive_code_unique_source) + (dst_positive_scale_unique_source)) + ((dst_positive_scale_unique_source) + (dst_positive_scale_unique_source))) + (((dst_negative_code_unique_source) + (dst_negative_scale_unique_source)) * S ((dst_negative_code_unique_source) + (dst_negative_scale_unique_source)) + ((dst_negative_scale_unique_source) + (dst_negative_scale_unique_source)))) * S ((((dst_positive_code_unique_source) + (dst_positive_scale_unique_source)) * S ((dst_positive_code_unique_source) + (dst_positive_scale_unique_source)) + ((dst_positive_scale_unique_source) + (dst_positive_scale_unique_source))) + (((dst_negative_code_unique_source) + (dst_negative_scale_unique_source)) * S ((dst_negative_code_unique_source) + (dst_negative_scale_unique_source)) + ((dst_negative_scale_unique_source) + (dst_negative_scale_unique_source)))) + ((((dst_negative_code_unique_source) + (dst_negative_scale_unique_source)) * S ((dst_negative_code_unique_source) + (dst_negative_scale_unique_source)) + ((dst_negative_scale_unique_source) + (dst_negative_scale_unique_source))) + (((dst_negative_code_unique_source) + (dst_negative_scale_unique_source)) * S ((dst_negative_code_unique_source) + (dst_negative_scale_unique_source)) + ((dst_negative_scale_unique_source) + (dst_negative_scale_unique_source)))))) /\ (forall dst_index_unique_source. (exists pvs_le_gap_unique_sourcedomain. pvs_le_gap_unique_sourcedomain + (dst_index_unique_source) = (0)) -> exists dst_positive_unique_source dst_negative_unique_source dst_value_unique_source. ((((exists ff_h_pvs_unique_sourceentrypositive. ff_h_pvs_unique_sourceentrypositive + S (dst_positive_unique_source) = S ((S (dst_index_unique_source)) * dst_positive_scale_unique_source)) /\ exists ff_q_pvs_unique_sourceentrypositive. dst_positive_code_unique_source = ff_q_pvs_unique_sourceentrypositive * S ((S (dst_index_unique_source)) * dst_positive_scale_unique_source) + (dst_positive_unique_source))) /\ (((((exists ff_h_pvs_unique_sourceentrynegative. ff_h_pvs_unique_sourceentrynegative + S (dst_negative_unique_source) = S ((S (dst_index_unique_source)) * dst_negative_scale_unique_source)) /\ exists ff_q_pvs_unique_sourceentrynegative. dst_negative_code_unique_source = ff_q_pvs_unique_sourceentrynegative * S ((S (dst_index_unique_source)) * dst_negative_scale_unique_source) + (dst_negative_unique_source))) /\ (exists ge_balance_positive_unique_sourceentryvalue ge_balance_negative_unique_sourceentryvalue. (((((dst_value_unique_source) = 2 * (ge_balance_positive_unique_sourceentryvalue) /\ (ge_balance_negative_unique_sourceentryvalue) = 0) \/ exists ge_signed_half_unique_sourceentryvaluedecode. (((dst_value_unique_source) = 2 * ge_signed_half_unique_sourceentryvaluedecode + 1 /\ (ge_balance_positive_unique_sourceentryvalue) = 0) /\ (ge_balance_negative_unique_sourceentryvalue) = S ge_signed_half_unique_sourceentryvaluedecode))) /\ ((dst_positive_unique_source) + ge_balance_negative_unique_sourceentryvalue = (dst_negative_unique_source) + ge_balance_positive_unique_sourceentryvalue))))))))) -> exists R. ((((exists dst_positive_code_unique_resultsource_table dst_positive_scale_unique_resultsource_table dst_negative_code_unique_resultsource_table dst_negative_scale_unique_resultsource_table. (((F) = (((((dst_positive_code_unique_resultsource_table) + (dst_positive_scale_unique_resultsource_table)) * S ((dst_positive_code_unique_resultsource_table) + (dst_positive_scale_unique_resultsource_table)) + ((dst_positive_scale_unique_resultsource_table) + (dst_positive_scale_unique_resultsource_table))) + (((dst_negative_code_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)) * S ((dst_negative_code_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)) + ((dst_negative_scale_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)))) * S ((((dst_positive_code_unique_resultsource_table) + (dst_positive_scale_unique_resultsource_table)) * S ((dst_positive_code_unique_resultsource_table) + (dst_positive_scale_unique_resultsource_table)) + ((dst_positive_scale_unique_resultsource_table) + (dst_positive_scale_unique_resultsource_table))) + (((dst_negative_code_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)) * S ((dst_negative_code_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)) + ((dst_negative_scale_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)))) + ((((dst_negative_code_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)) * S ((dst_negative_code_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)) + ((dst_negative_scale_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table))) + (((dst_negative_code_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)) * S ((dst_negative_code_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)) + ((dst_negative_scale_unique_resultsource_table) + (dst_negative_scale_unique_resultsource_table)))))) /\ (forall dst_index_unique_resultsource_table. (exists pvs_le_gap_unique_resultsource_tabledomain. pvs_le_gap_unique_resultsource_tabledomain + (dst_index_unique_resultsource_table) = (0)) -> exists dst_positive_unique_resultsource_table dst_negative_unique_resultsource_table dst_value_unique_resultsource_table. ((((exists ff_h_pvs_unique_resultsource_tableentrypositive. ff_h_pvs_unique_resultsource_tableentrypositive + S (dst_positive_unique_resultsource_table) = S ((S (dst_index_unique_resultsource_table)) * dst_positive_scale_unique_resultsource_table)) /\ exists ff_q_pvs_unique_resultsource_tableentrypositive. dst_positive_code_unique_resultsource_table = ff_q_pvs_unique_resultsource_tableentrypositive * S ((S (dst_index_unique_resultsource_table)) * dst_positive_scale_unique_resultsource_table) + (dst_positive_unique_resultsource_table))) /\ (((((exists ff_h_pvs_unique_resultsource_tableentrynegative. ff_h_pvs_unique_resultsource_tableentrynegative + S (dst_negative_unique_resultsource_table) = S ((S (dst_index_unique_resultsource_table)) * dst_negative_scale_unique_resultsource_table)) /\ exists ff_q_pvs_unique_resultsource_tableentrynegative. dst_negative_code_unique_resultsource_table = ff_q_pvs_unique_resultsource_tableentrynegative * S ((S (dst_index_unique_resultsource_table)) * dst_negative_scale_unique_resultsource_table) + (dst_negative_unique_resultsource_table))) /\ (exists ge_balance_positive_unique_resultsource_tableentryvalue ge_balance_negative_unique_resultsource_tableentryvalue. (((((dst_value_unique_resultsource_table) = 2 * (ge_balance_positive_unique_resultsource_tableentryvalue) /\ (ge_balance_negative_unique_resultsource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_resultsource_tableentryvaluedecode. (((dst_value_unique_resultsource_table) = 2 * ge_signed_half_unique_resultsource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_resultsource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_resultsource_tableentryvalue) = S ge_signed_half_unique_resultsource_tableentryvaluedecode))) /\ ((dst_positive_unique_resultsource_table) + ge_balance_negative_unique_resultsource_tableentryvalue = (dst_negative_unique_resultsource_table) + ge_balance_positive_unique_resultsource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_resultrow_table dst_positive_scale_unique_resultrow_table dst_negative_code_unique_resultrow_table dst_negative_scale_unique_resultrow_table. (((R) = (((((dst_positive_code_unique_resultrow_table) + (dst_positive_scale_unique_resultrow_table)) * S ((dst_positive_code_unique_resultrow_table) + (dst_positive_scale_unique_resultrow_table)) + ((dst_positive_scale_unique_resultrow_table) + (dst_positive_scale_unique_resultrow_table))) + (((dst_negative_code_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)) * S ((dst_negative_code_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)) + ((dst_negative_scale_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)))) * S ((((dst_positive_code_unique_resultrow_table) + (dst_positive_scale_unique_resultrow_table)) * S ((dst_positive_code_unique_resultrow_table) + (dst_positive_scale_unique_resultrow_table)) + ((dst_positive_scale_unique_resultrow_table) + (dst_positive_scale_unique_resultrow_table))) + (((dst_negative_code_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)) * S ((dst_negative_code_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)) + ((dst_negative_scale_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)))) + ((((dst_negative_code_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)) * S ((dst_negative_code_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)) + ((dst_negative_scale_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table))) + (((dst_negative_code_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)) * S ((dst_negative_code_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)) + ((dst_negative_scale_unique_resultrow_table) + (dst_negative_scale_unique_resultrow_table)))))) /\ (forall dst_index_unique_resultrow_table. (exists pvs_le_gap_unique_resultrow_tabledomain. pvs_le_gap_unique_resultrow_tabledomain + (dst_index_unique_resultrow_table) = (m)) -> exists dst_positive_unique_resultrow_table dst_negative_unique_resultrow_table dst_value_unique_resultrow_table. ((((exists ff_h_pvs_unique_resultrow_tableentrypositive. ff_h_pvs_unique_resultrow_tableentrypositive + S (dst_positive_unique_resultrow_table) = S ((S (dst_index_unique_resultrow_table)) * dst_positive_scale_unique_resultrow_table)) /\ exists ff_q_pvs_unique_resultrow_tableentrypositive. dst_positive_code_unique_resultrow_table = ff_q_pvs_unique_resultrow_tableentrypositive * S ((S (dst_index_unique_resultrow_table)) * dst_positive_scale_unique_resultrow_table) + (dst_positive_unique_resultrow_table))) /\ (((((exists ff_h_pvs_unique_resultrow_tableentrynegative. ff_h_pvs_unique_resultrow_tableentrynegative + S (dst_negative_unique_resultrow_table) = S ((S (dst_index_unique_resultrow_table)) * dst_negative_scale_unique_resultrow_table)) /\ exists ff_q_pvs_unique_resultrow_tableentrynegative. dst_negative_code_unique_resultrow_table = ff_q_pvs_unique_resultrow_tableentrynegative * S ((S (dst_index_unique_resultrow_table)) * dst_negative_scale_unique_resultrow_table) + (dst_negative_unique_resultrow_table))) /\ (exists ge_balance_positive_unique_resultrow_tableentryvalue ge_balance_negative_unique_resultrow_tableentryvalue. (((((dst_value_unique_resultrow_table) = 2 * (ge_balance_positive_unique_resultrow_tableentryvalue) /\ (ge_balance_negative_unique_resultrow_tableentryvalue) = 0) \/ exists ge_signed_half_unique_resultrow_tableentryvaluedecode. (((dst_value_unique_resultrow_table) = 2 * ge_signed_half_unique_resultrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_resultrow_tableentryvalue) = 0) /\ (ge_balance_negative_unique_resultrow_tableentryvalue) = S ge_signed_half_unique_resultrow_tableentryvaluedecode))) /\ ((dst_positive_unique_resultrow_table) + ge_balance_negative_unique_resultrow_tableentryvalue = (dst_negative_unique_resultrow_table) + ge_balance_positive_unique_resultrow_tableentryvalue))))))))) /\ (forall srt_index_unique_result. (exists pvs_gap_unique_resultbound. pvs_gap_unique_resultbound + S (srt_index_unique_result) = (m)) -> exists srt_value_unique_result. (((exists dst_positive_code_unique_resultrowentry dst_positive_scale_unique_resultrowentry dst_negative_code_unique_resultrowentry dst_negative_scale_unique_resultrowentry dst_positive_unique_resultrowentry dst_negative_unique_resultrowentry. (((R) = (((((dst_positive_code_unique_resultrowentry) + (dst_positive_scale_unique_resultrowentry)) * S ((dst_positive_code_unique_resultrowentry) + (dst_positive_scale_unique_resultrowentry)) + ((dst_positive_scale_unique_resultrowentry) + (dst_positive_scale_unique_resultrowentry))) + (((dst_negative_code_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)) * S ((dst_negative_code_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)) + ((dst_negative_scale_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)))) * S ((((dst_positive_code_unique_resultrowentry) + (dst_positive_scale_unique_resultrowentry)) * S ((dst_positive_code_unique_resultrowentry) + (dst_positive_scale_unique_resultrowentry)) + ((dst_positive_scale_unique_resultrowentry) + (dst_positive_scale_unique_resultrowentry))) + (((dst_negative_code_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)) * S ((dst_negative_code_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)) + ((dst_negative_scale_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)))) + ((((dst_negative_code_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)) * S ((dst_negative_code_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)) + ((dst_negative_scale_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry))) + (((dst_negative_code_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)) * S ((dst_negative_code_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)) + ((dst_negative_scale_unique_resultrowentry) + (dst_negative_scale_unique_resultrowentry)))))) /\ (((((exists ff_h_pvs_unique_resultrowentrypositive. ff_h_pvs_unique_resultrowentrypositive + S (dst_positive_unique_resultrowentry) = S ((S (srt_index_unique_result)) * dst_positive_scale_unique_resultrowentry)) /\ exists ff_q_pvs_unique_resultrowentrypositive. dst_positive_code_unique_resultrowentry = ff_q_pvs_unique_resultrowentrypositive * S ((S (srt_index_unique_result)) * dst_positive_scale_unique_resultrowentry) + (dst_positive_unique_resultrowentry))) /\ (((((exists ff_h_pvs_unique_resultrowentrynegative. ff_h_pvs_unique_resultrowentrynegative + S (dst_negative_unique_resultrowentry) = S ((S (srt_index_unique_result)) * dst_negative_scale_unique_resultrowentry)) /\ exists ff_q_pvs_unique_resultrowentrynegative. dst_negative_code_unique_resultrowentry = ff_q_pvs_unique_resultrowentrynegative * S ((S (srt_index_unique_result)) * dst_negative_scale_unique_resultrowentry) + (dst_negative_unique_resultrowentry))) /\ (exists ge_balance_positive_unique_resultrowentryvalue ge_balance_negative_unique_resultrowentryvalue. (((((srt_value_unique_result) = 2 * (ge_balance_positive_unique_resultrowentryvalue) /\ (ge_balance_negative_unique_resultrowentryvalue) = 0) \/ exists ge_signed_half_unique_resultrowentryvaluedecode. (((srt_value_unique_result) = 2 * ge_signed_half_unique_resultrowentryvaluedecode + 1 /\ (ge_balance_positive_unique_resultrowentryvalue) = 0) /\ (ge_balance_negative_unique_resultrowentryvalue) = S ge_signed_half_unique_resultrowentryvaluedecode))) /\ ((dst_positive_unique_resultrowentry) + ge_balance_negative_unique_resultrowentryvalue = (dst_negative_unique_resultrowentry) + ge_balance_positive_unique_resultrowentryvalue))))))))) /\ (exists srs_slice_unique_resultrowrow_sum. ((((exists dst_positive_code_unique_resultrowrow_sumslicesource_table dst_positive_scale_unique_resultrowrow_sumslicesource_table dst_negative_code_unique_resultrowrow_sumslicesource_table dst_negative_scale_unique_resultrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_unique_resultrowrow_sumslicesource_table) + (dst_positive_scale_unique_resultrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_resultrowrow_sumslicesource_table) + (dst_positive_scale_unique_resultrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_resultrowrow_sumslicesource_table) + (dst_positive_scale_unique_resultrowrow_sumslicesource_table))) + (((dst_negative_code_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)))) * S ((((dst_positive_code_unique_resultrowrow_sumslicesource_table) + (dst_positive_scale_unique_resultrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_resultrowrow_sumslicesource_table) + (dst_positive_scale_unique_resultrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_resultrowrow_sumslicesource_table) + (dst_positive_scale_unique_resultrowrow_sumslicesource_table))) + (((dst_negative_code_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)))) + ((((dst_negative_code_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table))) + (((dst_negative_code_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_resultrowrow_sumslicesource_table) + (dst_negative_scale_unique_resultrowrow_sumslicesource_table)))))) /\ (forall dst_index_unique_resultrowrow_sumslicesource_table. (exists pvs_le_gap_unique_resultrowrow_sumslicesource_tabledomain. pvs_le_gap_unique_resultrowrow_sumslicesource_tabledomain + (dst_index_unique_resultrowrow_sumslicesource_table) = (0)) -> exists dst_positive_unique_resultrowrow_sumslicesource_table dst_negative_unique_resultrowrow_sumslicesource_table dst_value_unique_resultrowrow_sumslicesource_table. ((((exists ff_h_pvs_unique_resultrowrow_sumslicesource_tableentrypositive. ff_h_pvs_unique_resultrowrow_sumslicesource_tableentrypositive + S (dst_positive_unique_resultrowrow_sumslicesource_table) = S ((S (dst_index_unique_resultrowrow_sumslicesource_table)) * dst_positive_scale_unique_resultrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_resultrowrow_sumslicesource_tableentrypositive. dst_positive_code_unique_resultrowrow_sumslicesource_table = ff_q_pvs_unique_resultrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_unique_resultrowrow_sumslicesource_table)) * dst_positive_scale_unique_resultrowrow_sumslicesource_table) + (dst_positive_unique_resultrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_unique_resultrowrow_sumslicesource_tableentrynegative. ff_h_pvs_unique_resultrowrow_sumslicesource_tableentrynegative + S (dst_negative_unique_resultrowrow_sumslicesource_table) = S ((S (dst_index_unique_resultrowrow_sumslicesource_table)) * dst_negative_scale_unique_resultrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_resultrowrow_sumslicesource_tableentrynegative. dst_negative_code_unique_resultrowrow_sumslicesource_table = ff_q_pvs_unique_resultrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_unique_resultrowrow_sumslicesource_table)) * dst_negative_scale_unique_resultrowrow_sumslicesource_table) + (dst_negative_unique_resultrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_unique_resultrowrow_sumslicesource_tableentryvalue ge_balance_negative_unique_resultrowrow_sumslicesource_tableentryvalue. (((((dst_value_unique_resultrowrow_sumslicesource_table) = 2 * (ge_balance_positive_unique_resultrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_unique_resultrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_resultrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_unique_resultrowrow_sumslicesource_table) = 2 * ge_signed_half_unique_resultrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_resultrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_resultrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_unique_resultrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_unique_resultrowrow_sumslicesource_table) + ge_balance_negative_unique_resultrowrow_sumslicesource_tableentryvalue = (dst_negative_unique_resultrowrow_sumslicesource_table) + ge_balance_positive_unique_resultrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_resultrowrow_sumsliceoutput_table dst_positive_scale_unique_resultrowrow_sumsliceoutput_table dst_negative_code_unique_resultrowrow_sumsliceoutput_table dst_negative_scale_unique_resultrowrow_sumsliceoutput_table. (((srs_slice_unique_resultrowrow_sum) = (((((dst_positive_code_unique_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_resultrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_resultrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_resultrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_unique_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_resultrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_resultrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_resultrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_unique_resultrowrow_sumsliceoutput_table. (exists pvs_le_gap_unique_resultrowrow_sumsliceoutput_tabledomain. pvs_le_gap_unique_resultrowrow_sumsliceoutput_tabledomain + (dst_index_unique_resultrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_unique_resultrowrow_sumsliceoutput_table dst_negative_unique_resultrowrow_sumsliceoutput_table dst_value_unique_resultrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_unique_resultrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_unique_resultrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_unique_resultrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_resultrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_resultrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_resultrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_unique_resultrowrow_sumsliceoutput_table = ff_q_pvs_unique_resultrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_unique_resultrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_resultrowrow_sumsliceoutput_table) + (dst_positive_unique_resultrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_unique_resultrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_unique_resultrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_unique_resultrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_resultrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_resultrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_resultrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_unique_resultrowrow_sumsliceoutput_table = ff_q_pvs_unique_resultrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_unique_resultrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_resultrowrow_sumsliceoutput_table) + (dst_negative_unique_resultrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_unique_resultrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_unique_resultrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_unique_resultrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_unique_resultrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_unique_resultrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_unique_resultrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_unique_resultrowrow_sumsliceoutput_table) = 2 * ge_signed_half_unique_resultrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_resultrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_unique_resultrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_unique_resultrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_unique_resultrowrow_sumsliceoutput_table) + ge_balance_negative_unique_resultrowrow_sumsliceoutput_tableentryvalue = (dst_negative_unique_resultrowrow_sumsliceoutput_table) + ge_balance_positive_unique_resultrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_unique_resultrowrow_sumslice. (exists pvs_gap_unique_resultrowrow_sumslicebound. pvs_gap_unique_resultrowrow_sumslicebound + S (srs_index_unique_resultrowrow_sumslice) = (n)) -> exists srs_value_unique_resultrowrow_sumslice. (((exists dst_positive_code_unique_resultrowrow_sumsliceentrysource dst_positive_scale_unique_resultrowrow_sumsliceentrysource dst_negative_code_unique_resultrowrow_sumsliceentrysource dst_negative_scale_unique_resultrowrow_sumsliceentrysource dst_positive_unique_resultrowrow_sumsliceentrysource dst_negative_unique_resultrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_unique_resultrowrow_sumsliceentrysource) + (dst_positive_scale_unique_resultrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_resultrowrow_sumsliceentrysource) + (dst_positive_scale_unique_resultrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_resultrowrow_sumsliceentrysource) + (dst_positive_scale_unique_resultrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_unique_resultrowrow_sumsliceentrysource) + (dst_positive_scale_unique_resultrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_resultrowrow_sumsliceentrysource) + (dst_positive_scale_unique_resultrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_resultrowrow_sumsliceentrysource) + (dst_positive_scale_unique_resultrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)))) + ((((dst_negative_code_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_resultrowrow_sumsliceentrysource) + (dst_negative_scale_unique_resultrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_unique_resultrowrow_sumsliceentrysourcepositive. ff_h_pvs_unique_resultrowrow_sumsliceentrysourcepositive + S (dst_positive_unique_resultrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_result)))) + ((t) * (srs_index_unique_resultrowrow_sumslice))))) * dst_positive_scale_unique_resultrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_resultrowrow_sumsliceentrysourcepositive. dst_positive_code_unique_resultrowrow_sumsliceentrysource = ff_q_pvs_unique_resultrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_unique_result)))) + ((t) * (srs_index_unique_resultrowrow_sumslice))))) * dst_positive_scale_unique_resultrowrow_sumsliceentrysource) + (dst_positive_unique_resultrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_unique_resultrowrow_sumsliceentrysourcenegative. ff_h_pvs_unique_resultrowrow_sumsliceentrysourcenegative + S (dst_negative_unique_resultrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_result)))) + ((t) * (srs_index_unique_resultrowrow_sumslice))))) * dst_negative_scale_unique_resultrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_resultrowrow_sumsliceentrysourcenegative. dst_negative_code_unique_resultrowrow_sumsliceentrysource = ff_q_pvs_unique_resultrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_unique_result)))) + ((t) * (srs_index_unique_resultrowrow_sumslice))))) * dst_negative_scale_unique_resultrowrow_sumsliceentrysource) + (dst_negative_unique_resultrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_unique_resultrowrow_sumsliceentrysourcevalue ge_balance_negative_unique_resultrowrow_sumsliceentrysourcevalue. (((((srs_value_unique_resultrowrow_sumslice) = 2 * (ge_balance_positive_unique_resultrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_unique_resultrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_unique_resultrowrow_sumsliceentrysourcevaluedecode. (((srs_value_unique_resultrowrow_sumslice) = 2 * ge_signed_half_unique_resultrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_unique_resultrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_unique_resultrowrow_sumsliceentrysourcevalue) = S ge_signed_half_unique_resultrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_unique_resultrowrow_sumsliceentrysource) + ge_balance_negative_unique_resultrowrow_sumsliceentrysourcevalue = (dst_negative_unique_resultrowrow_sumsliceentrysource) + ge_balance_positive_unique_resultrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_unique_resultrowrow_sumsliceentryoutput dst_positive_scale_unique_resultrowrow_sumsliceentryoutput dst_negative_code_unique_resultrowrow_sumsliceentryoutput dst_negative_scale_unique_resultrowrow_sumsliceentryoutput dst_positive_unique_resultrowrow_sumsliceentryoutput dst_negative_unique_resultrowrow_sumsliceentryoutput. (((srs_slice_unique_resultrowrow_sum) = (((((dst_positive_code_unique_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_resultrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_resultrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_resultrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_unique_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_resultrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_resultrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_resultrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_unique_resultrowrow_sumsliceentryoutputpositive. ff_h_pvs_unique_resultrowrow_sumsliceentryoutputpositive + S (dst_positive_unique_resultrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_resultrowrow_sumslice)) * dst_positive_scale_unique_resultrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_resultrowrow_sumsliceentryoutputpositive. dst_positive_code_unique_resultrowrow_sumsliceentryoutput = ff_q_pvs_unique_resultrowrow_sumsliceentryoutputpositive * S ((S (srs_index_unique_resultrowrow_sumslice)) * dst_positive_scale_unique_resultrowrow_sumsliceentryoutput) + (dst_positive_unique_resultrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_unique_resultrowrow_sumsliceentryoutputnegative. ff_h_pvs_unique_resultrowrow_sumsliceentryoutputnegative + S (dst_negative_unique_resultrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_resultrowrow_sumslice)) * dst_negative_scale_unique_resultrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_resultrowrow_sumsliceentryoutputnegative. dst_negative_code_unique_resultrowrow_sumsliceentryoutput = ff_q_pvs_unique_resultrowrow_sumsliceentryoutputnegative * S ((S (srs_index_unique_resultrowrow_sumslice)) * dst_negative_scale_unique_resultrowrow_sumsliceentryoutput) + (dst_negative_unique_resultrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_unique_resultrowrow_sumsliceentryoutputvalue ge_balance_negative_unique_resultrowrow_sumsliceentryoutputvalue. (((((srs_value_unique_resultrowrow_sumslice) = 2 * (ge_balance_positive_unique_resultrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_unique_resultrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_unique_resultrowrow_sumsliceentryoutputvaluedecode. (((srs_value_unique_resultrowrow_sumslice) = 2 * ge_signed_half_unique_resultrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_unique_resultrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_unique_resultrowrow_sumsliceentryoutputvalue) = S ge_signed_half_unique_resultrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_unique_resultrowrow_sumsliceentryoutput) + ge_balance_negative_unique_resultrowrow_sumsliceentryoutputvalue = (dst_negative_unique_resultrowrow_sumsliceentryoutput) + ge_balance_positive_unique_resultrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_unique_resultrowrow_sumsum dst_positive_scale_unique_resultrowrow_sumsum dst_negative_code_unique_resultrowrow_sumsum dst_negative_scale_unique_resultrowrow_sumsum dst_positive_sum_unique_resultrowrow_sumsum dst_negative_sum_unique_resultrowrow_sumsum. (((srs_slice_unique_resultrowrow_sum) = (((((dst_positive_code_unique_resultrowrow_sumsum) + (dst_positive_scale_unique_resultrowrow_sumsum)) * S ((dst_positive_code_unique_resultrowrow_sumsum) + (dst_positive_scale_unique_resultrowrow_sumsum)) + ((dst_positive_scale_unique_resultrowrow_sumsum) + (dst_positive_scale_unique_resultrowrow_sumsum))) + (((dst_negative_code_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)) * S ((dst_negative_code_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)) + ((dst_negative_scale_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)))) * S ((((dst_positive_code_unique_resultrowrow_sumsum) + (dst_positive_scale_unique_resultrowrow_sumsum)) * S ((dst_positive_code_unique_resultrowrow_sumsum) + (dst_positive_scale_unique_resultrowrow_sumsum)) + ((dst_positive_scale_unique_resultrowrow_sumsum) + (dst_positive_scale_unique_resultrowrow_sumsum))) + (((dst_negative_code_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)) * S ((dst_negative_code_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)) + ((dst_negative_scale_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)))) + ((((dst_negative_code_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)) * S ((dst_negative_code_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)) + ((dst_negative_scale_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum))) + (((dst_negative_code_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)) * S ((dst_negative_code_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)) + ((dst_negative_scale_unique_resultrowrow_sumsum) + (dst_negative_scale_unique_resultrowrow_sumsum)))))) /\ (((exists fs_u_dst_unique_resultrowrow_sumsumpositive fs_v_dst_unique_resultrowrow_sumsumpositive. ((((exists fs_h_dst_unique_resultrowrow_sumsumpositive_body_start. fs_h_dst_unique_resultrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_resultrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_resultrowrow_sumsumpositive_body_start. fs_u_dst_unique_resultrowrow_sumsumpositive = fs_q_dst_unique_resultrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_unique_resultrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_unique_resultrowrow_sumsumpositive_body_terminal. fs_h_dst_unique_resultrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_unique_resultrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_resultrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_resultrowrow_sumsumpositive_body_terminal. fs_u_dst_unique_resultrowrow_sumsumpositive = fs_q_dst_unique_resultrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_unique_resultrowrow_sumsumpositive) + (dst_positive_sum_unique_resultrowrow_sumsum))) /\ forall fs_i_dst_unique_resultrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_unique_resultrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_unique_resultrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_unique_resultrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_unique_resultrowrow_sumsumpositive_body_steps fs_r_dst_unique_resultrowrow_sumsumpositive_body_steps fs_s_dst_unique_resultrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_unique_resultrowrow_sumsumpositive_body_steps_summand. fs_h_dst_unique_resultrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_unique_resultrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_resultrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_resultrowrow_sumsum)) /\ exists fs_q_dst_unique_resultrowrow_sumsumpositive_body_steps_summand. dst_positive_code_unique_resultrowrow_sumsum = fs_q_dst_unique_resultrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_unique_resultrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_resultrowrow_sumsum) + (fs_a_dst_unique_resultrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_resultrowrow_sumsumpositive_body_steps_partial. fs_h_dst_unique_resultrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_unique_resultrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_resultrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_resultrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_resultrowrow_sumsumpositive_body_steps_partial. fs_u_dst_unique_resultrowrow_sumsumpositive = fs_q_dst_unique_resultrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_unique_resultrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_resultrowrow_sumsumpositive) + (fs_r_dst_unique_resultrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_resultrowrow_sumsumpositive_body_steps_successor. fs_h_dst_unique_resultrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_unique_resultrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_unique_resultrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_resultrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_resultrowrow_sumsumpositive_body_steps_successor. fs_u_dst_unique_resultrowrow_sumsumpositive = fs_q_dst_unique_resultrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_unique_resultrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_resultrowrow_sumsumpositive) + (fs_s_dst_unique_resultrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_unique_resultrowrow_sumsumpositive_body_steps = fs_r_dst_unique_resultrowrow_sumsumpositive_body_steps + fs_a_dst_unique_resultrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_unique_resultrowrow_sumsumnegative fs_v_dst_unique_resultrowrow_sumsumnegative. ((((exists fs_h_dst_unique_resultrowrow_sumsumnegative_body_start. fs_h_dst_unique_resultrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_resultrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_resultrowrow_sumsumnegative_body_start. fs_u_dst_unique_resultrowrow_sumsumnegative = fs_q_dst_unique_resultrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_unique_resultrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_unique_resultrowrow_sumsumnegative_body_terminal. fs_h_dst_unique_resultrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_unique_resultrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_resultrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_resultrowrow_sumsumnegative_body_terminal. fs_u_dst_unique_resultrowrow_sumsumnegative = fs_q_dst_unique_resultrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_unique_resultrowrow_sumsumnegative) + (dst_negative_sum_unique_resultrowrow_sumsum))) /\ forall fs_i_dst_unique_resultrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_unique_resultrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_unique_resultrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_unique_resultrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_unique_resultrowrow_sumsumnegative_body_steps fs_r_dst_unique_resultrowrow_sumsumnegative_body_steps fs_s_dst_unique_resultrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_unique_resultrowrow_sumsumnegative_body_steps_summand. fs_h_dst_unique_resultrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_unique_resultrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_resultrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_resultrowrow_sumsum)) /\ exists fs_q_dst_unique_resultrowrow_sumsumnegative_body_steps_summand. dst_negative_code_unique_resultrowrow_sumsum = fs_q_dst_unique_resultrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_unique_resultrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_resultrowrow_sumsum) + (fs_a_dst_unique_resultrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_resultrowrow_sumsumnegative_body_steps_partial. fs_h_dst_unique_resultrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_unique_resultrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_resultrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_resultrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_resultrowrow_sumsumnegative_body_steps_partial. fs_u_dst_unique_resultrowrow_sumsumnegative = fs_q_dst_unique_resultrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_unique_resultrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_resultrowrow_sumsumnegative) + (fs_r_dst_unique_resultrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_resultrowrow_sumsumnegative_body_steps_successor. fs_h_dst_unique_resultrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_unique_resultrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_unique_resultrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_resultrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_resultrowrow_sumsumnegative_body_steps_successor. fs_u_dst_unique_resultrowrow_sumsumnegative = fs_q_dst_unique_resultrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_unique_resultrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_resultrowrow_sumsumnegative) + (fs_s_dst_unique_resultrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_unique_resultrowrow_sumsumnegative_body_steps = fs_r_dst_unique_resultrowrow_sumsumnegative_body_steps + fs_a_dst_unique_resultrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_unique_resultrowrow_sumsumresult ge_balance_negative_unique_resultrowrow_sumsumresult. (((((srt_value_unique_result) = 2 * (ge_balance_positive_unique_resultrowrow_sumsumresult) /\ (ge_balance_negative_unique_resultrowrow_sumsumresult) = 0) \/ exists ge_signed_half_unique_resultrowrow_sumsumresultdecode. (((srt_value_unique_result) = 2 * ge_signed_half_unique_resultrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_unique_resultrowrow_sumsumresult) = 0) /\ (ge_balance_negative_unique_resultrowrow_sumsumresult) = S ge_signed_half_unique_resultrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_unique_resultrowrow_sumsum) + ge_balance_negative_unique_resultrowrow_sumsumresult = (dst_negative_sum_unique_resultrowrow_sumsum) + ge_balance_positive_unique_resultrowrow_sumsumresult)))))))))))))))))) /\ (forall Q. (((exists dst_positive_code_unique_othersource_table dst_positive_scale_unique_othersource_table dst_negative_code_unique_othersource_table dst_negative_scale_unique_othersource_table. (((F) = (((((dst_positive_code_unique_othersource_table) + (dst_positive_scale_unique_othersource_table)) * S ((dst_positive_code_unique_othersource_table) + (dst_positive_scale_unique_othersource_table)) + ((dst_positive_scale_unique_othersource_table) + (dst_positive_scale_unique_othersource_table))) + (((dst_negative_code_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)) * S ((dst_negative_code_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)) + ((dst_negative_scale_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)))) * S ((((dst_positive_code_unique_othersource_table) + (dst_positive_scale_unique_othersource_table)) * S ((dst_positive_code_unique_othersource_table) + (dst_positive_scale_unique_othersource_table)) + ((dst_positive_scale_unique_othersource_table) + (dst_positive_scale_unique_othersource_table))) + (((dst_negative_code_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)) * S ((dst_negative_code_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)) + ((dst_negative_scale_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)))) + ((((dst_negative_code_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)) * S ((dst_negative_code_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)) + ((dst_negative_scale_unique_othersource_table) + (dst_negative_scale_unique_othersource_table))) + (((dst_negative_code_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)) * S ((dst_negative_code_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)) + ((dst_negative_scale_unique_othersource_table) + (dst_negative_scale_unique_othersource_table)))))) /\ (forall dst_index_unique_othersource_table. (exists pvs_le_gap_unique_othersource_tabledomain. pvs_le_gap_unique_othersource_tabledomain + (dst_index_unique_othersource_table) = (0)) -> exists dst_positive_unique_othersource_table dst_negative_unique_othersource_table dst_value_unique_othersource_table. ((((exists ff_h_pvs_unique_othersource_tableentrypositive. ff_h_pvs_unique_othersource_tableentrypositive + S (dst_positive_unique_othersource_table) = S ((S (dst_index_unique_othersource_table)) * dst_positive_scale_unique_othersource_table)) /\ exists ff_q_pvs_unique_othersource_tableentrypositive. dst_positive_code_unique_othersource_table = ff_q_pvs_unique_othersource_tableentrypositive * S ((S (dst_index_unique_othersource_table)) * dst_positive_scale_unique_othersource_table) + (dst_positive_unique_othersource_table))) /\ (((((exists ff_h_pvs_unique_othersource_tableentrynegative. ff_h_pvs_unique_othersource_tableentrynegative + S (dst_negative_unique_othersource_table) = S ((S (dst_index_unique_othersource_table)) * dst_negative_scale_unique_othersource_table)) /\ exists ff_q_pvs_unique_othersource_tableentrynegative. dst_negative_code_unique_othersource_table = ff_q_pvs_unique_othersource_tableentrynegative * S ((S (dst_index_unique_othersource_table)) * dst_negative_scale_unique_othersource_table) + (dst_negative_unique_othersource_table))) /\ (exists ge_balance_positive_unique_othersource_tableentryvalue ge_balance_negative_unique_othersource_tableentryvalue. (((((dst_value_unique_othersource_table) = 2 * (ge_balance_positive_unique_othersource_tableentryvalue) /\ (ge_balance_negative_unique_othersource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_othersource_tableentryvaluedecode. (((dst_value_unique_othersource_table) = 2 * ge_signed_half_unique_othersource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_othersource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_othersource_tableentryvalue) = S ge_signed_half_unique_othersource_tableentryvaluedecode))) /\ ((dst_positive_unique_othersource_table) + ge_balance_negative_unique_othersource_tableentryvalue = (dst_negative_unique_othersource_table) + ge_balance_positive_unique_othersource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_otherrow_table dst_positive_scale_unique_otherrow_table dst_negative_code_unique_otherrow_table dst_negative_scale_unique_otherrow_table. (((Q) = (((((dst_positive_code_unique_otherrow_table) + (dst_positive_scale_unique_otherrow_table)) * S ((dst_positive_code_unique_otherrow_table) + (dst_positive_scale_unique_otherrow_table)) + ((dst_positive_scale_unique_otherrow_table) + (dst_positive_scale_unique_otherrow_table))) + (((dst_negative_code_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)) * S ((dst_negative_code_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)) + ((dst_negative_scale_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)))) * S ((((dst_positive_code_unique_otherrow_table) + (dst_positive_scale_unique_otherrow_table)) * S ((dst_positive_code_unique_otherrow_table) + (dst_positive_scale_unique_otherrow_table)) + ((dst_positive_scale_unique_otherrow_table) + (dst_positive_scale_unique_otherrow_table))) + (((dst_negative_code_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)) * S ((dst_negative_code_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)) + ((dst_negative_scale_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)))) + ((((dst_negative_code_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)) * S ((dst_negative_code_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)) + ((dst_negative_scale_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table))) + (((dst_negative_code_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)) * S ((dst_negative_code_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)) + ((dst_negative_scale_unique_otherrow_table) + (dst_negative_scale_unique_otherrow_table)))))) /\ (forall dst_index_unique_otherrow_table. (exists pvs_le_gap_unique_otherrow_tabledomain. pvs_le_gap_unique_otherrow_tabledomain + (dst_index_unique_otherrow_table) = (m)) -> exists dst_positive_unique_otherrow_table dst_negative_unique_otherrow_table dst_value_unique_otherrow_table. ((((exists ff_h_pvs_unique_otherrow_tableentrypositive. ff_h_pvs_unique_otherrow_tableentrypositive + S (dst_positive_unique_otherrow_table) = S ((S (dst_index_unique_otherrow_table)) * dst_positive_scale_unique_otherrow_table)) /\ exists ff_q_pvs_unique_otherrow_tableentrypositive. dst_positive_code_unique_otherrow_table = ff_q_pvs_unique_otherrow_tableentrypositive * S ((S (dst_index_unique_otherrow_table)) * dst_positive_scale_unique_otherrow_table) + (dst_positive_unique_otherrow_table))) /\ (((((exists ff_h_pvs_unique_otherrow_tableentrynegative. ff_h_pvs_unique_otherrow_tableentrynegative + S (dst_negative_unique_otherrow_table) = S ((S (dst_index_unique_otherrow_table)) * dst_negative_scale_unique_otherrow_table)) /\ exists ff_q_pvs_unique_otherrow_tableentrynegative. dst_negative_code_unique_otherrow_table = ff_q_pvs_unique_otherrow_tableentrynegative * S ((S (dst_index_unique_otherrow_table)) * dst_negative_scale_unique_otherrow_table) + (dst_negative_unique_otherrow_table))) /\ (exists ge_balance_positive_unique_otherrow_tableentryvalue ge_balance_negative_unique_otherrow_tableentryvalue. (((((dst_value_unique_otherrow_table) = 2 * (ge_balance_positive_unique_otherrow_tableentryvalue) /\ (ge_balance_negative_unique_otherrow_tableentryvalue) = 0) \/ exists ge_signed_half_unique_otherrow_tableentryvaluedecode. (((dst_value_unique_otherrow_table) = 2 * ge_signed_half_unique_otherrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_otherrow_tableentryvalue) = 0) /\ (ge_balance_negative_unique_otherrow_tableentryvalue) = S ge_signed_half_unique_otherrow_tableentryvaluedecode))) /\ ((dst_positive_unique_otherrow_table) + ge_balance_negative_unique_otherrow_tableentryvalue = (dst_negative_unique_otherrow_table) + ge_balance_positive_unique_otherrow_tableentryvalue))))))))) /\ (forall srt_index_unique_other. (exists pvs_gap_unique_otherbound. pvs_gap_unique_otherbound + S (srt_index_unique_other) = (m)) -> exists srt_value_unique_other. (((exists dst_positive_code_unique_otherrowentry dst_positive_scale_unique_otherrowentry dst_negative_code_unique_otherrowentry dst_negative_scale_unique_otherrowentry dst_positive_unique_otherrowentry dst_negative_unique_otherrowentry. (((Q) = (((((dst_positive_code_unique_otherrowentry) + (dst_positive_scale_unique_otherrowentry)) * S ((dst_positive_code_unique_otherrowentry) + (dst_positive_scale_unique_otherrowentry)) + ((dst_positive_scale_unique_otherrowentry) + (dst_positive_scale_unique_otherrowentry))) + (((dst_negative_code_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)) * S ((dst_negative_code_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)) + ((dst_negative_scale_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)))) * S ((((dst_positive_code_unique_otherrowentry) + (dst_positive_scale_unique_otherrowentry)) * S ((dst_positive_code_unique_otherrowentry) + (dst_positive_scale_unique_otherrowentry)) + ((dst_positive_scale_unique_otherrowentry) + (dst_positive_scale_unique_otherrowentry))) + (((dst_negative_code_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)) * S ((dst_negative_code_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)) + ((dst_negative_scale_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)))) + ((((dst_negative_code_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)) * S ((dst_negative_code_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)) + ((dst_negative_scale_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry))) + (((dst_negative_code_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)) * S ((dst_negative_code_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)) + ((dst_negative_scale_unique_otherrowentry) + (dst_negative_scale_unique_otherrowentry)))))) /\ (((((exists ff_h_pvs_unique_otherrowentrypositive. ff_h_pvs_unique_otherrowentrypositive + S (dst_positive_unique_otherrowentry) = S ((S (srt_index_unique_other)) * dst_positive_scale_unique_otherrowentry)) /\ exists ff_q_pvs_unique_otherrowentrypositive. dst_positive_code_unique_otherrowentry = ff_q_pvs_unique_otherrowentrypositive * S ((S (srt_index_unique_other)) * dst_positive_scale_unique_otherrowentry) + (dst_positive_unique_otherrowentry))) /\ (((((exists ff_h_pvs_unique_otherrowentrynegative. ff_h_pvs_unique_otherrowentrynegative + S (dst_negative_unique_otherrowentry) = S ((S (srt_index_unique_other)) * dst_negative_scale_unique_otherrowentry)) /\ exists ff_q_pvs_unique_otherrowentrynegative. dst_negative_code_unique_otherrowentry = ff_q_pvs_unique_otherrowentrynegative * S ((S (srt_index_unique_other)) * dst_negative_scale_unique_otherrowentry) + (dst_negative_unique_otherrowentry))) /\ (exists ge_balance_positive_unique_otherrowentryvalue ge_balance_negative_unique_otherrowentryvalue. (((((srt_value_unique_other) = 2 * (ge_balance_positive_unique_otherrowentryvalue) /\ (ge_balance_negative_unique_otherrowentryvalue) = 0) \/ exists ge_signed_half_unique_otherrowentryvaluedecode. (((srt_value_unique_other) = 2 * ge_signed_half_unique_otherrowentryvaluedecode + 1 /\ (ge_balance_positive_unique_otherrowentryvalue) = 0) /\ (ge_balance_negative_unique_otherrowentryvalue) = S ge_signed_half_unique_otherrowentryvaluedecode))) /\ ((dst_positive_unique_otherrowentry) + ge_balance_negative_unique_otherrowentryvalue = (dst_negative_unique_otherrowentry) + ge_balance_positive_unique_otherrowentryvalue))))))))) /\ (exists srs_slice_unique_otherrowrow_sum. ((((exists dst_positive_code_unique_otherrowrow_sumslicesource_table dst_positive_scale_unique_otherrowrow_sumslicesource_table dst_negative_code_unique_otherrowrow_sumslicesource_table dst_negative_scale_unique_otherrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_unique_otherrowrow_sumslicesource_table) + (dst_positive_scale_unique_otherrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_otherrowrow_sumslicesource_table) + (dst_positive_scale_unique_otherrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_otherrowrow_sumslicesource_table) + (dst_positive_scale_unique_otherrowrow_sumslicesource_table))) + (((dst_negative_code_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)))) * S ((((dst_positive_code_unique_otherrowrow_sumslicesource_table) + (dst_positive_scale_unique_otherrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_otherrowrow_sumslicesource_table) + (dst_positive_scale_unique_otherrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_otherrowrow_sumslicesource_table) + (dst_positive_scale_unique_otherrowrow_sumslicesource_table))) + (((dst_negative_code_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)))) + ((((dst_negative_code_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table))) + (((dst_negative_code_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_otherrowrow_sumslicesource_table) + (dst_negative_scale_unique_otherrowrow_sumslicesource_table)))))) /\ (forall dst_index_unique_otherrowrow_sumslicesource_table. (exists pvs_le_gap_unique_otherrowrow_sumslicesource_tabledomain. pvs_le_gap_unique_otherrowrow_sumslicesource_tabledomain + (dst_index_unique_otherrowrow_sumslicesource_table) = (0)) -> exists dst_positive_unique_otherrowrow_sumslicesource_table dst_negative_unique_otherrowrow_sumslicesource_table dst_value_unique_otherrowrow_sumslicesource_table. ((((exists ff_h_pvs_unique_otherrowrow_sumslicesource_tableentrypositive. ff_h_pvs_unique_otherrowrow_sumslicesource_tableentrypositive + S (dst_positive_unique_otherrowrow_sumslicesource_table) = S ((S (dst_index_unique_otherrowrow_sumslicesource_table)) * dst_positive_scale_unique_otherrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_otherrowrow_sumslicesource_tableentrypositive. dst_positive_code_unique_otherrowrow_sumslicesource_table = ff_q_pvs_unique_otherrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_unique_otherrowrow_sumslicesource_table)) * dst_positive_scale_unique_otherrowrow_sumslicesource_table) + (dst_positive_unique_otherrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_unique_otherrowrow_sumslicesource_tableentrynegative. ff_h_pvs_unique_otherrowrow_sumslicesource_tableentrynegative + S (dst_negative_unique_otherrowrow_sumslicesource_table) = S ((S (dst_index_unique_otherrowrow_sumslicesource_table)) * dst_negative_scale_unique_otherrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_otherrowrow_sumslicesource_tableentrynegative. dst_negative_code_unique_otherrowrow_sumslicesource_table = ff_q_pvs_unique_otherrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_unique_otherrowrow_sumslicesource_table)) * dst_negative_scale_unique_otherrowrow_sumslicesource_table) + (dst_negative_unique_otherrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_unique_otherrowrow_sumslicesource_tableentryvalue ge_balance_negative_unique_otherrowrow_sumslicesource_tableentryvalue. (((((dst_value_unique_otherrowrow_sumslicesource_table) = 2 * (ge_balance_positive_unique_otherrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_unique_otherrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_otherrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_unique_otherrowrow_sumslicesource_table) = 2 * ge_signed_half_unique_otherrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_otherrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_otherrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_unique_otherrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_unique_otherrowrow_sumslicesource_table) + ge_balance_negative_unique_otherrowrow_sumslicesource_tableentryvalue = (dst_negative_unique_otherrowrow_sumslicesource_table) + ge_balance_positive_unique_otherrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_otherrowrow_sumsliceoutput_table dst_positive_scale_unique_otherrowrow_sumsliceoutput_table dst_negative_code_unique_otherrowrow_sumsliceoutput_table dst_negative_scale_unique_otherrowrow_sumsliceoutput_table. (((srs_slice_unique_otherrowrow_sum) = (((((dst_positive_code_unique_otherrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_otherrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_otherrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_otherrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_otherrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_otherrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_unique_otherrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_otherrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_otherrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_otherrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_otherrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_otherrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_unique_otherrowrow_sumsliceoutput_table. (exists pvs_le_gap_unique_otherrowrow_sumsliceoutput_tabledomain. pvs_le_gap_unique_otherrowrow_sumsliceoutput_tabledomain + (dst_index_unique_otherrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_unique_otherrowrow_sumsliceoutput_table dst_negative_unique_otherrowrow_sumsliceoutput_table dst_value_unique_otherrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_unique_otherrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_unique_otherrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_unique_otherrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_otherrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_otherrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_otherrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_unique_otherrowrow_sumsliceoutput_table = ff_q_pvs_unique_otherrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_unique_otherrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_otherrowrow_sumsliceoutput_table) + (dst_positive_unique_otherrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_unique_otherrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_unique_otherrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_unique_otherrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_otherrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_otherrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_otherrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_unique_otherrowrow_sumsliceoutput_table = ff_q_pvs_unique_otherrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_unique_otherrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_otherrowrow_sumsliceoutput_table) + (dst_negative_unique_otherrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_unique_otherrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_unique_otherrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_unique_otherrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_unique_otherrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_unique_otherrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_unique_otherrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_unique_otherrowrow_sumsliceoutput_table) = 2 * ge_signed_half_unique_otherrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_otherrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_unique_otherrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_unique_otherrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_unique_otherrowrow_sumsliceoutput_table) + ge_balance_negative_unique_otherrowrow_sumsliceoutput_tableentryvalue = (dst_negative_unique_otherrowrow_sumsliceoutput_table) + ge_balance_positive_unique_otherrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_unique_otherrowrow_sumslice. (exists pvs_gap_unique_otherrowrow_sumslicebound. pvs_gap_unique_otherrowrow_sumslicebound + S (srs_index_unique_otherrowrow_sumslice) = (n)) -> exists srs_value_unique_otherrowrow_sumslice. (((exists dst_positive_code_unique_otherrowrow_sumsliceentrysource dst_positive_scale_unique_otherrowrow_sumsliceentrysource dst_negative_code_unique_otherrowrow_sumsliceentrysource dst_negative_scale_unique_otherrowrow_sumsliceentrysource dst_positive_unique_otherrowrow_sumsliceentrysource dst_negative_unique_otherrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_unique_otherrowrow_sumsliceentrysource) + (dst_positive_scale_unique_otherrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_otherrowrow_sumsliceentrysource) + (dst_positive_scale_unique_otherrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_otherrowrow_sumsliceentrysource) + (dst_positive_scale_unique_otherrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_unique_otherrowrow_sumsliceentrysource) + (dst_positive_scale_unique_otherrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_otherrowrow_sumsliceentrysource) + (dst_positive_scale_unique_otherrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_otherrowrow_sumsliceentrysource) + (dst_positive_scale_unique_otherrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)))) + ((((dst_negative_code_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_otherrowrow_sumsliceentrysource) + (dst_negative_scale_unique_otherrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_unique_otherrowrow_sumsliceentrysourcepositive. ff_h_pvs_unique_otherrowrow_sumsliceentrysourcepositive + S (dst_positive_unique_otherrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_other)))) + ((t) * (srs_index_unique_otherrowrow_sumslice))))) * dst_positive_scale_unique_otherrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_otherrowrow_sumsliceentrysourcepositive. dst_positive_code_unique_otherrowrow_sumsliceentrysource = ff_q_pvs_unique_otherrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_unique_other)))) + ((t) * (srs_index_unique_otherrowrow_sumslice))))) * dst_positive_scale_unique_otherrowrow_sumsliceentrysource) + (dst_positive_unique_otherrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_unique_otherrowrow_sumsliceentrysourcenegative. ff_h_pvs_unique_otherrowrow_sumsliceentrysourcenegative + S (dst_negative_unique_otherrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_other)))) + ((t) * (srs_index_unique_otherrowrow_sumslice))))) * dst_negative_scale_unique_otherrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_otherrowrow_sumsliceentrysourcenegative. dst_negative_code_unique_otherrowrow_sumsliceentrysource = ff_q_pvs_unique_otherrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_unique_other)))) + ((t) * (srs_index_unique_otherrowrow_sumslice))))) * dst_negative_scale_unique_otherrowrow_sumsliceentrysource) + (dst_negative_unique_otherrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_unique_otherrowrow_sumsliceentrysourcevalue ge_balance_negative_unique_otherrowrow_sumsliceentrysourcevalue. (((((srs_value_unique_otherrowrow_sumslice) = 2 * (ge_balance_positive_unique_otherrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_unique_otherrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_unique_otherrowrow_sumsliceentrysourcevaluedecode. (((srs_value_unique_otherrowrow_sumslice) = 2 * ge_signed_half_unique_otherrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_unique_otherrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_unique_otherrowrow_sumsliceentrysourcevalue) = S ge_signed_half_unique_otherrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_unique_otherrowrow_sumsliceentrysource) + ge_balance_negative_unique_otherrowrow_sumsliceentrysourcevalue = (dst_negative_unique_otherrowrow_sumsliceentrysource) + ge_balance_positive_unique_otherrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_unique_otherrowrow_sumsliceentryoutput dst_positive_scale_unique_otherrowrow_sumsliceentryoutput dst_negative_code_unique_otherrowrow_sumsliceentryoutput dst_negative_scale_unique_otherrowrow_sumsliceentryoutput dst_positive_unique_otherrowrow_sumsliceentryoutput dst_negative_unique_otherrowrow_sumsliceentryoutput. (((srs_slice_unique_otherrowrow_sum) = (((((dst_positive_code_unique_otherrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_otherrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_otherrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_otherrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_otherrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_otherrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_unique_otherrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_otherrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_otherrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_otherrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_otherrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_otherrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_unique_otherrowrow_sumsliceentryoutputpositive. ff_h_pvs_unique_otherrowrow_sumsliceentryoutputpositive + S (dst_positive_unique_otherrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_otherrowrow_sumslice)) * dst_positive_scale_unique_otherrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_otherrowrow_sumsliceentryoutputpositive. dst_positive_code_unique_otherrowrow_sumsliceentryoutput = ff_q_pvs_unique_otherrowrow_sumsliceentryoutputpositive * S ((S (srs_index_unique_otherrowrow_sumslice)) * dst_positive_scale_unique_otherrowrow_sumsliceentryoutput) + (dst_positive_unique_otherrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_unique_otherrowrow_sumsliceentryoutputnegative. ff_h_pvs_unique_otherrowrow_sumsliceentryoutputnegative + S (dst_negative_unique_otherrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_otherrowrow_sumslice)) * dst_negative_scale_unique_otherrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_otherrowrow_sumsliceentryoutputnegative. dst_negative_code_unique_otherrowrow_sumsliceentryoutput = ff_q_pvs_unique_otherrowrow_sumsliceentryoutputnegative * S ((S (srs_index_unique_otherrowrow_sumslice)) * dst_negative_scale_unique_otherrowrow_sumsliceentryoutput) + (dst_negative_unique_otherrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_unique_otherrowrow_sumsliceentryoutputvalue ge_balance_negative_unique_otherrowrow_sumsliceentryoutputvalue. (((((srs_value_unique_otherrowrow_sumslice) = 2 * (ge_balance_positive_unique_otherrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_unique_otherrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_unique_otherrowrow_sumsliceentryoutputvaluedecode. (((srs_value_unique_otherrowrow_sumslice) = 2 * ge_signed_half_unique_otherrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_unique_otherrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_unique_otherrowrow_sumsliceentryoutputvalue) = S ge_signed_half_unique_otherrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_unique_otherrowrow_sumsliceentryoutput) + ge_balance_negative_unique_otherrowrow_sumsliceentryoutputvalue = (dst_negative_unique_otherrowrow_sumsliceentryoutput) + ge_balance_positive_unique_otherrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_unique_otherrowrow_sumsum dst_positive_scale_unique_otherrowrow_sumsum dst_negative_code_unique_otherrowrow_sumsum dst_negative_scale_unique_otherrowrow_sumsum dst_positive_sum_unique_otherrowrow_sumsum dst_negative_sum_unique_otherrowrow_sumsum. (((srs_slice_unique_otherrowrow_sum) = (((((dst_positive_code_unique_otherrowrow_sumsum) + (dst_positive_scale_unique_otherrowrow_sumsum)) * S ((dst_positive_code_unique_otherrowrow_sumsum) + (dst_positive_scale_unique_otherrowrow_sumsum)) + ((dst_positive_scale_unique_otherrowrow_sumsum) + (dst_positive_scale_unique_otherrowrow_sumsum))) + (((dst_negative_code_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)) * S ((dst_negative_code_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)) + ((dst_negative_scale_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)))) * S ((((dst_positive_code_unique_otherrowrow_sumsum) + (dst_positive_scale_unique_otherrowrow_sumsum)) * S ((dst_positive_code_unique_otherrowrow_sumsum) + (dst_positive_scale_unique_otherrowrow_sumsum)) + ((dst_positive_scale_unique_otherrowrow_sumsum) + (dst_positive_scale_unique_otherrowrow_sumsum))) + (((dst_negative_code_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)) * S ((dst_negative_code_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)) + ((dst_negative_scale_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)))) + ((((dst_negative_code_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)) * S ((dst_negative_code_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)) + ((dst_negative_scale_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum))) + (((dst_negative_code_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)) * S ((dst_negative_code_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)) + ((dst_negative_scale_unique_otherrowrow_sumsum) + (dst_negative_scale_unique_otherrowrow_sumsum)))))) /\ (((exists fs_u_dst_unique_otherrowrow_sumsumpositive fs_v_dst_unique_otherrowrow_sumsumpositive. ((((exists fs_h_dst_unique_otherrowrow_sumsumpositive_body_start. fs_h_dst_unique_otherrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_otherrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_otherrowrow_sumsumpositive_body_start. fs_u_dst_unique_otherrowrow_sumsumpositive = fs_q_dst_unique_otherrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_unique_otherrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_unique_otherrowrow_sumsumpositive_body_terminal. fs_h_dst_unique_otherrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_unique_otherrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_otherrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_otherrowrow_sumsumpositive_body_terminal. fs_u_dst_unique_otherrowrow_sumsumpositive = fs_q_dst_unique_otherrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_unique_otherrowrow_sumsumpositive) + (dst_positive_sum_unique_otherrowrow_sumsum))) /\ forall fs_i_dst_unique_otherrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_unique_otherrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_unique_otherrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_unique_otherrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_unique_otherrowrow_sumsumpositive_body_steps fs_r_dst_unique_otherrowrow_sumsumpositive_body_steps fs_s_dst_unique_otherrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_unique_otherrowrow_sumsumpositive_body_steps_summand. fs_h_dst_unique_otherrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_unique_otherrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_otherrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_otherrowrow_sumsum)) /\ exists fs_q_dst_unique_otherrowrow_sumsumpositive_body_steps_summand. dst_positive_code_unique_otherrowrow_sumsum = fs_q_dst_unique_otherrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_unique_otherrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_otherrowrow_sumsum) + (fs_a_dst_unique_otherrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_otherrowrow_sumsumpositive_body_steps_partial. fs_h_dst_unique_otherrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_unique_otherrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_otherrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_otherrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_otherrowrow_sumsumpositive_body_steps_partial. fs_u_dst_unique_otherrowrow_sumsumpositive = fs_q_dst_unique_otherrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_unique_otherrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_otherrowrow_sumsumpositive) + (fs_r_dst_unique_otherrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_otherrowrow_sumsumpositive_body_steps_successor. fs_h_dst_unique_otherrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_unique_otherrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_unique_otherrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_otherrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_otherrowrow_sumsumpositive_body_steps_successor. fs_u_dst_unique_otherrowrow_sumsumpositive = fs_q_dst_unique_otherrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_unique_otherrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_otherrowrow_sumsumpositive) + (fs_s_dst_unique_otherrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_unique_otherrowrow_sumsumpositive_body_steps = fs_r_dst_unique_otherrowrow_sumsumpositive_body_steps + fs_a_dst_unique_otherrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_unique_otherrowrow_sumsumnegative fs_v_dst_unique_otherrowrow_sumsumnegative. ((((exists fs_h_dst_unique_otherrowrow_sumsumnegative_body_start. fs_h_dst_unique_otherrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_otherrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_otherrowrow_sumsumnegative_body_start. fs_u_dst_unique_otherrowrow_sumsumnegative = fs_q_dst_unique_otherrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_unique_otherrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_unique_otherrowrow_sumsumnegative_body_terminal. fs_h_dst_unique_otherrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_unique_otherrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_otherrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_otherrowrow_sumsumnegative_body_terminal. fs_u_dst_unique_otherrowrow_sumsumnegative = fs_q_dst_unique_otherrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_unique_otherrowrow_sumsumnegative) + (dst_negative_sum_unique_otherrowrow_sumsum))) /\ forall fs_i_dst_unique_otherrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_unique_otherrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_unique_otherrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_unique_otherrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_unique_otherrowrow_sumsumnegative_body_steps fs_r_dst_unique_otherrowrow_sumsumnegative_body_steps fs_s_dst_unique_otherrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_unique_otherrowrow_sumsumnegative_body_steps_summand. fs_h_dst_unique_otherrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_unique_otherrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_otherrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_otherrowrow_sumsum)) /\ exists fs_q_dst_unique_otherrowrow_sumsumnegative_body_steps_summand. dst_negative_code_unique_otherrowrow_sumsum = fs_q_dst_unique_otherrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_unique_otherrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_otherrowrow_sumsum) + (fs_a_dst_unique_otherrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_otherrowrow_sumsumnegative_body_steps_partial. fs_h_dst_unique_otherrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_unique_otherrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_otherrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_otherrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_otherrowrow_sumsumnegative_body_steps_partial. fs_u_dst_unique_otherrowrow_sumsumnegative = fs_q_dst_unique_otherrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_unique_otherrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_otherrowrow_sumsumnegative) + (fs_r_dst_unique_otherrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_otherrowrow_sumsumnegative_body_steps_successor. fs_h_dst_unique_otherrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_unique_otherrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_unique_otherrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_otherrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_otherrowrow_sumsumnegative_body_steps_successor. fs_u_dst_unique_otherrowrow_sumsumnegative = fs_q_dst_unique_otherrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_unique_otherrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_otherrowrow_sumsumnegative) + (fs_s_dst_unique_otherrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_unique_otherrowrow_sumsumnegative_body_steps = fs_r_dst_unique_otherrowrow_sumsumnegative_body_steps + fs_a_dst_unique_otherrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_unique_otherrowrow_sumsumresult ge_balance_negative_unique_otherrowrow_sumsumresult. (((((srt_value_unique_other) = 2 * (ge_balance_positive_unique_otherrowrow_sumsumresult) /\ (ge_balance_negative_unique_otherrowrow_sumsumresult) = 0) \/ exists ge_signed_half_unique_otherrowrow_sumsumresultdecode. (((srt_value_unique_other) = 2 * ge_signed_half_unique_otherrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_unique_otherrowrow_sumsumresult) = 0) /\ (ge_balance_negative_unique_otherrowrow_sumsumresult) = S ge_signed_half_unique_otherrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_unique_otherrowrow_sumsum) + ge_balance_negative_unique_otherrowrow_sumsumresult = (dst_negative_sum_unique_otherrowrow_sumsum) + ge_balance_positive_unique_otherrowrow_sumsumresult)))))))))))))))))) -> (forall dst_index_unique_equal dst_first_unique_equal dst_second_unique_equal. (exists pvs_gap_unique_equalbound. pvs_gap_unique_equalbound + S (dst_index_unique_equal) = (m)) -> (exists dst_positive_code_unique_equalfirst dst_positive_scale_unique_equalfirst dst_negative_code_unique_equalfirst dst_negative_scale_unique_equalfirst dst_positive_unique_equalfirst dst_negative_unique_equalfirst. (((R) = (((((dst_positive_code_unique_equalfirst) + (dst_positive_scale_unique_equalfirst)) * S ((dst_positive_code_unique_equalfirst) + (dst_positive_scale_unique_equalfirst)) + ((dst_positive_scale_unique_equalfirst) + (dst_positive_scale_unique_equalfirst))) + (((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) * S ((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) + ((dst_negative_scale_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)))) * S ((((dst_positive_code_unique_equalfirst) + (dst_positive_scale_unique_equalfirst)) * S ((dst_positive_code_unique_equalfirst) + (dst_positive_scale_unique_equalfirst)) + ((dst_positive_scale_unique_equalfirst) + (dst_positive_scale_unique_equalfirst))) + (((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) * S ((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) + ((dst_negative_scale_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)))) + ((((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) * S ((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) + ((dst_negative_scale_unique_equalfirst) + (dst_negative_scale_unique_equalfirst))) + (((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) * S ((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) + ((dst_negative_scale_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)))))) /\ (((((exists ff_h_pvs_unique_equalfirstpositive. ff_h_pvs_unique_equalfirstpositive + S (dst_positive_unique_equalfirst) = S ((S (dst_index_unique_equal)) * dst_positive_scale_unique_equalfirst)) /\ exists ff_q_pvs_unique_equalfirstpositive. dst_positive_code_unique_equalfirst = ff_q_pvs_unique_equalfirstpositive * S ((S (dst_index_unique_equal)) * dst_positive_scale_unique_equalfirst) + (dst_positive_unique_equalfirst))) /\ (((((exists ff_h_pvs_unique_equalfirstnegative. ff_h_pvs_unique_equalfirstnegative + S (dst_negative_unique_equalfirst) = S ((S (dst_index_unique_equal)) * dst_negative_scale_unique_equalfirst)) /\ exists ff_q_pvs_unique_equalfirstnegative. dst_negative_code_unique_equalfirst = ff_q_pvs_unique_equalfirstnegative * S ((S (dst_index_unique_equal)) * dst_negative_scale_unique_equalfirst) + (dst_negative_unique_equalfirst))) /\ (exists ge_balance_positive_unique_equalfirstvalue ge_balance_negative_unique_equalfirstvalue. (((((dst_first_unique_equal) = 2 * (ge_balance_positive_unique_equalfirstvalue) /\ (ge_balance_negative_unique_equalfirstvalue) = 0) \/ exists ge_signed_half_unique_equalfirstvaluedecode. (((dst_first_unique_equal) = 2 * ge_signed_half_unique_equalfirstvaluedecode + 1 /\ (ge_balance_positive_unique_equalfirstvalue) = 0) /\ (ge_balance_negative_unique_equalfirstvalue) = S ge_signed_half_unique_equalfirstvaluedecode))) /\ ((dst_positive_unique_equalfirst) + ge_balance_negative_unique_equalfirstvalue = (dst_negative_unique_equalfirst) + ge_balance_positive_unique_equalfirstvalue))))))))) -> (exists dst_positive_code_unique_equalsecond dst_positive_scale_unique_equalsecond dst_negative_code_unique_equalsecond dst_negative_scale_unique_equalsecond dst_positive_unique_equalsecond dst_negative_unique_equalsecond. (((Q) = (((((dst_positive_code_unique_equalsecond) + (dst_positive_scale_unique_equalsecond)) * S ((dst_positive_code_unique_equalsecond) + (dst_positive_scale_unique_equalsecond)) + ((dst_positive_scale_unique_equalsecond) + (dst_positive_scale_unique_equalsecond))) + (((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) * S ((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) + ((dst_negative_scale_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)))) * S ((((dst_positive_code_unique_equalsecond) + (dst_positive_scale_unique_equalsecond)) * S ((dst_positive_code_unique_equalsecond) + (dst_positive_scale_unique_equalsecond)) + ((dst_positive_scale_unique_equalsecond) + (dst_positive_scale_unique_equalsecond))) + (((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) * S ((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) + ((dst_negative_scale_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)))) + ((((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) * S ((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) + ((dst_negative_scale_unique_equalsecond) + (dst_negative_scale_unique_equalsecond))) + (((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) * S ((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) + ((dst_negative_scale_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)))))) /\ (((((exists ff_h_pvs_unique_equalsecondpositive. ff_h_pvs_unique_equalsecondpositive + S (dst_positive_unique_equalsecond) = S ((S (dst_index_unique_equal)) * dst_positive_scale_unique_equalsecond)) /\ exists ff_q_pvs_unique_equalsecondpositive. dst_positive_code_unique_equalsecond = ff_q_pvs_unique_equalsecondpositive * S ((S (dst_index_unique_equal)) * dst_positive_scale_unique_equalsecond) + (dst_positive_unique_equalsecond))) /\ (((((exists ff_h_pvs_unique_equalsecondnegative. ff_h_pvs_unique_equalsecondnegative + S (dst_negative_unique_equalsecond) = S ((S (dst_index_unique_equal)) * dst_negative_scale_unique_equalsecond)) /\ exists ff_q_pvs_unique_equalsecondnegative. dst_negative_code_unique_equalsecond = ff_q_pvs_unique_equalsecondnegative * S ((S (dst_index_unique_equal)) * dst_negative_scale_unique_equalsecond) + (dst_negative_unique_equalsecond))) /\ (exists ge_balance_positive_unique_equalsecondvalue ge_balance_negative_unique_equalsecondvalue. (((((dst_second_unique_equal) = 2 * (ge_balance_positive_unique_equalsecondvalue) /\ (ge_balance_negative_unique_equalsecondvalue) = 0) \/ exists ge_signed_half_unique_equalsecondvaluedecode. (((dst_second_unique_equal) = 2 * ge_signed_half_unique_equalsecondvaluedecode + 1 /\ (ge_balance_positive_unique_equalsecondvalue) = 0) /\ (ge_balance_negative_unique_equalsecondvalue) = S ge_signed_half_unique_equalsecondvaluedecode))) /\ ((dst_positive_unique_equalsecond) + ge_balance_negative_unique_equalsecondvalue = (dst_negative_unique_equalsecond) + ge_balance_positive_unique_equalsecondvalue))))))))) -> dst_first_unique_equal = dst_second_unique_equal)))

Constructive proof overview

Generated structural guide

Construct a genuine row-sum table and prove its precise extensional uniqueness at every i<m.

The unchanged tactic script uses 2 declared prerequisites and contains 33 exact native proof lines.

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

Proof neighborhood

Direct dependencies

Direct dependents

none

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

33 script commands · 9 reading checkpoints · 1 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 (2)

Long local formulas use this family’s existing definitions. Each new abbreviation was expanded back to the identical native formula, including its free-variable context. The original edition is preserved below.

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 n
  7. L7
    intro hF
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.

  1. L8
    have hr : ∃ R. ArithRowSums(F,R,o,s,t,m,n)Definitions: ArithRowSums
  2. L9
    specialize signed_rectangular_row_sums_exists (m)
  3. L10
    specialize signed_rectangular_row_sums_exists (F)
  4. L11
    specialize signed_rectangular_row_sums_exists (o)
  5. L12
    specialize signed_rectangular_row_sums_exists (s)
  6. L13
    specialize signed_rectangular_row_sums_exists (t)
  7. L14
    specialize signed_rectangular_row_sums_exists (n)
  8. L15
    apply signed_rectangular_row_sums_exists
  9. L16
    exact hF
03Separate the logical casesL17–17

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

  1. L17
    cases hr
04Construct an explicit witnessL18–18

Supply the displayed value, then prove that it has the required property.

  1. L18
    exists x
05Separate the logical casesL19–19

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

  1. L19
    split
06Use earlier factsL20–20

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

  1. L20
    exact hr_witness
07Fix variables and assumptionsL21–22

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

  1. L21
    intro Q
  2. L22
    intro hQ
08Use earlier factsL23–32

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

  1. L23
    specialize signed_rectangular_row_sums_extensional_unique (F)
  2. L24
    specialize signed_rectangular_row_sums_extensional_unique (x)
  3. L25
    specialize signed_rectangular_row_sums_extensional_unique (Q)
  4. L26
    specialize signed_rectangular_row_sums_extensional_unique (o)
  5. L27
    specialize signed_rectangular_row_sums_extensional_unique (s)
  6. L28
    specialize signed_rectangular_row_sums_extensional_unique (t)
  7. L29
    specialize signed_rectangular_row_sums_extensional_unique (m)
  8. L30
    specialize signed_rectangular_row_sums_extensional_unique (n)
  9. L31
    apply signed_rectangular_row_sums_extensional_unique
  10. L32
    exact hr_witness
09Use earlier factsL33–33

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

  1. L33
    exact hQ

Library-wide reading audit

Original exact command ledger · 33 lines
  1. 0001intro F
  2. 0002intro o
  3. 0003intro s
  4. 0004intro t
  5. 0005intro m
  6. 0006intro n
  7. 0007intro hF
  8. 0008have hr : exists R. (((exists dst_positive_code_unique_constructsource_table dst_positive_scale_unique_constructsource_table dst_negative_code_unique_constructsource_table dst_negative_scale_unique_constructsource_table. (((F) = (((((dst_positive_code_unique_constructsource_table) + (dst_positive_scale_unique_constructsource_table)) * S ((dst_positive_code_unique_constructsource_table) + (dst_positive_scale_unique_constructsource_table)) + ((dst_positive_scale_unique_constructsource_table) + (dst_positive_scale_unique_constructsource_table))) + (((dst_negative_code_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)) * S ((dst_negative_code_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)) + ((dst_negative_scale_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)))) * S ((((dst_positive_code_unique_constructsource_table) + (dst_positive_scale_unique_constructsource_table)) * S ((dst_positive_code_unique_constructsource_table) + (dst_positive_scale_unique_constructsource_table)) + ((dst_positive_scale_unique_constructsource_table) + (dst_positive_scale_unique_constructsource_table))) + (((dst_negative_code_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)) * S ((dst_negative_code_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)) + ((dst_negative_scale_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)))) + ((((dst_negative_code_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)) * S ((dst_negative_code_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)) + ((dst_negative_scale_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table))) + (((dst_negative_code_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)) * S ((dst_negative_code_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)) + ((dst_negative_scale_unique_constructsource_table) + (dst_negative_scale_unique_constructsource_table)))))) /\ (forall dst_index_unique_constructsource_table. (exists pvs_le_gap_unique_constructsource_tabledomain. pvs_le_gap_unique_constructsource_tabledomain + (dst_index_unique_constructsource_table) = (0)) -> exists dst_positive_unique_constructsource_table dst_negative_unique_constructsource_table dst_value_unique_constructsource_table. ((((exists ff_h_pvs_unique_constructsource_tableentrypositive. ff_h_pvs_unique_constructsource_tableentrypositive + S (dst_positive_unique_constructsource_table) = S ((S (dst_index_unique_constructsource_table)) * dst_positive_scale_unique_constructsource_table)) /\ exists ff_q_pvs_unique_constructsource_tableentrypositive. dst_positive_code_unique_constructsource_table = ff_q_pvs_unique_constructsource_tableentrypositive * S ((S (dst_index_unique_constructsource_table)) * dst_positive_scale_unique_constructsource_table) + (dst_positive_unique_constructsource_table))) /\ (((((exists ff_h_pvs_unique_constructsource_tableentrynegative. ff_h_pvs_unique_constructsource_tableentrynegative + S (dst_negative_unique_constructsource_table) = S ((S (dst_index_unique_constructsource_table)) * dst_negative_scale_unique_constructsource_table)) /\ exists ff_q_pvs_unique_constructsource_tableentrynegative. dst_negative_code_unique_constructsource_table = ff_q_pvs_unique_constructsource_tableentrynegative * S ((S (dst_index_unique_constructsource_table)) * dst_negative_scale_unique_constructsource_table) + (dst_negative_unique_constructsource_table))) /\ (exists ge_balance_positive_unique_constructsource_tableentryvalue ge_balance_negative_unique_constructsource_tableentryvalue. (((((dst_value_unique_constructsource_table) = 2 * (ge_balance_positive_unique_constructsource_tableentryvalue) /\ (ge_balance_negative_unique_constructsource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_constructsource_tableentryvaluedecode. (((dst_value_unique_constructsource_table) = 2 * ge_signed_half_unique_constructsource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_constructsource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_constructsource_tableentryvalue) = S ge_signed_half_unique_constructsource_tableentryvaluedecode))) /\ ((dst_positive_unique_constructsource_table) + ge_balance_negative_unique_constructsource_tableentryvalue = (dst_negative_unique_constructsource_table) + ge_balance_positive_unique_constructsource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_constructrow_table dst_positive_scale_unique_constructrow_table dst_negative_code_unique_constructrow_table dst_negative_scale_unique_constructrow_table. (((R) = (((((dst_positive_code_unique_constructrow_table) + (dst_positive_scale_unique_constructrow_table)) * S ((dst_positive_code_unique_constructrow_table) + (dst_positive_scale_unique_constructrow_table)) + ((dst_positive_scale_unique_constructrow_table) + (dst_positive_scale_unique_constructrow_table))) + (((dst_negative_code_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)) * S ((dst_negative_code_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)) + ((dst_negative_scale_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)))) * S ((((dst_positive_code_unique_constructrow_table) + (dst_positive_scale_unique_constructrow_table)) * S ((dst_positive_code_unique_constructrow_table) + (dst_positive_scale_unique_constructrow_table)) + ((dst_positive_scale_unique_constructrow_table) + (dst_positive_scale_unique_constructrow_table))) + (((dst_negative_code_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)) * S ((dst_negative_code_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)) + ((dst_negative_scale_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)))) + ((((dst_negative_code_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)) * S ((dst_negative_code_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)) + ((dst_negative_scale_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table))) + (((dst_negative_code_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)) * S ((dst_negative_code_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)) + ((dst_negative_scale_unique_constructrow_table) + (dst_negative_scale_unique_constructrow_table)))))) /\ (forall dst_index_unique_constructrow_table. (exists pvs_le_gap_unique_constructrow_tabledomain. pvs_le_gap_unique_constructrow_tabledomain + (dst_index_unique_constructrow_table) = (m)) -> exists dst_positive_unique_constructrow_table dst_negative_unique_constructrow_table dst_value_unique_constructrow_table. ((((exists ff_h_pvs_unique_constructrow_tableentrypositive. ff_h_pvs_unique_constructrow_tableentrypositive + S (dst_positive_unique_constructrow_table) = S ((S (dst_index_unique_constructrow_table)) * dst_positive_scale_unique_constructrow_table)) /\ exists ff_q_pvs_unique_constructrow_tableentrypositive. dst_positive_code_unique_constructrow_table = ff_q_pvs_unique_constructrow_tableentrypositive * S ((S (dst_index_unique_constructrow_table)) * dst_positive_scale_unique_constructrow_table) + (dst_positive_unique_constructrow_table))) /\ (((((exists ff_h_pvs_unique_constructrow_tableentrynegative. ff_h_pvs_unique_constructrow_tableentrynegative + S (dst_negative_unique_constructrow_table) = S ((S (dst_index_unique_constructrow_table)) * dst_negative_scale_unique_constructrow_table)) /\ exists ff_q_pvs_unique_constructrow_tableentrynegative. dst_negative_code_unique_constructrow_table = ff_q_pvs_unique_constructrow_tableentrynegative * S ((S (dst_index_unique_constructrow_table)) * dst_negative_scale_unique_constructrow_table) + (dst_negative_unique_constructrow_table))) /\ (exists ge_balance_positive_unique_constructrow_tableentryvalue ge_balance_negative_unique_constructrow_tableentryvalue. (((((dst_value_unique_constructrow_table) = 2 * (ge_balance_positive_unique_constructrow_tableentryvalue) /\ (ge_balance_negative_unique_constructrow_tableentryvalue) = 0) \/ exists ge_signed_half_unique_constructrow_tableentryvaluedecode. (((dst_value_unique_constructrow_table) = 2 * ge_signed_half_unique_constructrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_constructrow_tableentryvalue) = 0) /\ (ge_balance_negative_unique_constructrow_tableentryvalue) = S ge_signed_half_unique_constructrow_tableentryvaluedecode))) /\ ((dst_positive_unique_constructrow_table) + ge_balance_negative_unique_constructrow_tableentryvalue = (dst_negative_unique_constructrow_table) + ge_balance_positive_unique_constructrow_tableentryvalue))))))))) /\ (forall srt_index_unique_construct. (exists pvs_gap_unique_constructbound. pvs_gap_unique_constructbound + S (srt_index_unique_construct) = (m)) -> exists srt_value_unique_construct. (((exists dst_positive_code_unique_constructrowentry dst_positive_scale_unique_constructrowentry dst_negative_code_unique_constructrowentry dst_negative_scale_unique_constructrowentry dst_positive_unique_constructrowentry dst_negative_unique_constructrowentry. (((R) = (((((dst_positive_code_unique_constructrowentry) + (dst_positive_scale_unique_constructrowentry)) * S ((dst_positive_code_unique_constructrowentry) + (dst_positive_scale_unique_constructrowentry)) + ((dst_positive_scale_unique_constructrowentry) + (dst_positive_scale_unique_constructrowentry))) + (((dst_negative_code_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)) * S ((dst_negative_code_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)) + ((dst_negative_scale_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)))) * S ((((dst_positive_code_unique_constructrowentry) + (dst_positive_scale_unique_constructrowentry)) * S ((dst_positive_code_unique_constructrowentry) + (dst_positive_scale_unique_constructrowentry)) + ((dst_positive_scale_unique_constructrowentry) + (dst_positive_scale_unique_constructrowentry))) + (((dst_negative_code_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)) * S ((dst_negative_code_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)) + ((dst_negative_scale_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)))) + ((((dst_negative_code_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)) * S ((dst_negative_code_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)) + ((dst_negative_scale_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry))) + (((dst_negative_code_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)) * S ((dst_negative_code_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)) + ((dst_negative_scale_unique_constructrowentry) + (dst_negative_scale_unique_constructrowentry)))))) /\ (((((exists ff_h_pvs_unique_constructrowentrypositive. ff_h_pvs_unique_constructrowentrypositive + S (dst_positive_unique_constructrowentry) = S ((S (srt_index_unique_construct)) * dst_positive_scale_unique_constructrowentry)) /\ exists ff_q_pvs_unique_constructrowentrypositive. dst_positive_code_unique_constructrowentry = ff_q_pvs_unique_constructrowentrypositive * S ((S (srt_index_unique_construct)) * dst_positive_scale_unique_constructrowentry) + (dst_positive_unique_constructrowentry))) /\ (((((exists ff_h_pvs_unique_constructrowentrynegative. ff_h_pvs_unique_constructrowentrynegative + S (dst_negative_unique_constructrowentry) = S ((S (srt_index_unique_construct)) * dst_negative_scale_unique_constructrowentry)) /\ exists ff_q_pvs_unique_constructrowentrynegative. dst_negative_code_unique_constructrowentry = ff_q_pvs_unique_constructrowentrynegative * S ((S (srt_index_unique_construct)) * dst_negative_scale_unique_constructrowentry) + (dst_negative_unique_constructrowentry))) /\ (exists ge_balance_positive_unique_constructrowentryvalue ge_balance_negative_unique_constructrowentryvalue. (((((srt_value_unique_construct) = 2 * (ge_balance_positive_unique_constructrowentryvalue) /\ (ge_balance_negative_unique_constructrowentryvalue) = 0) \/ exists ge_signed_half_unique_constructrowentryvaluedecode. (((srt_value_unique_construct) = 2 * ge_signed_half_unique_constructrowentryvaluedecode + 1 /\ (ge_balance_positive_unique_constructrowentryvalue) = 0) /\ (ge_balance_negative_unique_constructrowentryvalue) = S ge_signed_half_unique_constructrowentryvaluedecode))) /\ ((dst_positive_unique_constructrowentry) + ge_balance_negative_unique_constructrowentryvalue = (dst_negative_unique_constructrowentry) + ge_balance_positive_unique_constructrowentryvalue))))))))) /\ (exists srs_slice_unique_constructrowrow_sum. ((((exists dst_positive_code_unique_constructrowrow_sumslicesource_table dst_positive_scale_unique_constructrowrow_sumslicesource_table dst_negative_code_unique_constructrowrow_sumslicesource_table dst_negative_scale_unique_constructrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_unique_constructrowrow_sumslicesource_table) + (dst_positive_scale_unique_constructrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_constructrowrow_sumslicesource_table) + (dst_positive_scale_unique_constructrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_constructrowrow_sumslicesource_table) + (dst_positive_scale_unique_constructrowrow_sumslicesource_table))) + (((dst_negative_code_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)))) * S ((((dst_positive_code_unique_constructrowrow_sumslicesource_table) + (dst_positive_scale_unique_constructrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_constructrowrow_sumslicesource_table) + (dst_positive_scale_unique_constructrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_constructrowrow_sumslicesource_table) + (dst_positive_scale_unique_constructrowrow_sumslicesource_table))) + (((dst_negative_code_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)))) + ((((dst_negative_code_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table))) + (((dst_negative_code_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_constructrowrow_sumslicesource_table) + (dst_negative_scale_unique_constructrowrow_sumslicesource_table)))))) /\ (forall dst_index_unique_constructrowrow_sumslicesource_table. (exists pvs_le_gap_unique_constructrowrow_sumslicesource_tabledomain. pvs_le_gap_unique_constructrowrow_sumslicesource_tabledomain + (dst_index_unique_constructrowrow_sumslicesource_table) = (0)) -> exists dst_positive_unique_constructrowrow_sumslicesource_table dst_negative_unique_constructrowrow_sumslicesource_table dst_value_unique_constructrowrow_sumslicesource_table. ((((exists ff_h_pvs_unique_constructrowrow_sumslicesource_tableentrypositive. ff_h_pvs_unique_constructrowrow_sumslicesource_tableentrypositive + S (dst_positive_unique_constructrowrow_sumslicesource_table) = S ((S (dst_index_unique_constructrowrow_sumslicesource_table)) * dst_positive_scale_unique_constructrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_constructrowrow_sumslicesource_tableentrypositive. dst_positive_code_unique_constructrowrow_sumslicesource_table = ff_q_pvs_unique_constructrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_unique_constructrowrow_sumslicesource_table)) * dst_positive_scale_unique_constructrowrow_sumslicesource_table) + (dst_positive_unique_constructrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_unique_constructrowrow_sumslicesource_tableentrynegative. ff_h_pvs_unique_constructrowrow_sumslicesource_tableentrynegative + S (dst_negative_unique_constructrowrow_sumslicesource_table) = S ((S (dst_index_unique_constructrowrow_sumslicesource_table)) * dst_negative_scale_unique_constructrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_constructrowrow_sumslicesource_tableentrynegative. dst_negative_code_unique_constructrowrow_sumslicesource_table = ff_q_pvs_unique_constructrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_unique_constructrowrow_sumslicesource_table)) * dst_negative_scale_unique_constructrowrow_sumslicesource_table) + (dst_negative_unique_constructrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_unique_constructrowrow_sumslicesource_tableentryvalue ge_balance_negative_unique_constructrowrow_sumslicesource_tableentryvalue. (((((dst_value_unique_constructrowrow_sumslicesource_table) = 2 * (ge_balance_positive_unique_constructrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_unique_constructrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_constructrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_unique_constructrowrow_sumslicesource_table) = 2 * ge_signed_half_unique_constructrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_constructrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_constructrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_unique_constructrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_unique_constructrowrow_sumslicesource_table) + ge_balance_negative_unique_constructrowrow_sumslicesource_tableentryvalue = (dst_negative_unique_constructrowrow_sumslicesource_table) + ge_balance_positive_unique_constructrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_constructrowrow_sumsliceoutput_table dst_positive_scale_unique_constructrowrow_sumsliceoutput_table dst_negative_code_unique_constructrowrow_sumsliceoutput_table dst_negative_scale_unique_constructrowrow_sumsliceoutput_table. (((srs_slice_unique_constructrowrow_sum) = (((((dst_positive_code_unique_constructrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_constructrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_constructrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_constructrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_constructrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_constructrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_unique_constructrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_constructrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_constructrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_constructrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_constructrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_constructrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_unique_constructrowrow_sumsliceoutput_table. (exists pvs_le_gap_unique_constructrowrow_sumsliceoutput_tabledomain. pvs_le_gap_unique_constructrowrow_sumsliceoutput_tabledomain + (dst_index_unique_constructrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_unique_constructrowrow_sumsliceoutput_table dst_negative_unique_constructrowrow_sumsliceoutput_table dst_value_unique_constructrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_unique_constructrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_unique_constructrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_unique_constructrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_constructrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_constructrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_constructrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_unique_constructrowrow_sumsliceoutput_table = ff_q_pvs_unique_constructrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_unique_constructrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_constructrowrow_sumsliceoutput_table) + (dst_positive_unique_constructrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_unique_constructrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_unique_constructrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_unique_constructrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_constructrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_constructrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_constructrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_unique_constructrowrow_sumsliceoutput_table = ff_q_pvs_unique_constructrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_unique_constructrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_constructrowrow_sumsliceoutput_table) + (dst_negative_unique_constructrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_unique_constructrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_unique_constructrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_unique_constructrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_unique_constructrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_unique_constructrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_unique_constructrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_unique_constructrowrow_sumsliceoutput_table) = 2 * ge_signed_half_unique_constructrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_constructrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_unique_constructrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_unique_constructrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_unique_constructrowrow_sumsliceoutput_table) + ge_balance_negative_unique_constructrowrow_sumsliceoutput_tableentryvalue = (dst_negative_unique_constructrowrow_sumsliceoutput_table) + ge_balance_positive_unique_constructrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_unique_constructrowrow_sumslice. (exists pvs_gap_unique_constructrowrow_sumslicebound. pvs_gap_unique_constructrowrow_sumslicebound + S (srs_index_unique_constructrowrow_sumslice) = (n)) -> exists srs_value_unique_constructrowrow_sumslice. (((exists dst_positive_code_unique_constructrowrow_sumsliceentrysource dst_positive_scale_unique_constructrowrow_sumsliceentrysource dst_negative_code_unique_constructrowrow_sumsliceentrysource dst_negative_scale_unique_constructrowrow_sumsliceentrysource dst_positive_unique_constructrowrow_sumsliceentrysource dst_negative_unique_constructrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_unique_constructrowrow_sumsliceentrysource) + (dst_positive_scale_unique_constructrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_constructrowrow_sumsliceentrysource) + (dst_positive_scale_unique_constructrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_constructrowrow_sumsliceentrysource) + (dst_positive_scale_unique_constructrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_unique_constructrowrow_sumsliceentrysource) + (dst_positive_scale_unique_constructrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_constructrowrow_sumsliceentrysource) + (dst_positive_scale_unique_constructrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_constructrowrow_sumsliceentrysource) + (dst_positive_scale_unique_constructrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)))) + ((((dst_negative_code_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_constructrowrow_sumsliceentrysource) + (dst_negative_scale_unique_constructrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_unique_constructrowrow_sumsliceentrysourcepositive. ff_h_pvs_unique_constructrowrow_sumsliceentrysourcepositive + S (dst_positive_unique_constructrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_construct)))) + ((t) * (srs_index_unique_constructrowrow_sumslice))))) * dst_positive_scale_unique_constructrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_constructrowrow_sumsliceentrysourcepositive. dst_positive_code_unique_constructrowrow_sumsliceentrysource = ff_q_pvs_unique_constructrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_unique_construct)))) + ((t) * (srs_index_unique_constructrowrow_sumslice))))) * dst_positive_scale_unique_constructrowrow_sumsliceentrysource) + (dst_positive_unique_constructrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_unique_constructrowrow_sumsliceentrysourcenegative. ff_h_pvs_unique_constructrowrow_sumsliceentrysourcenegative + S (dst_negative_unique_constructrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_construct)))) + ((t) * (srs_index_unique_constructrowrow_sumslice))))) * dst_negative_scale_unique_constructrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_constructrowrow_sumsliceentrysourcenegative. dst_negative_code_unique_constructrowrow_sumsliceentrysource = ff_q_pvs_unique_constructrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_unique_construct)))) + ((t) * (srs_index_unique_constructrowrow_sumslice))))) * dst_negative_scale_unique_constructrowrow_sumsliceentrysource) + (dst_negative_unique_constructrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_unique_constructrowrow_sumsliceentrysourcevalue ge_balance_negative_unique_constructrowrow_sumsliceentrysourcevalue. (((((srs_value_unique_constructrowrow_sumslice) = 2 * (ge_balance_positive_unique_constructrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_unique_constructrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_unique_constructrowrow_sumsliceentrysourcevaluedecode. (((srs_value_unique_constructrowrow_sumslice) = 2 * ge_signed_half_unique_constructrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_unique_constructrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_unique_constructrowrow_sumsliceentrysourcevalue) = S ge_signed_half_unique_constructrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_unique_constructrowrow_sumsliceentrysource) + ge_balance_negative_unique_constructrowrow_sumsliceentrysourcevalue = (dst_negative_unique_constructrowrow_sumsliceentrysource) + ge_balance_positive_unique_constructrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_unique_constructrowrow_sumsliceentryoutput dst_positive_scale_unique_constructrowrow_sumsliceentryoutput dst_negative_code_unique_constructrowrow_sumsliceentryoutput dst_negative_scale_unique_constructrowrow_sumsliceentryoutput dst_positive_unique_constructrowrow_sumsliceentryoutput dst_negative_unique_constructrowrow_sumsliceentryoutput. (((srs_slice_unique_constructrowrow_sum) = (((((dst_positive_code_unique_constructrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_constructrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_constructrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_constructrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_constructrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_constructrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_unique_constructrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_constructrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_constructrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_constructrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_constructrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_constructrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_unique_constructrowrow_sumsliceentryoutputpositive. ff_h_pvs_unique_constructrowrow_sumsliceentryoutputpositive + S (dst_positive_unique_constructrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_constructrowrow_sumslice)) * dst_positive_scale_unique_constructrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_constructrowrow_sumsliceentryoutputpositive. dst_positive_code_unique_constructrowrow_sumsliceentryoutput = ff_q_pvs_unique_constructrowrow_sumsliceentryoutputpositive * S ((S (srs_index_unique_constructrowrow_sumslice)) * dst_positive_scale_unique_constructrowrow_sumsliceentryoutput) + (dst_positive_unique_constructrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_unique_constructrowrow_sumsliceentryoutputnegative. ff_h_pvs_unique_constructrowrow_sumsliceentryoutputnegative + S (dst_negative_unique_constructrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_constructrowrow_sumslice)) * dst_negative_scale_unique_constructrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_constructrowrow_sumsliceentryoutputnegative. dst_negative_code_unique_constructrowrow_sumsliceentryoutput = ff_q_pvs_unique_constructrowrow_sumsliceentryoutputnegative * S ((S (srs_index_unique_constructrowrow_sumslice)) * dst_negative_scale_unique_constructrowrow_sumsliceentryoutput) + (dst_negative_unique_constructrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_unique_constructrowrow_sumsliceentryoutputvalue ge_balance_negative_unique_constructrowrow_sumsliceentryoutputvalue. (((((srs_value_unique_constructrowrow_sumslice) = 2 * (ge_balance_positive_unique_constructrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_unique_constructrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_unique_constructrowrow_sumsliceentryoutputvaluedecode. (((srs_value_unique_constructrowrow_sumslice) = 2 * ge_signed_half_unique_constructrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_unique_constructrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_unique_constructrowrow_sumsliceentryoutputvalue) = S ge_signed_half_unique_constructrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_unique_constructrowrow_sumsliceentryoutput) + ge_balance_negative_unique_constructrowrow_sumsliceentryoutputvalue = (dst_negative_unique_constructrowrow_sumsliceentryoutput) + ge_balance_positive_unique_constructrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_unique_constructrowrow_sumsum dst_positive_scale_unique_constructrowrow_sumsum dst_negative_code_unique_constructrowrow_sumsum dst_negative_scale_unique_constructrowrow_sumsum dst_positive_sum_unique_constructrowrow_sumsum dst_negative_sum_unique_constructrowrow_sumsum. (((srs_slice_unique_constructrowrow_sum) = (((((dst_positive_code_unique_constructrowrow_sumsum) + (dst_positive_scale_unique_constructrowrow_sumsum)) * S ((dst_positive_code_unique_constructrowrow_sumsum) + (dst_positive_scale_unique_constructrowrow_sumsum)) + ((dst_positive_scale_unique_constructrowrow_sumsum) + (dst_positive_scale_unique_constructrowrow_sumsum))) + (((dst_negative_code_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)) * S ((dst_negative_code_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)) + ((dst_negative_scale_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)))) * S ((((dst_positive_code_unique_constructrowrow_sumsum) + (dst_positive_scale_unique_constructrowrow_sumsum)) * S ((dst_positive_code_unique_constructrowrow_sumsum) + (dst_positive_scale_unique_constructrowrow_sumsum)) + ((dst_positive_scale_unique_constructrowrow_sumsum) + (dst_positive_scale_unique_constructrowrow_sumsum))) + (((dst_negative_code_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)) * S ((dst_negative_code_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)) + ((dst_negative_scale_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)))) + ((((dst_negative_code_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)) * S ((dst_negative_code_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)) + ((dst_negative_scale_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum))) + (((dst_negative_code_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)) * S ((dst_negative_code_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)) + ((dst_negative_scale_unique_constructrowrow_sumsum) + (dst_negative_scale_unique_constructrowrow_sumsum)))))) /\ (((exists fs_u_dst_unique_constructrowrow_sumsumpositive fs_v_dst_unique_constructrowrow_sumsumpositive. ((((exists fs_h_dst_unique_constructrowrow_sumsumpositive_body_start. fs_h_dst_unique_constructrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_constructrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_constructrowrow_sumsumpositive_body_start. fs_u_dst_unique_constructrowrow_sumsumpositive = fs_q_dst_unique_constructrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_unique_constructrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_unique_constructrowrow_sumsumpositive_body_terminal. fs_h_dst_unique_constructrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_unique_constructrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_constructrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_constructrowrow_sumsumpositive_body_terminal. fs_u_dst_unique_constructrowrow_sumsumpositive = fs_q_dst_unique_constructrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_unique_constructrowrow_sumsumpositive) + (dst_positive_sum_unique_constructrowrow_sumsum))) /\ forall fs_i_dst_unique_constructrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_unique_constructrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_unique_constructrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_unique_constructrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_unique_constructrowrow_sumsumpositive_body_steps fs_r_dst_unique_constructrowrow_sumsumpositive_body_steps fs_s_dst_unique_constructrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_unique_constructrowrow_sumsumpositive_body_steps_summand. fs_h_dst_unique_constructrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_unique_constructrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_constructrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_constructrowrow_sumsum)) /\ exists fs_q_dst_unique_constructrowrow_sumsumpositive_body_steps_summand. dst_positive_code_unique_constructrowrow_sumsum = fs_q_dst_unique_constructrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_unique_constructrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_constructrowrow_sumsum) + (fs_a_dst_unique_constructrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_constructrowrow_sumsumpositive_body_steps_partial. fs_h_dst_unique_constructrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_unique_constructrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_constructrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_constructrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_constructrowrow_sumsumpositive_body_steps_partial. fs_u_dst_unique_constructrowrow_sumsumpositive = fs_q_dst_unique_constructrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_unique_constructrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_constructrowrow_sumsumpositive) + (fs_r_dst_unique_constructrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_constructrowrow_sumsumpositive_body_steps_successor. fs_h_dst_unique_constructrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_unique_constructrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_unique_constructrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_constructrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_constructrowrow_sumsumpositive_body_steps_successor. fs_u_dst_unique_constructrowrow_sumsumpositive = fs_q_dst_unique_constructrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_unique_constructrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_constructrowrow_sumsumpositive) + (fs_s_dst_unique_constructrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_unique_constructrowrow_sumsumpositive_body_steps = fs_r_dst_unique_constructrowrow_sumsumpositive_body_steps + fs_a_dst_unique_constructrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_unique_constructrowrow_sumsumnegative fs_v_dst_unique_constructrowrow_sumsumnegative. ((((exists fs_h_dst_unique_constructrowrow_sumsumnegative_body_start. fs_h_dst_unique_constructrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_constructrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_constructrowrow_sumsumnegative_body_start. fs_u_dst_unique_constructrowrow_sumsumnegative = fs_q_dst_unique_constructrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_unique_constructrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_unique_constructrowrow_sumsumnegative_body_terminal. fs_h_dst_unique_constructrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_unique_constructrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_constructrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_constructrowrow_sumsumnegative_body_terminal. fs_u_dst_unique_constructrowrow_sumsumnegative = fs_q_dst_unique_constructrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_unique_constructrowrow_sumsumnegative) + (dst_negative_sum_unique_constructrowrow_sumsum))) /\ forall fs_i_dst_unique_constructrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_unique_constructrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_unique_constructrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_unique_constructrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_unique_constructrowrow_sumsumnegative_body_steps fs_r_dst_unique_constructrowrow_sumsumnegative_body_steps fs_s_dst_unique_constructrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_unique_constructrowrow_sumsumnegative_body_steps_summand. fs_h_dst_unique_constructrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_unique_constructrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_constructrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_constructrowrow_sumsum)) /\ exists fs_q_dst_unique_constructrowrow_sumsumnegative_body_steps_summand. dst_negative_code_unique_constructrowrow_sumsum = fs_q_dst_unique_constructrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_unique_constructrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_constructrowrow_sumsum) + (fs_a_dst_unique_constructrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_constructrowrow_sumsumnegative_body_steps_partial. fs_h_dst_unique_constructrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_unique_constructrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_constructrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_constructrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_constructrowrow_sumsumnegative_body_steps_partial. fs_u_dst_unique_constructrowrow_sumsumnegative = fs_q_dst_unique_constructrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_unique_constructrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_constructrowrow_sumsumnegative) + (fs_r_dst_unique_constructrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_constructrowrow_sumsumnegative_body_steps_successor. fs_h_dst_unique_constructrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_unique_constructrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_unique_constructrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_constructrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_constructrowrow_sumsumnegative_body_steps_successor. fs_u_dst_unique_constructrowrow_sumsumnegative = fs_q_dst_unique_constructrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_unique_constructrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_constructrowrow_sumsumnegative) + (fs_s_dst_unique_constructrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_unique_constructrowrow_sumsumnegative_body_steps = fs_r_dst_unique_constructrowrow_sumsumnegative_body_steps + fs_a_dst_unique_constructrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_unique_constructrowrow_sumsumresult ge_balance_negative_unique_constructrowrow_sumsumresult. (((((srt_value_unique_construct) = 2 * (ge_balance_positive_unique_constructrowrow_sumsumresult) /\ (ge_balance_negative_unique_constructrowrow_sumsumresult) = 0) \/ exists ge_signed_half_unique_constructrowrow_sumsumresultdecode. (((srt_value_unique_construct) = 2 * ge_signed_half_unique_constructrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_unique_constructrowrow_sumsumresult) = 0) /\ (ge_balance_negative_unique_constructrowrow_sumsumresult) = S ge_signed_half_unique_constructrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_unique_constructrowrow_sumsum) + ge_balance_negative_unique_constructrowrow_sumsumresult = (dst_negative_sum_unique_constructrowrow_sumsum) + ge_balance_positive_unique_constructrowrow_sumsumresult))))))))))))))))))
  9. 0009specialize signed_rectangular_row_sums_exists (m)
  10. 0010specialize signed_rectangular_row_sums_exists (F)
  11. 0011specialize signed_rectangular_row_sums_exists (o)
  12. 0012specialize signed_rectangular_row_sums_exists (s)
  13. 0013specialize signed_rectangular_row_sums_exists (t)
  14. 0014specialize signed_rectangular_row_sums_exists (n)
  15. 0015apply signed_rectangular_row_sums_exists
  16. 0016exact hF
  17. 0017cases hr
  18. 0018exists x
  19. 0019split
  20. 0020exact hr_witness
  21. 0021intro Q
  22. 0022intro hQ
  23. 0023specialize signed_rectangular_row_sums_extensional_unique (F)
  24. 0024specialize signed_rectangular_row_sums_extensional_unique (x)
  25. 0025specialize signed_rectangular_row_sums_extensional_unique (Q)
  26. 0026specialize signed_rectangular_row_sums_extensional_unique (o)
  27. 0027specialize signed_rectangular_row_sums_extensional_unique (s)
  28. 0028specialize signed_rectangular_row_sums_extensional_unique (t)
  29. 0029specialize signed_rectangular_row_sums_extensional_unique (m)
  30. 0030specialize signed_rectangular_row_sums_extensional_unique (n)
  31. 0031apply signed_rectangular_row_sums_extensional_unique
  32. 0032exact hr_witness
  33. 0033exact hQ