MX0049

signed_support_incidence_column_sums_equal

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

Every actual incidence column-sum table agrees with the represented target values on precisely the strict target window.

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 A B r s L M T C. (((exists dst_positive_code_column_equal_supportsource_table dst_positive_scale_column_equal_supportsource_table dst_negative_code_column_equal_supportsource_table dst_negative_scale_column_equal_supportsource_table. (((A) = (((((dst_positive_code_column_equal_supportsource_table) + (dst_positive_scale_column_equal_supportsource_table)) * S ((dst_positive_code_column_equal_supportsource_table) + (dst_positive_scale_column_equal_supportsource_table)) + ((dst_positive_scale_column_equal_supportsource_table) + (dst_positive_scale_column_equal_supportsource_table))) + (((dst_negative_code_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)) * S ((dst_negative_code_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)) + ((dst_negative_scale_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)))) * S ((((dst_positive_code_column_equal_supportsource_table) + (dst_positive_scale_column_equal_supportsource_table)) * S ((dst_positive_code_column_equal_supportsource_table) + (dst_positive_scale_column_equal_supportsource_table)) + ((dst_positive_scale_column_equal_supportsource_table) + (dst_positive_scale_column_equal_supportsource_table))) + (((dst_negative_code_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)) * S ((dst_negative_code_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)) + ((dst_negative_scale_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)))) + ((((dst_negative_code_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)) * S ((dst_negative_code_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)) + ((dst_negative_scale_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table))) + (((dst_negative_code_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)) * S ((dst_negative_code_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)) + ((dst_negative_scale_column_equal_supportsource_table) + (dst_negative_scale_column_equal_supportsource_table)))))) /\ (forall dst_index_column_equal_supportsource_table. (exists pvs_le_gap_column_equal_supportsource_tabledomain. pvs_le_gap_column_equal_supportsource_tabledomain + (dst_index_column_equal_supportsource_table) = (0)) -> exists dst_positive_column_equal_supportsource_table dst_negative_column_equal_supportsource_table dst_value_column_equal_supportsource_table. ((((exists ff_h_pvs_column_equal_supportsource_tableentrypositive. ff_h_pvs_column_equal_supportsource_tableentrypositive + S (dst_positive_column_equal_supportsource_table) = S ((S (dst_index_column_equal_supportsource_table)) * dst_positive_scale_column_equal_supportsource_table)) /\ exists ff_q_pvs_column_equal_supportsource_tableentrypositive. dst_positive_code_column_equal_supportsource_table = ff_q_pvs_column_equal_supportsource_tableentrypositive * S ((S (dst_index_column_equal_supportsource_table)) * dst_positive_scale_column_equal_supportsource_table) + (dst_positive_column_equal_supportsource_table))) /\ (((((exists ff_h_pvs_column_equal_supportsource_tableentrynegative. ff_h_pvs_column_equal_supportsource_tableentrynegative + S (dst_negative_column_equal_supportsource_table) = S ((S (dst_index_column_equal_supportsource_table)) * dst_negative_scale_column_equal_supportsource_table)) /\ exists ff_q_pvs_column_equal_supportsource_tableentrynegative. dst_negative_code_column_equal_supportsource_table = ff_q_pvs_column_equal_supportsource_tableentrynegative * S ((S (dst_index_column_equal_supportsource_table)) * dst_negative_scale_column_equal_supportsource_table) + (dst_negative_column_equal_supportsource_table))) /\ (exists ge_balance_positive_column_equal_supportsource_tableentryvalue ge_balance_negative_column_equal_supportsource_tableentryvalue. (((((dst_value_column_equal_supportsource_table) = 2 * (ge_balance_positive_column_equal_supportsource_tableentryvalue) /\ (ge_balance_negative_column_equal_supportsource_tableentryvalue) = 0) \/ exists ge_signed_half_column_equal_supportsource_tableentryvaluedecode. (((dst_value_column_equal_supportsource_table) = 2 * ge_signed_half_column_equal_supportsource_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_equal_supportsource_tableentryvalue) = 0) /\ (ge_balance_negative_column_equal_supportsource_tableentryvalue) = S ge_signed_half_column_equal_supportsource_tableentryvaluedecode))) /\ ((dst_positive_column_equal_supportsource_table) + ge_balance_negative_column_equal_supportsource_tableentryvalue = (dst_negative_column_equal_supportsource_table) + ge_balance_positive_column_equal_supportsource_tableentryvalue))))))))) /\ (((exists dst_positive_code_column_equal_supporttarget_table dst_positive_scale_column_equal_supporttarget_table dst_negative_code_column_equal_supporttarget_table dst_negative_scale_column_equal_supporttarget_table. (((B) = (((((dst_positive_code_column_equal_supporttarget_table) + (dst_positive_scale_column_equal_supporttarget_table)) * S ((dst_positive_code_column_equal_supporttarget_table) + (dst_positive_scale_column_equal_supporttarget_table)) + ((dst_positive_scale_column_equal_supporttarget_table) + (dst_positive_scale_column_equal_supporttarget_table))) + (((dst_negative_code_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)) * S ((dst_negative_code_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)) + ((dst_negative_scale_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)))) * S ((((dst_positive_code_column_equal_supporttarget_table) + (dst_positive_scale_column_equal_supporttarget_table)) * S ((dst_positive_code_column_equal_supporttarget_table) + (dst_positive_scale_column_equal_supporttarget_table)) + ((dst_positive_scale_column_equal_supporttarget_table) + (dst_positive_scale_column_equal_supporttarget_table))) + (((dst_negative_code_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)) * S ((dst_negative_code_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)) + ((dst_negative_scale_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)))) + ((((dst_negative_code_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)) * S ((dst_negative_code_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)) + ((dst_negative_scale_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table))) + (((dst_negative_code_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)) * S ((dst_negative_code_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)) + ((dst_negative_scale_column_equal_supporttarget_table) + (dst_negative_scale_column_equal_supporttarget_table)))))) /\ (forall dst_index_column_equal_supporttarget_table. (exists pvs_le_gap_column_equal_supporttarget_tabledomain. pvs_le_gap_column_equal_supporttarget_tabledomain + (dst_index_column_equal_supporttarget_table) = (0)) -> exists dst_positive_column_equal_supporttarget_table dst_negative_column_equal_supporttarget_table dst_value_column_equal_supporttarget_table. ((((exists ff_h_pvs_column_equal_supporttarget_tableentrypositive. ff_h_pvs_column_equal_supporttarget_tableentrypositive + S (dst_positive_column_equal_supporttarget_table) = S ((S (dst_index_column_equal_supporttarget_table)) * dst_positive_scale_column_equal_supporttarget_table)) /\ exists ff_q_pvs_column_equal_supporttarget_tableentrypositive. dst_positive_code_column_equal_supporttarget_table = ff_q_pvs_column_equal_supporttarget_tableentrypositive * S ((S (dst_index_column_equal_supporttarget_table)) * dst_positive_scale_column_equal_supporttarget_table) + (dst_positive_column_equal_supporttarget_table))) /\ (((((exists ff_h_pvs_column_equal_supporttarget_tableentrynegative. ff_h_pvs_column_equal_supporttarget_tableentrynegative + S (dst_negative_column_equal_supporttarget_table) = S ((S (dst_index_column_equal_supporttarget_table)) * dst_negative_scale_column_equal_supporttarget_table)) /\ exists ff_q_pvs_column_equal_supporttarget_tableentrynegative. dst_negative_code_column_equal_supporttarget_table = ff_q_pvs_column_equal_supporttarget_tableentrynegative * S ((S (dst_index_column_equal_supporttarget_table)) * dst_negative_scale_column_equal_supporttarget_table) + (dst_negative_column_equal_supporttarget_table))) /\ (exists ge_balance_positive_column_equal_supporttarget_tableentryvalue ge_balance_negative_column_equal_supporttarget_tableentryvalue. (((((dst_value_column_equal_supporttarget_table) = 2 * (ge_balance_positive_column_equal_supporttarget_tableentryvalue) /\ (ge_balance_negative_column_equal_supporttarget_tableentryvalue) = 0) \/ exists ge_signed_half_column_equal_supporttarget_tableentryvaluedecode. (((dst_value_column_equal_supporttarget_table) = 2 * ge_signed_half_column_equal_supporttarget_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_equal_supporttarget_tableentryvalue) = 0) /\ (ge_balance_negative_column_equal_supporttarget_tableentryvalue) = S ge_signed_half_column_equal_supporttarget_tableentryvaluedecode))) /\ ((dst_positive_column_equal_supporttarget_table) + ge_balance_negative_column_equal_supporttarget_tableentryvalue = (dst_negative_column_equal_supporttarget_table) + ge_balance_positive_column_equal_supporttarget_tableentryvalue))))))))) /\ (((forall ssr_source_column_equal_supportpreserve ssr_value_column_equal_supportpreserve. (exists pvs_gap_column_equal_supportpreservesource_bound. pvs_gap_column_equal_supportpreservesource_bound + S (ssr_source_column_equal_supportpreserve) = (L)) -> (exists dst_positive_code_column_equal_supportpreservesource_value dst_positive_scale_column_equal_supportpreservesource_value dst_negative_code_column_equal_supportpreservesource_value dst_negative_scale_column_equal_supportpreservesource_value dst_positive_column_equal_supportpreservesource_value dst_negative_column_equal_supportpreservesource_value. (((A) = (((((dst_positive_code_column_equal_supportpreservesource_value) + (dst_positive_scale_column_equal_supportpreservesource_value)) * S ((dst_positive_code_column_equal_supportpreservesource_value) + (dst_positive_scale_column_equal_supportpreservesource_value)) + ((dst_positive_scale_column_equal_supportpreservesource_value) + (dst_positive_scale_column_equal_supportpreservesource_value))) + (((dst_negative_code_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)) * S ((dst_negative_code_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)) + ((dst_negative_scale_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)))) * S ((((dst_positive_code_column_equal_supportpreservesource_value) + (dst_positive_scale_column_equal_supportpreservesource_value)) * S ((dst_positive_code_column_equal_supportpreservesource_value) + (dst_positive_scale_column_equal_supportpreservesource_value)) + ((dst_positive_scale_column_equal_supportpreservesource_value) + (dst_positive_scale_column_equal_supportpreservesource_value))) + (((dst_negative_code_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)) * S ((dst_negative_code_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)) + ((dst_negative_scale_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)))) + ((((dst_negative_code_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)) * S ((dst_negative_code_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)) + ((dst_negative_scale_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value))) + (((dst_negative_code_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)) * S ((dst_negative_code_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)) + ((dst_negative_scale_column_equal_supportpreservesource_value) + (dst_negative_scale_column_equal_supportpreservesource_value)))))) /\ (((((exists ff_h_pvs_column_equal_supportpreservesource_valuepositive. ff_h_pvs_column_equal_supportpreservesource_valuepositive + S (dst_positive_column_equal_supportpreservesource_value) = S ((S (ssr_source_column_equal_supportpreserve)) * dst_positive_scale_column_equal_supportpreservesource_value)) /\ exists ff_q_pvs_column_equal_supportpreservesource_valuepositive. dst_positive_code_column_equal_supportpreservesource_value = ff_q_pvs_column_equal_supportpreservesource_valuepositive * S ((S (ssr_source_column_equal_supportpreserve)) * dst_positive_scale_column_equal_supportpreservesource_value) + (dst_positive_column_equal_supportpreservesource_value))) /\ (((((exists ff_h_pvs_column_equal_supportpreservesource_valuenegative. ff_h_pvs_column_equal_supportpreservesource_valuenegative + S (dst_negative_column_equal_supportpreservesource_value) = S ((S (ssr_source_column_equal_supportpreserve)) * dst_negative_scale_column_equal_supportpreservesource_value)) /\ exists ff_q_pvs_column_equal_supportpreservesource_valuenegative. dst_negative_code_column_equal_supportpreservesource_value = ff_q_pvs_column_equal_supportpreservesource_valuenegative * S ((S (ssr_source_column_equal_supportpreserve)) * dst_negative_scale_column_equal_supportpreservesource_value) + (dst_negative_column_equal_supportpreservesource_value))) /\ (exists ge_balance_positive_column_equal_supportpreservesource_valuevalue ge_balance_negative_column_equal_supportpreservesource_valuevalue. (((((ssr_value_column_equal_supportpreserve) = 2 * (ge_balance_positive_column_equal_supportpreservesource_valuevalue) /\ (ge_balance_negative_column_equal_supportpreservesource_valuevalue) = 0) \/ exists ge_signed_half_column_equal_supportpreservesource_valuevaluedecode. (((ssr_value_column_equal_supportpreserve) = 2 * ge_signed_half_column_equal_supportpreservesource_valuevaluedecode + 1 /\ (ge_balance_positive_column_equal_supportpreservesource_valuevalue) = 0) /\ (ge_balance_negative_column_equal_supportpreservesource_valuevalue) = S ge_signed_half_column_equal_supportpreservesource_valuevaluedecode))) /\ ((dst_positive_column_equal_supportpreservesource_value) + ge_balance_negative_column_equal_supportpreservesource_valuevalue = (dst_negative_column_equal_supportpreservesource_value) + ge_balance_positive_column_equal_supportpreservesource_valuevalue))))))))) -> ~(ssr_value_column_equal_supportpreserve=0) -> exists ssr_target_column_equal_supportpreserve. ((((exists ff_h_pvs_column_equal_supportpreservemap. ff_h_pvs_column_equal_supportpreservemap + S (ssr_target_column_equal_supportpreserve) = S ((S (ssr_source_column_equal_supportpreserve)) * s)) /\ exists ff_q_pvs_column_equal_supportpreservemap. r = ff_q_pvs_column_equal_supportpreservemap * S ((S (ssr_source_column_equal_supportpreserve)) * s) + (ssr_target_column_equal_supportpreserve))) /\ (((exists pvs_gap_column_equal_supportpreservetarget_bound. pvs_gap_column_equal_supportpreservetarget_bound + S (ssr_target_column_equal_supportpreserve) = (M)) /\ (exists dst_positive_code_column_equal_supportpreservetarget_value dst_positive_scale_column_equal_supportpreservetarget_value dst_negative_code_column_equal_supportpreservetarget_value dst_negative_scale_column_equal_supportpreservetarget_value dst_positive_column_equal_supportpreservetarget_value dst_negative_column_equal_supportpreservetarget_value. (((B) = (((((dst_positive_code_column_equal_supportpreservetarget_value) + (dst_positive_scale_column_equal_supportpreservetarget_value)) * S ((dst_positive_code_column_equal_supportpreservetarget_value) + (dst_positive_scale_column_equal_supportpreservetarget_value)) + ((dst_positive_scale_column_equal_supportpreservetarget_value) + (dst_positive_scale_column_equal_supportpreservetarget_value))) + (((dst_negative_code_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)) * S ((dst_negative_code_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)) + ((dst_negative_scale_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)))) * S ((((dst_positive_code_column_equal_supportpreservetarget_value) + (dst_positive_scale_column_equal_supportpreservetarget_value)) * S ((dst_positive_code_column_equal_supportpreservetarget_value) + (dst_positive_scale_column_equal_supportpreservetarget_value)) + ((dst_positive_scale_column_equal_supportpreservetarget_value) + (dst_positive_scale_column_equal_supportpreservetarget_value))) + (((dst_negative_code_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)) * S ((dst_negative_code_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)) + ((dst_negative_scale_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)))) + ((((dst_negative_code_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)) * S ((dst_negative_code_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)) + ((dst_negative_scale_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value))) + (((dst_negative_code_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)) * S ((dst_negative_code_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)) + ((dst_negative_scale_column_equal_supportpreservetarget_value) + (dst_negative_scale_column_equal_supportpreservetarget_value)))))) /\ (((((exists ff_h_pvs_column_equal_supportpreservetarget_valuepositive. ff_h_pvs_column_equal_supportpreservetarget_valuepositive + S (dst_positive_column_equal_supportpreservetarget_value) = S ((S (ssr_target_column_equal_supportpreserve)) * dst_positive_scale_column_equal_supportpreservetarget_value)) /\ exists ff_q_pvs_column_equal_supportpreservetarget_valuepositive. dst_positive_code_column_equal_supportpreservetarget_value = ff_q_pvs_column_equal_supportpreservetarget_valuepositive * S ((S (ssr_target_column_equal_supportpreserve)) * dst_positive_scale_column_equal_supportpreservetarget_value) + (dst_positive_column_equal_supportpreservetarget_value))) /\ (((((exists ff_h_pvs_column_equal_supportpreservetarget_valuenegative. ff_h_pvs_column_equal_supportpreservetarget_valuenegative + S (dst_negative_column_equal_supportpreservetarget_value) = S ((S (ssr_target_column_equal_supportpreserve)) * dst_negative_scale_column_equal_supportpreservetarget_value)) /\ exists ff_q_pvs_column_equal_supportpreservetarget_valuenegative. dst_negative_code_column_equal_supportpreservetarget_value = ff_q_pvs_column_equal_supportpreservetarget_valuenegative * S ((S (ssr_target_column_equal_supportpreserve)) * dst_negative_scale_column_equal_supportpreservetarget_value) + (dst_negative_column_equal_supportpreservetarget_value))) /\ (exists ge_balance_positive_column_equal_supportpreservetarget_valuevalue ge_balance_negative_column_equal_supportpreservetarget_valuevalue. (((((ssr_value_column_equal_supportpreserve) = 2 * (ge_balance_positive_column_equal_supportpreservetarget_valuevalue) /\ (ge_balance_negative_column_equal_supportpreservetarget_valuevalue) = 0) \/ exists ge_signed_half_column_equal_supportpreservetarget_valuevaluedecode. (((ssr_value_column_equal_supportpreserve) = 2 * ge_signed_half_column_equal_supportpreservetarget_valuevaluedecode + 1 /\ (ge_balance_positive_column_equal_supportpreservetarget_valuevalue) = 0) /\ (ge_balance_negative_column_equal_supportpreservetarget_valuevalue) = S ge_signed_half_column_equal_supportpreservetarget_valuevaluedecode))) /\ ((dst_positive_column_equal_supportpreservetarget_value) + ge_balance_negative_column_equal_supportpreservetarget_valuevalue = (dst_negative_column_equal_supportpreservetarget_value) + ge_balance_positive_column_equal_supportpreservetarget_valuevalue))))))))))))) /\ (((forall ssr_first_column_equal_supportinjective ssr_second_column_equal_supportinjective ssr_image_column_equal_supportinjective ssr_a_column_equal_supportinjective ssr_b_column_equal_supportinjective. (exists pvs_gap_column_equal_supportinjectivefirst_bound. pvs_gap_column_equal_supportinjectivefirst_bound + S (ssr_first_column_equal_supportinjective) = (L)) -> (exists pvs_gap_column_equal_supportinjectivesecond_bound. pvs_gap_column_equal_supportinjectivesecond_bound + S (ssr_second_column_equal_supportinjective) = (L)) -> (exists dst_positive_code_column_equal_supportinjectivefirst_value dst_positive_scale_column_equal_supportinjectivefirst_value dst_negative_code_column_equal_supportinjectivefirst_value dst_negative_scale_column_equal_supportinjectivefirst_value dst_positive_column_equal_supportinjectivefirst_value dst_negative_column_equal_supportinjectivefirst_value. (((A) = (((((dst_positive_code_column_equal_supportinjectivefirst_value) + (dst_positive_scale_column_equal_supportinjectivefirst_value)) * S ((dst_positive_code_column_equal_supportinjectivefirst_value) + (dst_positive_scale_column_equal_supportinjectivefirst_value)) + ((dst_positive_scale_column_equal_supportinjectivefirst_value) + (dst_positive_scale_column_equal_supportinjectivefirst_value))) + (((dst_negative_code_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)) * S ((dst_negative_code_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)) + ((dst_negative_scale_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)))) * S ((((dst_positive_code_column_equal_supportinjectivefirst_value) + (dst_positive_scale_column_equal_supportinjectivefirst_value)) * S ((dst_positive_code_column_equal_supportinjectivefirst_value) + (dst_positive_scale_column_equal_supportinjectivefirst_value)) + ((dst_positive_scale_column_equal_supportinjectivefirst_value) + (dst_positive_scale_column_equal_supportinjectivefirst_value))) + (((dst_negative_code_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)) * S ((dst_negative_code_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)) + ((dst_negative_scale_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)))) + ((((dst_negative_code_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)) * S ((dst_negative_code_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)) + ((dst_negative_scale_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value))) + (((dst_negative_code_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)) * S ((dst_negative_code_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)) + ((dst_negative_scale_column_equal_supportinjectivefirst_value) + (dst_negative_scale_column_equal_supportinjectivefirst_value)))))) /\ (((((exists ff_h_pvs_column_equal_supportinjectivefirst_valuepositive. ff_h_pvs_column_equal_supportinjectivefirst_valuepositive + S (dst_positive_column_equal_supportinjectivefirst_value) = S ((S (ssr_first_column_equal_supportinjective)) * dst_positive_scale_column_equal_supportinjectivefirst_value)) /\ exists ff_q_pvs_column_equal_supportinjectivefirst_valuepositive. dst_positive_code_column_equal_supportinjectivefirst_value = ff_q_pvs_column_equal_supportinjectivefirst_valuepositive * S ((S (ssr_first_column_equal_supportinjective)) * dst_positive_scale_column_equal_supportinjectivefirst_value) + (dst_positive_column_equal_supportinjectivefirst_value))) /\ (((((exists ff_h_pvs_column_equal_supportinjectivefirst_valuenegative. ff_h_pvs_column_equal_supportinjectivefirst_valuenegative + S (dst_negative_column_equal_supportinjectivefirst_value) = S ((S (ssr_first_column_equal_supportinjective)) * dst_negative_scale_column_equal_supportinjectivefirst_value)) /\ exists ff_q_pvs_column_equal_supportinjectivefirst_valuenegative. dst_negative_code_column_equal_supportinjectivefirst_value = ff_q_pvs_column_equal_supportinjectivefirst_valuenegative * S ((S (ssr_first_column_equal_supportinjective)) * dst_negative_scale_column_equal_supportinjectivefirst_value) + (dst_negative_column_equal_supportinjectivefirst_value))) /\ (exists ge_balance_positive_column_equal_supportinjectivefirst_valuevalue ge_balance_negative_column_equal_supportinjectivefirst_valuevalue. (((((ssr_a_column_equal_supportinjective) = 2 * (ge_balance_positive_column_equal_supportinjectivefirst_valuevalue) /\ (ge_balance_negative_column_equal_supportinjectivefirst_valuevalue) = 0) \/ exists ge_signed_half_column_equal_supportinjectivefirst_valuevaluedecode. (((ssr_a_column_equal_supportinjective) = 2 * ge_signed_half_column_equal_supportinjectivefirst_valuevaluedecode + 1 /\ (ge_balance_positive_column_equal_supportinjectivefirst_valuevalue) = 0) /\ (ge_balance_negative_column_equal_supportinjectivefirst_valuevalue) = S ge_signed_half_column_equal_supportinjectivefirst_valuevaluedecode))) /\ ((dst_positive_column_equal_supportinjectivefirst_value) + ge_balance_negative_column_equal_supportinjectivefirst_valuevalue = (dst_negative_column_equal_supportinjectivefirst_value) + ge_balance_positive_column_equal_supportinjectivefirst_valuevalue))))))))) -> ~(ssr_a_column_equal_supportinjective=0) -> (exists dst_positive_code_column_equal_supportinjectivesecond_value dst_positive_scale_column_equal_supportinjectivesecond_value dst_negative_code_column_equal_supportinjectivesecond_value dst_negative_scale_column_equal_supportinjectivesecond_value dst_positive_column_equal_supportinjectivesecond_value dst_negative_column_equal_supportinjectivesecond_value. (((A) = (((((dst_positive_code_column_equal_supportinjectivesecond_value) + (dst_positive_scale_column_equal_supportinjectivesecond_value)) * S ((dst_positive_code_column_equal_supportinjectivesecond_value) + (dst_positive_scale_column_equal_supportinjectivesecond_value)) + ((dst_positive_scale_column_equal_supportinjectivesecond_value) + (dst_positive_scale_column_equal_supportinjectivesecond_value))) + (((dst_negative_code_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)) * S ((dst_negative_code_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)) + ((dst_negative_scale_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)))) * S ((((dst_positive_code_column_equal_supportinjectivesecond_value) + (dst_positive_scale_column_equal_supportinjectivesecond_value)) * S ((dst_positive_code_column_equal_supportinjectivesecond_value) + (dst_positive_scale_column_equal_supportinjectivesecond_value)) + ((dst_positive_scale_column_equal_supportinjectivesecond_value) + (dst_positive_scale_column_equal_supportinjectivesecond_value))) + (((dst_negative_code_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)) * S ((dst_negative_code_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)) + ((dst_negative_scale_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)))) + ((((dst_negative_code_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)) * S ((dst_negative_code_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)) + ((dst_negative_scale_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value))) + (((dst_negative_code_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)) * S ((dst_negative_code_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)) + ((dst_negative_scale_column_equal_supportinjectivesecond_value) + (dst_negative_scale_column_equal_supportinjectivesecond_value)))))) /\ (((((exists ff_h_pvs_column_equal_supportinjectivesecond_valuepositive. ff_h_pvs_column_equal_supportinjectivesecond_valuepositive + S (dst_positive_column_equal_supportinjectivesecond_value) = S ((S (ssr_second_column_equal_supportinjective)) * dst_positive_scale_column_equal_supportinjectivesecond_value)) /\ exists ff_q_pvs_column_equal_supportinjectivesecond_valuepositive. dst_positive_code_column_equal_supportinjectivesecond_value = ff_q_pvs_column_equal_supportinjectivesecond_valuepositive * S ((S (ssr_second_column_equal_supportinjective)) * dst_positive_scale_column_equal_supportinjectivesecond_value) + (dst_positive_column_equal_supportinjectivesecond_value))) /\ (((((exists ff_h_pvs_column_equal_supportinjectivesecond_valuenegative. ff_h_pvs_column_equal_supportinjectivesecond_valuenegative + S (dst_negative_column_equal_supportinjectivesecond_value) = S ((S (ssr_second_column_equal_supportinjective)) * dst_negative_scale_column_equal_supportinjectivesecond_value)) /\ exists ff_q_pvs_column_equal_supportinjectivesecond_valuenegative. dst_negative_code_column_equal_supportinjectivesecond_value = ff_q_pvs_column_equal_supportinjectivesecond_valuenegative * S ((S (ssr_second_column_equal_supportinjective)) * dst_negative_scale_column_equal_supportinjectivesecond_value) + (dst_negative_column_equal_supportinjectivesecond_value))) /\ (exists ge_balance_positive_column_equal_supportinjectivesecond_valuevalue ge_balance_negative_column_equal_supportinjectivesecond_valuevalue. (((((ssr_b_column_equal_supportinjective) = 2 * (ge_balance_positive_column_equal_supportinjectivesecond_valuevalue) /\ (ge_balance_negative_column_equal_supportinjectivesecond_valuevalue) = 0) \/ exists ge_signed_half_column_equal_supportinjectivesecond_valuevaluedecode. (((ssr_b_column_equal_supportinjective) = 2 * ge_signed_half_column_equal_supportinjectivesecond_valuevaluedecode + 1 /\ (ge_balance_positive_column_equal_supportinjectivesecond_valuevalue) = 0) /\ (ge_balance_negative_column_equal_supportinjectivesecond_valuevalue) = S ge_signed_half_column_equal_supportinjectivesecond_valuevaluedecode))) /\ ((dst_positive_column_equal_supportinjectivesecond_value) + ge_balance_negative_column_equal_supportinjectivesecond_valuevalue = (dst_negative_column_equal_supportinjectivesecond_value) + ge_balance_positive_column_equal_supportinjectivesecond_valuevalue))))))))) -> ~(ssr_b_column_equal_supportinjective=0) -> (((exists ff_h_pvs_column_equal_supportinjectivefirst_map. ff_h_pvs_column_equal_supportinjectivefirst_map + S (ssr_image_column_equal_supportinjective) = S ((S (ssr_first_column_equal_supportinjective)) * s)) /\ exists ff_q_pvs_column_equal_supportinjectivefirst_map. r = ff_q_pvs_column_equal_supportinjectivefirst_map * S ((S (ssr_first_column_equal_supportinjective)) * s) + (ssr_image_column_equal_supportinjective))) -> (((exists ff_h_pvs_column_equal_supportinjectivesecond_map. ff_h_pvs_column_equal_supportinjectivesecond_map + S (ssr_image_column_equal_supportinjective) = S ((S (ssr_second_column_equal_supportinjective)) * s)) /\ exists ff_q_pvs_column_equal_supportinjectivesecond_map. r = ff_q_pvs_column_equal_supportinjectivesecond_map * S ((S (ssr_second_column_equal_supportinjective)) * s) + (ssr_image_column_equal_supportinjective))) -> ssr_first_column_equal_supportinjective=ssr_second_column_equal_supportinjective) /\ (forall ssr_target_column_equal_supportcover ssr_value_column_equal_supportcover. (exists pvs_gap_column_equal_supportcovertarget_bound. pvs_gap_column_equal_supportcovertarget_bound + S (ssr_target_column_equal_supportcover) = (M)) -> (exists dst_positive_code_column_equal_supportcovertarget_value dst_positive_scale_column_equal_supportcovertarget_value dst_negative_code_column_equal_supportcovertarget_value dst_negative_scale_column_equal_supportcovertarget_value dst_positive_column_equal_supportcovertarget_value dst_negative_column_equal_supportcovertarget_value. (((B) = (((((dst_positive_code_column_equal_supportcovertarget_value) + (dst_positive_scale_column_equal_supportcovertarget_value)) * S ((dst_positive_code_column_equal_supportcovertarget_value) + (dst_positive_scale_column_equal_supportcovertarget_value)) + ((dst_positive_scale_column_equal_supportcovertarget_value) + (dst_positive_scale_column_equal_supportcovertarget_value))) + (((dst_negative_code_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)) * S ((dst_negative_code_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)) + ((dst_negative_scale_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)))) * S ((((dst_positive_code_column_equal_supportcovertarget_value) + (dst_positive_scale_column_equal_supportcovertarget_value)) * S ((dst_positive_code_column_equal_supportcovertarget_value) + (dst_positive_scale_column_equal_supportcovertarget_value)) + ((dst_positive_scale_column_equal_supportcovertarget_value) + (dst_positive_scale_column_equal_supportcovertarget_value))) + (((dst_negative_code_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)) * S ((dst_negative_code_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)) + ((dst_negative_scale_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)))) + ((((dst_negative_code_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)) * S ((dst_negative_code_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)) + ((dst_negative_scale_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value))) + (((dst_negative_code_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)) * S ((dst_negative_code_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)) + ((dst_negative_scale_column_equal_supportcovertarget_value) + (dst_negative_scale_column_equal_supportcovertarget_value)))))) /\ (((((exists ff_h_pvs_column_equal_supportcovertarget_valuepositive. ff_h_pvs_column_equal_supportcovertarget_valuepositive + S (dst_positive_column_equal_supportcovertarget_value) = S ((S (ssr_target_column_equal_supportcover)) * dst_positive_scale_column_equal_supportcovertarget_value)) /\ exists ff_q_pvs_column_equal_supportcovertarget_valuepositive. dst_positive_code_column_equal_supportcovertarget_value = ff_q_pvs_column_equal_supportcovertarget_valuepositive * S ((S (ssr_target_column_equal_supportcover)) * dst_positive_scale_column_equal_supportcovertarget_value) + (dst_positive_column_equal_supportcovertarget_value))) /\ (((((exists ff_h_pvs_column_equal_supportcovertarget_valuenegative. ff_h_pvs_column_equal_supportcovertarget_valuenegative + S (dst_negative_column_equal_supportcovertarget_value) = S ((S (ssr_target_column_equal_supportcover)) * dst_negative_scale_column_equal_supportcovertarget_value)) /\ exists ff_q_pvs_column_equal_supportcovertarget_valuenegative. dst_negative_code_column_equal_supportcovertarget_value = ff_q_pvs_column_equal_supportcovertarget_valuenegative * S ((S (ssr_target_column_equal_supportcover)) * dst_negative_scale_column_equal_supportcovertarget_value) + (dst_negative_column_equal_supportcovertarget_value))) /\ (exists ge_balance_positive_column_equal_supportcovertarget_valuevalue ge_balance_negative_column_equal_supportcovertarget_valuevalue. (((((ssr_value_column_equal_supportcover) = 2 * (ge_balance_positive_column_equal_supportcovertarget_valuevalue) /\ (ge_balance_negative_column_equal_supportcovertarget_valuevalue) = 0) \/ exists ge_signed_half_column_equal_supportcovertarget_valuevaluedecode. (((ssr_value_column_equal_supportcover) = 2 * ge_signed_half_column_equal_supportcovertarget_valuevaluedecode + 1 /\ (ge_balance_positive_column_equal_supportcovertarget_valuevalue) = 0) /\ (ge_balance_negative_column_equal_supportcovertarget_valuevalue) = S ge_signed_half_column_equal_supportcovertarget_valuevaluedecode))) /\ ((dst_positive_column_equal_supportcovertarget_value) + ge_balance_negative_column_equal_supportcovertarget_valuevalue = (dst_negative_column_equal_supportcovertarget_value) + ge_balance_positive_column_equal_supportcovertarget_valuevalue))))))))) -> ~(ssr_value_column_equal_supportcover=0) -> exists ssr_source_column_equal_supportcover. ((exists pvs_gap_column_equal_supportcoversource_bound. pvs_gap_column_equal_supportcoversource_bound + S (ssr_source_column_equal_supportcover) = (L)) /\ (((((exists ff_h_pvs_column_equal_supportcovermap. ff_h_pvs_column_equal_supportcovermap + S (ssr_target_column_equal_supportcover) = S ((S (ssr_source_column_equal_supportcover)) * s)) /\ exists ff_q_pvs_column_equal_supportcovermap. r = ff_q_pvs_column_equal_supportcovermap * S ((S (ssr_source_column_equal_supportcover)) * s) + (ssr_target_column_equal_supportcover))) /\ (exists dst_positive_code_column_equal_supportcoversource_value dst_positive_scale_column_equal_supportcoversource_value dst_negative_code_column_equal_supportcoversource_value dst_negative_scale_column_equal_supportcoversource_value dst_positive_column_equal_supportcoversource_value dst_negative_column_equal_supportcoversource_value. (((A) = (((((dst_positive_code_column_equal_supportcoversource_value) + (dst_positive_scale_column_equal_supportcoversource_value)) * S ((dst_positive_code_column_equal_supportcoversource_value) + (dst_positive_scale_column_equal_supportcoversource_value)) + ((dst_positive_scale_column_equal_supportcoversource_value) + (dst_positive_scale_column_equal_supportcoversource_value))) + (((dst_negative_code_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)) * S ((dst_negative_code_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)) + ((dst_negative_scale_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)))) * S ((((dst_positive_code_column_equal_supportcoversource_value) + (dst_positive_scale_column_equal_supportcoversource_value)) * S ((dst_positive_code_column_equal_supportcoversource_value) + (dst_positive_scale_column_equal_supportcoversource_value)) + ((dst_positive_scale_column_equal_supportcoversource_value) + (dst_positive_scale_column_equal_supportcoversource_value))) + (((dst_negative_code_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)) * S ((dst_negative_code_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)) + ((dst_negative_scale_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)))) + ((((dst_negative_code_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)) * S ((dst_negative_code_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)) + ((dst_negative_scale_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value))) + (((dst_negative_code_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)) * S ((dst_negative_code_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)) + ((dst_negative_scale_column_equal_supportcoversource_value) + (dst_negative_scale_column_equal_supportcoversource_value)))))) /\ (((((exists ff_h_pvs_column_equal_supportcoversource_valuepositive. ff_h_pvs_column_equal_supportcoversource_valuepositive + S (dst_positive_column_equal_supportcoversource_value) = S ((S (ssr_source_column_equal_supportcover)) * dst_positive_scale_column_equal_supportcoversource_value)) /\ exists ff_q_pvs_column_equal_supportcoversource_valuepositive. dst_positive_code_column_equal_supportcoversource_value = ff_q_pvs_column_equal_supportcoversource_valuepositive * S ((S (ssr_source_column_equal_supportcover)) * dst_positive_scale_column_equal_supportcoversource_value) + (dst_positive_column_equal_supportcoversource_value))) /\ (((((exists ff_h_pvs_column_equal_supportcoversource_valuenegative. ff_h_pvs_column_equal_supportcoversource_valuenegative + S (dst_negative_column_equal_supportcoversource_value) = S ((S (ssr_source_column_equal_supportcover)) * dst_negative_scale_column_equal_supportcoversource_value)) /\ exists ff_q_pvs_column_equal_supportcoversource_valuenegative. dst_negative_code_column_equal_supportcoversource_value = ff_q_pvs_column_equal_supportcoversource_valuenegative * S ((S (ssr_source_column_equal_supportcover)) * dst_negative_scale_column_equal_supportcoversource_value) + (dst_negative_column_equal_supportcoversource_value))) /\ (exists ge_balance_positive_column_equal_supportcoversource_valuevalue ge_balance_negative_column_equal_supportcoversource_valuevalue. (((((ssr_value_column_equal_supportcover) = 2 * (ge_balance_positive_column_equal_supportcoversource_valuevalue) /\ (ge_balance_negative_column_equal_supportcoversource_valuevalue) = 0) \/ exists ge_signed_half_column_equal_supportcoversource_valuevaluedecode. (((ssr_value_column_equal_supportcover) = 2 * ge_signed_half_column_equal_supportcoversource_valuevaluedecode + 1 /\ (ge_balance_positive_column_equal_supportcoversource_valuevalue) = 0) /\ (ge_balance_negative_column_equal_supportcoversource_valuevalue) = S ge_signed_half_column_equal_supportcoversource_valuevaluedecode))) /\ ((dst_positive_column_equal_supportcoversource_value) + ge_balance_negative_column_equal_supportcoversource_valuevalue = (dst_negative_column_equal_supportcoversource_value) + ge_balance_positive_column_equal_supportcoversource_valuevalue))))))))))))))))))))) -> (((exists dst_positive_code_column_equal_gridsource dst_positive_scale_column_equal_gridsource dst_negative_code_column_equal_gridsource dst_negative_scale_column_equal_gridsource. (((A) = (((((dst_positive_code_column_equal_gridsource) + (dst_positive_scale_column_equal_gridsource)) * S ((dst_positive_code_column_equal_gridsource) + (dst_positive_scale_column_equal_gridsource)) + ((dst_positive_scale_column_equal_gridsource) + (dst_positive_scale_column_equal_gridsource))) + (((dst_negative_code_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)) * S ((dst_negative_code_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)) + ((dst_negative_scale_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)))) * S ((((dst_positive_code_column_equal_gridsource) + (dst_positive_scale_column_equal_gridsource)) * S ((dst_positive_code_column_equal_gridsource) + (dst_positive_scale_column_equal_gridsource)) + ((dst_positive_scale_column_equal_gridsource) + (dst_positive_scale_column_equal_gridsource))) + (((dst_negative_code_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)) * S ((dst_negative_code_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)) + ((dst_negative_scale_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)))) + ((((dst_negative_code_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)) * S ((dst_negative_code_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)) + ((dst_negative_scale_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource))) + (((dst_negative_code_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)) * S ((dst_negative_code_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)) + ((dst_negative_scale_column_equal_gridsource) + (dst_negative_scale_column_equal_gridsource)))))) /\ (forall dst_index_column_equal_gridsource. (exists pvs_le_gap_column_equal_gridsourcedomain. pvs_le_gap_column_equal_gridsourcedomain + (dst_index_column_equal_gridsource) = (0)) -> exists dst_positive_column_equal_gridsource dst_negative_column_equal_gridsource dst_value_column_equal_gridsource. ((((exists ff_h_pvs_column_equal_gridsourceentrypositive. ff_h_pvs_column_equal_gridsourceentrypositive + S (dst_positive_column_equal_gridsource) = S ((S (dst_index_column_equal_gridsource)) * dst_positive_scale_column_equal_gridsource)) /\ exists ff_q_pvs_column_equal_gridsourceentrypositive. dst_positive_code_column_equal_gridsource = ff_q_pvs_column_equal_gridsourceentrypositive * S ((S (dst_index_column_equal_gridsource)) * dst_positive_scale_column_equal_gridsource) + (dst_positive_column_equal_gridsource))) /\ (((((exists ff_h_pvs_column_equal_gridsourceentrynegative. ff_h_pvs_column_equal_gridsourceentrynegative + S (dst_negative_column_equal_gridsource) = S ((S (dst_index_column_equal_gridsource)) * dst_negative_scale_column_equal_gridsource)) /\ exists ff_q_pvs_column_equal_gridsourceentrynegative. dst_negative_code_column_equal_gridsource = ff_q_pvs_column_equal_gridsourceentrynegative * S ((S (dst_index_column_equal_gridsource)) * dst_negative_scale_column_equal_gridsource) + (dst_negative_column_equal_gridsource))) /\ (exists ge_balance_positive_column_equal_gridsourceentryvalue ge_balance_negative_column_equal_gridsourceentryvalue. (((((dst_value_column_equal_gridsource) = 2 * (ge_balance_positive_column_equal_gridsourceentryvalue) /\ (ge_balance_negative_column_equal_gridsourceentryvalue) = 0) \/ exists ge_signed_half_column_equal_gridsourceentryvaluedecode. (((dst_value_column_equal_gridsource) = 2 * ge_signed_half_column_equal_gridsourceentryvaluedecode + 1 /\ (ge_balance_positive_column_equal_gridsourceentryvalue) = 0) /\ (ge_balance_negative_column_equal_gridsourceentryvalue) = S ge_signed_half_column_equal_gridsourceentryvaluedecode))) /\ ((dst_positive_column_equal_gridsource) + ge_balance_negative_column_equal_gridsourceentryvalue = (dst_negative_column_equal_gridsource) + ge_balance_positive_column_equal_gridsourceentryvalue))))))))) /\ (((exists dst_positive_code_column_equal_gridtable dst_positive_scale_column_equal_gridtable dst_negative_code_column_equal_gridtable dst_negative_scale_column_equal_gridtable. (((T) = (((((dst_positive_code_column_equal_gridtable) + (dst_positive_scale_column_equal_gridtable)) * S ((dst_positive_code_column_equal_gridtable) + (dst_positive_scale_column_equal_gridtable)) + ((dst_positive_scale_column_equal_gridtable) + (dst_positive_scale_column_equal_gridtable))) + (((dst_negative_code_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)) * S ((dst_negative_code_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)) + ((dst_negative_scale_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)))) * S ((((dst_positive_code_column_equal_gridtable) + (dst_positive_scale_column_equal_gridtable)) * S ((dst_positive_code_column_equal_gridtable) + (dst_positive_scale_column_equal_gridtable)) + ((dst_positive_scale_column_equal_gridtable) + (dst_positive_scale_column_equal_gridtable))) + (((dst_negative_code_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)) * S ((dst_negative_code_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)) + ((dst_negative_scale_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)))) + ((((dst_negative_code_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)) * S ((dst_negative_code_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)) + ((dst_negative_scale_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable))) + (((dst_negative_code_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)) * S ((dst_negative_code_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)) + ((dst_negative_scale_column_equal_gridtable) + (dst_negative_scale_column_equal_gridtable)))))) /\ (forall dst_index_column_equal_gridtable. (exists pvs_le_gap_column_equal_gridtabledomain. pvs_le_gap_column_equal_gridtabledomain + (dst_index_column_equal_gridtable) = ((L)*(S (M)))) -> exists dst_positive_column_equal_gridtable dst_negative_column_equal_gridtable dst_value_column_equal_gridtable. ((((exists ff_h_pvs_column_equal_gridtableentrypositive. ff_h_pvs_column_equal_gridtableentrypositive + S (dst_positive_column_equal_gridtable) = S ((S (dst_index_column_equal_gridtable)) * dst_positive_scale_column_equal_gridtable)) /\ exists ff_q_pvs_column_equal_gridtableentrypositive. dst_positive_code_column_equal_gridtable = ff_q_pvs_column_equal_gridtableentrypositive * S ((S (dst_index_column_equal_gridtable)) * dst_positive_scale_column_equal_gridtable) + (dst_positive_column_equal_gridtable))) /\ (((((exists ff_h_pvs_column_equal_gridtableentrynegative. ff_h_pvs_column_equal_gridtableentrynegative + S (dst_negative_column_equal_gridtable) = S ((S (dst_index_column_equal_gridtable)) * dst_negative_scale_column_equal_gridtable)) /\ exists ff_q_pvs_column_equal_gridtableentrynegative. dst_negative_code_column_equal_gridtable = ff_q_pvs_column_equal_gridtableentrynegative * S ((S (dst_index_column_equal_gridtable)) * dst_negative_scale_column_equal_gridtable) + (dst_negative_column_equal_gridtable))) /\ (exists ge_balance_positive_column_equal_gridtableentryvalue ge_balance_negative_column_equal_gridtableentryvalue. (((((dst_value_column_equal_gridtable) = 2 * (ge_balance_positive_column_equal_gridtableentryvalue) /\ (ge_balance_negative_column_equal_gridtableentryvalue) = 0) \/ exists ge_signed_half_column_equal_gridtableentryvaluedecode. (((dst_value_column_equal_gridtable) = 2 * ge_signed_half_column_equal_gridtableentryvaluedecode + 1 /\ (ge_balance_positive_column_equal_gridtableentryvalue) = 0) /\ (ge_balance_negative_column_equal_gridtableentryvalue) = S ge_signed_half_column_equal_gridtableentryvaluedecode))) /\ ((dst_positive_column_equal_gridtable) + ge_balance_negative_column_equal_gridtableentryvalue = (dst_negative_column_equal_gridtable) + ge_balance_positive_column_equal_gridtableentryvalue))))))))) /\ (forall ssr_grid_row_column_equal_grid ssr_grid_column_column_equal_grid ssr_grid_value_column_equal_grid. (exists pvs_gap_column_equal_gridrow_bound. pvs_gap_column_equal_gridrow_bound + S (ssr_grid_row_column_equal_grid) = (L)) -> (exists pvs_gap_column_equal_gridcolumn_bound. pvs_gap_column_equal_gridcolumn_bound + S (ssr_grid_column_column_equal_grid) = (M)) -> (exists dst_positive_code_column_equal_gridlookup dst_positive_scale_column_equal_gridlookup dst_negative_code_column_equal_gridlookup dst_negative_scale_column_equal_gridlookup dst_positive_column_equal_gridlookup dst_negative_column_equal_gridlookup. (((T) = (((((dst_positive_code_column_equal_gridlookup) + (dst_positive_scale_column_equal_gridlookup)) * S ((dst_positive_code_column_equal_gridlookup) + (dst_positive_scale_column_equal_gridlookup)) + ((dst_positive_scale_column_equal_gridlookup) + (dst_positive_scale_column_equal_gridlookup))) + (((dst_negative_code_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)) * S ((dst_negative_code_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)) + ((dst_negative_scale_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)))) * S ((((dst_positive_code_column_equal_gridlookup) + (dst_positive_scale_column_equal_gridlookup)) * S ((dst_positive_code_column_equal_gridlookup) + (dst_positive_scale_column_equal_gridlookup)) + ((dst_positive_scale_column_equal_gridlookup) + (dst_positive_scale_column_equal_gridlookup))) + (((dst_negative_code_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)) * S ((dst_negative_code_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)) + ((dst_negative_scale_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)))) + ((((dst_negative_code_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)) * S ((dst_negative_code_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)) + ((dst_negative_scale_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup))) + (((dst_negative_code_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)) * S ((dst_negative_code_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)) + ((dst_negative_scale_column_equal_gridlookup) + (dst_negative_scale_column_equal_gridlookup)))))) /\ (((((exists ff_h_pvs_column_equal_gridlookuppositive. ff_h_pvs_column_equal_gridlookuppositive + S (dst_positive_column_equal_gridlookup) = S ((S (((S (M))*(ssr_grid_row_column_equal_grid)+(ssr_grid_column_column_equal_grid)))) * dst_positive_scale_column_equal_gridlookup)) /\ exists ff_q_pvs_column_equal_gridlookuppositive. dst_positive_code_column_equal_gridlookup = ff_q_pvs_column_equal_gridlookuppositive * S ((S (((S (M))*(ssr_grid_row_column_equal_grid)+(ssr_grid_column_column_equal_grid)))) * dst_positive_scale_column_equal_gridlookup) + (dst_positive_column_equal_gridlookup))) /\ (((((exists ff_h_pvs_column_equal_gridlookupnegative. ff_h_pvs_column_equal_gridlookupnegative + S (dst_negative_column_equal_gridlookup) = S ((S (((S (M))*(ssr_grid_row_column_equal_grid)+(ssr_grid_column_column_equal_grid)))) * dst_negative_scale_column_equal_gridlookup)) /\ exists ff_q_pvs_column_equal_gridlookupnegative. dst_negative_code_column_equal_gridlookup = ff_q_pvs_column_equal_gridlookupnegative * S ((S (((S (M))*(ssr_grid_row_column_equal_grid)+(ssr_grid_column_column_equal_grid)))) * dst_negative_scale_column_equal_gridlookup) + (dst_negative_column_equal_gridlookup))) /\ (exists ge_balance_positive_column_equal_gridlookupvalue ge_balance_negative_column_equal_gridlookupvalue. (((((ssr_grid_value_column_equal_grid) = 2 * (ge_balance_positive_column_equal_gridlookupvalue) /\ (ge_balance_negative_column_equal_gridlookupvalue) = 0) \/ exists ge_signed_half_column_equal_gridlookupvaluedecode. (((ssr_grid_value_column_equal_grid) = 2 * ge_signed_half_column_equal_gridlookupvaluedecode + 1 /\ (ge_balance_positive_column_equal_gridlookupvalue) = 0) /\ (ge_balance_negative_column_equal_gridlookupvalue) = S ge_signed_half_column_equal_gridlookupvaluedecode))) /\ ((dst_positive_column_equal_gridlookup) + ge_balance_negative_column_equal_gridlookupvalue = (dst_negative_column_equal_gridlookup) + ge_balance_positive_column_equal_gridlookupvalue))))))))) -> (exists ssr_entry_value_column_equal_gridentry ssr_entry_image_column_equal_gridentry. ((exists dst_positive_code_column_equal_gridentrysource dst_positive_scale_column_equal_gridentrysource dst_negative_code_column_equal_gridentrysource dst_negative_scale_column_equal_gridentrysource dst_positive_column_equal_gridentrysource dst_negative_column_equal_gridentrysource. (((A) = (((((dst_positive_code_column_equal_gridentrysource) + (dst_positive_scale_column_equal_gridentrysource)) * S ((dst_positive_code_column_equal_gridentrysource) + (dst_positive_scale_column_equal_gridentrysource)) + ((dst_positive_scale_column_equal_gridentrysource) + (dst_positive_scale_column_equal_gridentrysource))) + (((dst_negative_code_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)) * S ((dst_negative_code_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)) + ((dst_negative_scale_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)))) * S ((((dst_positive_code_column_equal_gridentrysource) + (dst_positive_scale_column_equal_gridentrysource)) * S ((dst_positive_code_column_equal_gridentrysource) + (dst_positive_scale_column_equal_gridentrysource)) + ((dst_positive_scale_column_equal_gridentrysource) + (dst_positive_scale_column_equal_gridentrysource))) + (((dst_negative_code_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)) * S ((dst_negative_code_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)) + ((dst_negative_scale_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)))) + ((((dst_negative_code_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)) * S ((dst_negative_code_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)) + ((dst_negative_scale_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource))) + (((dst_negative_code_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)) * S ((dst_negative_code_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)) + ((dst_negative_scale_column_equal_gridentrysource) + (dst_negative_scale_column_equal_gridentrysource)))))) /\ (((((exists ff_h_pvs_column_equal_gridentrysourcepositive. ff_h_pvs_column_equal_gridentrysourcepositive + S (dst_positive_column_equal_gridentrysource) = S ((S (ssr_grid_row_column_equal_grid)) * dst_positive_scale_column_equal_gridentrysource)) /\ exists ff_q_pvs_column_equal_gridentrysourcepositive. dst_positive_code_column_equal_gridentrysource = ff_q_pvs_column_equal_gridentrysourcepositive * S ((S (ssr_grid_row_column_equal_grid)) * dst_positive_scale_column_equal_gridentrysource) + (dst_positive_column_equal_gridentrysource))) /\ (((((exists ff_h_pvs_column_equal_gridentrysourcenegative. ff_h_pvs_column_equal_gridentrysourcenegative + S (dst_negative_column_equal_gridentrysource) = S ((S (ssr_grid_row_column_equal_grid)) * dst_negative_scale_column_equal_gridentrysource)) /\ exists ff_q_pvs_column_equal_gridentrysourcenegative. dst_negative_code_column_equal_gridentrysource = ff_q_pvs_column_equal_gridentrysourcenegative * S ((S (ssr_grid_row_column_equal_grid)) * dst_negative_scale_column_equal_gridentrysource) + (dst_negative_column_equal_gridentrysource))) /\ (exists ge_balance_positive_column_equal_gridentrysourcevalue ge_balance_negative_column_equal_gridentrysourcevalue. (((((ssr_entry_value_column_equal_gridentry) = 2 * (ge_balance_positive_column_equal_gridentrysourcevalue) /\ (ge_balance_negative_column_equal_gridentrysourcevalue) = 0) \/ exists ge_signed_half_column_equal_gridentrysourcevaluedecode. (((ssr_entry_value_column_equal_gridentry) = 2 * ge_signed_half_column_equal_gridentrysourcevaluedecode + 1 /\ (ge_balance_positive_column_equal_gridentrysourcevalue) = 0) /\ (ge_balance_negative_column_equal_gridentrysourcevalue) = S ge_signed_half_column_equal_gridentrysourcevaluedecode))) /\ ((dst_positive_column_equal_gridentrysource) + ge_balance_negative_column_equal_gridentrysourcevalue = (dst_negative_column_equal_gridentrysource) + ge_balance_positive_column_equal_gridentrysourcevalue))))))))) /\ (((((exists ff_h_pvs_column_equal_gridentrymap. ff_h_pvs_column_equal_gridentrymap + S (ssr_entry_image_column_equal_gridentry) = S ((S (ssr_grid_row_column_equal_grid)) * s)) /\ exists ff_q_pvs_column_equal_gridentrymap. r = ff_q_pvs_column_equal_gridentrymap * S ((S (ssr_grid_row_column_equal_grid)) * s) + (ssr_entry_image_column_equal_gridentry))) /\ (((((ssr_grid_column_column_equal_grid)=(ssr_entry_image_column_equal_gridentry)) /\ ((ssr_grid_value_column_equal_grid)=(ssr_entry_value_column_equal_gridentry)))) \/ (((~((ssr_grid_column_column_equal_grid)=(ssr_entry_image_column_equal_gridentry))) /\ ((ssr_grid_value_column_equal_grid)=0))))))))))))) -> (((exists dst_positive_code_column_equal_rowssource_table dst_positive_scale_column_equal_rowssource_table dst_negative_code_column_equal_rowssource_table dst_negative_scale_column_equal_rowssource_table. (((T) = (((((dst_positive_code_column_equal_rowssource_table) + (dst_positive_scale_column_equal_rowssource_table)) * S ((dst_positive_code_column_equal_rowssource_table) + (dst_positive_scale_column_equal_rowssource_table)) + ((dst_positive_scale_column_equal_rowssource_table) + (dst_positive_scale_column_equal_rowssource_table))) + (((dst_negative_code_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)) * S ((dst_negative_code_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)) + ((dst_negative_scale_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)))) * S ((((dst_positive_code_column_equal_rowssource_table) + (dst_positive_scale_column_equal_rowssource_table)) * S ((dst_positive_code_column_equal_rowssource_table) + (dst_positive_scale_column_equal_rowssource_table)) + ((dst_positive_scale_column_equal_rowssource_table) + (dst_positive_scale_column_equal_rowssource_table))) + (((dst_negative_code_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)) * S ((dst_negative_code_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)) + ((dst_negative_scale_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)))) + ((((dst_negative_code_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)) * S ((dst_negative_code_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)) + ((dst_negative_scale_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table))) + (((dst_negative_code_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)) * S ((dst_negative_code_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)) + ((dst_negative_scale_column_equal_rowssource_table) + (dst_negative_scale_column_equal_rowssource_table)))))) /\ (forall dst_index_column_equal_rowssource_table. (exists pvs_le_gap_column_equal_rowssource_tabledomain. pvs_le_gap_column_equal_rowssource_tabledomain + (dst_index_column_equal_rowssource_table) = (0)) -> exists dst_positive_column_equal_rowssource_table dst_negative_column_equal_rowssource_table dst_value_column_equal_rowssource_table. ((((exists ff_h_pvs_column_equal_rowssource_tableentrypositive. ff_h_pvs_column_equal_rowssource_tableentrypositive + S (dst_positive_column_equal_rowssource_table) = S ((S (dst_index_column_equal_rowssource_table)) * dst_positive_scale_column_equal_rowssource_table)) /\ exists ff_q_pvs_column_equal_rowssource_tableentrypositive. dst_positive_code_column_equal_rowssource_table = ff_q_pvs_column_equal_rowssource_tableentrypositive * S ((S (dst_index_column_equal_rowssource_table)) * dst_positive_scale_column_equal_rowssource_table) + (dst_positive_column_equal_rowssource_table))) /\ (((((exists ff_h_pvs_column_equal_rowssource_tableentrynegative. ff_h_pvs_column_equal_rowssource_tableentrynegative + S (dst_negative_column_equal_rowssource_table) = S ((S (dst_index_column_equal_rowssource_table)) * dst_negative_scale_column_equal_rowssource_table)) /\ exists ff_q_pvs_column_equal_rowssource_tableentrynegative. dst_negative_code_column_equal_rowssource_table = ff_q_pvs_column_equal_rowssource_tableentrynegative * S ((S (dst_index_column_equal_rowssource_table)) * dst_negative_scale_column_equal_rowssource_table) + (dst_negative_column_equal_rowssource_table))) /\ (exists ge_balance_positive_column_equal_rowssource_tableentryvalue ge_balance_negative_column_equal_rowssource_tableentryvalue. (((((dst_value_column_equal_rowssource_table) = 2 * (ge_balance_positive_column_equal_rowssource_tableentryvalue) /\ (ge_balance_negative_column_equal_rowssource_tableentryvalue) = 0) \/ exists ge_signed_half_column_equal_rowssource_tableentryvaluedecode. (((dst_value_column_equal_rowssource_table) = 2 * ge_signed_half_column_equal_rowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_equal_rowssource_tableentryvalue) = 0) /\ (ge_balance_negative_column_equal_rowssource_tableentryvalue) = S ge_signed_half_column_equal_rowssource_tableentryvaluedecode))) /\ ((dst_positive_column_equal_rowssource_table) + ge_balance_negative_column_equal_rowssource_tableentryvalue = (dst_negative_column_equal_rowssource_table) + ge_balance_positive_column_equal_rowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_column_equal_rowsrow_table dst_positive_scale_column_equal_rowsrow_table dst_negative_code_column_equal_rowsrow_table dst_negative_scale_column_equal_rowsrow_table. (((C) = (((((dst_positive_code_column_equal_rowsrow_table) + (dst_positive_scale_column_equal_rowsrow_table)) * S ((dst_positive_code_column_equal_rowsrow_table) + (dst_positive_scale_column_equal_rowsrow_table)) + ((dst_positive_scale_column_equal_rowsrow_table) + (dst_positive_scale_column_equal_rowsrow_table))) + (((dst_negative_code_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)) * S ((dst_negative_code_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)) + ((dst_negative_scale_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)))) * S ((((dst_positive_code_column_equal_rowsrow_table) + (dst_positive_scale_column_equal_rowsrow_table)) * S ((dst_positive_code_column_equal_rowsrow_table) + (dst_positive_scale_column_equal_rowsrow_table)) + ((dst_positive_scale_column_equal_rowsrow_table) + (dst_positive_scale_column_equal_rowsrow_table))) + (((dst_negative_code_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)) * S ((dst_negative_code_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)) + ((dst_negative_scale_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)))) + ((((dst_negative_code_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)) * S ((dst_negative_code_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)) + ((dst_negative_scale_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table))) + (((dst_negative_code_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)) * S ((dst_negative_code_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)) + ((dst_negative_scale_column_equal_rowsrow_table) + (dst_negative_scale_column_equal_rowsrow_table)))))) /\ (forall dst_index_column_equal_rowsrow_table. (exists pvs_le_gap_column_equal_rowsrow_tabledomain. pvs_le_gap_column_equal_rowsrow_tabledomain + (dst_index_column_equal_rowsrow_table) = (M)) -> exists dst_positive_column_equal_rowsrow_table dst_negative_column_equal_rowsrow_table dst_value_column_equal_rowsrow_table. ((((exists ff_h_pvs_column_equal_rowsrow_tableentrypositive. ff_h_pvs_column_equal_rowsrow_tableentrypositive + S (dst_positive_column_equal_rowsrow_table) = S ((S (dst_index_column_equal_rowsrow_table)) * dst_positive_scale_column_equal_rowsrow_table)) /\ exists ff_q_pvs_column_equal_rowsrow_tableentrypositive. dst_positive_code_column_equal_rowsrow_table = ff_q_pvs_column_equal_rowsrow_tableentrypositive * S ((S (dst_index_column_equal_rowsrow_table)) * dst_positive_scale_column_equal_rowsrow_table) + (dst_positive_column_equal_rowsrow_table))) /\ (((((exists ff_h_pvs_column_equal_rowsrow_tableentrynegative. ff_h_pvs_column_equal_rowsrow_tableentrynegative + S (dst_negative_column_equal_rowsrow_table) = S ((S (dst_index_column_equal_rowsrow_table)) * dst_negative_scale_column_equal_rowsrow_table)) /\ exists ff_q_pvs_column_equal_rowsrow_tableentrynegative. dst_negative_code_column_equal_rowsrow_table = ff_q_pvs_column_equal_rowsrow_tableentrynegative * S ((S (dst_index_column_equal_rowsrow_table)) * dst_negative_scale_column_equal_rowsrow_table) + (dst_negative_column_equal_rowsrow_table))) /\ (exists ge_balance_positive_column_equal_rowsrow_tableentryvalue ge_balance_negative_column_equal_rowsrow_tableentryvalue. (((((dst_value_column_equal_rowsrow_table) = 2 * (ge_balance_positive_column_equal_rowsrow_tableentryvalue) /\ (ge_balance_negative_column_equal_rowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_column_equal_rowsrow_tableentryvaluedecode. (((dst_value_column_equal_rowsrow_table) = 2 * ge_signed_half_column_equal_rowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_equal_rowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_column_equal_rowsrow_tableentryvalue) = S ge_signed_half_column_equal_rowsrow_tableentryvaluedecode))) /\ ((dst_positive_column_equal_rowsrow_table) + ge_balance_negative_column_equal_rowsrow_tableentryvalue = (dst_negative_column_equal_rowsrow_table) + ge_balance_positive_column_equal_rowsrow_tableentryvalue))))))))) /\ (forall srt_index_column_equal_rows. (exists pvs_gap_column_equal_rowsbound. pvs_gap_column_equal_rowsbound + S (srt_index_column_equal_rows) = (M)) -> exists srt_value_column_equal_rows. (((exists dst_positive_code_column_equal_rowsrowentry dst_positive_scale_column_equal_rowsrowentry dst_negative_code_column_equal_rowsrowentry dst_negative_scale_column_equal_rowsrowentry dst_positive_column_equal_rowsrowentry dst_negative_column_equal_rowsrowentry. (((C) = (((((dst_positive_code_column_equal_rowsrowentry) + (dst_positive_scale_column_equal_rowsrowentry)) * S ((dst_positive_code_column_equal_rowsrowentry) + (dst_positive_scale_column_equal_rowsrowentry)) + ((dst_positive_scale_column_equal_rowsrowentry) + (dst_positive_scale_column_equal_rowsrowentry))) + (((dst_negative_code_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)) * S ((dst_negative_code_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)) + ((dst_negative_scale_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)))) * S ((((dst_positive_code_column_equal_rowsrowentry) + (dst_positive_scale_column_equal_rowsrowentry)) * S ((dst_positive_code_column_equal_rowsrowentry) + (dst_positive_scale_column_equal_rowsrowentry)) + ((dst_positive_scale_column_equal_rowsrowentry) + (dst_positive_scale_column_equal_rowsrowentry))) + (((dst_negative_code_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)) * S ((dst_negative_code_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)) + ((dst_negative_scale_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)))) + ((((dst_negative_code_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)) * S ((dst_negative_code_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)) + ((dst_negative_scale_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry))) + (((dst_negative_code_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)) * S ((dst_negative_code_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)) + ((dst_negative_scale_column_equal_rowsrowentry) + (dst_negative_scale_column_equal_rowsrowentry)))))) /\ (((((exists ff_h_pvs_column_equal_rowsrowentrypositive. ff_h_pvs_column_equal_rowsrowentrypositive + S (dst_positive_column_equal_rowsrowentry) = S ((S (srt_index_column_equal_rows)) * dst_positive_scale_column_equal_rowsrowentry)) /\ exists ff_q_pvs_column_equal_rowsrowentrypositive. dst_positive_code_column_equal_rowsrowentry = ff_q_pvs_column_equal_rowsrowentrypositive * S ((S (srt_index_column_equal_rows)) * dst_positive_scale_column_equal_rowsrowentry) + (dst_positive_column_equal_rowsrowentry))) /\ (((((exists ff_h_pvs_column_equal_rowsrowentrynegative. ff_h_pvs_column_equal_rowsrowentrynegative + S (dst_negative_column_equal_rowsrowentry) = S ((S (srt_index_column_equal_rows)) * dst_negative_scale_column_equal_rowsrowentry)) /\ exists ff_q_pvs_column_equal_rowsrowentrynegative. dst_negative_code_column_equal_rowsrowentry = ff_q_pvs_column_equal_rowsrowentrynegative * S ((S (srt_index_column_equal_rows)) * dst_negative_scale_column_equal_rowsrowentry) + (dst_negative_column_equal_rowsrowentry))) /\ (exists ge_balance_positive_column_equal_rowsrowentryvalue ge_balance_negative_column_equal_rowsrowentryvalue. (((((srt_value_column_equal_rows) = 2 * (ge_balance_positive_column_equal_rowsrowentryvalue) /\ (ge_balance_negative_column_equal_rowsrowentryvalue) = 0) \/ exists ge_signed_half_column_equal_rowsrowentryvaluedecode. (((srt_value_column_equal_rows) = 2 * ge_signed_half_column_equal_rowsrowentryvaluedecode + 1 /\ (ge_balance_positive_column_equal_rowsrowentryvalue) = 0) /\ (ge_balance_negative_column_equal_rowsrowentryvalue) = S ge_signed_half_column_equal_rowsrowentryvaluedecode))) /\ ((dst_positive_column_equal_rowsrowentry) + ge_balance_negative_column_equal_rowsrowentryvalue = (dst_negative_column_equal_rowsrowentry) + ge_balance_positive_column_equal_rowsrowentryvalue))))))))) /\ (exists srs_slice_column_equal_rowsrowrow_sum. ((((exists dst_positive_code_column_equal_rowsrowrow_sumslicesource_table dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table dst_negative_code_column_equal_rowsrowrow_sumslicesource_table dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table. (((T) = (((((dst_positive_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table)) * S ((dst_positive_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table)) + ((dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table) + (dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table)) * S ((dst_positive_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table)) + ((dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table) + (dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_column_equal_rowsrowrow_sumslicesource_table. (exists pvs_le_gap_column_equal_rowsrowrow_sumslicesource_tabledomain. pvs_le_gap_column_equal_rowsrowrow_sumslicesource_tabledomain + (dst_index_column_equal_rowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_column_equal_rowsrowrow_sumslicesource_table dst_negative_column_equal_rowsrowrow_sumslicesource_table dst_value_column_equal_rowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_column_equal_rowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_column_equal_rowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_column_equal_rowsrowrow_sumslicesource_table) = S ((S (dst_index_column_equal_rowsrowrow_sumslicesource_table)) * dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_column_equal_rowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_column_equal_rowsrowrow_sumslicesource_table = ff_q_pvs_column_equal_rowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_column_equal_rowsrowrow_sumslicesource_table)) * dst_positive_scale_column_equal_rowsrowrow_sumslicesource_table) + (dst_positive_column_equal_rowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_column_equal_rowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_column_equal_rowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_column_equal_rowsrowrow_sumslicesource_table) = S ((S (dst_index_column_equal_rowsrowrow_sumslicesource_table)) * dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_column_equal_rowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_column_equal_rowsrowrow_sumslicesource_table = ff_q_pvs_column_equal_rowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_column_equal_rowsrowrow_sumslicesource_table)) * dst_negative_scale_column_equal_rowsrowrow_sumslicesource_table) + (dst_negative_column_equal_rowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_column_equal_rowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_column_equal_rowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_column_equal_rowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_column_equal_rowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_column_equal_rowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_column_equal_rowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_column_equal_rowsrowrow_sumslicesource_table) = 2 * ge_signed_half_column_equal_rowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_equal_rowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_column_equal_rowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_column_equal_rowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_column_equal_rowsrowrow_sumslicesource_table) + ge_balance_negative_column_equal_rowsrowrow_sumslicesource_tableentryvalue = (dst_negative_column_equal_rowsrowrow_sumslicesource_table) + ge_balance_positive_column_equal_rowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_column_equal_rowsrowrow_sumsliceoutput_table dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table. (((srs_slice_column_equal_rowsrowrow_sum) = (((((dst_positive_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_column_equal_rowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_column_equal_rowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_column_equal_rowsrowrow_sumsliceoutput_tabledomain + (dst_index_column_equal_rowsrowrow_sumsliceoutput_table) = (L)) -> exists dst_positive_column_equal_rowsrowrow_sumsliceoutput_table dst_negative_column_equal_rowsrowrow_sumsliceoutput_table dst_value_column_equal_rowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_column_equal_rowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_column_equal_rowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_column_equal_rowsrowrow_sumsliceoutput_table) = S ((S (dst_index_column_equal_rowsrowrow_sumsliceoutput_table)) * dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_column_equal_rowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_column_equal_rowsrowrow_sumsliceoutput_table = ff_q_pvs_column_equal_rowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_column_equal_rowsrowrow_sumsliceoutput_table)) * dst_positive_scale_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_positive_column_equal_rowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_column_equal_rowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_column_equal_rowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_column_equal_rowsrowrow_sumsliceoutput_table) = S ((S (dst_index_column_equal_rowsrowrow_sumsliceoutput_table)) * dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_column_equal_rowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_column_equal_rowsrowrow_sumsliceoutput_table = ff_q_pvs_column_equal_rowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_column_equal_rowsrowrow_sumsliceoutput_table)) * dst_negative_scale_column_equal_rowsrowrow_sumsliceoutput_table) + (dst_negative_column_equal_rowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_column_equal_rowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_column_equal_rowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_column_equal_rowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_column_equal_rowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_column_equal_rowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_column_equal_rowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_column_equal_rowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_column_equal_rowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_equal_rowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_column_equal_rowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_column_equal_rowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_column_equal_rowsrowrow_sumsliceoutput_table) + ge_balance_negative_column_equal_rowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_column_equal_rowsrowrow_sumsliceoutput_table) + ge_balance_positive_column_equal_rowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_column_equal_rowsrowrow_sumslice. (exists pvs_gap_column_equal_rowsrowrow_sumslicebound. pvs_gap_column_equal_rowsrowrow_sumslicebound + S (srs_index_column_equal_rowsrowrow_sumslice) = (L)) -> exists srs_value_column_equal_rowsrowrow_sumslice. (((exists dst_positive_code_column_equal_rowsrowrow_sumsliceentrysource dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource dst_positive_column_equal_rowsrowrow_sumsliceentrysource dst_negative_column_equal_rowsrowrow_sumsliceentrysource. (((T) = (((((dst_positive_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_column_equal_rowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_column_equal_rowsrowrow_sumsliceentrysourcepositive + S (dst_positive_column_equal_rowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((1) * (srt_index_column_equal_rows)))) + ((S M) * (srs_index_column_equal_rowsrowrow_sumslice))))) * dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_column_equal_rowsrowrow_sumsliceentrysourcepositive. dst_positive_code_column_equal_rowsrowrow_sumsliceentrysource = ff_q_pvs_column_equal_rowsrowrow_sumsliceentrysourcepositive * S ((S (((((0) + ((1) * (srt_index_column_equal_rows)))) + ((S M) * (srs_index_column_equal_rowsrowrow_sumslice))))) * dst_positive_scale_column_equal_rowsrowrow_sumsliceentrysource) + (dst_positive_column_equal_rowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_column_equal_rowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_column_equal_rowsrowrow_sumsliceentrysourcenegative + S (dst_negative_column_equal_rowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((1) * (srt_index_column_equal_rows)))) + ((S M) * (srs_index_column_equal_rowsrowrow_sumslice))))) * dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_column_equal_rowsrowrow_sumsliceentrysourcenegative. dst_negative_code_column_equal_rowsrowrow_sumsliceentrysource = ff_q_pvs_column_equal_rowsrowrow_sumsliceentrysourcenegative * S ((S (((((0) + ((1) * (srt_index_column_equal_rows)))) + ((S M) * (srs_index_column_equal_rowsrowrow_sumslice))))) * dst_negative_scale_column_equal_rowsrowrow_sumsliceentrysource) + (dst_negative_column_equal_rowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_column_equal_rowsrowrow_sumsliceentrysourcevalue ge_balance_negative_column_equal_rowsrowrow_sumsliceentrysourcevalue. (((((srs_value_column_equal_rowsrowrow_sumslice) = 2 * (ge_balance_positive_column_equal_rowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_column_equal_rowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_column_equal_rowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_column_equal_rowsrowrow_sumslice) = 2 * ge_signed_half_column_equal_rowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_column_equal_rowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_column_equal_rowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_column_equal_rowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_column_equal_rowsrowrow_sumsliceentrysource) + ge_balance_negative_column_equal_rowsrowrow_sumsliceentrysourcevalue = (dst_negative_column_equal_rowsrowrow_sumsliceentrysource) + ge_balance_positive_column_equal_rowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_column_equal_rowsrowrow_sumsliceentryoutput dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput dst_positive_column_equal_rowsrowrow_sumsliceentryoutput dst_negative_column_equal_rowsrowrow_sumsliceentryoutput. (((srs_slice_column_equal_rowsrowrow_sum) = (((((dst_positive_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_column_equal_rowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_column_equal_rowsrowrow_sumsliceentryoutputpositive + S (dst_positive_column_equal_rowsrowrow_sumsliceentryoutput) = S ((S (srs_index_column_equal_rowsrowrow_sumslice)) * dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_column_equal_rowsrowrow_sumsliceentryoutputpositive. dst_positive_code_column_equal_rowsrowrow_sumsliceentryoutput = ff_q_pvs_column_equal_rowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_column_equal_rowsrowrow_sumslice)) * dst_positive_scale_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_positive_column_equal_rowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_column_equal_rowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_column_equal_rowsrowrow_sumsliceentryoutputnegative + S (dst_negative_column_equal_rowsrowrow_sumsliceentryoutput) = S ((S (srs_index_column_equal_rowsrowrow_sumslice)) * dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_column_equal_rowsrowrow_sumsliceentryoutputnegative. dst_negative_code_column_equal_rowsrowrow_sumsliceentryoutput = ff_q_pvs_column_equal_rowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_column_equal_rowsrowrow_sumslice)) * dst_negative_scale_column_equal_rowsrowrow_sumsliceentryoutput) + (dst_negative_column_equal_rowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_column_equal_rowsrowrow_sumsliceentryoutputvalue ge_balance_negative_column_equal_rowsrowrow_sumsliceentryoutputvalue. (((((srs_value_column_equal_rowsrowrow_sumslice) = 2 * (ge_balance_positive_column_equal_rowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_column_equal_rowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_column_equal_rowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_column_equal_rowsrowrow_sumslice) = 2 * ge_signed_half_column_equal_rowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_column_equal_rowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_column_equal_rowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_column_equal_rowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_column_equal_rowsrowrow_sumsliceentryoutput) + ge_balance_negative_column_equal_rowsrowrow_sumsliceentryoutputvalue = (dst_negative_column_equal_rowsrowrow_sumsliceentryoutput) + ge_balance_positive_column_equal_rowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_column_equal_rowsrowrow_sumsum dst_positive_scale_column_equal_rowsrowrow_sumsum dst_negative_code_column_equal_rowsrowrow_sumsum dst_negative_scale_column_equal_rowsrowrow_sumsum dst_positive_sum_column_equal_rowsrowrow_sumsum dst_negative_sum_column_equal_rowsrowrow_sumsum. (((srs_slice_column_equal_rowsrowrow_sum) = (((((dst_positive_code_column_equal_rowsrowrow_sumsum) + (dst_positive_scale_column_equal_rowsrowrow_sumsum)) * S ((dst_positive_code_column_equal_rowsrowrow_sumsum) + (dst_positive_scale_column_equal_rowsrowrow_sumsum)) + ((dst_positive_scale_column_equal_rowsrowrow_sumsum) + (dst_positive_scale_column_equal_rowsrowrow_sumsum))) + (((dst_negative_code_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)))) * S ((((dst_positive_code_column_equal_rowsrowrow_sumsum) + (dst_positive_scale_column_equal_rowsrowrow_sumsum)) * S ((dst_positive_code_column_equal_rowsrowrow_sumsum) + (dst_positive_scale_column_equal_rowsrowrow_sumsum)) + ((dst_positive_scale_column_equal_rowsrowrow_sumsum) + (dst_positive_scale_column_equal_rowsrowrow_sumsum))) + (((dst_negative_code_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)))) + ((((dst_negative_code_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum))) + (((dst_negative_code_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)) * S ((dst_negative_code_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)) + ((dst_negative_scale_column_equal_rowsrowrow_sumsum) + (dst_negative_scale_column_equal_rowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_column_equal_rowsrowrow_sumsumpositive fs_v_dst_column_equal_rowsrowrow_sumsumpositive. ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_start. fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_column_equal_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_start. fs_u_dst_column_equal_rowsrowrow_sumsumpositive = fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_column_equal_rowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_terminal. fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_column_equal_rowsrowrow_sumsum) = S ((S (L)) * fs_v_dst_column_equal_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_terminal. fs_u_dst_column_equal_rowsrowrow_sumsumpositive = fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_terminal * S ((S (L)) * fs_v_dst_column_equal_rowsrowrow_sumsumpositive) + (dst_positive_sum_column_equal_rowsrowrow_sumsum))) /\ forall fs_i_dst_column_equal_rowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_column_equal_rowsrowrow_sumsumpositive_body_steps = L) -> exists fs_a_dst_column_equal_rowsrowrow_sumsumpositive_body_steps fs_r_dst_column_equal_rowsrowrow_sumsumpositive_body_steps fs_s_dst_column_equal_rowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_column_equal_rowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_column_equal_rowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_column_equal_rowsrowrow_sumsum)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_column_equal_rowsrowrow_sumsum = fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_column_equal_rowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_column_equal_rowsrowrow_sumsum) + (fs_a_dst_column_equal_rowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_column_equal_rowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_column_equal_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_column_equal_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_column_equal_rowsrowrow_sumsumpositive = fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_column_equal_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_column_equal_rowsrowrow_sumsumpositive) + (fs_r_dst_column_equal_rowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_column_equal_rowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_column_equal_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_column_equal_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_column_equal_rowsrowrow_sumsumpositive = fs_q_dst_column_equal_rowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_column_equal_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_column_equal_rowsrowrow_sumsumpositive) + (fs_s_dst_column_equal_rowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_column_equal_rowsrowrow_sumsumpositive_body_steps = fs_r_dst_column_equal_rowsrowrow_sumsumpositive_body_steps + fs_a_dst_column_equal_rowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_column_equal_rowsrowrow_sumsumnegative fs_v_dst_column_equal_rowsrowrow_sumsumnegative. ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_start. fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_column_equal_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_start. fs_u_dst_column_equal_rowsrowrow_sumsumnegative = fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_column_equal_rowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_terminal. fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_column_equal_rowsrowrow_sumsum) = S ((S (L)) * fs_v_dst_column_equal_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_terminal. fs_u_dst_column_equal_rowsrowrow_sumsumnegative = fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_terminal * S ((S (L)) * fs_v_dst_column_equal_rowsrowrow_sumsumnegative) + (dst_negative_sum_column_equal_rowsrowrow_sumsum))) /\ forall fs_i_dst_column_equal_rowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_column_equal_rowsrowrow_sumsumnegative_body_steps = L) -> exists fs_a_dst_column_equal_rowsrowrow_sumsumnegative_body_steps fs_r_dst_column_equal_rowsrowrow_sumsumnegative_body_steps fs_s_dst_column_equal_rowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_column_equal_rowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_column_equal_rowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_column_equal_rowsrowrow_sumsum)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_column_equal_rowsrowrow_sumsum = fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_column_equal_rowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_column_equal_rowsrowrow_sumsum) + (fs_a_dst_column_equal_rowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_column_equal_rowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_column_equal_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_column_equal_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_column_equal_rowsrowrow_sumsumnegative = fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_column_equal_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_column_equal_rowsrowrow_sumsumnegative) + (fs_r_dst_column_equal_rowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_column_equal_rowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_column_equal_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_column_equal_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_column_equal_rowsrowrow_sumsumnegative = fs_q_dst_column_equal_rowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_column_equal_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_column_equal_rowsrowrow_sumsumnegative) + (fs_s_dst_column_equal_rowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_column_equal_rowsrowrow_sumsumnegative_body_steps = fs_r_dst_column_equal_rowsrowrow_sumsumnegative_body_steps + fs_a_dst_column_equal_rowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_column_equal_rowsrowrow_sumsumresult ge_balance_negative_column_equal_rowsrowrow_sumsumresult. (((((srt_value_column_equal_rows) = 2 * (ge_balance_positive_column_equal_rowsrowrow_sumsumresult) /\ (ge_balance_negative_column_equal_rowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_column_equal_rowsrowrow_sumsumresultdecode. (((srt_value_column_equal_rows) = 2 * ge_signed_half_column_equal_rowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_column_equal_rowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_column_equal_rowsrowrow_sumsumresult) = S ge_signed_half_column_equal_rowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_column_equal_rowsrowrow_sumsum) + ge_balance_negative_column_equal_rowsrowrow_sumsumresult = (dst_negative_sum_column_equal_rowsrowrow_sumsum) + ge_balance_positive_column_equal_rowsrowrow_sumsumresult)))))))))))))))))) -> (forall dst_index_column_equal_result dst_first_column_equal_result dst_second_column_equal_result. (exists pvs_gap_column_equal_resultbound. pvs_gap_column_equal_resultbound + S (dst_index_column_equal_result) = (M)) -> (exists dst_positive_code_column_equal_resultfirst dst_positive_scale_column_equal_resultfirst dst_negative_code_column_equal_resultfirst dst_negative_scale_column_equal_resultfirst dst_positive_column_equal_resultfirst dst_negative_column_equal_resultfirst. (((B) = (((((dst_positive_code_column_equal_resultfirst) + (dst_positive_scale_column_equal_resultfirst)) * S ((dst_positive_code_column_equal_resultfirst) + (dst_positive_scale_column_equal_resultfirst)) + ((dst_positive_scale_column_equal_resultfirst) + (dst_positive_scale_column_equal_resultfirst))) + (((dst_negative_code_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)) * S ((dst_negative_code_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)) + ((dst_negative_scale_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)))) * S ((((dst_positive_code_column_equal_resultfirst) + (dst_positive_scale_column_equal_resultfirst)) * S ((dst_positive_code_column_equal_resultfirst) + (dst_positive_scale_column_equal_resultfirst)) + ((dst_positive_scale_column_equal_resultfirst) + (dst_positive_scale_column_equal_resultfirst))) + (((dst_negative_code_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)) * S ((dst_negative_code_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)) + ((dst_negative_scale_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)))) + ((((dst_negative_code_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)) * S ((dst_negative_code_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)) + ((dst_negative_scale_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst))) + (((dst_negative_code_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)) * S ((dst_negative_code_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)) + ((dst_negative_scale_column_equal_resultfirst) + (dst_negative_scale_column_equal_resultfirst)))))) /\ (((((exists ff_h_pvs_column_equal_resultfirstpositive. ff_h_pvs_column_equal_resultfirstpositive + S (dst_positive_column_equal_resultfirst) = S ((S (dst_index_column_equal_result)) * dst_positive_scale_column_equal_resultfirst)) /\ exists ff_q_pvs_column_equal_resultfirstpositive. dst_positive_code_column_equal_resultfirst = ff_q_pvs_column_equal_resultfirstpositive * S ((S (dst_index_column_equal_result)) * dst_positive_scale_column_equal_resultfirst) + (dst_positive_column_equal_resultfirst))) /\ (((((exists ff_h_pvs_column_equal_resultfirstnegative. ff_h_pvs_column_equal_resultfirstnegative + S (dst_negative_column_equal_resultfirst) = S ((S (dst_index_column_equal_result)) * dst_negative_scale_column_equal_resultfirst)) /\ exists ff_q_pvs_column_equal_resultfirstnegative. dst_negative_code_column_equal_resultfirst = ff_q_pvs_column_equal_resultfirstnegative * S ((S (dst_index_column_equal_result)) * dst_negative_scale_column_equal_resultfirst) + (dst_negative_column_equal_resultfirst))) /\ (exists ge_balance_positive_column_equal_resultfirstvalue ge_balance_negative_column_equal_resultfirstvalue. (((((dst_first_column_equal_result) = 2 * (ge_balance_positive_column_equal_resultfirstvalue) /\ (ge_balance_negative_column_equal_resultfirstvalue) = 0) \/ exists ge_signed_half_column_equal_resultfirstvaluedecode. (((dst_first_column_equal_result) = 2 * ge_signed_half_column_equal_resultfirstvaluedecode + 1 /\ (ge_balance_positive_column_equal_resultfirstvalue) = 0) /\ (ge_balance_negative_column_equal_resultfirstvalue) = S ge_signed_half_column_equal_resultfirstvaluedecode))) /\ ((dst_positive_column_equal_resultfirst) + ge_balance_negative_column_equal_resultfirstvalue = (dst_negative_column_equal_resultfirst) + ge_balance_positive_column_equal_resultfirstvalue))))))))) -> (exists dst_positive_code_column_equal_resultsecond dst_positive_scale_column_equal_resultsecond dst_negative_code_column_equal_resultsecond dst_negative_scale_column_equal_resultsecond dst_positive_column_equal_resultsecond dst_negative_column_equal_resultsecond. (((C) = (((((dst_positive_code_column_equal_resultsecond) + (dst_positive_scale_column_equal_resultsecond)) * S ((dst_positive_code_column_equal_resultsecond) + (dst_positive_scale_column_equal_resultsecond)) + ((dst_positive_scale_column_equal_resultsecond) + (dst_positive_scale_column_equal_resultsecond))) + (((dst_negative_code_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)) * S ((dst_negative_code_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)) + ((dst_negative_scale_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)))) * S ((((dst_positive_code_column_equal_resultsecond) + (dst_positive_scale_column_equal_resultsecond)) * S ((dst_positive_code_column_equal_resultsecond) + (dst_positive_scale_column_equal_resultsecond)) + ((dst_positive_scale_column_equal_resultsecond) + (dst_positive_scale_column_equal_resultsecond))) + (((dst_negative_code_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)) * S ((dst_negative_code_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)) + ((dst_negative_scale_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)))) + ((((dst_negative_code_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)) * S ((dst_negative_code_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)) + ((dst_negative_scale_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond))) + (((dst_negative_code_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)) * S ((dst_negative_code_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)) + ((dst_negative_scale_column_equal_resultsecond) + (dst_negative_scale_column_equal_resultsecond)))))) /\ (((((exists ff_h_pvs_column_equal_resultsecondpositive. ff_h_pvs_column_equal_resultsecondpositive + S (dst_positive_column_equal_resultsecond) = S ((S (dst_index_column_equal_result)) * dst_positive_scale_column_equal_resultsecond)) /\ exists ff_q_pvs_column_equal_resultsecondpositive. dst_positive_code_column_equal_resultsecond = ff_q_pvs_column_equal_resultsecondpositive * S ((S (dst_index_column_equal_result)) * dst_positive_scale_column_equal_resultsecond) + (dst_positive_column_equal_resultsecond))) /\ (((((exists ff_h_pvs_column_equal_resultsecondnegative. ff_h_pvs_column_equal_resultsecondnegative + S (dst_negative_column_equal_resultsecond) = S ((S (dst_index_column_equal_result)) * dst_negative_scale_column_equal_resultsecond)) /\ exists ff_q_pvs_column_equal_resultsecondnegative. dst_negative_code_column_equal_resultsecond = ff_q_pvs_column_equal_resultsecondnegative * S ((S (dst_index_column_equal_result)) * dst_negative_scale_column_equal_resultsecond) + (dst_negative_column_equal_resultsecond))) /\ (exists ge_balance_positive_column_equal_resultsecondvalue ge_balance_negative_column_equal_resultsecondvalue. (((((dst_second_column_equal_result) = 2 * (ge_balance_positive_column_equal_resultsecondvalue) /\ (ge_balance_negative_column_equal_resultsecondvalue) = 0) \/ exists ge_signed_half_column_equal_resultsecondvaluedecode. (((dst_second_column_equal_result) = 2 * ge_signed_half_column_equal_resultsecondvaluedecode + 1 /\ (ge_balance_positive_column_equal_resultsecondvalue) = 0) /\ (ge_balance_negative_column_equal_resultsecondvalue) = S ge_signed_half_column_equal_resultsecondvaluedecode))) /\ ((dst_positive_column_equal_resultsecond) + ge_balance_negative_column_equal_resultsecondvalue = (dst_negative_column_equal_resultsecond) + ge_balance_positive_column_equal_resultsecondvalue))))))))) -> dst_first_column_equal_result = dst_second_column_equal_result)

Constructive proof overview

Generated structural guide

Every actual incidence column-sum table agrees with the represented target values on precisely the strict target window.

The unchanged tactic script uses 2 declared prerequisites and contains 48 exact native proof lines.

Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

MX0047 signed_support_incidence_column_sum_value signed_rectangular_row_sums_lookup Alpha 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

48 script commands · 7 reading checkpoints · 1 local claims

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

Named ingredients (1)
01Fix variables and assumptionsL1–10

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

  1. L1
    intro A
  2. L2
    intro B
  3. L3
    intro r
  4. L4
    intro s
  5. L5
    intro L
  6. L6
    intro M
  7. L7
    intro T
  8. L8
    intro C
  9. L9
    intro hp
  10. L10
    intro hg
02Fix variables and assumptionsL11–17

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

  1. L11
    intro hc
  2. L12
    intro j
  3. L13
    intro a
  4. L14
    intro b
  5. L15
    intro hj
  6. L16
    intro ha
  7. L17
    intro hb
03Establish heL18–27

Establish this local claim before using it. It is not an additional assumption.

  1. L18
    have he : b=a
  2. L19
    specialize signed_support_incidence_column_sum_value (A)
  3. L20
    specialize signed_support_incidence_column_sum_value (B)
  4. L21
    specialize signed_support_incidence_column_sum_value (r)
  5. L22
    specialize signed_support_incidence_column_sum_value (s)
  6. L23
    specialize signed_support_incidence_column_sum_value (L)
  7. L24
    specialize signed_support_incidence_column_sum_value (M)
  8. L25
    specialize signed_support_incidence_column_sum_value (T)
  9. L26
    specialize signed_support_incidence_column_sum_value (j)
  10. L27
    specialize signed_support_incidence_column_sum_value (a)
04Use earlier factsL28–37

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

  1. L28
    specialize signed_support_incidence_column_sum_value (b)
  2. L29
    apply signed_support_incidence_column_sum_value
  3. L30
    exact hp
  4. L31
    exact hg
  5. L32
    exact hj
  6. L33
    exact ha
  7. L34
    specialize signed_rectangular_row_sums_lookup (T)
  8. L35
    specialize signed_rectangular_row_sums_lookup (C)
  9. L36
    specialize signed_rectangular_row_sums_lookup (0)
  10. L37
    specialize signed_rectangular_row_sums_lookup (1)
05Use earlier factsL38–46

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

  1. L38
    specialize signed_rectangular_row_sums_lookup (S M)
  2. L39
    specialize signed_rectangular_row_sums_lookup (M)
  3. L40
    specialize signed_rectangular_row_sums_lookup (L)
  4. L41
    specialize signed_rectangular_row_sums_lookup (j)
  5. L42
    specialize signed_rectangular_row_sums_lookup (b)
  6. L43
    apply signed_rectangular_row_sums_lookup
  7. L44
    exact hc
  8. L45
    exact hj
  9. L46
    exact hb
06Calculate and transport equalitiesL47–47

Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.

  1. L47
    symm
07Use earlier factsL48–48

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

  1. L48
    exact he

Library-wide reading audit

Original exact command ledger · 48 lines
  1. 0001intro A
  2. 0002intro B
  3. 0003intro r
  4. 0004intro s
  5. 0005intro L
  6. 0006intro M
  7. 0007intro T
  8. 0008intro C
  9. 0009intro hp
  10. 0010intro hg
  11. 0011intro hc
  12. 0012intro j
  13. 0013intro a
  14. 0014intro b
  15. 0015intro hj
  16. 0016intro ha
  17. 0017intro hb
  18. 0018have he : b=a
  19. 0019specialize signed_support_incidence_column_sum_value (A)
  20. 0020specialize signed_support_incidence_column_sum_value (B)
  21. 0021specialize signed_support_incidence_column_sum_value (r)
  22. 0022specialize signed_support_incidence_column_sum_value (s)
  23. 0023specialize signed_support_incidence_column_sum_value (L)
  24. 0024specialize signed_support_incidence_column_sum_value (M)
  25. 0025specialize signed_support_incidence_column_sum_value (T)
  26. 0026specialize signed_support_incidence_column_sum_value (j)
  27. 0027specialize signed_support_incidence_column_sum_value (a)
  28. 0028specialize signed_support_incidence_column_sum_value (b)
  29. 0029apply signed_support_incidence_column_sum_value
  30. 0030exact hp
  31. 0031exact hg
  32. 0032exact hj
  33. 0033exact ha
  34. 0034specialize signed_rectangular_row_sums_lookup (T)
  35. 0035specialize signed_rectangular_row_sums_lookup (C)
  36. 0036specialize signed_rectangular_row_sums_lookup (0)
  37. 0037specialize signed_rectangular_row_sums_lookup (1)
  38. 0038specialize signed_rectangular_row_sums_lookup (S M)
  39. 0039specialize signed_rectangular_row_sums_lookup (M)
  40. 0040specialize signed_rectangular_row_sums_lookup (L)
  41. 0041specialize signed_rectangular_row_sums_lookup (j)
  42. 0042specialize signed_rectangular_row_sums_lookup (b)
  43. 0043apply signed_rectangular_row_sums_lookup
  44. 0044exact hc
  45. 0045exact hj
  46. 0046exact hb
  47. 0047symm
  48. 0048exact he