RS0011

signed_rectangular_row_sums_restrict_outer

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

Removing the last row preserves every actual earlier row sum and the same output encoding.

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 R o s t m n. (((exists dst_positive_code_restrict_sourcesource_table dst_positive_scale_restrict_sourcesource_table dst_negative_code_restrict_sourcesource_table dst_negative_scale_restrict_sourcesource_table. (((F) = (((((dst_positive_code_restrict_sourcesource_table) + (dst_positive_scale_restrict_sourcesource_table)) * S ((dst_positive_code_restrict_sourcesource_table) + (dst_positive_scale_restrict_sourcesource_table)) + ((dst_positive_scale_restrict_sourcesource_table) + (dst_positive_scale_restrict_sourcesource_table))) + (((dst_negative_code_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)) * S ((dst_negative_code_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)) + ((dst_negative_scale_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)))) * S ((((dst_positive_code_restrict_sourcesource_table) + (dst_positive_scale_restrict_sourcesource_table)) * S ((dst_positive_code_restrict_sourcesource_table) + (dst_positive_scale_restrict_sourcesource_table)) + ((dst_positive_scale_restrict_sourcesource_table) + (dst_positive_scale_restrict_sourcesource_table))) + (((dst_negative_code_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)) * S ((dst_negative_code_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)) + ((dst_negative_scale_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)))) + ((((dst_negative_code_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)) * S ((dst_negative_code_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)) + ((dst_negative_scale_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table))) + (((dst_negative_code_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)) * S ((dst_negative_code_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)) + ((dst_negative_scale_restrict_sourcesource_table) + (dst_negative_scale_restrict_sourcesource_table)))))) /\ (forall dst_index_restrict_sourcesource_table. (exists pvs_le_gap_restrict_sourcesource_tabledomain. pvs_le_gap_restrict_sourcesource_tabledomain + (dst_index_restrict_sourcesource_table) = (0)) -> exists dst_positive_restrict_sourcesource_table dst_negative_restrict_sourcesource_table dst_value_restrict_sourcesource_table. ((((exists ff_h_pvs_restrict_sourcesource_tableentrypositive. ff_h_pvs_restrict_sourcesource_tableentrypositive + S (dst_positive_restrict_sourcesource_table) = S ((S (dst_index_restrict_sourcesource_table)) * dst_positive_scale_restrict_sourcesource_table)) /\ exists ff_q_pvs_restrict_sourcesource_tableentrypositive. dst_positive_code_restrict_sourcesource_table = ff_q_pvs_restrict_sourcesource_tableentrypositive * S ((S (dst_index_restrict_sourcesource_table)) * dst_positive_scale_restrict_sourcesource_table) + (dst_positive_restrict_sourcesource_table))) /\ (((((exists ff_h_pvs_restrict_sourcesource_tableentrynegative. ff_h_pvs_restrict_sourcesource_tableentrynegative + S (dst_negative_restrict_sourcesource_table) = S ((S (dst_index_restrict_sourcesource_table)) * dst_negative_scale_restrict_sourcesource_table)) /\ exists ff_q_pvs_restrict_sourcesource_tableentrynegative. dst_negative_code_restrict_sourcesource_table = ff_q_pvs_restrict_sourcesource_tableentrynegative * S ((S (dst_index_restrict_sourcesource_table)) * dst_negative_scale_restrict_sourcesource_table) + (dst_negative_restrict_sourcesource_table))) /\ (exists ge_balance_positive_restrict_sourcesource_tableentryvalue ge_balance_negative_restrict_sourcesource_tableentryvalue. (((((dst_value_restrict_sourcesource_table) = 2 * (ge_balance_positive_restrict_sourcesource_tableentryvalue) /\ (ge_balance_negative_restrict_sourcesource_tableentryvalue) = 0) \/ exists ge_signed_half_restrict_sourcesource_tableentryvaluedecode. (((dst_value_restrict_sourcesource_table) = 2 * ge_signed_half_restrict_sourcesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_sourcesource_tableentryvalue) = 0) /\ (ge_balance_negative_restrict_sourcesource_tableentryvalue) = S ge_signed_half_restrict_sourcesource_tableentryvaluedecode))) /\ ((dst_positive_restrict_sourcesource_table) + ge_balance_negative_restrict_sourcesource_tableentryvalue = (dst_negative_restrict_sourcesource_table) + ge_balance_positive_restrict_sourcesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_restrict_sourcerow_table dst_positive_scale_restrict_sourcerow_table dst_negative_code_restrict_sourcerow_table dst_negative_scale_restrict_sourcerow_table. (((R) = (((((dst_positive_code_restrict_sourcerow_table) + (dst_positive_scale_restrict_sourcerow_table)) * S ((dst_positive_code_restrict_sourcerow_table) + (dst_positive_scale_restrict_sourcerow_table)) + ((dst_positive_scale_restrict_sourcerow_table) + (dst_positive_scale_restrict_sourcerow_table))) + (((dst_negative_code_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)) * S ((dst_negative_code_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)) + ((dst_negative_scale_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)))) * S ((((dst_positive_code_restrict_sourcerow_table) + (dst_positive_scale_restrict_sourcerow_table)) * S ((dst_positive_code_restrict_sourcerow_table) + (dst_positive_scale_restrict_sourcerow_table)) + ((dst_positive_scale_restrict_sourcerow_table) + (dst_positive_scale_restrict_sourcerow_table))) + (((dst_negative_code_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)) * S ((dst_negative_code_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)) + ((dst_negative_scale_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)))) + ((((dst_negative_code_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)) * S ((dst_negative_code_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)) + ((dst_negative_scale_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table))) + (((dst_negative_code_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)) * S ((dst_negative_code_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)) + ((dst_negative_scale_restrict_sourcerow_table) + (dst_negative_scale_restrict_sourcerow_table)))))) /\ (forall dst_index_restrict_sourcerow_table. (exists pvs_le_gap_restrict_sourcerow_tabledomain. pvs_le_gap_restrict_sourcerow_tabledomain + (dst_index_restrict_sourcerow_table) = (S m)) -> exists dst_positive_restrict_sourcerow_table dst_negative_restrict_sourcerow_table dst_value_restrict_sourcerow_table. ((((exists ff_h_pvs_restrict_sourcerow_tableentrypositive. ff_h_pvs_restrict_sourcerow_tableentrypositive + S (dst_positive_restrict_sourcerow_table) = S ((S (dst_index_restrict_sourcerow_table)) * dst_positive_scale_restrict_sourcerow_table)) /\ exists ff_q_pvs_restrict_sourcerow_tableentrypositive. dst_positive_code_restrict_sourcerow_table = ff_q_pvs_restrict_sourcerow_tableentrypositive * S ((S (dst_index_restrict_sourcerow_table)) * dst_positive_scale_restrict_sourcerow_table) + (dst_positive_restrict_sourcerow_table))) /\ (((((exists ff_h_pvs_restrict_sourcerow_tableentrynegative. ff_h_pvs_restrict_sourcerow_tableentrynegative + S (dst_negative_restrict_sourcerow_table) = S ((S (dst_index_restrict_sourcerow_table)) * dst_negative_scale_restrict_sourcerow_table)) /\ exists ff_q_pvs_restrict_sourcerow_tableentrynegative. dst_negative_code_restrict_sourcerow_table = ff_q_pvs_restrict_sourcerow_tableentrynegative * S ((S (dst_index_restrict_sourcerow_table)) * dst_negative_scale_restrict_sourcerow_table) + (dst_negative_restrict_sourcerow_table))) /\ (exists ge_balance_positive_restrict_sourcerow_tableentryvalue ge_balance_negative_restrict_sourcerow_tableentryvalue. (((((dst_value_restrict_sourcerow_table) = 2 * (ge_balance_positive_restrict_sourcerow_tableentryvalue) /\ (ge_balance_negative_restrict_sourcerow_tableentryvalue) = 0) \/ exists ge_signed_half_restrict_sourcerow_tableentryvaluedecode. (((dst_value_restrict_sourcerow_table) = 2 * ge_signed_half_restrict_sourcerow_tableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_sourcerow_tableentryvalue) = 0) /\ (ge_balance_negative_restrict_sourcerow_tableentryvalue) = S ge_signed_half_restrict_sourcerow_tableentryvaluedecode))) /\ ((dst_positive_restrict_sourcerow_table) + ge_balance_negative_restrict_sourcerow_tableentryvalue = (dst_negative_restrict_sourcerow_table) + ge_balance_positive_restrict_sourcerow_tableentryvalue))))))))) /\ (forall srt_index_restrict_source. (exists pvs_gap_restrict_sourcebound. pvs_gap_restrict_sourcebound + S (srt_index_restrict_source) = (S m)) -> exists srt_value_restrict_source. (((exists dst_positive_code_restrict_sourcerowentry dst_positive_scale_restrict_sourcerowentry dst_negative_code_restrict_sourcerowentry dst_negative_scale_restrict_sourcerowentry dst_positive_restrict_sourcerowentry dst_negative_restrict_sourcerowentry. (((R) = (((((dst_positive_code_restrict_sourcerowentry) + (dst_positive_scale_restrict_sourcerowentry)) * S ((dst_positive_code_restrict_sourcerowentry) + (dst_positive_scale_restrict_sourcerowentry)) + ((dst_positive_scale_restrict_sourcerowentry) + (dst_positive_scale_restrict_sourcerowentry))) + (((dst_negative_code_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)) * S ((dst_negative_code_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)) + ((dst_negative_scale_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)))) * S ((((dst_positive_code_restrict_sourcerowentry) + (dst_positive_scale_restrict_sourcerowentry)) * S ((dst_positive_code_restrict_sourcerowentry) + (dst_positive_scale_restrict_sourcerowentry)) + ((dst_positive_scale_restrict_sourcerowentry) + (dst_positive_scale_restrict_sourcerowentry))) + (((dst_negative_code_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)) * S ((dst_negative_code_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)) + ((dst_negative_scale_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)))) + ((((dst_negative_code_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)) * S ((dst_negative_code_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)) + ((dst_negative_scale_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry))) + (((dst_negative_code_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)) * S ((dst_negative_code_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)) + ((dst_negative_scale_restrict_sourcerowentry) + (dst_negative_scale_restrict_sourcerowentry)))))) /\ (((((exists ff_h_pvs_restrict_sourcerowentrypositive. ff_h_pvs_restrict_sourcerowentrypositive + S (dst_positive_restrict_sourcerowentry) = S ((S (srt_index_restrict_source)) * dst_positive_scale_restrict_sourcerowentry)) /\ exists ff_q_pvs_restrict_sourcerowentrypositive. dst_positive_code_restrict_sourcerowentry = ff_q_pvs_restrict_sourcerowentrypositive * S ((S (srt_index_restrict_source)) * dst_positive_scale_restrict_sourcerowentry) + (dst_positive_restrict_sourcerowentry))) /\ (((((exists ff_h_pvs_restrict_sourcerowentrynegative. ff_h_pvs_restrict_sourcerowentrynegative + S (dst_negative_restrict_sourcerowentry) = S ((S (srt_index_restrict_source)) * dst_negative_scale_restrict_sourcerowentry)) /\ exists ff_q_pvs_restrict_sourcerowentrynegative. dst_negative_code_restrict_sourcerowentry = ff_q_pvs_restrict_sourcerowentrynegative * S ((S (srt_index_restrict_source)) * dst_negative_scale_restrict_sourcerowentry) + (dst_negative_restrict_sourcerowentry))) /\ (exists ge_balance_positive_restrict_sourcerowentryvalue ge_balance_negative_restrict_sourcerowentryvalue. (((((srt_value_restrict_source) = 2 * (ge_balance_positive_restrict_sourcerowentryvalue) /\ (ge_balance_negative_restrict_sourcerowentryvalue) = 0) \/ exists ge_signed_half_restrict_sourcerowentryvaluedecode. (((srt_value_restrict_source) = 2 * ge_signed_half_restrict_sourcerowentryvaluedecode + 1 /\ (ge_balance_positive_restrict_sourcerowentryvalue) = 0) /\ (ge_balance_negative_restrict_sourcerowentryvalue) = S ge_signed_half_restrict_sourcerowentryvaluedecode))) /\ ((dst_positive_restrict_sourcerowentry) + ge_balance_negative_restrict_sourcerowentryvalue = (dst_negative_restrict_sourcerowentry) + ge_balance_positive_restrict_sourcerowentryvalue))))))))) /\ (exists srs_slice_restrict_sourcerowrow_sum. ((((exists dst_positive_code_restrict_sourcerowrow_sumslicesource_table dst_positive_scale_restrict_sourcerowrow_sumslicesource_table dst_negative_code_restrict_sourcerowrow_sumslicesource_table dst_negative_scale_restrict_sourcerowrow_sumslicesource_table. (((F) = (((((dst_positive_code_restrict_sourcerowrow_sumslicesource_table) + (dst_positive_scale_restrict_sourcerowrow_sumslicesource_table)) * S ((dst_positive_code_restrict_sourcerowrow_sumslicesource_table) + (dst_positive_scale_restrict_sourcerowrow_sumslicesource_table)) + ((dst_positive_scale_restrict_sourcerowrow_sumslicesource_table) + (dst_positive_scale_restrict_sourcerowrow_sumslicesource_table))) + (((dst_negative_code_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)) * S ((dst_negative_code_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)) + ((dst_negative_scale_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)))) * S ((((dst_positive_code_restrict_sourcerowrow_sumslicesource_table) + (dst_positive_scale_restrict_sourcerowrow_sumslicesource_table)) * S ((dst_positive_code_restrict_sourcerowrow_sumslicesource_table) + (dst_positive_scale_restrict_sourcerowrow_sumslicesource_table)) + ((dst_positive_scale_restrict_sourcerowrow_sumslicesource_table) + (dst_positive_scale_restrict_sourcerowrow_sumslicesource_table))) + (((dst_negative_code_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)) * S ((dst_negative_code_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)) + ((dst_negative_scale_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)))) + ((((dst_negative_code_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)) * S ((dst_negative_code_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)) + ((dst_negative_scale_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table))) + (((dst_negative_code_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)) * S ((dst_negative_code_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)) + ((dst_negative_scale_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)))))) /\ (forall dst_index_restrict_sourcerowrow_sumslicesource_table. (exists pvs_le_gap_restrict_sourcerowrow_sumslicesource_tabledomain. pvs_le_gap_restrict_sourcerowrow_sumslicesource_tabledomain + (dst_index_restrict_sourcerowrow_sumslicesource_table) = (0)) -> exists dst_positive_restrict_sourcerowrow_sumslicesource_table dst_negative_restrict_sourcerowrow_sumslicesource_table dst_value_restrict_sourcerowrow_sumslicesource_table. ((((exists ff_h_pvs_restrict_sourcerowrow_sumslicesource_tableentrypositive. ff_h_pvs_restrict_sourcerowrow_sumslicesource_tableentrypositive + S (dst_positive_restrict_sourcerowrow_sumslicesource_table) = S ((S (dst_index_restrict_sourcerowrow_sumslicesource_table)) * dst_positive_scale_restrict_sourcerowrow_sumslicesource_table)) /\ exists ff_q_pvs_restrict_sourcerowrow_sumslicesource_tableentrypositive. dst_positive_code_restrict_sourcerowrow_sumslicesource_table = ff_q_pvs_restrict_sourcerowrow_sumslicesource_tableentrypositive * S ((S (dst_index_restrict_sourcerowrow_sumslicesource_table)) * dst_positive_scale_restrict_sourcerowrow_sumslicesource_table) + (dst_positive_restrict_sourcerowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_restrict_sourcerowrow_sumslicesource_tableentrynegative. ff_h_pvs_restrict_sourcerowrow_sumslicesource_tableentrynegative + S (dst_negative_restrict_sourcerowrow_sumslicesource_table) = S ((S (dst_index_restrict_sourcerowrow_sumslicesource_table)) * dst_negative_scale_restrict_sourcerowrow_sumslicesource_table)) /\ exists ff_q_pvs_restrict_sourcerowrow_sumslicesource_tableentrynegative. dst_negative_code_restrict_sourcerowrow_sumslicesource_table = ff_q_pvs_restrict_sourcerowrow_sumslicesource_tableentrynegative * S ((S (dst_index_restrict_sourcerowrow_sumslicesource_table)) * dst_negative_scale_restrict_sourcerowrow_sumslicesource_table) + (dst_negative_restrict_sourcerowrow_sumslicesource_table))) /\ (exists ge_balance_positive_restrict_sourcerowrow_sumslicesource_tableentryvalue ge_balance_negative_restrict_sourcerowrow_sumslicesource_tableentryvalue. (((((dst_value_restrict_sourcerowrow_sumslicesource_table) = 2 * (ge_balance_positive_restrict_sourcerowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_restrict_sourcerowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_restrict_sourcerowrow_sumslicesource_tableentryvaluedecode. (((dst_value_restrict_sourcerowrow_sumslicesource_table) = 2 * ge_signed_half_restrict_sourcerowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_sourcerowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_restrict_sourcerowrow_sumslicesource_tableentryvalue) = S ge_signed_half_restrict_sourcerowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_restrict_sourcerowrow_sumslicesource_table) + ge_balance_negative_restrict_sourcerowrow_sumslicesource_tableentryvalue = (dst_negative_restrict_sourcerowrow_sumslicesource_table) + ge_balance_positive_restrict_sourcerowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_restrict_sourcerowrow_sumsliceoutput_table dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table. (((srs_slice_restrict_sourcerowrow_sum) = (((((dst_positive_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table)) * S ((dst_positive_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table)) + ((dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table))) + (((dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table)) * S ((dst_positive_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table)) + ((dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table))) + (((dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)))) + ((((dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table))) + (((dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)))))) /\ (forall dst_index_restrict_sourcerowrow_sumsliceoutput_table. (exists pvs_le_gap_restrict_sourcerowrow_sumsliceoutput_tabledomain. pvs_le_gap_restrict_sourcerowrow_sumsliceoutput_tabledomain + (dst_index_restrict_sourcerowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_restrict_sourcerowrow_sumsliceoutput_table dst_negative_restrict_sourcerowrow_sumsliceoutput_table dst_value_restrict_sourcerowrow_sumsliceoutput_table. ((((exists ff_h_pvs_restrict_sourcerowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_restrict_sourcerowrow_sumsliceoutput_tableentrypositive + S (dst_positive_restrict_sourcerowrow_sumsliceoutput_table) = S ((S (dst_index_restrict_sourcerowrow_sumsliceoutput_table)) * dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_restrict_sourcerowrow_sumsliceoutput_tableentrypositive. dst_positive_code_restrict_sourcerowrow_sumsliceoutput_table = ff_q_pvs_restrict_sourcerowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_restrict_sourcerowrow_sumsliceoutput_table)) * dst_positive_scale_restrict_sourcerowrow_sumsliceoutput_table) + (dst_positive_restrict_sourcerowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_restrict_sourcerowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_restrict_sourcerowrow_sumsliceoutput_tableentrynegative + S (dst_negative_restrict_sourcerowrow_sumsliceoutput_table) = S ((S (dst_index_restrict_sourcerowrow_sumsliceoutput_table)) * dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_restrict_sourcerowrow_sumsliceoutput_tableentrynegative. dst_negative_code_restrict_sourcerowrow_sumsliceoutput_table = ff_q_pvs_restrict_sourcerowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_restrict_sourcerowrow_sumsliceoutput_table)) * dst_negative_scale_restrict_sourcerowrow_sumsliceoutput_table) + (dst_negative_restrict_sourcerowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_restrict_sourcerowrow_sumsliceoutput_tableentryvalue ge_balance_negative_restrict_sourcerowrow_sumsliceoutput_tableentryvalue. (((((dst_value_restrict_sourcerowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_restrict_sourcerowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_restrict_sourcerowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_restrict_sourcerowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_restrict_sourcerowrow_sumsliceoutput_table) = 2 * ge_signed_half_restrict_sourcerowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_sourcerowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_restrict_sourcerowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_restrict_sourcerowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_restrict_sourcerowrow_sumsliceoutput_table) + ge_balance_negative_restrict_sourcerowrow_sumsliceoutput_tableentryvalue = (dst_negative_restrict_sourcerowrow_sumsliceoutput_table) + ge_balance_positive_restrict_sourcerowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_restrict_sourcerowrow_sumslice. (exists pvs_gap_restrict_sourcerowrow_sumslicebound. pvs_gap_restrict_sourcerowrow_sumslicebound + S (srs_index_restrict_sourcerowrow_sumslice) = (n)) -> exists srs_value_restrict_sourcerowrow_sumslice. (((exists dst_positive_code_restrict_sourcerowrow_sumsliceentrysource dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource dst_negative_code_restrict_sourcerowrow_sumsliceentrysource dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource dst_positive_restrict_sourcerowrow_sumsliceentrysource dst_negative_restrict_sourcerowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource)) * S ((dst_positive_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource)) + ((dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource))) + (((dst_negative_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)))) * S ((((dst_positive_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource)) * S ((dst_positive_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource)) + ((dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource))) + (((dst_negative_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)))) + ((((dst_negative_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource))) + (((dst_negative_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_restrict_sourcerowrow_sumsliceentrysourcepositive. ff_h_pvs_restrict_sourcerowrow_sumsliceentrysourcepositive + S (dst_positive_restrict_sourcerowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_restrict_source)))) + ((t) * (srs_index_restrict_sourcerowrow_sumslice))))) * dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource)) /\ exists ff_q_pvs_restrict_sourcerowrow_sumsliceentrysourcepositive. dst_positive_code_restrict_sourcerowrow_sumsliceentrysource = ff_q_pvs_restrict_sourcerowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_restrict_source)))) + ((t) * (srs_index_restrict_sourcerowrow_sumslice))))) * dst_positive_scale_restrict_sourcerowrow_sumsliceentrysource) + (dst_positive_restrict_sourcerowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_restrict_sourcerowrow_sumsliceentrysourcenegative. ff_h_pvs_restrict_sourcerowrow_sumsliceentrysourcenegative + S (dst_negative_restrict_sourcerowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_restrict_source)))) + ((t) * (srs_index_restrict_sourcerowrow_sumslice))))) * dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource)) /\ exists ff_q_pvs_restrict_sourcerowrow_sumsliceentrysourcenegative. dst_negative_code_restrict_sourcerowrow_sumsliceentrysource = ff_q_pvs_restrict_sourcerowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_restrict_source)))) + ((t) * (srs_index_restrict_sourcerowrow_sumslice))))) * dst_negative_scale_restrict_sourcerowrow_sumsliceentrysource) + (dst_negative_restrict_sourcerowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_restrict_sourcerowrow_sumsliceentrysourcevalue ge_balance_negative_restrict_sourcerowrow_sumsliceentrysourcevalue. (((((srs_value_restrict_sourcerowrow_sumslice) = 2 * (ge_balance_positive_restrict_sourcerowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_restrict_sourcerowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_restrict_sourcerowrow_sumsliceentrysourcevaluedecode. (((srs_value_restrict_sourcerowrow_sumslice) = 2 * ge_signed_half_restrict_sourcerowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_restrict_sourcerowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_restrict_sourcerowrow_sumsliceentrysourcevalue) = S ge_signed_half_restrict_sourcerowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_restrict_sourcerowrow_sumsliceentrysource) + ge_balance_negative_restrict_sourcerowrow_sumsliceentrysourcevalue = (dst_negative_restrict_sourcerowrow_sumsliceentrysource) + ge_balance_positive_restrict_sourcerowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_restrict_sourcerowrow_sumsliceentryoutput dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput dst_positive_restrict_sourcerowrow_sumsliceentryoutput dst_negative_restrict_sourcerowrow_sumsliceentryoutput. (((srs_slice_restrict_sourcerowrow_sum) = (((((dst_positive_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput)) * S ((dst_positive_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput)) + ((dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput))) + (((dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput)) * S ((dst_positive_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput)) + ((dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput))) + (((dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)))) + ((((dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput))) + (((dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)) * S ((dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)) + ((dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_restrict_sourcerowrow_sumsliceentryoutputpositive. ff_h_pvs_restrict_sourcerowrow_sumsliceentryoutputpositive + S (dst_positive_restrict_sourcerowrow_sumsliceentryoutput) = S ((S (srs_index_restrict_sourcerowrow_sumslice)) * dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_restrict_sourcerowrow_sumsliceentryoutputpositive. dst_positive_code_restrict_sourcerowrow_sumsliceentryoutput = ff_q_pvs_restrict_sourcerowrow_sumsliceentryoutputpositive * S ((S (srs_index_restrict_sourcerowrow_sumslice)) * dst_positive_scale_restrict_sourcerowrow_sumsliceentryoutput) + (dst_positive_restrict_sourcerowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_restrict_sourcerowrow_sumsliceentryoutputnegative. ff_h_pvs_restrict_sourcerowrow_sumsliceentryoutputnegative + S (dst_negative_restrict_sourcerowrow_sumsliceentryoutput) = S ((S (srs_index_restrict_sourcerowrow_sumslice)) * dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_restrict_sourcerowrow_sumsliceentryoutputnegative. dst_negative_code_restrict_sourcerowrow_sumsliceentryoutput = ff_q_pvs_restrict_sourcerowrow_sumsliceentryoutputnegative * S ((S (srs_index_restrict_sourcerowrow_sumslice)) * dst_negative_scale_restrict_sourcerowrow_sumsliceentryoutput) + (dst_negative_restrict_sourcerowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_restrict_sourcerowrow_sumsliceentryoutputvalue ge_balance_negative_restrict_sourcerowrow_sumsliceentryoutputvalue. (((((srs_value_restrict_sourcerowrow_sumslice) = 2 * (ge_balance_positive_restrict_sourcerowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_restrict_sourcerowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_restrict_sourcerowrow_sumsliceentryoutputvaluedecode. (((srs_value_restrict_sourcerowrow_sumslice) = 2 * ge_signed_half_restrict_sourcerowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_restrict_sourcerowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_restrict_sourcerowrow_sumsliceentryoutputvalue) = S ge_signed_half_restrict_sourcerowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_restrict_sourcerowrow_sumsliceentryoutput) + ge_balance_negative_restrict_sourcerowrow_sumsliceentryoutputvalue = (dst_negative_restrict_sourcerowrow_sumsliceentryoutput) + ge_balance_positive_restrict_sourcerowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_restrict_sourcerowrow_sumsum dst_positive_scale_restrict_sourcerowrow_sumsum dst_negative_code_restrict_sourcerowrow_sumsum dst_negative_scale_restrict_sourcerowrow_sumsum dst_positive_sum_restrict_sourcerowrow_sumsum dst_negative_sum_restrict_sourcerowrow_sumsum. (((srs_slice_restrict_sourcerowrow_sum) = (((((dst_positive_code_restrict_sourcerowrow_sumsum) + (dst_positive_scale_restrict_sourcerowrow_sumsum)) * S ((dst_positive_code_restrict_sourcerowrow_sumsum) + (dst_positive_scale_restrict_sourcerowrow_sumsum)) + ((dst_positive_scale_restrict_sourcerowrow_sumsum) + (dst_positive_scale_restrict_sourcerowrow_sumsum))) + (((dst_negative_code_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)) * S ((dst_negative_code_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)) + ((dst_negative_scale_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)))) * S ((((dst_positive_code_restrict_sourcerowrow_sumsum) + (dst_positive_scale_restrict_sourcerowrow_sumsum)) * S ((dst_positive_code_restrict_sourcerowrow_sumsum) + (dst_positive_scale_restrict_sourcerowrow_sumsum)) + ((dst_positive_scale_restrict_sourcerowrow_sumsum) + (dst_positive_scale_restrict_sourcerowrow_sumsum))) + (((dst_negative_code_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)) * S ((dst_negative_code_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)) + ((dst_negative_scale_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)))) + ((((dst_negative_code_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)) * S ((dst_negative_code_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)) + ((dst_negative_scale_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum))) + (((dst_negative_code_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)) * S ((dst_negative_code_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)) + ((dst_negative_scale_restrict_sourcerowrow_sumsum) + (dst_negative_scale_restrict_sourcerowrow_sumsum)))))) /\ (((exists fs_u_dst_restrict_sourcerowrow_sumsumpositive fs_v_dst_restrict_sourcerowrow_sumsumpositive. ((((exists fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_start. fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_restrict_sourcerowrow_sumsumpositive)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_start. fs_u_dst_restrict_sourcerowrow_sumsumpositive = fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_restrict_sourcerowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_terminal. fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_terminal + S (dst_positive_sum_restrict_sourcerowrow_sumsum) = S ((S (n)) * fs_v_dst_restrict_sourcerowrow_sumsumpositive)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_terminal. fs_u_dst_restrict_sourcerowrow_sumsumpositive = fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_restrict_sourcerowrow_sumsumpositive) + (dst_positive_sum_restrict_sourcerowrow_sumsum))) /\ forall fs_i_dst_restrict_sourcerowrow_sumsumpositive_body_steps. (exists fs_lt_dst_restrict_sourcerowrow_sumsumpositive_body_steps_bound. fs_lt_dst_restrict_sourcerowrow_sumsumpositive_body_steps_bound + S fs_i_dst_restrict_sourcerowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_restrict_sourcerowrow_sumsumpositive_body_steps fs_r_dst_restrict_sourcerowrow_sumsumpositive_body_steps fs_s_dst_restrict_sourcerowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_steps_summand. fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_restrict_sourcerowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_restrict_sourcerowrow_sumsumpositive_body_steps)) * dst_positive_scale_restrict_sourcerowrow_sumsum)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_steps_summand. dst_positive_code_restrict_sourcerowrow_sumsum = fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_restrict_sourcerowrow_sumsumpositive_body_steps)) * dst_positive_scale_restrict_sourcerowrow_sumsum) + (fs_a_dst_restrict_sourcerowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_steps_partial. fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_restrict_sourcerowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_restrict_sourcerowrow_sumsumpositive_body_steps)) * fs_v_dst_restrict_sourcerowrow_sumsumpositive)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_steps_partial. fs_u_dst_restrict_sourcerowrow_sumsumpositive = fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_restrict_sourcerowrow_sumsumpositive_body_steps)) * fs_v_dst_restrict_sourcerowrow_sumsumpositive) + (fs_r_dst_restrict_sourcerowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_steps_successor. fs_h_dst_restrict_sourcerowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_restrict_sourcerowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_restrict_sourcerowrow_sumsumpositive_body_steps)) * fs_v_dst_restrict_sourcerowrow_sumsumpositive)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_steps_successor. fs_u_dst_restrict_sourcerowrow_sumsumpositive = fs_q_dst_restrict_sourcerowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_restrict_sourcerowrow_sumsumpositive_body_steps)) * fs_v_dst_restrict_sourcerowrow_sumsumpositive) + (fs_s_dst_restrict_sourcerowrow_sumsumpositive_body_steps))) /\ fs_s_dst_restrict_sourcerowrow_sumsumpositive_body_steps = fs_r_dst_restrict_sourcerowrow_sumsumpositive_body_steps + fs_a_dst_restrict_sourcerowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_restrict_sourcerowrow_sumsumnegative fs_v_dst_restrict_sourcerowrow_sumsumnegative. ((((exists fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_start. fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_restrict_sourcerowrow_sumsumnegative)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_start. fs_u_dst_restrict_sourcerowrow_sumsumnegative = fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_restrict_sourcerowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_terminal. fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_terminal + S (dst_negative_sum_restrict_sourcerowrow_sumsum) = S ((S (n)) * fs_v_dst_restrict_sourcerowrow_sumsumnegative)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_terminal. fs_u_dst_restrict_sourcerowrow_sumsumnegative = fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_restrict_sourcerowrow_sumsumnegative) + (dst_negative_sum_restrict_sourcerowrow_sumsum))) /\ forall fs_i_dst_restrict_sourcerowrow_sumsumnegative_body_steps. (exists fs_lt_dst_restrict_sourcerowrow_sumsumnegative_body_steps_bound. fs_lt_dst_restrict_sourcerowrow_sumsumnegative_body_steps_bound + S fs_i_dst_restrict_sourcerowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_restrict_sourcerowrow_sumsumnegative_body_steps fs_r_dst_restrict_sourcerowrow_sumsumnegative_body_steps fs_s_dst_restrict_sourcerowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_steps_summand. fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_restrict_sourcerowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_restrict_sourcerowrow_sumsumnegative_body_steps)) * dst_negative_scale_restrict_sourcerowrow_sumsum)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_steps_summand. dst_negative_code_restrict_sourcerowrow_sumsum = fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_restrict_sourcerowrow_sumsumnegative_body_steps)) * dst_negative_scale_restrict_sourcerowrow_sumsum) + (fs_a_dst_restrict_sourcerowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_steps_partial. fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_restrict_sourcerowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_restrict_sourcerowrow_sumsumnegative_body_steps)) * fs_v_dst_restrict_sourcerowrow_sumsumnegative)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_steps_partial. fs_u_dst_restrict_sourcerowrow_sumsumnegative = fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_restrict_sourcerowrow_sumsumnegative_body_steps)) * fs_v_dst_restrict_sourcerowrow_sumsumnegative) + (fs_r_dst_restrict_sourcerowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_steps_successor. fs_h_dst_restrict_sourcerowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_restrict_sourcerowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_restrict_sourcerowrow_sumsumnegative_body_steps)) * fs_v_dst_restrict_sourcerowrow_sumsumnegative)) /\ exists fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_steps_successor. fs_u_dst_restrict_sourcerowrow_sumsumnegative = fs_q_dst_restrict_sourcerowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_restrict_sourcerowrow_sumsumnegative_body_steps)) * fs_v_dst_restrict_sourcerowrow_sumsumnegative) + (fs_s_dst_restrict_sourcerowrow_sumsumnegative_body_steps))) /\ fs_s_dst_restrict_sourcerowrow_sumsumnegative_body_steps = fs_r_dst_restrict_sourcerowrow_sumsumnegative_body_steps + fs_a_dst_restrict_sourcerowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_restrict_sourcerowrow_sumsumresult ge_balance_negative_restrict_sourcerowrow_sumsumresult. (((((srt_value_restrict_source) = 2 * (ge_balance_positive_restrict_sourcerowrow_sumsumresult) /\ (ge_balance_negative_restrict_sourcerowrow_sumsumresult) = 0) \/ exists ge_signed_half_restrict_sourcerowrow_sumsumresultdecode. (((srt_value_restrict_source) = 2 * ge_signed_half_restrict_sourcerowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_restrict_sourcerowrow_sumsumresult) = 0) /\ (ge_balance_negative_restrict_sourcerowrow_sumsumresult) = S ge_signed_half_restrict_sourcerowrow_sumsumresultdecode))) /\ ((dst_positive_sum_restrict_sourcerowrow_sumsum) + ge_balance_negative_restrict_sourcerowrow_sumsumresult = (dst_negative_sum_restrict_sourcerowrow_sumsum) + ge_balance_positive_restrict_sourcerowrow_sumsumresult)))))))))))))))))) -> (((exists dst_positive_code_restrict_resultsource_table dst_positive_scale_restrict_resultsource_table dst_negative_code_restrict_resultsource_table dst_negative_scale_restrict_resultsource_table. (((F) = (((((dst_positive_code_restrict_resultsource_table) + (dst_positive_scale_restrict_resultsource_table)) * S ((dst_positive_code_restrict_resultsource_table) + (dst_positive_scale_restrict_resultsource_table)) + ((dst_positive_scale_restrict_resultsource_table) + (dst_positive_scale_restrict_resultsource_table))) + (((dst_negative_code_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)) * S ((dst_negative_code_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)) + ((dst_negative_scale_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)))) * S ((((dst_positive_code_restrict_resultsource_table) + (dst_positive_scale_restrict_resultsource_table)) * S ((dst_positive_code_restrict_resultsource_table) + (dst_positive_scale_restrict_resultsource_table)) + ((dst_positive_scale_restrict_resultsource_table) + (dst_positive_scale_restrict_resultsource_table))) + (((dst_negative_code_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)) * S ((dst_negative_code_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)) + ((dst_negative_scale_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)))) + ((((dst_negative_code_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)) * S ((dst_negative_code_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)) + ((dst_negative_scale_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table))) + (((dst_negative_code_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)) * S ((dst_negative_code_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)) + ((dst_negative_scale_restrict_resultsource_table) + (dst_negative_scale_restrict_resultsource_table)))))) /\ (forall dst_index_restrict_resultsource_table. (exists pvs_le_gap_restrict_resultsource_tabledomain. pvs_le_gap_restrict_resultsource_tabledomain + (dst_index_restrict_resultsource_table) = (0)) -> exists dst_positive_restrict_resultsource_table dst_negative_restrict_resultsource_table dst_value_restrict_resultsource_table. ((((exists ff_h_pvs_restrict_resultsource_tableentrypositive. ff_h_pvs_restrict_resultsource_tableentrypositive + S (dst_positive_restrict_resultsource_table) = S ((S (dst_index_restrict_resultsource_table)) * dst_positive_scale_restrict_resultsource_table)) /\ exists ff_q_pvs_restrict_resultsource_tableentrypositive. dst_positive_code_restrict_resultsource_table = ff_q_pvs_restrict_resultsource_tableentrypositive * S ((S (dst_index_restrict_resultsource_table)) * dst_positive_scale_restrict_resultsource_table) + (dst_positive_restrict_resultsource_table))) /\ (((((exists ff_h_pvs_restrict_resultsource_tableentrynegative. ff_h_pvs_restrict_resultsource_tableentrynegative + S (dst_negative_restrict_resultsource_table) = S ((S (dst_index_restrict_resultsource_table)) * dst_negative_scale_restrict_resultsource_table)) /\ exists ff_q_pvs_restrict_resultsource_tableentrynegative. dst_negative_code_restrict_resultsource_table = ff_q_pvs_restrict_resultsource_tableentrynegative * S ((S (dst_index_restrict_resultsource_table)) * dst_negative_scale_restrict_resultsource_table) + (dst_negative_restrict_resultsource_table))) /\ (exists ge_balance_positive_restrict_resultsource_tableentryvalue ge_balance_negative_restrict_resultsource_tableentryvalue. (((((dst_value_restrict_resultsource_table) = 2 * (ge_balance_positive_restrict_resultsource_tableentryvalue) /\ (ge_balance_negative_restrict_resultsource_tableentryvalue) = 0) \/ exists ge_signed_half_restrict_resultsource_tableentryvaluedecode. (((dst_value_restrict_resultsource_table) = 2 * ge_signed_half_restrict_resultsource_tableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_resultsource_tableentryvalue) = 0) /\ (ge_balance_negative_restrict_resultsource_tableentryvalue) = S ge_signed_half_restrict_resultsource_tableentryvaluedecode))) /\ ((dst_positive_restrict_resultsource_table) + ge_balance_negative_restrict_resultsource_tableentryvalue = (dst_negative_restrict_resultsource_table) + ge_balance_positive_restrict_resultsource_tableentryvalue))))))))) /\ (((exists dst_positive_code_restrict_resultrow_table dst_positive_scale_restrict_resultrow_table dst_negative_code_restrict_resultrow_table dst_negative_scale_restrict_resultrow_table. (((R) = (((((dst_positive_code_restrict_resultrow_table) + (dst_positive_scale_restrict_resultrow_table)) * S ((dst_positive_code_restrict_resultrow_table) + (dst_positive_scale_restrict_resultrow_table)) + ((dst_positive_scale_restrict_resultrow_table) + (dst_positive_scale_restrict_resultrow_table))) + (((dst_negative_code_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)) * S ((dst_negative_code_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)) + ((dst_negative_scale_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)))) * S ((((dst_positive_code_restrict_resultrow_table) + (dst_positive_scale_restrict_resultrow_table)) * S ((dst_positive_code_restrict_resultrow_table) + (dst_positive_scale_restrict_resultrow_table)) + ((dst_positive_scale_restrict_resultrow_table) + (dst_positive_scale_restrict_resultrow_table))) + (((dst_negative_code_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)) * S ((dst_negative_code_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)) + ((dst_negative_scale_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)))) + ((((dst_negative_code_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)) * S ((dst_negative_code_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)) + ((dst_negative_scale_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table))) + (((dst_negative_code_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)) * S ((dst_negative_code_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)) + ((dst_negative_scale_restrict_resultrow_table) + (dst_negative_scale_restrict_resultrow_table)))))) /\ (forall dst_index_restrict_resultrow_table. (exists pvs_le_gap_restrict_resultrow_tabledomain. pvs_le_gap_restrict_resultrow_tabledomain + (dst_index_restrict_resultrow_table) = (m)) -> exists dst_positive_restrict_resultrow_table dst_negative_restrict_resultrow_table dst_value_restrict_resultrow_table. ((((exists ff_h_pvs_restrict_resultrow_tableentrypositive. ff_h_pvs_restrict_resultrow_tableentrypositive + S (dst_positive_restrict_resultrow_table) = S ((S (dst_index_restrict_resultrow_table)) * dst_positive_scale_restrict_resultrow_table)) /\ exists ff_q_pvs_restrict_resultrow_tableentrypositive. dst_positive_code_restrict_resultrow_table = ff_q_pvs_restrict_resultrow_tableentrypositive * S ((S (dst_index_restrict_resultrow_table)) * dst_positive_scale_restrict_resultrow_table) + (dst_positive_restrict_resultrow_table))) /\ (((((exists ff_h_pvs_restrict_resultrow_tableentrynegative. ff_h_pvs_restrict_resultrow_tableentrynegative + S (dst_negative_restrict_resultrow_table) = S ((S (dst_index_restrict_resultrow_table)) * dst_negative_scale_restrict_resultrow_table)) /\ exists ff_q_pvs_restrict_resultrow_tableentrynegative. dst_negative_code_restrict_resultrow_table = ff_q_pvs_restrict_resultrow_tableentrynegative * S ((S (dst_index_restrict_resultrow_table)) * dst_negative_scale_restrict_resultrow_table) + (dst_negative_restrict_resultrow_table))) /\ (exists ge_balance_positive_restrict_resultrow_tableentryvalue ge_balance_negative_restrict_resultrow_tableentryvalue. (((((dst_value_restrict_resultrow_table) = 2 * (ge_balance_positive_restrict_resultrow_tableentryvalue) /\ (ge_balance_negative_restrict_resultrow_tableentryvalue) = 0) \/ exists ge_signed_half_restrict_resultrow_tableentryvaluedecode. (((dst_value_restrict_resultrow_table) = 2 * ge_signed_half_restrict_resultrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_resultrow_tableentryvalue) = 0) /\ (ge_balance_negative_restrict_resultrow_tableentryvalue) = S ge_signed_half_restrict_resultrow_tableentryvaluedecode))) /\ ((dst_positive_restrict_resultrow_table) + ge_balance_negative_restrict_resultrow_tableentryvalue = (dst_negative_restrict_resultrow_table) + ge_balance_positive_restrict_resultrow_tableentryvalue))))))))) /\ (forall srt_index_restrict_result. (exists pvs_gap_restrict_resultbound. pvs_gap_restrict_resultbound + S (srt_index_restrict_result) = (m)) -> exists srt_value_restrict_result. (((exists dst_positive_code_restrict_resultrowentry dst_positive_scale_restrict_resultrowentry dst_negative_code_restrict_resultrowentry dst_negative_scale_restrict_resultrowentry dst_positive_restrict_resultrowentry dst_negative_restrict_resultrowentry. (((R) = (((((dst_positive_code_restrict_resultrowentry) + (dst_positive_scale_restrict_resultrowentry)) * S ((dst_positive_code_restrict_resultrowentry) + (dst_positive_scale_restrict_resultrowentry)) + ((dst_positive_scale_restrict_resultrowentry) + (dst_positive_scale_restrict_resultrowentry))) + (((dst_negative_code_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)) * S ((dst_negative_code_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)) + ((dst_negative_scale_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)))) * S ((((dst_positive_code_restrict_resultrowentry) + (dst_positive_scale_restrict_resultrowentry)) * S ((dst_positive_code_restrict_resultrowentry) + (dst_positive_scale_restrict_resultrowentry)) + ((dst_positive_scale_restrict_resultrowentry) + (dst_positive_scale_restrict_resultrowentry))) + (((dst_negative_code_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)) * S ((dst_negative_code_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)) + ((dst_negative_scale_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)))) + ((((dst_negative_code_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)) * S ((dst_negative_code_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)) + ((dst_negative_scale_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry))) + (((dst_negative_code_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)) * S ((dst_negative_code_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)) + ((dst_negative_scale_restrict_resultrowentry) + (dst_negative_scale_restrict_resultrowentry)))))) /\ (((((exists ff_h_pvs_restrict_resultrowentrypositive. ff_h_pvs_restrict_resultrowentrypositive + S (dst_positive_restrict_resultrowentry) = S ((S (srt_index_restrict_result)) * dst_positive_scale_restrict_resultrowentry)) /\ exists ff_q_pvs_restrict_resultrowentrypositive. dst_positive_code_restrict_resultrowentry = ff_q_pvs_restrict_resultrowentrypositive * S ((S (srt_index_restrict_result)) * dst_positive_scale_restrict_resultrowentry) + (dst_positive_restrict_resultrowentry))) /\ (((((exists ff_h_pvs_restrict_resultrowentrynegative. ff_h_pvs_restrict_resultrowentrynegative + S (dst_negative_restrict_resultrowentry) = S ((S (srt_index_restrict_result)) * dst_negative_scale_restrict_resultrowentry)) /\ exists ff_q_pvs_restrict_resultrowentrynegative. dst_negative_code_restrict_resultrowentry = ff_q_pvs_restrict_resultrowentrynegative * S ((S (srt_index_restrict_result)) * dst_negative_scale_restrict_resultrowentry) + (dst_negative_restrict_resultrowentry))) /\ (exists ge_balance_positive_restrict_resultrowentryvalue ge_balance_negative_restrict_resultrowentryvalue. (((((srt_value_restrict_result) = 2 * (ge_balance_positive_restrict_resultrowentryvalue) /\ (ge_balance_negative_restrict_resultrowentryvalue) = 0) \/ exists ge_signed_half_restrict_resultrowentryvaluedecode. (((srt_value_restrict_result) = 2 * ge_signed_half_restrict_resultrowentryvaluedecode + 1 /\ (ge_balance_positive_restrict_resultrowentryvalue) = 0) /\ (ge_balance_negative_restrict_resultrowentryvalue) = S ge_signed_half_restrict_resultrowentryvaluedecode))) /\ ((dst_positive_restrict_resultrowentry) + ge_balance_negative_restrict_resultrowentryvalue = (dst_negative_restrict_resultrowentry) + ge_balance_positive_restrict_resultrowentryvalue))))))))) /\ (exists srs_slice_restrict_resultrowrow_sum. ((((exists dst_positive_code_restrict_resultrowrow_sumslicesource_table dst_positive_scale_restrict_resultrowrow_sumslicesource_table dst_negative_code_restrict_resultrowrow_sumslicesource_table dst_negative_scale_restrict_resultrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_restrict_resultrowrow_sumslicesource_table) + (dst_positive_scale_restrict_resultrowrow_sumslicesource_table)) * S ((dst_positive_code_restrict_resultrowrow_sumslicesource_table) + (dst_positive_scale_restrict_resultrowrow_sumslicesource_table)) + ((dst_positive_scale_restrict_resultrowrow_sumslicesource_table) + (dst_positive_scale_restrict_resultrowrow_sumslicesource_table))) + (((dst_negative_code_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)) * S ((dst_negative_code_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)) + ((dst_negative_scale_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)))) * S ((((dst_positive_code_restrict_resultrowrow_sumslicesource_table) + (dst_positive_scale_restrict_resultrowrow_sumslicesource_table)) * S ((dst_positive_code_restrict_resultrowrow_sumslicesource_table) + (dst_positive_scale_restrict_resultrowrow_sumslicesource_table)) + ((dst_positive_scale_restrict_resultrowrow_sumslicesource_table) + (dst_positive_scale_restrict_resultrowrow_sumslicesource_table))) + (((dst_negative_code_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)) * S ((dst_negative_code_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)) + ((dst_negative_scale_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)))) + ((((dst_negative_code_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)) * S ((dst_negative_code_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)) + ((dst_negative_scale_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table))) + (((dst_negative_code_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)) * S ((dst_negative_code_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)) + ((dst_negative_scale_restrict_resultrowrow_sumslicesource_table) + (dst_negative_scale_restrict_resultrowrow_sumslicesource_table)))))) /\ (forall dst_index_restrict_resultrowrow_sumslicesource_table. (exists pvs_le_gap_restrict_resultrowrow_sumslicesource_tabledomain. pvs_le_gap_restrict_resultrowrow_sumslicesource_tabledomain + (dst_index_restrict_resultrowrow_sumslicesource_table) = (0)) -> exists dst_positive_restrict_resultrowrow_sumslicesource_table dst_negative_restrict_resultrowrow_sumslicesource_table dst_value_restrict_resultrowrow_sumslicesource_table. ((((exists ff_h_pvs_restrict_resultrowrow_sumslicesource_tableentrypositive. ff_h_pvs_restrict_resultrowrow_sumslicesource_tableentrypositive + S (dst_positive_restrict_resultrowrow_sumslicesource_table) = S ((S (dst_index_restrict_resultrowrow_sumslicesource_table)) * dst_positive_scale_restrict_resultrowrow_sumslicesource_table)) /\ exists ff_q_pvs_restrict_resultrowrow_sumslicesource_tableentrypositive. dst_positive_code_restrict_resultrowrow_sumslicesource_table = ff_q_pvs_restrict_resultrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_restrict_resultrowrow_sumslicesource_table)) * dst_positive_scale_restrict_resultrowrow_sumslicesource_table) + (dst_positive_restrict_resultrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_restrict_resultrowrow_sumslicesource_tableentrynegative. ff_h_pvs_restrict_resultrowrow_sumslicesource_tableentrynegative + S (dst_negative_restrict_resultrowrow_sumslicesource_table) = S ((S (dst_index_restrict_resultrowrow_sumslicesource_table)) * dst_negative_scale_restrict_resultrowrow_sumslicesource_table)) /\ exists ff_q_pvs_restrict_resultrowrow_sumslicesource_tableentrynegative. dst_negative_code_restrict_resultrowrow_sumslicesource_table = ff_q_pvs_restrict_resultrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_restrict_resultrowrow_sumslicesource_table)) * dst_negative_scale_restrict_resultrowrow_sumslicesource_table) + (dst_negative_restrict_resultrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_restrict_resultrowrow_sumslicesource_tableentryvalue ge_balance_negative_restrict_resultrowrow_sumslicesource_tableentryvalue. (((((dst_value_restrict_resultrowrow_sumslicesource_table) = 2 * (ge_balance_positive_restrict_resultrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_restrict_resultrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_restrict_resultrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_restrict_resultrowrow_sumslicesource_table) = 2 * ge_signed_half_restrict_resultrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_resultrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_restrict_resultrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_restrict_resultrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_restrict_resultrowrow_sumslicesource_table) + ge_balance_negative_restrict_resultrowrow_sumslicesource_tableentryvalue = (dst_negative_restrict_resultrowrow_sumslicesource_table) + ge_balance_positive_restrict_resultrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_restrict_resultrowrow_sumsliceoutput_table dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table dst_negative_code_restrict_resultrowrow_sumsliceoutput_table dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table. (((srs_slice_restrict_resultrowrow_sum) = (((((dst_positive_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table)) * S ((dst_positive_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table)) + ((dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table))) + (((dst_negative_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table)) * S ((dst_positive_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table)) + ((dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table) + (dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table))) + (((dst_negative_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table))) + (((dst_negative_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_restrict_resultrowrow_sumsliceoutput_table. (exists pvs_le_gap_restrict_resultrowrow_sumsliceoutput_tabledomain. pvs_le_gap_restrict_resultrowrow_sumsliceoutput_tabledomain + (dst_index_restrict_resultrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_restrict_resultrowrow_sumsliceoutput_table dst_negative_restrict_resultrowrow_sumsliceoutput_table dst_value_restrict_resultrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_restrict_resultrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_restrict_resultrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_restrict_resultrowrow_sumsliceoutput_table) = S ((S (dst_index_restrict_resultrowrow_sumsliceoutput_table)) * dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_restrict_resultrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_restrict_resultrowrow_sumsliceoutput_table = ff_q_pvs_restrict_resultrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_restrict_resultrowrow_sumsliceoutput_table)) * dst_positive_scale_restrict_resultrowrow_sumsliceoutput_table) + (dst_positive_restrict_resultrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_restrict_resultrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_restrict_resultrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_restrict_resultrowrow_sumsliceoutput_table) = S ((S (dst_index_restrict_resultrowrow_sumsliceoutput_table)) * dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_restrict_resultrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_restrict_resultrowrow_sumsliceoutput_table = ff_q_pvs_restrict_resultrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_restrict_resultrowrow_sumsliceoutput_table)) * dst_negative_scale_restrict_resultrowrow_sumsliceoutput_table) + (dst_negative_restrict_resultrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_restrict_resultrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_restrict_resultrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_restrict_resultrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_restrict_resultrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_restrict_resultrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_restrict_resultrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_restrict_resultrowrow_sumsliceoutput_table) = 2 * ge_signed_half_restrict_resultrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_resultrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_restrict_resultrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_restrict_resultrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_restrict_resultrowrow_sumsliceoutput_table) + ge_balance_negative_restrict_resultrowrow_sumsliceoutput_tableentryvalue = (dst_negative_restrict_resultrowrow_sumsliceoutput_table) + ge_balance_positive_restrict_resultrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_restrict_resultrowrow_sumslice. (exists pvs_gap_restrict_resultrowrow_sumslicebound. pvs_gap_restrict_resultrowrow_sumslicebound + S (srs_index_restrict_resultrowrow_sumslice) = (n)) -> exists srs_value_restrict_resultrowrow_sumslice. (((exists dst_positive_code_restrict_resultrowrow_sumsliceentrysource dst_positive_scale_restrict_resultrowrow_sumsliceentrysource dst_negative_code_restrict_resultrowrow_sumsliceentrysource dst_negative_scale_restrict_resultrowrow_sumsliceentrysource dst_positive_restrict_resultrowrow_sumsliceentrysource dst_negative_restrict_resultrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_restrict_resultrowrow_sumsliceentrysource) + (dst_positive_scale_restrict_resultrowrow_sumsliceentrysource)) * S ((dst_positive_code_restrict_resultrowrow_sumsliceentrysource) + (dst_positive_scale_restrict_resultrowrow_sumsliceentrysource)) + ((dst_positive_scale_restrict_resultrowrow_sumsliceentrysource) + (dst_positive_scale_restrict_resultrowrow_sumsliceentrysource))) + (((dst_negative_code_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_restrict_resultrowrow_sumsliceentrysource) + (dst_positive_scale_restrict_resultrowrow_sumsliceentrysource)) * S ((dst_positive_code_restrict_resultrowrow_sumsliceentrysource) + (dst_positive_scale_restrict_resultrowrow_sumsliceentrysource)) + ((dst_positive_scale_restrict_resultrowrow_sumsliceentrysource) + (dst_positive_scale_restrict_resultrowrow_sumsliceentrysource))) + (((dst_negative_code_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)))) + ((((dst_negative_code_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource))) + (((dst_negative_code_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_restrict_resultrowrow_sumsliceentrysourcepositive. ff_h_pvs_restrict_resultrowrow_sumsliceentrysourcepositive + S (dst_positive_restrict_resultrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_restrict_result)))) + ((t) * (srs_index_restrict_resultrowrow_sumslice))))) * dst_positive_scale_restrict_resultrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_restrict_resultrowrow_sumsliceentrysourcepositive. dst_positive_code_restrict_resultrowrow_sumsliceentrysource = ff_q_pvs_restrict_resultrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_restrict_result)))) + ((t) * (srs_index_restrict_resultrowrow_sumslice))))) * dst_positive_scale_restrict_resultrowrow_sumsliceentrysource) + (dst_positive_restrict_resultrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_restrict_resultrowrow_sumsliceentrysourcenegative. ff_h_pvs_restrict_resultrowrow_sumsliceentrysourcenegative + S (dst_negative_restrict_resultrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_restrict_result)))) + ((t) * (srs_index_restrict_resultrowrow_sumslice))))) * dst_negative_scale_restrict_resultrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_restrict_resultrowrow_sumsliceentrysourcenegative. dst_negative_code_restrict_resultrowrow_sumsliceentrysource = ff_q_pvs_restrict_resultrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_restrict_result)))) + ((t) * (srs_index_restrict_resultrowrow_sumslice))))) * dst_negative_scale_restrict_resultrowrow_sumsliceentrysource) + (dst_negative_restrict_resultrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_restrict_resultrowrow_sumsliceentrysourcevalue ge_balance_negative_restrict_resultrowrow_sumsliceentrysourcevalue. (((((srs_value_restrict_resultrowrow_sumslice) = 2 * (ge_balance_positive_restrict_resultrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_restrict_resultrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_restrict_resultrowrow_sumsliceentrysourcevaluedecode. (((srs_value_restrict_resultrowrow_sumslice) = 2 * ge_signed_half_restrict_resultrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_restrict_resultrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_restrict_resultrowrow_sumsliceentrysourcevalue) = S ge_signed_half_restrict_resultrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_restrict_resultrowrow_sumsliceentrysource) + ge_balance_negative_restrict_resultrowrow_sumsliceentrysourcevalue = (dst_negative_restrict_resultrowrow_sumsliceentrysource) + ge_balance_positive_restrict_resultrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_restrict_resultrowrow_sumsliceentryoutput dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput dst_negative_code_restrict_resultrowrow_sumsliceentryoutput dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput dst_positive_restrict_resultrowrow_sumsliceentryoutput dst_negative_restrict_resultrowrow_sumsliceentryoutput. (((srs_slice_restrict_resultrowrow_sum) = (((((dst_positive_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput)) * S ((dst_positive_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput)) + ((dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput))) + (((dst_negative_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput)) * S ((dst_positive_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput)) + ((dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput) + (dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput))) + (((dst_negative_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput))) + (((dst_negative_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)) * S ((dst_negative_code_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)) + ((dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_restrict_resultrowrow_sumsliceentryoutputpositive. ff_h_pvs_restrict_resultrowrow_sumsliceentryoutputpositive + S (dst_positive_restrict_resultrowrow_sumsliceentryoutput) = S ((S (srs_index_restrict_resultrowrow_sumslice)) * dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_restrict_resultrowrow_sumsliceentryoutputpositive. dst_positive_code_restrict_resultrowrow_sumsliceentryoutput = ff_q_pvs_restrict_resultrowrow_sumsliceentryoutputpositive * S ((S (srs_index_restrict_resultrowrow_sumslice)) * dst_positive_scale_restrict_resultrowrow_sumsliceentryoutput) + (dst_positive_restrict_resultrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_restrict_resultrowrow_sumsliceentryoutputnegative. ff_h_pvs_restrict_resultrowrow_sumsliceentryoutputnegative + S (dst_negative_restrict_resultrowrow_sumsliceentryoutput) = S ((S (srs_index_restrict_resultrowrow_sumslice)) * dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_restrict_resultrowrow_sumsliceentryoutputnegative. dst_negative_code_restrict_resultrowrow_sumsliceentryoutput = ff_q_pvs_restrict_resultrowrow_sumsliceentryoutputnegative * S ((S (srs_index_restrict_resultrowrow_sumslice)) * dst_negative_scale_restrict_resultrowrow_sumsliceentryoutput) + (dst_negative_restrict_resultrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_restrict_resultrowrow_sumsliceentryoutputvalue ge_balance_negative_restrict_resultrowrow_sumsliceentryoutputvalue. (((((srs_value_restrict_resultrowrow_sumslice) = 2 * (ge_balance_positive_restrict_resultrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_restrict_resultrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_restrict_resultrowrow_sumsliceentryoutputvaluedecode. (((srs_value_restrict_resultrowrow_sumslice) = 2 * ge_signed_half_restrict_resultrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_restrict_resultrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_restrict_resultrowrow_sumsliceentryoutputvalue) = S ge_signed_half_restrict_resultrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_restrict_resultrowrow_sumsliceentryoutput) + ge_balance_negative_restrict_resultrowrow_sumsliceentryoutputvalue = (dst_negative_restrict_resultrowrow_sumsliceentryoutput) + ge_balance_positive_restrict_resultrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_restrict_resultrowrow_sumsum dst_positive_scale_restrict_resultrowrow_sumsum dst_negative_code_restrict_resultrowrow_sumsum dst_negative_scale_restrict_resultrowrow_sumsum dst_positive_sum_restrict_resultrowrow_sumsum dst_negative_sum_restrict_resultrowrow_sumsum. (((srs_slice_restrict_resultrowrow_sum) = (((((dst_positive_code_restrict_resultrowrow_sumsum) + (dst_positive_scale_restrict_resultrowrow_sumsum)) * S ((dst_positive_code_restrict_resultrowrow_sumsum) + (dst_positive_scale_restrict_resultrowrow_sumsum)) + ((dst_positive_scale_restrict_resultrowrow_sumsum) + (dst_positive_scale_restrict_resultrowrow_sumsum))) + (((dst_negative_code_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)) * S ((dst_negative_code_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)) + ((dst_negative_scale_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)))) * S ((((dst_positive_code_restrict_resultrowrow_sumsum) + (dst_positive_scale_restrict_resultrowrow_sumsum)) * S ((dst_positive_code_restrict_resultrowrow_sumsum) + (dst_positive_scale_restrict_resultrowrow_sumsum)) + ((dst_positive_scale_restrict_resultrowrow_sumsum) + (dst_positive_scale_restrict_resultrowrow_sumsum))) + (((dst_negative_code_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)) * S ((dst_negative_code_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)) + ((dst_negative_scale_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)))) + ((((dst_negative_code_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)) * S ((dst_negative_code_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)) + ((dst_negative_scale_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum))) + (((dst_negative_code_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)) * S ((dst_negative_code_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)) + ((dst_negative_scale_restrict_resultrowrow_sumsum) + (dst_negative_scale_restrict_resultrowrow_sumsum)))))) /\ (((exists fs_u_dst_restrict_resultrowrow_sumsumpositive fs_v_dst_restrict_resultrowrow_sumsumpositive. ((((exists fs_h_dst_restrict_resultrowrow_sumsumpositive_body_start. fs_h_dst_restrict_resultrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_restrict_resultrowrow_sumsumpositive)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumpositive_body_start. fs_u_dst_restrict_resultrowrow_sumsumpositive = fs_q_dst_restrict_resultrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_restrict_resultrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_restrict_resultrowrow_sumsumpositive_body_terminal. fs_h_dst_restrict_resultrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_restrict_resultrowrow_sumsum) = S ((S (n)) * fs_v_dst_restrict_resultrowrow_sumsumpositive)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumpositive_body_terminal. fs_u_dst_restrict_resultrowrow_sumsumpositive = fs_q_dst_restrict_resultrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_restrict_resultrowrow_sumsumpositive) + (dst_positive_sum_restrict_resultrowrow_sumsum))) /\ forall fs_i_dst_restrict_resultrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_restrict_resultrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_restrict_resultrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_restrict_resultrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_restrict_resultrowrow_sumsumpositive_body_steps fs_r_dst_restrict_resultrowrow_sumsumpositive_body_steps fs_s_dst_restrict_resultrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_restrict_resultrowrow_sumsumpositive_body_steps_summand. fs_h_dst_restrict_resultrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_restrict_resultrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_restrict_resultrowrow_sumsumpositive_body_steps)) * dst_positive_scale_restrict_resultrowrow_sumsum)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumpositive_body_steps_summand. dst_positive_code_restrict_resultrowrow_sumsum = fs_q_dst_restrict_resultrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_restrict_resultrowrow_sumsumpositive_body_steps)) * dst_positive_scale_restrict_resultrowrow_sumsum) + (fs_a_dst_restrict_resultrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_restrict_resultrowrow_sumsumpositive_body_steps_partial. fs_h_dst_restrict_resultrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_restrict_resultrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_restrict_resultrowrow_sumsumpositive_body_steps)) * fs_v_dst_restrict_resultrowrow_sumsumpositive)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumpositive_body_steps_partial. fs_u_dst_restrict_resultrowrow_sumsumpositive = fs_q_dst_restrict_resultrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_restrict_resultrowrow_sumsumpositive_body_steps)) * fs_v_dst_restrict_resultrowrow_sumsumpositive) + (fs_r_dst_restrict_resultrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_restrict_resultrowrow_sumsumpositive_body_steps_successor. fs_h_dst_restrict_resultrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_restrict_resultrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_restrict_resultrowrow_sumsumpositive_body_steps)) * fs_v_dst_restrict_resultrowrow_sumsumpositive)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumpositive_body_steps_successor. fs_u_dst_restrict_resultrowrow_sumsumpositive = fs_q_dst_restrict_resultrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_restrict_resultrowrow_sumsumpositive_body_steps)) * fs_v_dst_restrict_resultrowrow_sumsumpositive) + (fs_s_dst_restrict_resultrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_restrict_resultrowrow_sumsumpositive_body_steps = fs_r_dst_restrict_resultrowrow_sumsumpositive_body_steps + fs_a_dst_restrict_resultrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_restrict_resultrowrow_sumsumnegative fs_v_dst_restrict_resultrowrow_sumsumnegative. ((((exists fs_h_dst_restrict_resultrowrow_sumsumnegative_body_start. fs_h_dst_restrict_resultrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_restrict_resultrowrow_sumsumnegative)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumnegative_body_start. fs_u_dst_restrict_resultrowrow_sumsumnegative = fs_q_dst_restrict_resultrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_restrict_resultrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_restrict_resultrowrow_sumsumnegative_body_terminal. fs_h_dst_restrict_resultrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_restrict_resultrowrow_sumsum) = S ((S (n)) * fs_v_dst_restrict_resultrowrow_sumsumnegative)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumnegative_body_terminal. fs_u_dst_restrict_resultrowrow_sumsumnegative = fs_q_dst_restrict_resultrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_restrict_resultrowrow_sumsumnegative) + (dst_negative_sum_restrict_resultrowrow_sumsum))) /\ forall fs_i_dst_restrict_resultrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_restrict_resultrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_restrict_resultrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_restrict_resultrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_restrict_resultrowrow_sumsumnegative_body_steps fs_r_dst_restrict_resultrowrow_sumsumnegative_body_steps fs_s_dst_restrict_resultrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_restrict_resultrowrow_sumsumnegative_body_steps_summand. fs_h_dst_restrict_resultrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_restrict_resultrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_restrict_resultrowrow_sumsumnegative_body_steps)) * dst_negative_scale_restrict_resultrowrow_sumsum)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumnegative_body_steps_summand. dst_negative_code_restrict_resultrowrow_sumsum = fs_q_dst_restrict_resultrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_restrict_resultrowrow_sumsumnegative_body_steps)) * dst_negative_scale_restrict_resultrowrow_sumsum) + (fs_a_dst_restrict_resultrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_restrict_resultrowrow_sumsumnegative_body_steps_partial. fs_h_dst_restrict_resultrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_restrict_resultrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_restrict_resultrowrow_sumsumnegative_body_steps)) * fs_v_dst_restrict_resultrowrow_sumsumnegative)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumnegative_body_steps_partial. fs_u_dst_restrict_resultrowrow_sumsumnegative = fs_q_dst_restrict_resultrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_restrict_resultrowrow_sumsumnegative_body_steps)) * fs_v_dst_restrict_resultrowrow_sumsumnegative) + (fs_r_dst_restrict_resultrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_restrict_resultrowrow_sumsumnegative_body_steps_successor. fs_h_dst_restrict_resultrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_restrict_resultrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_restrict_resultrowrow_sumsumnegative_body_steps)) * fs_v_dst_restrict_resultrowrow_sumsumnegative)) /\ exists fs_q_dst_restrict_resultrowrow_sumsumnegative_body_steps_successor. fs_u_dst_restrict_resultrowrow_sumsumnegative = fs_q_dst_restrict_resultrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_restrict_resultrowrow_sumsumnegative_body_steps)) * fs_v_dst_restrict_resultrowrow_sumsumnegative) + (fs_s_dst_restrict_resultrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_restrict_resultrowrow_sumsumnegative_body_steps = fs_r_dst_restrict_resultrowrow_sumsumnegative_body_steps + fs_a_dst_restrict_resultrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_restrict_resultrowrow_sumsumresult ge_balance_negative_restrict_resultrowrow_sumsumresult. (((((srt_value_restrict_result) = 2 * (ge_balance_positive_restrict_resultrowrow_sumsumresult) /\ (ge_balance_negative_restrict_resultrowrow_sumsumresult) = 0) \/ exists ge_signed_half_restrict_resultrowrow_sumsumresultdecode. (((srt_value_restrict_result) = 2 * ge_signed_half_restrict_resultrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_restrict_resultrowrow_sumsumresult) = 0) /\ (ge_balance_negative_restrict_resultrowrow_sumsumresult) = S ge_signed_half_restrict_resultrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_restrict_resultrowrow_sumsum) + ge_balance_negative_restrict_resultrowrow_sumsumresult = (dst_negative_sum_restrict_resultrowrow_sumsum) + ge_balance_positive_restrict_resultrowrow_sumsumresult))))))))))))))))))

Constructive proof overview

Generated structural guide

Removing the last row preserves every actual earlier row sum and the same output encoding.

The unchanged tactic script uses 2 declared prerequisites and contains 26 exact native proof lines.

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

Proof neighborhood

Direct dependencies

signed_table_domain_resize Alpha theorem; checked-use authorized le_succ Stable theorem; checked-use authorized

Direct dependents

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.

Read the argument

Proof checkpoints

26 script commands · 7 reading checkpoints · 0 local claims

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

01Fix variables and assumptionsL1–8

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

  1. L1
    intro F
  2. L2
    intro R
  3. L3
    intro o
  4. L4
    intro s
  5. L5
    intro t
  6. L6
    intro m
  7. L7
    intro n
  8. L8
    intro hr
02Separate the logical casesL9–11

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

  1. L9
    cases hr
  2. L10
    cases hr_right
  3. L11
    split
03Use earlier factsL12–12

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

  1. L12
    exact hr_left
04Separate the logical casesL13–13

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

  1. L13
    split
05Use earlier factsL14–18

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

  1. L14
    specialize signed_table_domain_resize (S m)
  2. L15
    specialize signed_table_domain_resize (m)
  3. L16
    specialize signed_table_domain_resize (R)
  4. L17
    apply signed_table_domain_resize
  5. L18
    exact hr_right_left
06Fix variables and assumptionsL19–20

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

  1. L19
    intro i
  2. L20
    intro hi
07Use earlier factsL21–26

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

  1. L21
    specialize hr_right_right (i)
  2. L22
    apply hr_right_right
  3. L23
    specialize le_succ (S i)
  4. L24
    specialize le_succ (m)
  5. L25
    apply le_succ
  6. L26
    exact hi

Library-wide reading audit

Original exact command ledger · 26 lines
  1. 0001intro F
  2. 0002intro R
  3. 0003intro o
  4. 0004intro s
  5. 0005intro t
  6. 0006intro m
  7. 0007intro n
  8. 0008intro hr
  9. 0009cases hr
  10. 0010cases hr_right
  11. 0011split
  12. 0012exact hr_left
  13. 0013split
  14. 0014specialize signed_table_domain_resize (S m)
  15. 0015specialize signed_table_domain_resize (m)
  16. 0016specialize signed_table_domain_resize (R)
  17. 0017apply signed_table_domain_resize
  18. 0018exact hr_right_left
  19. 0019intro i
  20. 0020intro hi
  21. 0021specialize hr_right_right (i)
  22. 0022apply hr_right_right
  23. 0023specialize le_succ (S i)
  24. 0024specialize le_succ (m)
  25. 0025apply le_succ
  26. 0026exact hi