MX0047

signed_support_incidence_column_sum_value

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

Target coverage supplies the actual nonzero spike; active injectivity excludes other nonzero cells and preservation handles zero targets.

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 j b z. (((exists dst_positive_code_column_value_supportsource_table dst_positive_scale_column_value_supportsource_table dst_negative_code_column_value_supportsource_table dst_negative_scale_column_value_supportsource_table. (((A) = (((((dst_positive_code_column_value_supportsource_table) + (dst_positive_scale_column_value_supportsource_table)) * S ((dst_positive_code_column_value_supportsource_table) + (dst_positive_scale_column_value_supportsource_table)) + ((dst_positive_scale_column_value_supportsource_table) + (dst_positive_scale_column_value_supportsource_table))) + (((dst_negative_code_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)) * S ((dst_negative_code_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)) + ((dst_negative_scale_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)))) * S ((((dst_positive_code_column_value_supportsource_table) + (dst_positive_scale_column_value_supportsource_table)) * S ((dst_positive_code_column_value_supportsource_table) + (dst_positive_scale_column_value_supportsource_table)) + ((dst_positive_scale_column_value_supportsource_table) + (dst_positive_scale_column_value_supportsource_table))) + (((dst_negative_code_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)) * S ((dst_negative_code_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)) + ((dst_negative_scale_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)))) + ((((dst_negative_code_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)) * S ((dst_negative_code_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)) + ((dst_negative_scale_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table))) + (((dst_negative_code_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)) * S ((dst_negative_code_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)) + ((dst_negative_scale_column_value_supportsource_table) + (dst_negative_scale_column_value_supportsource_table)))))) /\ (forall dst_index_column_value_supportsource_table. (exists pvs_le_gap_column_value_supportsource_tabledomain. pvs_le_gap_column_value_supportsource_tabledomain + (dst_index_column_value_supportsource_table) = (0)) -> exists dst_positive_column_value_supportsource_table dst_negative_column_value_supportsource_table dst_value_column_value_supportsource_table. ((((exists ff_h_pvs_column_value_supportsource_tableentrypositive. ff_h_pvs_column_value_supportsource_tableentrypositive + S (dst_positive_column_value_supportsource_table) = S ((S (dst_index_column_value_supportsource_table)) * dst_positive_scale_column_value_supportsource_table)) /\ exists ff_q_pvs_column_value_supportsource_tableentrypositive. dst_positive_code_column_value_supportsource_table = ff_q_pvs_column_value_supportsource_tableentrypositive * S ((S (dst_index_column_value_supportsource_table)) * dst_positive_scale_column_value_supportsource_table) + (dst_positive_column_value_supportsource_table))) /\ (((((exists ff_h_pvs_column_value_supportsource_tableentrynegative. ff_h_pvs_column_value_supportsource_tableentrynegative + S (dst_negative_column_value_supportsource_table) = S ((S (dst_index_column_value_supportsource_table)) * dst_negative_scale_column_value_supportsource_table)) /\ exists ff_q_pvs_column_value_supportsource_tableentrynegative. dst_negative_code_column_value_supportsource_table = ff_q_pvs_column_value_supportsource_tableentrynegative * S ((S (dst_index_column_value_supportsource_table)) * dst_negative_scale_column_value_supportsource_table) + (dst_negative_column_value_supportsource_table))) /\ (exists ge_balance_positive_column_value_supportsource_tableentryvalue ge_balance_negative_column_value_supportsource_tableentryvalue. (((((dst_value_column_value_supportsource_table) = 2 * (ge_balance_positive_column_value_supportsource_tableentryvalue) /\ (ge_balance_negative_column_value_supportsource_tableentryvalue) = 0) \/ exists ge_signed_half_column_value_supportsource_tableentryvaluedecode. (((dst_value_column_value_supportsource_table) = 2 * ge_signed_half_column_value_supportsource_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_value_supportsource_tableentryvalue) = 0) /\ (ge_balance_negative_column_value_supportsource_tableentryvalue) = S ge_signed_half_column_value_supportsource_tableentryvaluedecode))) /\ ((dst_positive_column_value_supportsource_table) + ge_balance_negative_column_value_supportsource_tableentryvalue = (dst_negative_column_value_supportsource_table) + ge_balance_positive_column_value_supportsource_tableentryvalue))))))))) /\ (((exists dst_positive_code_column_value_supporttarget_table dst_positive_scale_column_value_supporttarget_table dst_negative_code_column_value_supporttarget_table dst_negative_scale_column_value_supporttarget_table. (((B) = (((((dst_positive_code_column_value_supporttarget_table) + (dst_positive_scale_column_value_supporttarget_table)) * S ((dst_positive_code_column_value_supporttarget_table) + (dst_positive_scale_column_value_supporttarget_table)) + ((dst_positive_scale_column_value_supporttarget_table) + (dst_positive_scale_column_value_supporttarget_table))) + (((dst_negative_code_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)) * S ((dst_negative_code_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)) + ((dst_negative_scale_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)))) * S ((((dst_positive_code_column_value_supporttarget_table) + (dst_positive_scale_column_value_supporttarget_table)) * S ((dst_positive_code_column_value_supporttarget_table) + (dst_positive_scale_column_value_supporttarget_table)) + ((dst_positive_scale_column_value_supporttarget_table) + (dst_positive_scale_column_value_supporttarget_table))) + (((dst_negative_code_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)) * S ((dst_negative_code_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)) + ((dst_negative_scale_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)))) + ((((dst_negative_code_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)) * S ((dst_negative_code_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)) + ((dst_negative_scale_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table))) + (((dst_negative_code_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)) * S ((dst_negative_code_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)) + ((dst_negative_scale_column_value_supporttarget_table) + (dst_negative_scale_column_value_supporttarget_table)))))) /\ (forall dst_index_column_value_supporttarget_table. (exists pvs_le_gap_column_value_supporttarget_tabledomain. pvs_le_gap_column_value_supporttarget_tabledomain + (dst_index_column_value_supporttarget_table) = (0)) -> exists dst_positive_column_value_supporttarget_table dst_negative_column_value_supporttarget_table dst_value_column_value_supporttarget_table. ((((exists ff_h_pvs_column_value_supporttarget_tableentrypositive. ff_h_pvs_column_value_supporttarget_tableentrypositive + S (dst_positive_column_value_supporttarget_table) = S ((S (dst_index_column_value_supporttarget_table)) * dst_positive_scale_column_value_supporttarget_table)) /\ exists ff_q_pvs_column_value_supporttarget_tableentrypositive. dst_positive_code_column_value_supporttarget_table = ff_q_pvs_column_value_supporttarget_tableentrypositive * S ((S (dst_index_column_value_supporttarget_table)) * dst_positive_scale_column_value_supporttarget_table) + (dst_positive_column_value_supporttarget_table))) /\ (((((exists ff_h_pvs_column_value_supporttarget_tableentrynegative. ff_h_pvs_column_value_supporttarget_tableentrynegative + S (dst_negative_column_value_supporttarget_table) = S ((S (dst_index_column_value_supporttarget_table)) * dst_negative_scale_column_value_supporttarget_table)) /\ exists ff_q_pvs_column_value_supporttarget_tableentrynegative. dst_negative_code_column_value_supporttarget_table = ff_q_pvs_column_value_supporttarget_tableentrynegative * S ((S (dst_index_column_value_supporttarget_table)) * dst_negative_scale_column_value_supporttarget_table) + (dst_negative_column_value_supporttarget_table))) /\ (exists ge_balance_positive_column_value_supporttarget_tableentryvalue ge_balance_negative_column_value_supporttarget_tableentryvalue. (((((dst_value_column_value_supporttarget_table) = 2 * (ge_balance_positive_column_value_supporttarget_tableentryvalue) /\ (ge_balance_negative_column_value_supporttarget_tableentryvalue) = 0) \/ exists ge_signed_half_column_value_supporttarget_tableentryvaluedecode. (((dst_value_column_value_supporttarget_table) = 2 * ge_signed_half_column_value_supporttarget_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_value_supporttarget_tableentryvalue) = 0) /\ (ge_balance_negative_column_value_supporttarget_tableentryvalue) = S ge_signed_half_column_value_supporttarget_tableentryvaluedecode))) /\ ((dst_positive_column_value_supporttarget_table) + ge_balance_negative_column_value_supporttarget_tableentryvalue = (dst_negative_column_value_supporttarget_table) + ge_balance_positive_column_value_supporttarget_tableentryvalue))))))))) /\ (((forall ssr_source_column_value_supportpreserve ssr_value_column_value_supportpreserve. (exists pvs_gap_column_value_supportpreservesource_bound. pvs_gap_column_value_supportpreservesource_bound + S (ssr_source_column_value_supportpreserve) = (L)) -> (exists dst_positive_code_column_value_supportpreservesource_value dst_positive_scale_column_value_supportpreservesource_value dst_negative_code_column_value_supportpreservesource_value dst_negative_scale_column_value_supportpreservesource_value dst_positive_column_value_supportpreservesource_value dst_negative_column_value_supportpreservesource_value. (((A) = (((((dst_positive_code_column_value_supportpreservesource_value) + (dst_positive_scale_column_value_supportpreservesource_value)) * S ((dst_positive_code_column_value_supportpreservesource_value) + (dst_positive_scale_column_value_supportpreservesource_value)) + ((dst_positive_scale_column_value_supportpreservesource_value) + (dst_positive_scale_column_value_supportpreservesource_value))) + (((dst_negative_code_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)) * S ((dst_negative_code_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)) + ((dst_negative_scale_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)))) * S ((((dst_positive_code_column_value_supportpreservesource_value) + (dst_positive_scale_column_value_supportpreservesource_value)) * S ((dst_positive_code_column_value_supportpreservesource_value) + (dst_positive_scale_column_value_supportpreservesource_value)) + ((dst_positive_scale_column_value_supportpreservesource_value) + (dst_positive_scale_column_value_supportpreservesource_value))) + (((dst_negative_code_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)) * S ((dst_negative_code_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)) + ((dst_negative_scale_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)))) + ((((dst_negative_code_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)) * S ((dst_negative_code_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)) + ((dst_negative_scale_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value))) + (((dst_negative_code_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)) * S ((dst_negative_code_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)) + ((dst_negative_scale_column_value_supportpreservesource_value) + (dst_negative_scale_column_value_supportpreservesource_value)))))) /\ (((((exists ff_h_pvs_column_value_supportpreservesource_valuepositive. ff_h_pvs_column_value_supportpreservesource_valuepositive + S (dst_positive_column_value_supportpreservesource_value) = S ((S (ssr_source_column_value_supportpreserve)) * dst_positive_scale_column_value_supportpreservesource_value)) /\ exists ff_q_pvs_column_value_supportpreservesource_valuepositive. dst_positive_code_column_value_supportpreservesource_value = ff_q_pvs_column_value_supportpreservesource_valuepositive * S ((S (ssr_source_column_value_supportpreserve)) * dst_positive_scale_column_value_supportpreservesource_value) + (dst_positive_column_value_supportpreservesource_value))) /\ (((((exists ff_h_pvs_column_value_supportpreservesource_valuenegative. ff_h_pvs_column_value_supportpreservesource_valuenegative + S (dst_negative_column_value_supportpreservesource_value) = S ((S (ssr_source_column_value_supportpreserve)) * dst_negative_scale_column_value_supportpreservesource_value)) /\ exists ff_q_pvs_column_value_supportpreservesource_valuenegative. dst_negative_code_column_value_supportpreservesource_value = ff_q_pvs_column_value_supportpreservesource_valuenegative * S ((S (ssr_source_column_value_supportpreserve)) * dst_negative_scale_column_value_supportpreservesource_value) + (dst_negative_column_value_supportpreservesource_value))) /\ (exists ge_balance_positive_column_value_supportpreservesource_valuevalue ge_balance_negative_column_value_supportpreservesource_valuevalue. (((((ssr_value_column_value_supportpreserve) = 2 * (ge_balance_positive_column_value_supportpreservesource_valuevalue) /\ (ge_balance_negative_column_value_supportpreservesource_valuevalue) = 0) \/ exists ge_signed_half_column_value_supportpreservesource_valuevaluedecode. (((ssr_value_column_value_supportpreserve) = 2 * ge_signed_half_column_value_supportpreservesource_valuevaluedecode + 1 /\ (ge_balance_positive_column_value_supportpreservesource_valuevalue) = 0) /\ (ge_balance_negative_column_value_supportpreservesource_valuevalue) = S ge_signed_half_column_value_supportpreservesource_valuevaluedecode))) /\ ((dst_positive_column_value_supportpreservesource_value) + ge_balance_negative_column_value_supportpreservesource_valuevalue = (dst_negative_column_value_supportpreservesource_value) + ge_balance_positive_column_value_supportpreservesource_valuevalue))))))))) -> ~(ssr_value_column_value_supportpreserve=0) -> exists ssr_target_column_value_supportpreserve. ((((exists ff_h_pvs_column_value_supportpreservemap. ff_h_pvs_column_value_supportpreservemap + S (ssr_target_column_value_supportpreserve) = S ((S (ssr_source_column_value_supportpreserve)) * s)) /\ exists ff_q_pvs_column_value_supportpreservemap. r = ff_q_pvs_column_value_supportpreservemap * S ((S (ssr_source_column_value_supportpreserve)) * s) + (ssr_target_column_value_supportpreserve))) /\ (((exists pvs_gap_column_value_supportpreservetarget_bound. pvs_gap_column_value_supportpreservetarget_bound + S (ssr_target_column_value_supportpreserve) = (M)) /\ (exists dst_positive_code_column_value_supportpreservetarget_value dst_positive_scale_column_value_supportpreservetarget_value dst_negative_code_column_value_supportpreservetarget_value dst_negative_scale_column_value_supportpreservetarget_value dst_positive_column_value_supportpreservetarget_value dst_negative_column_value_supportpreservetarget_value. (((B) = (((((dst_positive_code_column_value_supportpreservetarget_value) + (dst_positive_scale_column_value_supportpreservetarget_value)) * S ((dst_positive_code_column_value_supportpreservetarget_value) + (dst_positive_scale_column_value_supportpreservetarget_value)) + ((dst_positive_scale_column_value_supportpreservetarget_value) + (dst_positive_scale_column_value_supportpreservetarget_value))) + (((dst_negative_code_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)) * S ((dst_negative_code_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)) + ((dst_negative_scale_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)))) * S ((((dst_positive_code_column_value_supportpreservetarget_value) + (dst_positive_scale_column_value_supportpreservetarget_value)) * S ((dst_positive_code_column_value_supportpreservetarget_value) + (dst_positive_scale_column_value_supportpreservetarget_value)) + ((dst_positive_scale_column_value_supportpreservetarget_value) + (dst_positive_scale_column_value_supportpreservetarget_value))) + (((dst_negative_code_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)) * S ((dst_negative_code_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)) + ((dst_negative_scale_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)))) + ((((dst_negative_code_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)) * S ((dst_negative_code_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)) + ((dst_negative_scale_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value))) + (((dst_negative_code_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)) * S ((dst_negative_code_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)) + ((dst_negative_scale_column_value_supportpreservetarget_value) + (dst_negative_scale_column_value_supportpreservetarget_value)))))) /\ (((((exists ff_h_pvs_column_value_supportpreservetarget_valuepositive. ff_h_pvs_column_value_supportpreservetarget_valuepositive + S (dst_positive_column_value_supportpreservetarget_value) = S ((S (ssr_target_column_value_supportpreserve)) * dst_positive_scale_column_value_supportpreservetarget_value)) /\ exists ff_q_pvs_column_value_supportpreservetarget_valuepositive. dst_positive_code_column_value_supportpreservetarget_value = ff_q_pvs_column_value_supportpreservetarget_valuepositive * S ((S (ssr_target_column_value_supportpreserve)) * dst_positive_scale_column_value_supportpreservetarget_value) + (dst_positive_column_value_supportpreservetarget_value))) /\ (((((exists ff_h_pvs_column_value_supportpreservetarget_valuenegative. ff_h_pvs_column_value_supportpreservetarget_valuenegative + S (dst_negative_column_value_supportpreservetarget_value) = S ((S (ssr_target_column_value_supportpreserve)) * dst_negative_scale_column_value_supportpreservetarget_value)) /\ exists ff_q_pvs_column_value_supportpreservetarget_valuenegative. dst_negative_code_column_value_supportpreservetarget_value = ff_q_pvs_column_value_supportpreservetarget_valuenegative * S ((S (ssr_target_column_value_supportpreserve)) * dst_negative_scale_column_value_supportpreservetarget_value) + (dst_negative_column_value_supportpreservetarget_value))) /\ (exists ge_balance_positive_column_value_supportpreservetarget_valuevalue ge_balance_negative_column_value_supportpreservetarget_valuevalue. (((((ssr_value_column_value_supportpreserve) = 2 * (ge_balance_positive_column_value_supportpreservetarget_valuevalue) /\ (ge_balance_negative_column_value_supportpreservetarget_valuevalue) = 0) \/ exists ge_signed_half_column_value_supportpreservetarget_valuevaluedecode. (((ssr_value_column_value_supportpreserve) = 2 * ge_signed_half_column_value_supportpreservetarget_valuevaluedecode + 1 /\ (ge_balance_positive_column_value_supportpreservetarget_valuevalue) = 0) /\ (ge_balance_negative_column_value_supportpreservetarget_valuevalue) = S ge_signed_half_column_value_supportpreservetarget_valuevaluedecode))) /\ ((dst_positive_column_value_supportpreservetarget_value) + ge_balance_negative_column_value_supportpreservetarget_valuevalue = (dst_negative_column_value_supportpreservetarget_value) + ge_balance_positive_column_value_supportpreservetarget_valuevalue))))))))))))) /\ (((forall ssr_first_column_value_supportinjective ssr_second_column_value_supportinjective ssr_image_column_value_supportinjective ssr_a_column_value_supportinjective ssr_b_column_value_supportinjective. (exists pvs_gap_column_value_supportinjectivefirst_bound. pvs_gap_column_value_supportinjectivefirst_bound + S (ssr_first_column_value_supportinjective) = (L)) -> (exists pvs_gap_column_value_supportinjectivesecond_bound. pvs_gap_column_value_supportinjectivesecond_bound + S (ssr_second_column_value_supportinjective) = (L)) -> (exists dst_positive_code_column_value_supportinjectivefirst_value dst_positive_scale_column_value_supportinjectivefirst_value dst_negative_code_column_value_supportinjectivefirst_value dst_negative_scale_column_value_supportinjectivefirst_value dst_positive_column_value_supportinjectivefirst_value dst_negative_column_value_supportinjectivefirst_value. (((A) = (((((dst_positive_code_column_value_supportinjectivefirst_value) + (dst_positive_scale_column_value_supportinjectivefirst_value)) * S ((dst_positive_code_column_value_supportinjectivefirst_value) + (dst_positive_scale_column_value_supportinjectivefirst_value)) + ((dst_positive_scale_column_value_supportinjectivefirst_value) + (dst_positive_scale_column_value_supportinjectivefirst_value))) + (((dst_negative_code_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)) * S ((dst_negative_code_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)) + ((dst_negative_scale_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)))) * S ((((dst_positive_code_column_value_supportinjectivefirst_value) + (dst_positive_scale_column_value_supportinjectivefirst_value)) * S ((dst_positive_code_column_value_supportinjectivefirst_value) + (dst_positive_scale_column_value_supportinjectivefirst_value)) + ((dst_positive_scale_column_value_supportinjectivefirst_value) + (dst_positive_scale_column_value_supportinjectivefirst_value))) + (((dst_negative_code_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)) * S ((dst_negative_code_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)) + ((dst_negative_scale_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)))) + ((((dst_negative_code_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)) * S ((dst_negative_code_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)) + ((dst_negative_scale_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value))) + (((dst_negative_code_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)) * S ((dst_negative_code_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)) + ((dst_negative_scale_column_value_supportinjectivefirst_value) + (dst_negative_scale_column_value_supportinjectivefirst_value)))))) /\ (((((exists ff_h_pvs_column_value_supportinjectivefirst_valuepositive. ff_h_pvs_column_value_supportinjectivefirst_valuepositive + S (dst_positive_column_value_supportinjectivefirst_value) = S ((S (ssr_first_column_value_supportinjective)) * dst_positive_scale_column_value_supportinjectivefirst_value)) /\ exists ff_q_pvs_column_value_supportinjectivefirst_valuepositive. dst_positive_code_column_value_supportinjectivefirst_value = ff_q_pvs_column_value_supportinjectivefirst_valuepositive * S ((S (ssr_first_column_value_supportinjective)) * dst_positive_scale_column_value_supportinjectivefirst_value) + (dst_positive_column_value_supportinjectivefirst_value))) /\ (((((exists ff_h_pvs_column_value_supportinjectivefirst_valuenegative. ff_h_pvs_column_value_supportinjectivefirst_valuenegative + S (dst_negative_column_value_supportinjectivefirst_value) = S ((S (ssr_first_column_value_supportinjective)) * dst_negative_scale_column_value_supportinjectivefirst_value)) /\ exists ff_q_pvs_column_value_supportinjectivefirst_valuenegative. dst_negative_code_column_value_supportinjectivefirst_value = ff_q_pvs_column_value_supportinjectivefirst_valuenegative * S ((S (ssr_first_column_value_supportinjective)) * dst_negative_scale_column_value_supportinjectivefirst_value) + (dst_negative_column_value_supportinjectivefirst_value))) /\ (exists ge_balance_positive_column_value_supportinjectivefirst_valuevalue ge_balance_negative_column_value_supportinjectivefirst_valuevalue. (((((ssr_a_column_value_supportinjective) = 2 * (ge_balance_positive_column_value_supportinjectivefirst_valuevalue) /\ (ge_balance_negative_column_value_supportinjectivefirst_valuevalue) = 0) \/ exists ge_signed_half_column_value_supportinjectivefirst_valuevaluedecode. (((ssr_a_column_value_supportinjective) = 2 * ge_signed_half_column_value_supportinjectivefirst_valuevaluedecode + 1 /\ (ge_balance_positive_column_value_supportinjectivefirst_valuevalue) = 0) /\ (ge_balance_negative_column_value_supportinjectivefirst_valuevalue) = S ge_signed_half_column_value_supportinjectivefirst_valuevaluedecode))) /\ ((dst_positive_column_value_supportinjectivefirst_value) + ge_balance_negative_column_value_supportinjectivefirst_valuevalue = (dst_negative_column_value_supportinjectivefirst_value) + ge_balance_positive_column_value_supportinjectivefirst_valuevalue))))))))) -> ~(ssr_a_column_value_supportinjective=0) -> (exists dst_positive_code_column_value_supportinjectivesecond_value dst_positive_scale_column_value_supportinjectivesecond_value dst_negative_code_column_value_supportinjectivesecond_value dst_negative_scale_column_value_supportinjectivesecond_value dst_positive_column_value_supportinjectivesecond_value dst_negative_column_value_supportinjectivesecond_value. (((A) = (((((dst_positive_code_column_value_supportinjectivesecond_value) + (dst_positive_scale_column_value_supportinjectivesecond_value)) * S ((dst_positive_code_column_value_supportinjectivesecond_value) + (dst_positive_scale_column_value_supportinjectivesecond_value)) + ((dst_positive_scale_column_value_supportinjectivesecond_value) + (dst_positive_scale_column_value_supportinjectivesecond_value))) + (((dst_negative_code_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)) * S ((dst_negative_code_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)) + ((dst_negative_scale_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)))) * S ((((dst_positive_code_column_value_supportinjectivesecond_value) + (dst_positive_scale_column_value_supportinjectivesecond_value)) * S ((dst_positive_code_column_value_supportinjectivesecond_value) + (dst_positive_scale_column_value_supportinjectivesecond_value)) + ((dst_positive_scale_column_value_supportinjectivesecond_value) + (dst_positive_scale_column_value_supportinjectivesecond_value))) + (((dst_negative_code_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)) * S ((dst_negative_code_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)) + ((dst_negative_scale_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)))) + ((((dst_negative_code_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)) * S ((dst_negative_code_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)) + ((dst_negative_scale_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value))) + (((dst_negative_code_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)) * S ((dst_negative_code_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)) + ((dst_negative_scale_column_value_supportinjectivesecond_value) + (dst_negative_scale_column_value_supportinjectivesecond_value)))))) /\ (((((exists ff_h_pvs_column_value_supportinjectivesecond_valuepositive. ff_h_pvs_column_value_supportinjectivesecond_valuepositive + S (dst_positive_column_value_supportinjectivesecond_value) = S ((S (ssr_second_column_value_supportinjective)) * dst_positive_scale_column_value_supportinjectivesecond_value)) /\ exists ff_q_pvs_column_value_supportinjectivesecond_valuepositive. dst_positive_code_column_value_supportinjectivesecond_value = ff_q_pvs_column_value_supportinjectivesecond_valuepositive * S ((S (ssr_second_column_value_supportinjective)) * dst_positive_scale_column_value_supportinjectivesecond_value) + (dst_positive_column_value_supportinjectivesecond_value))) /\ (((((exists ff_h_pvs_column_value_supportinjectivesecond_valuenegative. ff_h_pvs_column_value_supportinjectivesecond_valuenegative + S (dst_negative_column_value_supportinjectivesecond_value) = S ((S (ssr_second_column_value_supportinjective)) * dst_negative_scale_column_value_supportinjectivesecond_value)) /\ exists ff_q_pvs_column_value_supportinjectivesecond_valuenegative. dst_negative_code_column_value_supportinjectivesecond_value = ff_q_pvs_column_value_supportinjectivesecond_valuenegative * S ((S (ssr_second_column_value_supportinjective)) * dst_negative_scale_column_value_supportinjectivesecond_value) + (dst_negative_column_value_supportinjectivesecond_value))) /\ (exists ge_balance_positive_column_value_supportinjectivesecond_valuevalue ge_balance_negative_column_value_supportinjectivesecond_valuevalue. (((((ssr_b_column_value_supportinjective) = 2 * (ge_balance_positive_column_value_supportinjectivesecond_valuevalue) /\ (ge_balance_negative_column_value_supportinjectivesecond_valuevalue) = 0) \/ exists ge_signed_half_column_value_supportinjectivesecond_valuevaluedecode. (((ssr_b_column_value_supportinjective) = 2 * ge_signed_half_column_value_supportinjectivesecond_valuevaluedecode + 1 /\ (ge_balance_positive_column_value_supportinjectivesecond_valuevalue) = 0) /\ (ge_balance_negative_column_value_supportinjectivesecond_valuevalue) = S ge_signed_half_column_value_supportinjectivesecond_valuevaluedecode))) /\ ((dst_positive_column_value_supportinjectivesecond_value) + ge_balance_negative_column_value_supportinjectivesecond_valuevalue = (dst_negative_column_value_supportinjectivesecond_value) + ge_balance_positive_column_value_supportinjectivesecond_valuevalue))))))))) -> ~(ssr_b_column_value_supportinjective=0) -> (((exists ff_h_pvs_column_value_supportinjectivefirst_map. ff_h_pvs_column_value_supportinjectivefirst_map + S (ssr_image_column_value_supportinjective) = S ((S (ssr_first_column_value_supportinjective)) * s)) /\ exists ff_q_pvs_column_value_supportinjectivefirst_map. r = ff_q_pvs_column_value_supportinjectivefirst_map * S ((S (ssr_first_column_value_supportinjective)) * s) + (ssr_image_column_value_supportinjective))) -> (((exists ff_h_pvs_column_value_supportinjectivesecond_map. ff_h_pvs_column_value_supportinjectivesecond_map + S (ssr_image_column_value_supportinjective) = S ((S (ssr_second_column_value_supportinjective)) * s)) /\ exists ff_q_pvs_column_value_supportinjectivesecond_map. r = ff_q_pvs_column_value_supportinjectivesecond_map * S ((S (ssr_second_column_value_supportinjective)) * s) + (ssr_image_column_value_supportinjective))) -> ssr_first_column_value_supportinjective=ssr_second_column_value_supportinjective) /\ (forall ssr_target_column_value_supportcover ssr_value_column_value_supportcover. (exists pvs_gap_column_value_supportcovertarget_bound. pvs_gap_column_value_supportcovertarget_bound + S (ssr_target_column_value_supportcover) = (M)) -> (exists dst_positive_code_column_value_supportcovertarget_value dst_positive_scale_column_value_supportcovertarget_value dst_negative_code_column_value_supportcovertarget_value dst_negative_scale_column_value_supportcovertarget_value dst_positive_column_value_supportcovertarget_value dst_negative_column_value_supportcovertarget_value. (((B) = (((((dst_positive_code_column_value_supportcovertarget_value) + (dst_positive_scale_column_value_supportcovertarget_value)) * S ((dst_positive_code_column_value_supportcovertarget_value) + (dst_positive_scale_column_value_supportcovertarget_value)) + ((dst_positive_scale_column_value_supportcovertarget_value) + (dst_positive_scale_column_value_supportcovertarget_value))) + (((dst_negative_code_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)) * S ((dst_negative_code_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)) + ((dst_negative_scale_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)))) * S ((((dst_positive_code_column_value_supportcovertarget_value) + (dst_positive_scale_column_value_supportcovertarget_value)) * S ((dst_positive_code_column_value_supportcovertarget_value) + (dst_positive_scale_column_value_supportcovertarget_value)) + ((dst_positive_scale_column_value_supportcovertarget_value) + (dst_positive_scale_column_value_supportcovertarget_value))) + (((dst_negative_code_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)) * S ((dst_negative_code_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)) + ((dst_negative_scale_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)))) + ((((dst_negative_code_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)) * S ((dst_negative_code_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)) + ((dst_negative_scale_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value))) + (((dst_negative_code_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)) * S ((dst_negative_code_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)) + ((dst_negative_scale_column_value_supportcovertarget_value) + (dst_negative_scale_column_value_supportcovertarget_value)))))) /\ (((((exists ff_h_pvs_column_value_supportcovertarget_valuepositive. ff_h_pvs_column_value_supportcovertarget_valuepositive + S (dst_positive_column_value_supportcovertarget_value) = S ((S (ssr_target_column_value_supportcover)) * dst_positive_scale_column_value_supportcovertarget_value)) /\ exists ff_q_pvs_column_value_supportcovertarget_valuepositive. dst_positive_code_column_value_supportcovertarget_value = ff_q_pvs_column_value_supportcovertarget_valuepositive * S ((S (ssr_target_column_value_supportcover)) * dst_positive_scale_column_value_supportcovertarget_value) + (dst_positive_column_value_supportcovertarget_value))) /\ (((((exists ff_h_pvs_column_value_supportcovertarget_valuenegative. ff_h_pvs_column_value_supportcovertarget_valuenegative + S (dst_negative_column_value_supportcovertarget_value) = S ((S (ssr_target_column_value_supportcover)) * dst_negative_scale_column_value_supportcovertarget_value)) /\ exists ff_q_pvs_column_value_supportcovertarget_valuenegative. dst_negative_code_column_value_supportcovertarget_value = ff_q_pvs_column_value_supportcovertarget_valuenegative * S ((S (ssr_target_column_value_supportcover)) * dst_negative_scale_column_value_supportcovertarget_value) + (dst_negative_column_value_supportcovertarget_value))) /\ (exists ge_balance_positive_column_value_supportcovertarget_valuevalue ge_balance_negative_column_value_supportcovertarget_valuevalue. (((((ssr_value_column_value_supportcover) = 2 * (ge_balance_positive_column_value_supportcovertarget_valuevalue) /\ (ge_balance_negative_column_value_supportcovertarget_valuevalue) = 0) \/ exists ge_signed_half_column_value_supportcovertarget_valuevaluedecode. (((ssr_value_column_value_supportcover) = 2 * ge_signed_half_column_value_supportcovertarget_valuevaluedecode + 1 /\ (ge_balance_positive_column_value_supportcovertarget_valuevalue) = 0) /\ (ge_balance_negative_column_value_supportcovertarget_valuevalue) = S ge_signed_half_column_value_supportcovertarget_valuevaluedecode))) /\ ((dst_positive_column_value_supportcovertarget_value) + ge_balance_negative_column_value_supportcovertarget_valuevalue = (dst_negative_column_value_supportcovertarget_value) + ge_balance_positive_column_value_supportcovertarget_valuevalue))))))))) -> ~(ssr_value_column_value_supportcover=0) -> exists ssr_source_column_value_supportcover. ((exists pvs_gap_column_value_supportcoversource_bound. pvs_gap_column_value_supportcoversource_bound + S (ssr_source_column_value_supportcover) = (L)) /\ (((((exists ff_h_pvs_column_value_supportcovermap. ff_h_pvs_column_value_supportcovermap + S (ssr_target_column_value_supportcover) = S ((S (ssr_source_column_value_supportcover)) * s)) /\ exists ff_q_pvs_column_value_supportcovermap. r = ff_q_pvs_column_value_supportcovermap * S ((S (ssr_source_column_value_supportcover)) * s) + (ssr_target_column_value_supportcover))) /\ (exists dst_positive_code_column_value_supportcoversource_value dst_positive_scale_column_value_supportcoversource_value dst_negative_code_column_value_supportcoversource_value dst_negative_scale_column_value_supportcoversource_value dst_positive_column_value_supportcoversource_value dst_negative_column_value_supportcoversource_value. (((A) = (((((dst_positive_code_column_value_supportcoversource_value) + (dst_positive_scale_column_value_supportcoversource_value)) * S ((dst_positive_code_column_value_supportcoversource_value) + (dst_positive_scale_column_value_supportcoversource_value)) + ((dst_positive_scale_column_value_supportcoversource_value) + (dst_positive_scale_column_value_supportcoversource_value))) + (((dst_negative_code_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)) * S ((dst_negative_code_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)) + ((dst_negative_scale_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)))) * S ((((dst_positive_code_column_value_supportcoversource_value) + (dst_positive_scale_column_value_supportcoversource_value)) * S ((dst_positive_code_column_value_supportcoversource_value) + (dst_positive_scale_column_value_supportcoversource_value)) + ((dst_positive_scale_column_value_supportcoversource_value) + (dst_positive_scale_column_value_supportcoversource_value))) + (((dst_negative_code_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)) * S ((dst_negative_code_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)) + ((dst_negative_scale_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)))) + ((((dst_negative_code_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)) * S ((dst_negative_code_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)) + ((dst_negative_scale_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value))) + (((dst_negative_code_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)) * S ((dst_negative_code_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)) + ((dst_negative_scale_column_value_supportcoversource_value) + (dst_negative_scale_column_value_supportcoversource_value)))))) /\ (((((exists ff_h_pvs_column_value_supportcoversource_valuepositive. ff_h_pvs_column_value_supportcoversource_valuepositive + S (dst_positive_column_value_supportcoversource_value) = S ((S (ssr_source_column_value_supportcover)) * dst_positive_scale_column_value_supportcoversource_value)) /\ exists ff_q_pvs_column_value_supportcoversource_valuepositive. dst_positive_code_column_value_supportcoversource_value = ff_q_pvs_column_value_supportcoversource_valuepositive * S ((S (ssr_source_column_value_supportcover)) * dst_positive_scale_column_value_supportcoversource_value) + (dst_positive_column_value_supportcoversource_value))) /\ (((((exists ff_h_pvs_column_value_supportcoversource_valuenegative. ff_h_pvs_column_value_supportcoversource_valuenegative + S (dst_negative_column_value_supportcoversource_value) = S ((S (ssr_source_column_value_supportcover)) * dst_negative_scale_column_value_supportcoversource_value)) /\ exists ff_q_pvs_column_value_supportcoversource_valuenegative. dst_negative_code_column_value_supportcoversource_value = ff_q_pvs_column_value_supportcoversource_valuenegative * S ((S (ssr_source_column_value_supportcover)) * dst_negative_scale_column_value_supportcoversource_value) + (dst_negative_column_value_supportcoversource_value))) /\ (exists ge_balance_positive_column_value_supportcoversource_valuevalue ge_balance_negative_column_value_supportcoversource_valuevalue. (((((ssr_value_column_value_supportcover) = 2 * (ge_balance_positive_column_value_supportcoversource_valuevalue) /\ (ge_balance_negative_column_value_supportcoversource_valuevalue) = 0) \/ exists ge_signed_half_column_value_supportcoversource_valuevaluedecode. (((ssr_value_column_value_supportcover) = 2 * ge_signed_half_column_value_supportcoversource_valuevaluedecode + 1 /\ (ge_balance_positive_column_value_supportcoversource_valuevalue) = 0) /\ (ge_balance_negative_column_value_supportcoversource_valuevalue) = S ge_signed_half_column_value_supportcoversource_valuevaluedecode))) /\ ((dst_positive_column_value_supportcoversource_value) + ge_balance_negative_column_value_supportcoversource_valuevalue = (dst_negative_column_value_supportcoversource_value) + ge_balance_positive_column_value_supportcoversource_valuevalue))))))))))))))))))))) -> (((exists dst_positive_code_column_value_gridsource dst_positive_scale_column_value_gridsource dst_negative_code_column_value_gridsource dst_negative_scale_column_value_gridsource. (((A) = (((((dst_positive_code_column_value_gridsource) + (dst_positive_scale_column_value_gridsource)) * S ((dst_positive_code_column_value_gridsource) + (dst_positive_scale_column_value_gridsource)) + ((dst_positive_scale_column_value_gridsource) + (dst_positive_scale_column_value_gridsource))) + (((dst_negative_code_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)) * S ((dst_negative_code_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)) + ((dst_negative_scale_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)))) * S ((((dst_positive_code_column_value_gridsource) + (dst_positive_scale_column_value_gridsource)) * S ((dst_positive_code_column_value_gridsource) + (dst_positive_scale_column_value_gridsource)) + ((dst_positive_scale_column_value_gridsource) + (dst_positive_scale_column_value_gridsource))) + (((dst_negative_code_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)) * S ((dst_negative_code_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)) + ((dst_negative_scale_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)))) + ((((dst_negative_code_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)) * S ((dst_negative_code_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)) + ((dst_negative_scale_column_value_gridsource) + (dst_negative_scale_column_value_gridsource))) + (((dst_negative_code_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)) * S ((dst_negative_code_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)) + ((dst_negative_scale_column_value_gridsource) + (dst_negative_scale_column_value_gridsource)))))) /\ (forall dst_index_column_value_gridsource. (exists pvs_le_gap_column_value_gridsourcedomain. pvs_le_gap_column_value_gridsourcedomain + (dst_index_column_value_gridsource) = (0)) -> exists dst_positive_column_value_gridsource dst_negative_column_value_gridsource dst_value_column_value_gridsource. ((((exists ff_h_pvs_column_value_gridsourceentrypositive. ff_h_pvs_column_value_gridsourceentrypositive + S (dst_positive_column_value_gridsource) = S ((S (dst_index_column_value_gridsource)) * dst_positive_scale_column_value_gridsource)) /\ exists ff_q_pvs_column_value_gridsourceentrypositive. dst_positive_code_column_value_gridsource = ff_q_pvs_column_value_gridsourceentrypositive * S ((S (dst_index_column_value_gridsource)) * dst_positive_scale_column_value_gridsource) + (dst_positive_column_value_gridsource))) /\ (((((exists ff_h_pvs_column_value_gridsourceentrynegative. ff_h_pvs_column_value_gridsourceentrynegative + S (dst_negative_column_value_gridsource) = S ((S (dst_index_column_value_gridsource)) * dst_negative_scale_column_value_gridsource)) /\ exists ff_q_pvs_column_value_gridsourceentrynegative. dst_negative_code_column_value_gridsource = ff_q_pvs_column_value_gridsourceentrynegative * S ((S (dst_index_column_value_gridsource)) * dst_negative_scale_column_value_gridsource) + (dst_negative_column_value_gridsource))) /\ (exists ge_balance_positive_column_value_gridsourceentryvalue ge_balance_negative_column_value_gridsourceentryvalue. (((((dst_value_column_value_gridsource) = 2 * (ge_balance_positive_column_value_gridsourceentryvalue) /\ (ge_balance_negative_column_value_gridsourceentryvalue) = 0) \/ exists ge_signed_half_column_value_gridsourceentryvaluedecode. (((dst_value_column_value_gridsource) = 2 * ge_signed_half_column_value_gridsourceentryvaluedecode + 1 /\ (ge_balance_positive_column_value_gridsourceentryvalue) = 0) /\ (ge_balance_negative_column_value_gridsourceentryvalue) = S ge_signed_half_column_value_gridsourceentryvaluedecode))) /\ ((dst_positive_column_value_gridsource) + ge_balance_negative_column_value_gridsourceentryvalue = (dst_negative_column_value_gridsource) + ge_balance_positive_column_value_gridsourceentryvalue))))))))) /\ (((exists dst_positive_code_column_value_gridtable dst_positive_scale_column_value_gridtable dst_negative_code_column_value_gridtable dst_negative_scale_column_value_gridtable. (((T) = (((((dst_positive_code_column_value_gridtable) + (dst_positive_scale_column_value_gridtable)) * S ((dst_positive_code_column_value_gridtable) + (dst_positive_scale_column_value_gridtable)) + ((dst_positive_scale_column_value_gridtable) + (dst_positive_scale_column_value_gridtable))) + (((dst_negative_code_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)) * S ((dst_negative_code_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)) + ((dst_negative_scale_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)))) * S ((((dst_positive_code_column_value_gridtable) + (dst_positive_scale_column_value_gridtable)) * S ((dst_positive_code_column_value_gridtable) + (dst_positive_scale_column_value_gridtable)) + ((dst_positive_scale_column_value_gridtable) + (dst_positive_scale_column_value_gridtable))) + (((dst_negative_code_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)) * S ((dst_negative_code_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)) + ((dst_negative_scale_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)))) + ((((dst_negative_code_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)) * S ((dst_negative_code_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)) + ((dst_negative_scale_column_value_gridtable) + (dst_negative_scale_column_value_gridtable))) + (((dst_negative_code_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)) * S ((dst_negative_code_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)) + ((dst_negative_scale_column_value_gridtable) + (dst_negative_scale_column_value_gridtable)))))) /\ (forall dst_index_column_value_gridtable. (exists pvs_le_gap_column_value_gridtabledomain. pvs_le_gap_column_value_gridtabledomain + (dst_index_column_value_gridtable) = ((L)*(S (M)))) -> exists dst_positive_column_value_gridtable dst_negative_column_value_gridtable dst_value_column_value_gridtable. ((((exists ff_h_pvs_column_value_gridtableentrypositive. ff_h_pvs_column_value_gridtableentrypositive + S (dst_positive_column_value_gridtable) = S ((S (dst_index_column_value_gridtable)) * dst_positive_scale_column_value_gridtable)) /\ exists ff_q_pvs_column_value_gridtableentrypositive. dst_positive_code_column_value_gridtable = ff_q_pvs_column_value_gridtableentrypositive * S ((S (dst_index_column_value_gridtable)) * dst_positive_scale_column_value_gridtable) + (dst_positive_column_value_gridtable))) /\ (((((exists ff_h_pvs_column_value_gridtableentrynegative. ff_h_pvs_column_value_gridtableentrynegative + S (dst_negative_column_value_gridtable) = S ((S (dst_index_column_value_gridtable)) * dst_negative_scale_column_value_gridtable)) /\ exists ff_q_pvs_column_value_gridtableentrynegative. dst_negative_code_column_value_gridtable = ff_q_pvs_column_value_gridtableentrynegative * S ((S (dst_index_column_value_gridtable)) * dst_negative_scale_column_value_gridtable) + (dst_negative_column_value_gridtable))) /\ (exists ge_balance_positive_column_value_gridtableentryvalue ge_balance_negative_column_value_gridtableentryvalue. (((((dst_value_column_value_gridtable) = 2 * (ge_balance_positive_column_value_gridtableentryvalue) /\ (ge_balance_negative_column_value_gridtableentryvalue) = 0) \/ exists ge_signed_half_column_value_gridtableentryvaluedecode. (((dst_value_column_value_gridtable) = 2 * ge_signed_half_column_value_gridtableentryvaluedecode + 1 /\ (ge_balance_positive_column_value_gridtableentryvalue) = 0) /\ (ge_balance_negative_column_value_gridtableentryvalue) = S ge_signed_half_column_value_gridtableentryvaluedecode))) /\ ((dst_positive_column_value_gridtable) + ge_balance_negative_column_value_gridtableentryvalue = (dst_negative_column_value_gridtable) + ge_balance_positive_column_value_gridtableentryvalue))))))))) /\ (forall ssr_grid_row_column_value_grid ssr_grid_column_column_value_grid ssr_grid_value_column_value_grid. (exists pvs_gap_column_value_gridrow_bound. pvs_gap_column_value_gridrow_bound + S (ssr_grid_row_column_value_grid) = (L)) -> (exists pvs_gap_column_value_gridcolumn_bound. pvs_gap_column_value_gridcolumn_bound + S (ssr_grid_column_column_value_grid) = (M)) -> (exists dst_positive_code_column_value_gridlookup dst_positive_scale_column_value_gridlookup dst_negative_code_column_value_gridlookup dst_negative_scale_column_value_gridlookup dst_positive_column_value_gridlookup dst_negative_column_value_gridlookup. (((T) = (((((dst_positive_code_column_value_gridlookup) + (dst_positive_scale_column_value_gridlookup)) * S ((dst_positive_code_column_value_gridlookup) + (dst_positive_scale_column_value_gridlookup)) + ((dst_positive_scale_column_value_gridlookup) + (dst_positive_scale_column_value_gridlookup))) + (((dst_negative_code_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)) * S ((dst_negative_code_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)) + ((dst_negative_scale_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)))) * S ((((dst_positive_code_column_value_gridlookup) + (dst_positive_scale_column_value_gridlookup)) * S ((dst_positive_code_column_value_gridlookup) + (dst_positive_scale_column_value_gridlookup)) + ((dst_positive_scale_column_value_gridlookup) + (dst_positive_scale_column_value_gridlookup))) + (((dst_negative_code_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)) * S ((dst_negative_code_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)) + ((dst_negative_scale_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)))) + ((((dst_negative_code_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)) * S ((dst_negative_code_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)) + ((dst_negative_scale_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup))) + (((dst_negative_code_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)) * S ((dst_negative_code_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)) + ((dst_negative_scale_column_value_gridlookup) + (dst_negative_scale_column_value_gridlookup)))))) /\ (((((exists ff_h_pvs_column_value_gridlookuppositive. ff_h_pvs_column_value_gridlookuppositive + S (dst_positive_column_value_gridlookup) = S ((S (((S (M))*(ssr_grid_row_column_value_grid)+(ssr_grid_column_column_value_grid)))) * dst_positive_scale_column_value_gridlookup)) /\ exists ff_q_pvs_column_value_gridlookuppositive. dst_positive_code_column_value_gridlookup = ff_q_pvs_column_value_gridlookuppositive * S ((S (((S (M))*(ssr_grid_row_column_value_grid)+(ssr_grid_column_column_value_grid)))) * dst_positive_scale_column_value_gridlookup) + (dst_positive_column_value_gridlookup))) /\ (((((exists ff_h_pvs_column_value_gridlookupnegative. ff_h_pvs_column_value_gridlookupnegative + S (dst_negative_column_value_gridlookup) = S ((S (((S (M))*(ssr_grid_row_column_value_grid)+(ssr_grid_column_column_value_grid)))) * dst_negative_scale_column_value_gridlookup)) /\ exists ff_q_pvs_column_value_gridlookupnegative. dst_negative_code_column_value_gridlookup = ff_q_pvs_column_value_gridlookupnegative * S ((S (((S (M))*(ssr_grid_row_column_value_grid)+(ssr_grid_column_column_value_grid)))) * dst_negative_scale_column_value_gridlookup) + (dst_negative_column_value_gridlookup))) /\ (exists ge_balance_positive_column_value_gridlookupvalue ge_balance_negative_column_value_gridlookupvalue. (((((ssr_grid_value_column_value_grid) = 2 * (ge_balance_positive_column_value_gridlookupvalue) /\ (ge_balance_negative_column_value_gridlookupvalue) = 0) \/ exists ge_signed_half_column_value_gridlookupvaluedecode. (((ssr_grid_value_column_value_grid) = 2 * ge_signed_half_column_value_gridlookupvaluedecode + 1 /\ (ge_balance_positive_column_value_gridlookupvalue) = 0) /\ (ge_balance_negative_column_value_gridlookupvalue) = S ge_signed_half_column_value_gridlookupvaluedecode))) /\ ((dst_positive_column_value_gridlookup) + ge_balance_negative_column_value_gridlookupvalue = (dst_negative_column_value_gridlookup) + ge_balance_positive_column_value_gridlookupvalue))))))))) -> (exists ssr_entry_value_column_value_gridentry ssr_entry_image_column_value_gridentry. ((exists dst_positive_code_column_value_gridentrysource dst_positive_scale_column_value_gridentrysource dst_negative_code_column_value_gridentrysource dst_negative_scale_column_value_gridentrysource dst_positive_column_value_gridentrysource dst_negative_column_value_gridentrysource. (((A) = (((((dst_positive_code_column_value_gridentrysource) + (dst_positive_scale_column_value_gridentrysource)) * S ((dst_positive_code_column_value_gridentrysource) + (dst_positive_scale_column_value_gridentrysource)) + ((dst_positive_scale_column_value_gridentrysource) + (dst_positive_scale_column_value_gridentrysource))) + (((dst_negative_code_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)) * S ((dst_negative_code_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)) + ((dst_negative_scale_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)))) * S ((((dst_positive_code_column_value_gridentrysource) + (dst_positive_scale_column_value_gridentrysource)) * S ((dst_positive_code_column_value_gridentrysource) + (dst_positive_scale_column_value_gridentrysource)) + ((dst_positive_scale_column_value_gridentrysource) + (dst_positive_scale_column_value_gridentrysource))) + (((dst_negative_code_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)) * S ((dst_negative_code_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)) + ((dst_negative_scale_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)))) + ((((dst_negative_code_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)) * S ((dst_negative_code_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)) + ((dst_negative_scale_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource))) + (((dst_negative_code_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)) * S ((dst_negative_code_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)) + ((dst_negative_scale_column_value_gridentrysource) + (dst_negative_scale_column_value_gridentrysource)))))) /\ (((((exists ff_h_pvs_column_value_gridentrysourcepositive. ff_h_pvs_column_value_gridentrysourcepositive + S (dst_positive_column_value_gridentrysource) = S ((S (ssr_grid_row_column_value_grid)) * dst_positive_scale_column_value_gridentrysource)) /\ exists ff_q_pvs_column_value_gridentrysourcepositive. dst_positive_code_column_value_gridentrysource = ff_q_pvs_column_value_gridentrysourcepositive * S ((S (ssr_grid_row_column_value_grid)) * dst_positive_scale_column_value_gridentrysource) + (dst_positive_column_value_gridentrysource))) /\ (((((exists ff_h_pvs_column_value_gridentrysourcenegative. ff_h_pvs_column_value_gridentrysourcenegative + S (dst_negative_column_value_gridentrysource) = S ((S (ssr_grid_row_column_value_grid)) * dst_negative_scale_column_value_gridentrysource)) /\ exists ff_q_pvs_column_value_gridentrysourcenegative. dst_negative_code_column_value_gridentrysource = ff_q_pvs_column_value_gridentrysourcenegative * S ((S (ssr_grid_row_column_value_grid)) * dst_negative_scale_column_value_gridentrysource) + (dst_negative_column_value_gridentrysource))) /\ (exists ge_balance_positive_column_value_gridentrysourcevalue ge_balance_negative_column_value_gridentrysourcevalue. (((((ssr_entry_value_column_value_gridentry) = 2 * (ge_balance_positive_column_value_gridentrysourcevalue) /\ (ge_balance_negative_column_value_gridentrysourcevalue) = 0) \/ exists ge_signed_half_column_value_gridentrysourcevaluedecode. (((ssr_entry_value_column_value_gridentry) = 2 * ge_signed_half_column_value_gridentrysourcevaluedecode + 1 /\ (ge_balance_positive_column_value_gridentrysourcevalue) = 0) /\ (ge_balance_negative_column_value_gridentrysourcevalue) = S ge_signed_half_column_value_gridentrysourcevaluedecode))) /\ ((dst_positive_column_value_gridentrysource) + ge_balance_negative_column_value_gridentrysourcevalue = (dst_negative_column_value_gridentrysource) + ge_balance_positive_column_value_gridentrysourcevalue))))))))) /\ (((((exists ff_h_pvs_column_value_gridentrymap. ff_h_pvs_column_value_gridentrymap + S (ssr_entry_image_column_value_gridentry) = S ((S (ssr_grid_row_column_value_grid)) * s)) /\ exists ff_q_pvs_column_value_gridentrymap. r = ff_q_pvs_column_value_gridentrymap * S ((S (ssr_grid_row_column_value_grid)) * s) + (ssr_entry_image_column_value_gridentry))) /\ (((((ssr_grid_column_column_value_grid)=(ssr_entry_image_column_value_gridentry)) /\ ((ssr_grid_value_column_value_grid)=(ssr_entry_value_column_value_gridentry)))) \/ (((~((ssr_grid_column_column_value_grid)=(ssr_entry_image_column_value_gridentry))) /\ ((ssr_grid_value_column_value_grid)=0))))))))))))) -> (exists pvs_gap_column_value_bound. pvs_gap_column_value_bound + S (j) = (M)) -> (exists dst_positive_code_column_value_target dst_positive_scale_column_value_target dst_negative_code_column_value_target dst_negative_scale_column_value_target dst_positive_column_value_target dst_negative_column_value_target. (((B) = (((((dst_positive_code_column_value_target) + (dst_positive_scale_column_value_target)) * S ((dst_positive_code_column_value_target) + (dst_positive_scale_column_value_target)) + ((dst_positive_scale_column_value_target) + (dst_positive_scale_column_value_target))) + (((dst_negative_code_column_value_target) + (dst_negative_scale_column_value_target)) * S ((dst_negative_code_column_value_target) + (dst_negative_scale_column_value_target)) + ((dst_negative_scale_column_value_target) + (dst_negative_scale_column_value_target)))) * S ((((dst_positive_code_column_value_target) + (dst_positive_scale_column_value_target)) * S ((dst_positive_code_column_value_target) + (dst_positive_scale_column_value_target)) + ((dst_positive_scale_column_value_target) + (dst_positive_scale_column_value_target))) + (((dst_negative_code_column_value_target) + (dst_negative_scale_column_value_target)) * S ((dst_negative_code_column_value_target) + (dst_negative_scale_column_value_target)) + ((dst_negative_scale_column_value_target) + (dst_negative_scale_column_value_target)))) + ((((dst_negative_code_column_value_target) + (dst_negative_scale_column_value_target)) * S ((dst_negative_code_column_value_target) + (dst_negative_scale_column_value_target)) + ((dst_negative_scale_column_value_target) + (dst_negative_scale_column_value_target))) + (((dst_negative_code_column_value_target) + (dst_negative_scale_column_value_target)) * S ((dst_negative_code_column_value_target) + (dst_negative_scale_column_value_target)) + ((dst_negative_scale_column_value_target) + (dst_negative_scale_column_value_target)))))) /\ (((((exists ff_h_pvs_column_value_targetpositive. ff_h_pvs_column_value_targetpositive + S (dst_positive_column_value_target) = S ((S (j)) * dst_positive_scale_column_value_target)) /\ exists ff_q_pvs_column_value_targetpositive. dst_positive_code_column_value_target = ff_q_pvs_column_value_targetpositive * S ((S (j)) * dst_positive_scale_column_value_target) + (dst_positive_column_value_target))) /\ (((((exists ff_h_pvs_column_value_targetnegative. ff_h_pvs_column_value_targetnegative + S (dst_negative_column_value_target) = S ((S (j)) * dst_negative_scale_column_value_target)) /\ exists ff_q_pvs_column_value_targetnegative. dst_negative_code_column_value_target = ff_q_pvs_column_value_targetnegative * S ((S (j)) * dst_negative_scale_column_value_target) + (dst_negative_column_value_target))) /\ (exists ge_balance_positive_column_value_targetvalue ge_balance_negative_column_value_targetvalue. (((((b) = 2 * (ge_balance_positive_column_value_targetvalue) /\ (ge_balance_negative_column_value_targetvalue) = 0) \/ exists ge_signed_half_column_value_targetvaluedecode. (((b) = 2 * ge_signed_half_column_value_targetvaluedecode + 1 /\ (ge_balance_positive_column_value_targetvalue) = 0) /\ (ge_balance_negative_column_value_targetvalue) = S ge_signed_half_column_value_targetvaluedecode))) /\ ((dst_positive_column_value_target) + ge_balance_negative_column_value_targetvalue = (dst_negative_column_value_target) + ge_balance_positive_column_value_targetvalue))))))))) -> (exists srs_slice_column_value_sum. ((((exists dst_positive_code_column_value_sumslicesource_table dst_positive_scale_column_value_sumslicesource_table dst_negative_code_column_value_sumslicesource_table dst_negative_scale_column_value_sumslicesource_table. (((T) = (((((dst_positive_code_column_value_sumslicesource_table) + (dst_positive_scale_column_value_sumslicesource_table)) * S ((dst_positive_code_column_value_sumslicesource_table) + (dst_positive_scale_column_value_sumslicesource_table)) + ((dst_positive_scale_column_value_sumslicesource_table) + (dst_positive_scale_column_value_sumslicesource_table))) + (((dst_negative_code_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)) * S ((dst_negative_code_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)) + ((dst_negative_scale_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)))) * S ((((dst_positive_code_column_value_sumslicesource_table) + (dst_positive_scale_column_value_sumslicesource_table)) * S ((dst_positive_code_column_value_sumslicesource_table) + (dst_positive_scale_column_value_sumslicesource_table)) + ((dst_positive_scale_column_value_sumslicesource_table) + (dst_positive_scale_column_value_sumslicesource_table))) + (((dst_negative_code_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)) * S ((dst_negative_code_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)) + ((dst_negative_scale_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)))) + ((((dst_negative_code_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)) * S ((dst_negative_code_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)) + ((dst_negative_scale_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table))) + (((dst_negative_code_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)) * S ((dst_negative_code_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)) + ((dst_negative_scale_column_value_sumslicesource_table) + (dst_negative_scale_column_value_sumslicesource_table)))))) /\ (forall dst_index_column_value_sumslicesource_table. (exists pvs_le_gap_column_value_sumslicesource_tabledomain. pvs_le_gap_column_value_sumslicesource_tabledomain + (dst_index_column_value_sumslicesource_table) = (0)) -> exists dst_positive_column_value_sumslicesource_table dst_negative_column_value_sumslicesource_table dst_value_column_value_sumslicesource_table. ((((exists ff_h_pvs_column_value_sumslicesource_tableentrypositive. ff_h_pvs_column_value_sumslicesource_tableentrypositive + S (dst_positive_column_value_sumslicesource_table) = S ((S (dst_index_column_value_sumslicesource_table)) * dst_positive_scale_column_value_sumslicesource_table)) /\ exists ff_q_pvs_column_value_sumslicesource_tableentrypositive. dst_positive_code_column_value_sumslicesource_table = ff_q_pvs_column_value_sumslicesource_tableentrypositive * S ((S (dst_index_column_value_sumslicesource_table)) * dst_positive_scale_column_value_sumslicesource_table) + (dst_positive_column_value_sumslicesource_table))) /\ (((((exists ff_h_pvs_column_value_sumslicesource_tableentrynegative. ff_h_pvs_column_value_sumslicesource_tableentrynegative + S (dst_negative_column_value_sumslicesource_table) = S ((S (dst_index_column_value_sumslicesource_table)) * dst_negative_scale_column_value_sumslicesource_table)) /\ exists ff_q_pvs_column_value_sumslicesource_tableentrynegative. dst_negative_code_column_value_sumslicesource_table = ff_q_pvs_column_value_sumslicesource_tableentrynegative * S ((S (dst_index_column_value_sumslicesource_table)) * dst_negative_scale_column_value_sumslicesource_table) + (dst_negative_column_value_sumslicesource_table))) /\ (exists ge_balance_positive_column_value_sumslicesource_tableentryvalue ge_balance_negative_column_value_sumslicesource_tableentryvalue. (((((dst_value_column_value_sumslicesource_table) = 2 * (ge_balance_positive_column_value_sumslicesource_tableentryvalue) /\ (ge_balance_negative_column_value_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_column_value_sumslicesource_tableentryvaluedecode. (((dst_value_column_value_sumslicesource_table) = 2 * ge_signed_half_column_value_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_value_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_column_value_sumslicesource_tableentryvalue) = S ge_signed_half_column_value_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_column_value_sumslicesource_table) + ge_balance_negative_column_value_sumslicesource_tableentryvalue = (dst_negative_column_value_sumslicesource_table) + ge_balance_positive_column_value_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_column_value_sumsliceoutput_table dst_positive_scale_column_value_sumsliceoutput_table dst_negative_code_column_value_sumsliceoutput_table dst_negative_scale_column_value_sumsliceoutput_table. (((srs_slice_column_value_sum) = (((((dst_positive_code_column_value_sumsliceoutput_table) + (dst_positive_scale_column_value_sumsliceoutput_table)) * S ((dst_positive_code_column_value_sumsliceoutput_table) + (dst_positive_scale_column_value_sumsliceoutput_table)) + ((dst_positive_scale_column_value_sumsliceoutput_table) + (dst_positive_scale_column_value_sumsliceoutput_table))) + (((dst_negative_code_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)) * S ((dst_negative_code_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)) + ((dst_negative_scale_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)))) * S ((((dst_positive_code_column_value_sumsliceoutput_table) + (dst_positive_scale_column_value_sumsliceoutput_table)) * S ((dst_positive_code_column_value_sumsliceoutput_table) + (dst_positive_scale_column_value_sumsliceoutput_table)) + ((dst_positive_scale_column_value_sumsliceoutput_table) + (dst_positive_scale_column_value_sumsliceoutput_table))) + (((dst_negative_code_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)) * S ((dst_negative_code_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)) + ((dst_negative_scale_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)))) + ((((dst_negative_code_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)) * S ((dst_negative_code_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)) + ((dst_negative_scale_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table))) + (((dst_negative_code_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)) * S ((dst_negative_code_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)) + ((dst_negative_scale_column_value_sumsliceoutput_table) + (dst_negative_scale_column_value_sumsliceoutput_table)))))) /\ (forall dst_index_column_value_sumsliceoutput_table. (exists pvs_le_gap_column_value_sumsliceoutput_tabledomain. pvs_le_gap_column_value_sumsliceoutput_tabledomain + (dst_index_column_value_sumsliceoutput_table) = (L)) -> exists dst_positive_column_value_sumsliceoutput_table dst_negative_column_value_sumsliceoutput_table dst_value_column_value_sumsliceoutput_table. ((((exists ff_h_pvs_column_value_sumsliceoutput_tableentrypositive. ff_h_pvs_column_value_sumsliceoutput_tableentrypositive + S (dst_positive_column_value_sumsliceoutput_table) = S ((S (dst_index_column_value_sumsliceoutput_table)) * dst_positive_scale_column_value_sumsliceoutput_table)) /\ exists ff_q_pvs_column_value_sumsliceoutput_tableentrypositive. dst_positive_code_column_value_sumsliceoutput_table = ff_q_pvs_column_value_sumsliceoutput_tableentrypositive * S ((S (dst_index_column_value_sumsliceoutput_table)) * dst_positive_scale_column_value_sumsliceoutput_table) + (dst_positive_column_value_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_column_value_sumsliceoutput_tableentrynegative. ff_h_pvs_column_value_sumsliceoutput_tableentrynegative + S (dst_negative_column_value_sumsliceoutput_table) = S ((S (dst_index_column_value_sumsliceoutput_table)) * dst_negative_scale_column_value_sumsliceoutput_table)) /\ exists ff_q_pvs_column_value_sumsliceoutput_tableentrynegative. dst_negative_code_column_value_sumsliceoutput_table = ff_q_pvs_column_value_sumsliceoutput_tableentrynegative * S ((S (dst_index_column_value_sumsliceoutput_table)) * dst_negative_scale_column_value_sumsliceoutput_table) + (dst_negative_column_value_sumsliceoutput_table))) /\ (exists ge_balance_positive_column_value_sumsliceoutput_tableentryvalue ge_balance_negative_column_value_sumsliceoutput_tableentryvalue. (((((dst_value_column_value_sumsliceoutput_table) = 2 * (ge_balance_positive_column_value_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_column_value_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_column_value_sumsliceoutput_tableentryvaluedecode. (((dst_value_column_value_sumsliceoutput_table) = 2 * ge_signed_half_column_value_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_value_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_column_value_sumsliceoutput_tableentryvalue) = S ge_signed_half_column_value_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_column_value_sumsliceoutput_table) + ge_balance_negative_column_value_sumsliceoutput_tableentryvalue = (dst_negative_column_value_sumsliceoutput_table) + ge_balance_positive_column_value_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_column_value_sumslice. (exists pvs_gap_column_value_sumslicebound. pvs_gap_column_value_sumslicebound + S (srs_index_column_value_sumslice) = (L)) -> exists srs_value_column_value_sumslice. (((exists dst_positive_code_column_value_sumsliceentrysource dst_positive_scale_column_value_sumsliceentrysource dst_negative_code_column_value_sumsliceentrysource dst_negative_scale_column_value_sumsliceentrysource dst_positive_column_value_sumsliceentrysource dst_negative_column_value_sumsliceentrysource. (((T) = (((((dst_positive_code_column_value_sumsliceentrysource) + (dst_positive_scale_column_value_sumsliceentrysource)) * S ((dst_positive_code_column_value_sumsliceentrysource) + (dst_positive_scale_column_value_sumsliceentrysource)) + ((dst_positive_scale_column_value_sumsliceentrysource) + (dst_positive_scale_column_value_sumsliceentrysource))) + (((dst_negative_code_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)) * S ((dst_negative_code_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)) + ((dst_negative_scale_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)))) * S ((((dst_positive_code_column_value_sumsliceentrysource) + (dst_positive_scale_column_value_sumsliceentrysource)) * S ((dst_positive_code_column_value_sumsliceentrysource) + (dst_positive_scale_column_value_sumsliceentrysource)) + ((dst_positive_scale_column_value_sumsliceentrysource) + (dst_positive_scale_column_value_sumsliceentrysource))) + (((dst_negative_code_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)) * S ((dst_negative_code_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)) + ((dst_negative_scale_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)))) + ((((dst_negative_code_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)) * S ((dst_negative_code_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)) + ((dst_negative_scale_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource))) + (((dst_negative_code_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)) * S ((dst_negative_code_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)) + ((dst_negative_scale_column_value_sumsliceentrysource) + (dst_negative_scale_column_value_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_column_value_sumsliceentrysourcepositive. ff_h_pvs_column_value_sumsliceentrysourcepositive + S (dst_positive_column_value_sumsliceentrysource) = S ((S (((((0) + ((1) * (j)))) + ((S M) * (srs_index_column_value_sumslice))))) * dst_positive_scale_column_value_sumsliceentrysource)) /\ exists ff_q_pvs_column_value_sumsliceentrysourcepositive. dst_positive_code_column_value_sumsliceentrysource = ff_q_pvs_column_value_sumsliceentrysourcepositive * S ((S (((((0) + ((1) * (j)))) + ((S M) * (srs_index_column_value_sumslice))))) * dst_positive_scale_column_value_sumsliceentrysource) + (dst_positive_column_value_sumsliceentrysource))) /\ (((((exists ff_h_pvs_column_value_sumsliceentrysourcenegative. ff_h_pvs_column_value_sumsliceentrysourcenegative + S (dst_negative_column_value_sumsliceentrysource) = S ((S (((((0) + ((1) * (j)))) + ((S M) * (srs_index_column_value_sumslice))))) * dst_negative_scale_column_value_sumsliceentrysource)) /\ exists ff_q_pvs_column_value_sumsliceentrysourcenegative. dst_negative_code_column_value_sumsliceentrysource = ff_q_pvs_column_value_sumsliceentrysourcenegative * S ((S (((((0) + ((1) * (j)))) + ((S M) * (srs_index_column_value_sumslice))))) * dst_negative_scale_column_value_sumsliceentrysource) + (dst_negative_column_value_sumsliceentrysource))) /\ (exists ge_balance_positive_column_value_sumsliceentrysourcevalue ge_balance_negative_column_value_sumsliceentrysourcevalue. (((((srs_value_column_value_sumslice) = 2 * (ge_balance_positive_column_value_sumsliceentrysourcevalue) /\ (ge_balance_negative_column_value_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_column_value_sumsliceentrysourcevaluedecode. (((srs_value_column_value_sumslice) = 2 * ge_signed_half_column_value_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_column_value_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_column_value_sumsliceentrysourcevalue) = S ge_signed_half_column_value_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_column_value_sumsliceentrysource) + ge_balance_negative_column_value_sumsliceentrysourcevalue = (dst_negative_column_value_sumsliceentrysource) + ge_balance_positive_column_value_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_column_value_sumsliceentryoutput dst_positive_scale_column_value_sumsliceentryoutput dst_negative_code_column_value_sumsliceentryoutput dst_negative_scale_column_value_sumsliceentryoutput dst_positive_column_value_sumsliceentryoutput dst_negative_column_value_sumsliceentryoutput. (((srs_slice_column_value_sum) = (((((dst_positive_code_column_value_sumsliceentryoutput) + (dst_positive_scale_column_value_sumsliceentryoutput)) * S ((dst_positive_code_column_value_sumsliceentryoutput) + (dst_positive_scale_column_value_sumsliceentryoutput)) + ((dst_positive_scale_column_value_sumsliceentryoutput) + (dst_positive_scale_column_value_sumsliceentryoutput))) + (((dst_negative_code_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)) * S ((dst_negative_code_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)) + ((dst_negative_scale_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)))) * S ((((dst_positive_code_column_value_sumsliceentryoutput) + (dst_positive_scale_column_value_sumsliceentryoutput)) * S ((dst_positive_code_column_value_sumsliceentryoutput) + (dst_positive_scale_column_value_sumsliceentryoutput)) + ((dst_positive_scale_column_value_sumsliceentryoutput) + (dst_positive_scale_column_value_sumsliceentryoutput))) + (((dst_negative_code_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)) * S ((dst_negative_code_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)) + ((dst_negative_scale_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)))) + ((((dst_negative_code_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)) * S ((dst_negative_code_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)) + ((dst_negative_scale_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput))) + (((dst_negative_code_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)) * S ((dst_negative_code_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)) + ((dst_negative_scale_column_value_sumsliceentryoutput) + (dst_negative_scale_column_value_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_column_value_sumsliceentryoutputpositive. ff_h_pvs_column_value_sumsliceentryoutputpositive + S (dst_positive_column_value_sumsliceentryoutput) = S ((S (srs_index_column_value_sumslice)) * dst_positive_scale_column_value_sumsliceentryoutput)) /\ exists ff_q_pvs_column_value_sumsliceentryoutputpositive. dst_positive_code_column_value_sumsliceentryoutput = ff_q_pvs_column_value_sumsliceentryoutputpositive * S ((S (srs_index_column_value_sumslice)) * dst_positive_scale_column_value_sumsliceentryoutput) + (dst_positive_column_value_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_column_value_sumsliceentryoutputnegative. ff_h_pvs_column_value_sumsliceentryoutputnegative + S (dst_negative_column_value_sumsliceentryoutput) = S ((S (srs_index_column_value_sumslice)) * dst_negative_scale_column_value_sumsliceentryoutput)) /\ exists ff_q_pvs_column_value_sumsliceentryoutputnegative. dst_negative_code_column_value_sumsliceentryoutput = ff_q_pvs_column_value_sumsliceentryoutputnegative * S ((S (srs_index_column_value_sumslice)) * dst_negative_scale_column_value_sumsliceentryoutput) + (dst_negative_column_value_sumsliceentryoutput))) /\ (exists ge_balance_positive_column_value_sumsliceentryoutputvalue ge_balance_negative_column_value_sumsliceentryoutputvalue. (((((srs_value_column_value_sumslice) = 2 * (ge_balance_positive_column_value_sumsliceentryoutputvalue) /\ (ge_balance_negative_column_value_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_column_value_sumsliceentryoutputvaluedecode. (((srs_value_column_value_sumslice) = 2 * ge_signed_half_column_value_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_column_value_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_column_value_sumsliceentryoutputvalue) = S ge_signed_half_column_value_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_column_value_sumsliceentryoutput) + ge_balance_negative_column_value_sumsliceentryoutputvalue = (dst_negative_column_value_sumsliceentryoutput) + ge_balance_positive_column_value_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_column_value_sumsum dst_positive_scale_column_value_sumsum dst_negative_code_column_value_sumsum dst_negative_scale_column_value_sumsum dst_positive_sum_column_value_sumsum dst_negative_sum_column_value_sumsum. (((srs_slice_column_value_sum) = (((((dst_positive_code_column_value_sumsum) + (dst_positive_scale_column_value_sumsum)) * S ((dst_positive_code_column_value_sumsum) + (dst_positive_scale_column_value_sumsum)) + ((dst_positive_scale_column_value_sumsum) + (dst_positive_scale_column_value_sumsum))) + (((dst_negative_code_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)) * S ((dst_negative_code_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)) + ((dst_negative_scale_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)))) * S ((((dst_positive_code_column_value_sumsum) + (dst_positive_scale_column_value_sumsum)) * S ((dst_positive_code_column_value_sumsum) + (dst_positive_scale_column_value_sumsum)) + ((dst_positive_scale_column_value_sumsum) + (dst_positive_scale_column_value_sumsum))) + (((dst_negative_code_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)) * S ((dst_negative_code_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)) + ((dst_negative_scale_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)))) + ((((dst_negative_code_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)) * S ((dst_negative_code_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)) + ((dst_negative_scale_column_value_sumsum) + (dst_negative_scale_column_value_sumsum))) + (((dst_negative_code_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)) * S ((dst_negative_code_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)) + ((dst_negative_scale_column_value_sumsum) + (dst_negative_scale_column_value_sumsum)))))) /\ (((exists fs_u_dst_column_value_sumsumpositive fs_v_dst_column_value_sumsumpositive. ((((exists fs_h_dst_column_value_sumsumpositive_body_start. fs_h_dst_column_value_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_column_value_sumsumpositive)) /\ exists fs_q_dst_column_value_sumsumpositive_body_start. fs_u_dst_column_value_sumsumpositive = fs_q_dst_column_value_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_column_value_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_column_value_sumsumpositive_body_terminal. fs_h_dst_column_value_sumsumpositive_body_terminal + S (dst_positive_sum_column_value_sumsum) = S ((S (L)) * fs_v_dst_column_value_sumsumpositive)) /\ exists fs_q_dst_column_value_sumsumpositive_body_terminal. fs_u_dst_column_value_sumsumpositive = fs_q_dst_column_value_sumsumpositive_body_terminal * S ((S (L)) * fs_v_dst_column_value_sumsumpositive) + (dst_positive_sum_column_value_sumsum))) /\ forall fs_i_dst_column_value_sumsumpositive_body_steps. (exists fs_lt_dst_column_value_sumsumpositive_body_steps_bound. fs_lt_dst_column_value_sumsumpositive_body_steps_bound + S fs_i_dst_column_value_sumsumpositive_body_steps = L) -> exists fs_a_dst_column_value_sumsumpositive_body_steps fs_r_dst_column_value_sumsumpositive_body_steps fs_s_dst_column_value_sumsumpositive_body_steps. ((((exists fs_h_dst_column_value_sumsumpositive_body_steps_summand. fs_h_dst_column_value_sumsumpositive_body_steps_summand + S (fs_a_dst_column_value_sumsumpositive_body_steps) = S ((S (fs_i_dst_column_value_sumsumpositive_body_steps)) * dst_positive_scale_column_value_sumsum)) /\ exists fs_q_dst_column_value_sumsumpositive_body_steps_summand. dst_positive_code_column_value_sumsum = fs_q_dst_column_value_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_column_value_sumsumpositive_body_steps)) * dst_positive_scale_column_value_sumsum) + (fs_a_dst_column_value_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_column_value_sumsumpositive_body_steps_partial. fs_h_dst_column_value_sumsumpositive_body_steps_partial + S (fs_r_dst_column_value_sumsumpositive_body_steps) = S ((S (fs_i_dst_column_value_sumsumpositive_body_steps)) * fs_v_dst_column_value_sumsumpositive)) /\ exists fs_q_dst_column_value_sumsumpositive_body_steps_partial. fs_u_dst_column_value_sumsumpositive = fs_q_dst_column_value_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_column_value_sumsumpositive_body_steps)) * fs_v_dst_column_value_sumsumpositive) + (fs_r_dst_column_value_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_column_value_sumsumpositive_body_steps_successor. fs_h_dst_column_value_sumsumpositive_body_steps_successor + S (fs_s_dst_column_value_sumsumpositive_body_steps) = S ((S (S fs_i_dst_column_value_sumsumpositive_body_steps)) * fs_v_dst_column_value_sumsumpositive)) /\ exists fs_q_dst_column_value_sumsumpositive_body_steps_successor. fs_u_dst_column_value_sumsumpositive = fs_q_dst_column_value_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_column_value_sumsumpositive_body_steps)) * fs_v_dst_column_value_sumsumpositive) + (fs_s_dst_column_value_sumsumpositive_body_steps))) /\ fs_s_dst_column_value_sumsumpositive_body_steps = fs_r_dst_column_value_sumsumpositive_body_steps + fs_a_dst_column_value_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_column_value_sumsumnegative fs_v_dst_column_value_sumsumnegative. ((((exists fs_h_dst_column_value_sumsumnegative_body_start. fs_h_dst_column_value_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_column_value_sumsumnegative)) /\ exists fs_q_dst_column_value_sumsumnegative_body_start. fs_u_dst_column_value_sumsumnegative = fs_q_dst_column_value_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_column_value_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_column_value_sumsumnegative_body_terminal. fs_h_dst_column_value_sumsumnegative_body_terminal + S (dst_negative_sum_column_value_sumsum) = S ((S (L)) * fs_v_dst_column_value_sumsumnegative)) /\ exists fs_q_dst_column_value_sumsumnegative_body_terminal. fs_u_dst_column_value_sumsumnegative = fs_q_dst_column_value_sumsumnegative_body_terminal * S ((S (L)) * fs_v_dst_column_value_sumsumnegative) + (dst_negative_sum_column_value_sumsum))) /\ forall fs_i_dst_column_value_sumsumnegative_body_steps. (exists fs_lt_dst_column_value_sumsumnegative_body_steps_bound. fs_lt_dst_column_value_sumsumnegative_body_steps_bound + S fs_i_dst_column_value_sumsumnegative_body_steps = L) -> exists fs_a_dst_column_value_sumsumnegative_body_steps fs_r_dst_column_value_sumsumnegative_body_steps fs_s_dst_column_value_sumsumnegative_body_steps. ((((exists fs_h_dst_column_value_sumsumnegative_body_steps_summand. fs_h_dst_column_value_sumsumnegative_body_steps_summand + S (fs_a_dst_column_value_sumsumnegative_body_steps) = S ((S (fs_i_dst_column_value_sumsumnegative_body_steps)) * dst_negative_scale_column_value_sumsum)) /\ exists fs_q_dst_column_value_sumsumnegative_body_steps_summand. dst_negative_code_column_value_sumsum = fs_q_dst_column_value_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_column_value_sumsumnegative_body_steps)) * dst_negative_scale_column_value_sumsum) + (fs_a_dst_column_value_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_column_value_sumsumnegative_body_steps_partial. fs_h_dst_column_value_sumsumnegative_body_steps_partial + S (fs_r_dst_column_value_sumsumnegative_body_steps) = S ((S (fs_i_dst_column_value_sumsumnegative_body_steps)) * fs_v_dst_column_value_sumsumnegative)) /\ exists fs_q_dst_column_value_sumsumnegative_body_steps_partial. fs_u_dst_column_value_sumsumnegative = fs_q_dst_column_value_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_column_value_sumsumnegative_body_steps)) * fs_v_dst_column_value_sumsumnegative) + (fs_r_dst_column_value_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_column_value_sumsumnegative_body_steps_successor. fs_h_dst_column_value_sumsumnegative_body_steps_successor + S (fs_s_dst_column_value_sumsumnegative_body_steps) = S ((S (S fs_i_dst_column_value_sumsumnegative_body_steps)) * fs_v_dst_column_value_sumsumnegative)) /\ exists fs_q_dst_column_value_sumsumnegative_body_steps_successor. fs_u_dst_column_value_sumsumnegative = fs_q_dst_column_value_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_column_value_sumsumnegative_body_steps)) * fs_v_dst_column_value_sumsumnegative) + (fs_s_dst_column_value_sumsumnegative_body_steps))) /\ fs_s_dst_column_value_sumsumnegative_body_steps = fs_r_dst_column_value_sumsumnegative_body_steps + fs_a_dst_column_value_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_column_value_sumsumresult ge_balance_negative_column_value_sumsumresult. (((((z) = 2 * (ge_balance_positive_column_value_sumsumresult) /\ (ge_balance_negative_column_value_sumsumresult) = 0) \/ exists ge_signed_half_column_value_sumsumresultdecode. (((z) = 2 * ge_signed_half_column_value_sumsumresultdecode + 1 /\ (ge_balance_positive_column_value_sumsumresult) = 0) /\ (ge_balance_negative_column_value_sumsumresult) = S ge_signed_half_column_value_sumsumresultdecode))) /\ ((dst_positive_sum_column_value_sumsum) + ge_balance_negative_column_value_sumsumresult = (dst_negative_sum_column_value_sumsum) + ge_balance_positive_column_value_sumsumresult))))))))))) -> z=b

Constructive proof overview

Generated structural guide

Target coverage supplies the actual nonzero spike; active injectivity excludes other nonzero cells and preservation handles zero targets.

The unchanged tactic script uses 11 declared prerequisites and contains 225 exact native proof lines.

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

Proof neighborhood

Direct dependencies

eq_decidable Stable theorem; checked-use authorized signed_prefix_sum_zero_value Alpha theorem; checked-use authorized MX003C signed_support_incidence_nonzero_source_image MX0045 signed_support_incidence_column_lookup beta_at_unique Stable theorem; checked-use authorized divisor_signed_table_at_functional Alpha theorem; checked-use authorized MX0035 signed_prefix_sum_point_spike_value signed_table_domain_resize Alpha theorem; checked-use authorized signed_table_lookup_any Alpha theorem; checked-use authorized MX0039 signed_support_incidence_entry_functional MX0036 signed_support_incidence_entry_hit

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

225 script commands · 47 reading checkpoints · 10 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 (5)

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

01Fix variables and assumptionsL1–10

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 j
  9. L9
    intro b
  10. L10
    intro z
02Fix variables and assumptionsL11–15

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

  1. L11
    intro hp
  2. L12
    intro hg
  3. L13
    intro hj
  4. L14
    intro hb
  5. L15
    intro hs
03Separate the logical casesL16–21

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

  1. L16
    cases hp
  2. L17
    cases hp_right
  3. L18
    cases hp_right_right
  4. L19
    cases hp_right_right_right
  5. L20
    cases hs
  6. L21
    cases hs_witness
04Establish hcL22–25

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply eq decidable.

  1. L22
    have hc : b=0 \/ ~(b=0)
  2. L23
    specialize eq_decidable (b)
  3. L24
    specialize eq_decidable (0)
  4. L25
    apply eq_decidable
05Separate the logical casesL26–26

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

  1. L26
    cases hc
06Calculate and transport equalitiesL27–29

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

  1. L27
    rewrite hc_left at hb
  2. L28
    rewrite hc_left at hb
  3. L29
    rewrite hc_left
07Use earlier factsL30–33

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

  1. L30
    specialize signed_prefix_sum_zero_value (x)
  2. L31
    specialize signed_prefix_sum_zero_value (L)
  3. L32
    specialize signed_prefix_sum_zero_value (z)
  4. L33
    apply signed_prefix_sum_zero_value
08Fix variables and assumptionsL34–38

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

  1. L34
    intro i
  2. L35
    intro v
  3. L36
    intro h0i
  4. L37
    intro hi
  5. L38
    intro hv
09Establish hnL39–42

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply eq decidable.

  1. L39
    have hn : v=0 \/ ~(v=0)
  2. L40
    specialize eq_decidable (v)
  3. L41
    specialize eq_decidable (0)
  4. L42
    apply eq_decidable
10Separate the logical casesL43–43

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

  1. L43
    cases hn
11Use earlier factsL44–44

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

  1. L44
    exact hn_left
12Establish hsourceL45–54

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed support incidence nonzero source image.

  1. L45
    have hsource : ArithAt(A,i,v) ∧ BetaAt(r,s,i,j)Definitions: ArithAtBetaAt
  2. L46
    specialize signed_support_incidence_nonzero_source_image (A)
  3. L47
    specialize signed_support_incidence_nonzero_source_image (r)
  4. L48
    specialize signed_support_incidence_nonzero_source_image (s)
  5. L49
    specialize signed_support_incidence_nonzero_source_image (i)
  6. L50
    specialize signed_support_incidence_nonzero_source_image (j)
  7. L51
    specialize signed_support_incidence_nonzero_source_image (v)
  8. L52
    apply signed_support_incidence_nonzero_source_image
  9. L53
    specialize signed_support_incidence_column_lookup (A)
  10. L54
    specialize signed_support_incidence_column_lookup (r)
13Use earlier factsL55–64

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

  1. L55
    specialize signed_support_incidence_column_lookup (s)
  2. L56
    specialize signed_support_incidence_column_lookup (L)
  3. L57
    specialize signed_support_incidence_column_lookup (M)
  4. L58
    specialize signed_support_incidence_column_lookup (T)
  5. L59
    specialize signed_support_incidence_column_lookup (x)
  6. L60
    specialize signed_support_incidence_column_lookup (i)
  7. L61
    specialize signed_support_incidence_column_lookup (j)
  8. L62
    specialize signed_support_incidence_column_lookup (v)
  9. L63
    apply signed_support_incidence_column_lookup
  10. L64
    exact hg
14Use earlier factsL65–69

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

  1. L65
    exact hs_witness_left
  2. L66
    exact hi
  3. L67
    exact hj
  4. L68
    exact hv
  5. L69
    exact hn_right
15Separate the logical casesL70–70

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

  1. L70
    cases hsource
16Establish hmL71–77

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply hp right right left.

  1. L71
    have hm : ∃ k. BetaAt(r,s,i,k) ∧ (Lt(k,M) ∧ ArithAt(B,k,v))Definitions: ArithAtLtBetaAt
  2. L72
    specialize hp_right_right_left (i)
  3. L73
    specialize hp_right_right_left (v)
  4. L74
    apply hp_right_right_left
  5. L75
    exact hi
  6. L76
    exact hsource_left
  7. L77
    exact hn_right
17Separate the logical casesL78–80

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

  1. L78
    cases hm
  2. L79
    cases hm_witness
  3. L80
    cases hm_witness_right
18Establish heL81–90

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply beta at unique.

  1. L81
    have he : x1=j
  2. L82
    specialize beta_at_unique (r)
  3. L83
    specialize beta_at_unique (s)
  4. L84
    specialize beta_at_unique (i)
  5. L85
    specialize beta_at_unique (x1)
  6. L86
    specialize beta_at_unique (j)
  7. L87
    apply beta_at_unique
  8. L88
    exact hm_witness_left
  9. L89
    exact hsource_right
  10. L90
    rewrite he at hm_witness_right_right
19Calculate and transport equalitiesL91–93

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

  1. L91
    rewrite he at hm_witness_right_right
  2. L92
    rewrite he at hm_witness_right_right
  3. L93
    rewrite he at hm_witness_right_right
20Use earlier factsL94–101

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

  1. L94
    specialize divisor_signed_table_at_functional (B)
  2. L95
    specialize divisor_signed_table_at_functional (j)
  3. L96
    specialize divisor_signed_table_at_functional (v)
  4. L97
    specialize divisor_signed_table_at_functional (0)
  5. L98
    apply divisor_signed_table_at_functional
  6. L99
    exact hm_witness_right_right
  7. L100
    exact hb
  8. L101
    exact hs_witness_right
21Establish hmL102–108

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply hp right right right right.

  1. L102
    have hm : ∃ i. Lt(i,L) ∧ (BetaAt(r,s,i,j) ∧ ArithAt(A,i,b))Definitions: ArithAtLtBetaAt
  2. L103
    specialize hp_right_right_right_right (j)
  3. L104
    specialize hp_right_right_right_right (b)
  4. L105
    apply hp_right_right_right_right
  5. L106
    exact hj
  6. L107
    exact hb
  7. L108
    exact hc_right
22Separate the logical casesL109–111

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

  1. L109
    cases hm
  2. L110
    cases hm_witness
  3. L111
    cases hm_witness_right
23Use earlier factsL112–117

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

  1. L112
    specialize signed_prefix_sum_point_spike_value (x)
  2. L113
    specialize signed_prefix_sum_point_spike_value (L)
  3. L114
    specialize signed_prefix_sum_point_spike_value (x1)
  4. L115
    specialize signed_prefix_sum_point_spike_value (b)
  5. L116
    specialize signed_prefix_sum_point_spike_value (z)
  6. L117
    apply signed_prefix_sum_point_spike_value
24Separate the logical casesL118–119

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

  1. L118
    cases hs_witness_left
  2. L119
    cases hs_witness_left_right
25Use earlier factsL120–125

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

  1. L120
    specialize signed_table_domain_resize (L)
  2. L121
    specialize signed_table_domain_resize (0)
  3. L122
    specialize signed_table_domain_resize (x)
  4. L123
    apply signed_table_domain_resize
  5. L124
    exact hs_witness_left_right_left
  6. L125
    exact hm_witness_left
26Establish hvL126–130

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed table lookup any.

  1. L126
    have hv : ∃ v. ArithAt(x,x1,v)Definitions: ArithAt
  2. L127
    specialize signed_table_lookup_any (L)
  3. L128
    specialize signed_table_lookup_any (x)
  4. L129
    specialize signed_table_lookup_any (x1)
  5. L130
    apply signed_table_lookup_any
27Separate the logical casesL131–132

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

  1. L131
    cases hs_witness_left
  2. L132
    cases hs_witness_left_right
28Use earlier factsL133–133

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

  1. L133
    exact hs_witness_left_right_left
29Separate the logical casesL134–134

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

  1. L134
    cases hv
30Establish heL135–144

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed support incidence entry functional.

  1. L135
    have he : x2=b
  2. L136
    specialize signed_support_incidence_entry_functional (A)
  3. L137
    specialize signed_support_incidence_entry_functional (r)
  4. L138
    specialize signed_support_incidence_entry_functional (s)
  5. L139
    specialize signed_support_incidence_entry_functional (x1)
  6. L140
    specialize signed_support_incidence_entry_functional (j)
  7. L141
    specialize signed_support_incidence_entry_functional (x2)
  8. L142
    specialize signed_support_incidence_entry_functional (b)
  9. L143
    apply signed_support_incidence_entry_functional
  10. L144
    specialize signed_support_incidence_column_lookup (A)
31Use earlier factsL145–154

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

  1. L145
    specialize signed_support_incidence_column_lookup (r)
  2. L146
    specialize signed_support_incidence_column_lookup (s)
  3. L147
    specialize signed_support_incidence_column_lookup (L)
  4. L148
    specialize signed_support_incidence_column_lookup (M)
  5. L149
    specialize signed_support_incidence_column_lookup (T)
  6. L150
    specialize signed_support_incidence_column_lookup (x)
  7. L151
    specialize signed_support_incidence_column_lookup (x1)
  8. L152
    specialize signed_support_incidence_column_lookup (j)
  9. L153
    specialize signed_support_incidence_column_lookup (x2)
  10. L154
    apply signed_support_incidence_column_lookup
32Use earlier factsL155–164

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

  1. L155
    exact hg
  2. L156
    exact hs_witness_left
  3. L157
    exact hm_witness_left
  4. L158
    exact hj
  5. L159
    exact hv_witness
  6. L160
    specialize signed_support_incidence_entry_hit (A)
  7. L161
    specialize signed_support_incidence_entry_hit (r)
  8. L162
    specialize signed_support_incidence_entry_hit (s)
  9. L163
    specialize signed_support_incidence_entry_hit (x1)
  10. L164
    specialize signed_support_incidence_entry_hit (j)
33Use earlier factsL165–168

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

  1. L165
    specialize signed_support_incidence_entry_hit (b)
  2. L166
    apply signed_support_incidence_entry_hit
  3. L167
    exact hm_witness_right_right
  4. L168
    exact hm_witness_right_left
34Calculate and transport equalitiesL169–170

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

  1. L169
    rewrite he at hv_witness
  2. L170
    rewrite he at hv_witness
35Use earlier factsL171–171

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

  1. L171
    exact hv_witness
36Fix variables and assumptionsL172–176

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

  1. L172
    intro i
  2. L173
    intro v
  3. L174
    intro hi
  4. L175
    intro hne
  5. L176
    intro hv
37Establish hnL177–180

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply eq decidable.

  1. L177
    have hn : v=0 \/ ~(v=0)
  2. L178
    specialize eq_decidable (v)
  3. L179
    specialize eq_decidable (0)
  4. L180
    apply eq_decidable
38Separate the logical casesL181–181

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

  1. L181
    cases hn
39Use earlier factsL182–182

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

  1. L182
    exact hn_left
40Separate the logical casesL183–183

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

  1. L183
    exfalso
41Use earlier factsL184–184

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

  1. L184
    apply hne
42Establish hsourceL185–194

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed support incidence nonzero source image.

  1. L185
    have hsource : ArithAt(A,i,v) ∧ BetaAt(r,s,i,j)Definitions: ArithAtBetaAt
  2. L186
    specialize signed_support_incidence_nonzero_source_image (A)
  3. L187
    specialize signed_support_incidence_nonzero_source_image (r)
  4. L188
    specialize signed_support_incidence_nonzero_source_image (s)
  5. L189
    specialize signed_support_incidence_nonzero_source_image (i)
  6. L190
    specialize signed_support_incidence_nonzero_source_image (j)
  7. L191
    specialize signed_support_incidence_nonzero_source_image (v)
  8. L192
    apply signed_support_incidence_nonzero_source_image
  9. L193
    specialize signed_support_incidence_column_lookup (A)
  10. L194
    specialize signed_support_incidence_column_lookup (r)
43Use earlier factsL195–204

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

  1. L195
    specialize signed_support_incidence_column_lookup (s)
  2. L196
    specialize signed_support_incidence_column_lookup (L)
  3. L197
    specialize signed_support_incidence_column_lookup (M)
  4. L198
    specialize signed_support_incidence_column_lookup (T)
  5. L199
    specialize signed_support_incidence_column_lookup (x)
  6. L200
    specialize signed_support_incidence_column_lookup (i)
  7. L201
    specialize signed_support_incidence_column_lookup (j)
  8. L202
    specialize signed_support_incidence_column_lookup (v)
  9. L203
    apply signed_support_incidence_column_lookup
  10. L204
    exact hg
44Use earlier factsL205–209

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

  1. L205
    exact hs_witness_left
  2. L206
    exact hi
  3. L207
    exact hj
  4. L208
    exact hv
  5. L209
    exact hn_right
45Separate the logical casesL210–210

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

  1. L210
    cases hsource
46Use earlier factsL211–220

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

  1. L211
    specialize hp_right_right_right_left (i)
  2. L212
    specialize hp_right_right_right_left (x1)
  3. L213
    specialize hp_right_right_right_left (j)
  4. L214
    specialize hp_right_right_right_left (v)
  5. L215
    specialize hp_right_right_right_left (b)
  6. L216
    apply hp_right_right_right_left
  7. L217
    exact hi
  8. L218
    exact hm_witness_left
  9. L219
    exact hsource_left
  10. L220
    exact hn_right
47Use earlier factsL221–225

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

  1. L221
    exact hm_witness_right_right
  2. L222
    exact hc_right
  3. L223
    exact hsource_right
  4. L224
    exact hm_witness_right_left
  5. L225
    exact hs_witness_right

Library-wide reading audit

Original exact command ledger · 225 lines
  1. 0001intro A
  2. 0002intro B
  3. 0003intro r
  4. 0004intro s
  5. 0005intro L
  6. 0006intro M
  7. 0007intro T
  8. 0008intro j
  9. 0009intro b
  10. 0010intro z
  11. 0011intro hp
  12. 0012intro hg
  13. 0013intro hj
  14. 0014intro hb
  15. 0015intro hs
  16. 0016cases hp
  17. 0017cases hp_right
  18. 0018cases hp_right_right
  19. 0019cases hp_right_right_right
  20. 0020cases hs
  21. 0021cases hs_witness
  22. 0022have hc : b=0 \/ ~(b=0)
  23. 0023specialize eq_decidable (b)
  24. 0024specialize eq_decidable (0)
  25. 0025apply eq_decidable
  26. 0026cases hc
  27. 0027rewrite hc_left at hb
  28. 0028rewrite hc_left at hb
  29. 0029rewrite hc_left
  30. 0030specialize signed_prefix_sum_zero_value (x)
  31. 0031specialize signed_prefix_sum_zero_value (L)
  32. 0032specialize signed_prefix_sum_zero_value (z)
  33. 0033apply signed_prefix_sum_zero_value
  34. 0034intro i
  35. 0035intro v
  36. 0036intro h0i
  37. 0037intro hi
  38. 0038intro hv
  39. 0039have hn : v=0 \/ ~(v=0)
  40. 0040specialize eq_decidable (v)
  41. 0041specialize eq_decidable (0)
  42. 0042apply eq_decidable
  43. 0043cases hn
  44. 0044exact hn_left
  45. 0045have hsource : ((exists dst_positive_code_column_zero_source dst_positive_scale_column_zero_source dst_negative_code_column_zero_source dst_negative_scale_column_zero_source dst_positive_column_zero_source dst_negative_column_zero_source. (((A) = (((((dst_positive_code_column_zero_source) + (dst_positive_scale_column_zero_source)) * S ((dst_positive_code_column_zero_source) + (dst_positive_scale_column_zero_source)) + ((dst_positive_scale_column_zero_source) + (dst_positive_scale_column_zero_source))) + (((dst_negative_code_column_zero_source) + (dst_negative_scale_column_zero_source)) * S ((dst_negative_code_column_zero_source) + (dst_negative_scale_column_zero_source)) + ((dst_negative_scale_column_zero_source) + (dst_negative_scale_column_zero_source)))) * S ((((dst_positive_code_column_zero_source) + (dst_positive_scale_column_zero_source)) * S ((dst_positive_code_column_zero_source) + (dst_positive_scale_column_zero_source)) + ((dst_positive_scale_column_zero_source) + (dst_positive_scale_column_zero_source))) + (((dst_negative_code_column_zero_source) + (dst_negative_scale_column_zero_source)) * S ((dst_negative_code_column_zero_source) + (dst_negative_scale_column_zero_source)) + ((dst_negative_scale_column_zero_source) + (dst_negative_scale_column_zero_source)))) + ((((dst_negative_code_column_zero_source) + (dst_negative_scale_column_zero_source)) * S ((dst_negative_code_column_zero_source) + (dst_negative_scale_column_zero_source)) + ((dst_negative_scale_column_zero_source) + (dst_negative_scale_column_zero_source))) + (((dst_negative_code_column_zero_source) + (dst_negative_scale_column_zero_source)) * S ((dst_negative_code_column_zero_source) + (dst_negative_scale_column_zero_source)) + ((dst_negative_scale_column_zero_source) + (dst_negative_scale_column_zero_source)))))) /\ (((((exists ff_h_pvs_column_zero_sourcepositive. ff_h_pvs_column_zero_sourcepositive + S (dst_positive_column_zero_source) = S ((S (i)) * dst_positive_scale_column_zero_source)) /\ exists ff_q_pvs_column_zero_sourcepositive. dst_positive_code_column_zero_source = ff_q_pvs_column_zero_sourcepositive * S ((S (i)) * dst_positive_scale_column_zero_source) + (dst_positive_column_zero_source))) /\ (((((exists ff_h_pvs_column_zero_sourcenegative. ff_h_pvs_column_zero_sourcenegative + S (dst_negative_column_zero_source) = S ((S (i)) * dst_negative_scale_column_zero_source)) /\ exists ff_q_pvs_column_zero_sourcenegative. dst_negative_code_column_zero_source = ff_q_pvs_column_zero_sourcenegative * S ((S (i)) * dst_negative_scale_column_zero_source) + (dst_negative_column_zero_source))) /\ (exists ge_balance_positive_column_zero_sourcevalue ge_balance_negative_column_zero_sourcevalue. (((((v) = 2 * (ge_balance_positive_column_zero_sourcevalue) /\ (ge_balance_negative_column_zero_sourcevalue) = 0) \/ exists ge_signed_half_column_zero_sourcevaluedecode. (((v) = 2 * ge_signed_half_column_zero_sourcevaluedecode + 1 /\ (ge_balance_positive_column_zero_sourcevalue) = 0) /\ (ge_balance_negative_column_zero_sourcevalue) = S ge_signed_half_column_zero_sourcevaluedecode))) /\ ((dst_positive_column_zero_source) + ge_balance_negative_column_zero_sourcevalue = (dst_negative_column_zero_source) + ge_balance_positive_column_zero_sourcevalue))))))))) /\ (((exists ff_h_pvs_column_zero_map. ff_h_pvs_column_zero_map + S (j) = S ((S (i)) * s)) /\ exists ff_q_pvs_column_zero_map. r = ff_q_pvs_column_zero_map * S ((S (i)) * s) + (j))))
  46. 0046specialize signed_support_incidence_nonzero_source_image (A)
  47. 0047specialize signed_support_incidence_nonzero_source_image (r)
  48. 0048specialize signed_support_incidence_nonzero_source_image (s)
  49. 0049specialize signed_support_incidence_nonzero_source_image (i)
  50. 0050specialize signed_support_incidence_nonzero_source_image (j)
  51. 0051specialize signed_support_incidence_nonzero_source_image (v)
  52. 0052apply signed_support_incidence_nonzero_source_image
  53. 0053specialize signed_support_incidence_column_lookup (A)
  54. 0054specialize signed_support_incidence_column_lookup (r)
  55. 0055specialize signed_support_incidence_column_lookup (s)
  56. 0056specialize signed_support_incidence_column_lookup (L)
  57. 0057specialize signed_support_incidence_column_lookup (M)
  58. 0058specialize signed_support_incidence_column_lookup (T)
  59. 0059specialize signed_support_incidence_column_lookup (x)
  60. 0060specialize signed_support_incidence_column_lookup (i)
  61. 0061specialize signed_support_incidence_column_lookup (j)
  62. 0062specialize signed_support_incidence_column_lookup (v)
  63. 0063apply signed_support_incidence_column_lookup
  64. 0064exact hg
  65. 0065exact hs_witness_left
  66. 0066exact hi
  67. 0067exact hj
  68. 0068exact hv
  69. 0069exact hn_right
  70. 0070cases hsource
  71. 0071have hm : exists k. (((((exists ff_h_pvs_column_zero_preserved_map. ff_h_pvs_column_zero_preserved_map + S (k) = S ((S (i)) * s)) /\ exists ff_q_pvs_column_zero_preserved_map. r = ff_q_pvs_column_zero_preserved_map * S ((S (i)) * s) + (k))) /\ (((exists pvs_gap_column_zero_preserved_bound. pvs_gap_column_zero_preserved_bound + S (k) = (M)) /\ (exists dst_positive_code_column_zero_preserved_value dst_positive_scale_column_zero_preserved_value dst_negative_code_column_zero_preserved_value dst_negative_scale_column_zero_preserved_value dst_positive_column_zero_preserved_value dst_negative_column_zero_preserved_value. (((B) = (((((dst_positive_code_column_zero_preserved_value) + (dst_positive_scale_column_zero_preserved_value)) * S ((dst_positive_code_column_zero_preserved_value) + (dst_positive_scale_column_zero_preserved_value)) + ((dst_positive_scale_column_zero_preserved_value) + (dst_positive_scale_column_zero_preserved_value))) + (((dst_negative_code_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)) * S ((dst_negative_code_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)) + ((dst_negative_scale_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)))) * S ((((dst_positive_code_column_zero_preserved_value) + (dst_positive_scale_column_zero_preserved_value)) * S ((dst_positive_code_column_zero_preserved_value) + (dst_positive_scale_column_zero_preserved_value)) + ((dst_positive_scale_column_zero_preserved_value) + (dst_positive_scale_column_zero_preserved_value))) + (((dst_negative_code_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)) * S ((dst_negative_code_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)) + ((dst_negative_scale_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)))) + ((((dst_negative_code_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)) * S ((dst_negative_code_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)) + ((dst_negative_scale_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value))) + (((dst_negative_code_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)) * S ((dst_negative_code_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)) + ((dst_negative_scale_column_zero_preserved_value) + (dst_negative_scale_column_zero_preserved_value)))))) /\ (((((exists ff_h_pvs_column_zero_preserved_valuepositive. ff_h_pvs_column_zero_preserved_valuepositive + S (dst_positive_column_zero_preserved_value) = S ((S (k)) * dst_positive_scale_column_zero_preserved_value)) /\ exists ff_q_pvs_column_zero_preserved_valuepositive. dst_positive_code_column_zero_preserved_value = ff_q_pvs_column_zero_preserved_valuepositive * S ((S (k)) * dst_positive_scale_column_zero_preserved_value) + (dst_positive_column_zero_preserved_value))) /\ (((((exists ff_h_pvs_column_zero_preserved_valuenegative. ff_h_pvs_column_zero_preserved_valuenegative + S (dst_negative_column_zero_preserved_value) = S ((S (k)) * dst_negative_scale_column_zero_preserved_value)) /\ exists ff_q_pvs_column_zero_preserved_valuenegative. dst_negative_code_column_zero_preserved_value = ff_q_pvs_column_zero_preserved_valuenegative * S ((S (k)) * dst_negative_scale_column_zero_preserved_value) + (dst_negative_column_zero_preserved_value))) /\ (exists ge_balance_positive_column_zero_preserved_valuevalue ge_balance_negative_column_zero_preserved_valuevalue. (((((v) = 2 * (ge_balance_positive_column_zero_preserved_valuevalue) /\ (ge_balance_negative_column_zero_preserved_valuevalue) = 0) \/ exists ge_signed_half_column_zero_preserved_valuevaluedecode. (((v) = 2 * ge_signed_half_column_zero_preserved_valuevaluedecode + 1 /\ (ge_balance_positive_column_zero_preserved_valuevalue) = 0) /\ (ge_balance_negative_column_zero_preserved_valuevalue) = S ge_signed_half_column_zero_preserved_valuevaluedecode))) /\ ((dst_positive_column_zero_preserved_value) + ge_balance_negative_column_zero_preserved_valuevalue = (dst_negative_column_zero_preserved_value) + ge_balance_positive_column_zero_preserved_valuevalue)))))))))))))
  72. 0072specialize hp_right_right_left (i)
  73. 0073specialize hp_right_right_left (v)
  74. 0074apply hp_right_right_left
  75. 0075exact hi
  76. 0076exact hsource_left
  77. 0077exact hn_right
  78. 0078cases hm
  79. 0079cases hm_witness
  80. 0080cases hm_witness_right
  81. 0081have he : x1=j
  82. 0082specialize beta_at_unique (r)
  83. 0083specialize beta_at_unique (s)
  84. 0084specialize beta_at_unique (i)
  85. 0085specialize beta_at_unique (x1)
  86. 0086specialize beta_at_unique (j)
  87. 0087apply beta_at_unique
  88. 0088exact hm_witness_left
  89. 0089exact hsource_right
  90. 0090rewrite he at hm_witness_right_right
  91. 0091rewrite he at hm_witness_right_right
  92. 0092rewrite he at hm_witness_right_right
  93. 0093rewrite he at hm_witness_right_right
  94. 0094specialize divisor_signed_table_at_functional (B)
  95. 0095specialize divisor_signed_table_at_functional (j)
  96. 0096specialize divisor_signed_table_at_functional (v)
  97. 0097specialize divisor_signed_table_at_functional (0)
  98. 0098apply divisor_signed_table_at_functional
  99. 0099exact hm_witness_right_right
  100. 0100exact hb
  101. 0101exact hs_witness_right
  102. 0102have hm : exists i. (((exists pvs_gap_column_active_bound. pvs_gap_column_active_bound + S (i) = (L)) /\ (((((exists ff_h_pvs_column_active_map. ff_h_pvs_column_active_map + S (j) = S ((S (i)) * s)) /\ exists ff_q_pvs_column_active_map. r = ff_q_pvs_column_active_map * S ((S (i)) * s) + (j))) /\ (exists dst_positive_code_column_active_source dst_positive_scale_column_active_source dst_negative_code_column_active_source dst_negative_scale_column_active_source dst_positive_column_active_source dst_negative_column_active_source. (((A) = (((((dst_positive_code_column_active_source) + (dst_positive_scale_column_active_source)) * S ((dst_positive_code_column_active_source) + (dst_positive_scale_column_active_source)) + ((dst_positive_scale_column_active_source) + (dst_positive_scale_column_active_source))) + (((dst_negative_code_column_active_source) + (dst_negative_scale_column_active_source)) * S ((dst_negative_code_column_active_source) + (dst_negative_scale_column_active_source)) + ((dst_negative_scale_column_active_source) + (dst_negative_scale_column_active_source)))) * S ((((dst_positive_code_column_active_source) + (dst_positive_scale_column_active_source)) * S ((dst_positive_code_column_active_source) + (dst_positive_scale_column_active_source)) + ((dst_positive_scale_column_active_source) + (dst_positive_scale_column_active_source))) + (((dst_negative_code_column_active_source) + (dst_negative_scale_column_active_source)) * S ((dst_negative_code_column_active_source) + (dst_negative_scale_column_active_source)) + ((dst_negative_scale_column_active_source) + (dst_negative_scale_column_active_source)))) + ((((dst_negative_code_column_active_source) + (dst_negative_scale_column_active_source)) * S ((dst_negative_code_column_active_source) + (dst_negative_scale_column_active_source)) + ((dst_negative_scale_column_active_source) + (dst_negative_scale_column_active_source))) + (((dst_negative_code_column_active_source) + (dst_negative_scale_column_active_source)) * S ((dst_negative_code_column_active_source) + (dst_negative_scale_column_active_source)) + ((dst_negative_scale_column_active_source) + (dst_negative_scale_column_active_source)))))) /\ (((((exists ff_h_pvs_column_active_sourcepositive. ff_h_pvs_column_active_sourcepositive + S (dst_positive_column_active_source) = S ((S (i)) * dst_positive_scale_column_active_source)) /\ exists ff_q_pvs_column_active_sourcepositive. dst_positive_code_column_active_source = ff_q_pvs_column_active_sourcepositive * S ((S (i)) * dst_positive_scale_column_active_source) + (dst_positive_column_active_source))) /\ (((((exists ff_h_pvs_column_active_sourcenegative. ff_h_pvs_column_active_sourcenegative + S (dst_negative_column_active_source) = S ((S (i)) * dst_negative_scale_column_active_source)) /\ exists ff_q_pvs_column_active_sourcenegative. dst_negative_code_column_active_source = ff_q_pvs_column_active_sourcenegative * S ((S (i)) * dst_negative_scale_column_active_source) + (dst_negative_column_active_source))) /\ (exists ge_balance_positive_column_active_sourcevalue ge_balance_negative_column_active_sourcevalue. (((((b) = 2 * (ge_balance_positive_column_active_sourcevalue) /\ (ge_balance_negative_column_active_sourcevalue) = 0) \/ exists ge_signed_half_column_active_sourcevaluedecode. (((b) = 2 * ge_signed_half_column_active_sourcevaluedecode + 1 /\ (ge_balance_positive_column_active_sourcevalue) = 0) /\ (ge_balance_negative_column_active_sourcevalue) = S ge_signed_half_column_active_sourcevaluedecode))) /\ ((dst_positive_column_active_source) + ge_balance_negative_column_active_sourcevalue = (dst_negative_column_active_source) + ge_balance_positive_column_active_sourcevalue)))))))))))))
  103. 0103specialize hp_right_right_right_right (j)
  104. 0104specialize hp_right_right_right_right (b)
  105. 0105apply hp_right_right_right_right
  106. 0106exact hj
  107. 0107exact hb
  108. 0108exact hc_right
  109. 0109cases hm
  110. 0110cases hm_witness
  111. 0111cases hm_witness_right
  112. 0112specialize signed_prefix_sum_point_spike_value (x)
  113. 0113specialize signed_prefix_sum_point_spike_value (L)
  114. 0114specialize signed_prefix_sum_point_spike_value (x1)
  115. 0115specialize signed_prefix_sum_point_spike_value (b)
  116. 0116specialize signed_prefix_sum_point_spike_value (z)
  117. 0117apply signed_prefix_sum_point_spike_value
  118. 0118cases hs_witness_left
  119. 0119cases hs_witness_left_right
  120. 0120specialize signed_table_domain_resize (L)
  121. 0121specialize signed_table_domain_resize (0)
  122. 0122specialize signed_table_domain_resize (x)
  123. 0123apply signed_table_domain_resize
  124. 0124exact hs_witness_left_right_left
  125. 0125exact hm_witness_left
  126. 0126have hv : exists v. (exists dst_positive_code_column_spike_actual_lookup dst_positive_scale_column_spike_actual_lookup dst_negative_code_column_spike_actual_lookup dst_negative_scale_column_spike_actual_lookup dst_positive_column_spike_actual_lookup dst_negative_column_spike_actual_lookup. (((x) = (((((dst_positive_code_column_spike_actual_lookup) + (dst_positive_scale_column_spike_actual_lookup)) * S ((dst_positive_code_column_spike_actual_lookup) + (dst_positive_scale_column_spike_actual_lookup)) + ((dst_positive_scale_column_spike_actual_lookup) + (dst_positive_scale_column_spike_actual_lookup))) + (((dst_negative_code_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)) * S ((dst_negative_code_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)) + ((dst_negative_scale_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)))) * S ((((dst_positive_code_column_spike_actual_lookup) + (dst_positive_scale_column_spike_actual_lookup)) * S ((dst_positive_code_column_spike_actual_lookup) + (dst_positive_scale_column_spike_actual_lookup)) + ((dst_positive_scale_column_spike_actual_lookup) + (dst_positive_scale_column_spike_actual_lookup))) + (((dst_negative_code_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)) * S ((dst_negative_code_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)) + ((dst_negative_scale_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)))) + ((((dst_negative_code_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)) * S ((dst_negative_code_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)) + ((dst_negative_scale_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup))) + (((dst_negative_code_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)) * S ((dst_negative_code_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)) + ((dst_negative_scale_column_spike_actual_lookup) + (dst_negative_scale_column_spike_actual_lookup)))))) /\ (((((exists ff_h_pvs_column_spike_actual_lookuppositive. ff_h_pvs_column_spike_actual_lookuppositive + S (dst_positive_column_spike_actual_lookup) = S ((S (x1)) * dst_positive_scale_column_spike_actual_lookup)) /\ exists ff_q_pvs_column_spike_actual_lookuppositive. dst_positive_code_column_spike_actual_lookup = ff_q_pvs_column_spike_actual_lookuppositive * S ((S (x1)) * dst_positive_scale_column_spike_actual_lookup) + (dst_positive_column_spike_actual_lookup))) /\ (((((exists ff_h_pvs_column_spike_actual_lookupnegative. ff_h_pvs_column_spike_actual_lookupnegative + S (dst_negative_column_spike_actual_lookup) = S ((S (x1)) * dst_negative_scale_column_spike_actual_lookup)) /\ exists ff_q_pvs_column_spike_actual_lookupnegative. dst_negative_code_column_spike_actual_lookup = ff_q_pvs_column_spike_actual_lookupnegative * S ((S (x1)) * dst_negative_scale_column_spike_actual_lookup) + (dst_negative_column_spike_actual_lookup))) /\ (exists ge_balance_positive_column_spike_actual_lookupvalue ge_balance_negative_column_spike_actual_lookupvalue. (((((v) = 2 * (ge_balance_positive_column_spike_actual_lookupvalue) /\ (ge_balance_negative_column_spike_actual_lookupvalue) = 0) \/ exists ge_signed_half_column_spike_actual_lookupvaluedecode. (((v) = 2 * ge_signed_half_column_spike_actual_lookupvaluedecode + 1 /\ (ge_balance_positive_column_spike_actual_lookupvalue) = 0) /\ (ge_balance_negative_column_spike_actual_lookupvalue) = S ge_signed_half_column_spike_actual_lookupvaluedecode))) /\ ((dst_positive_column_spike_actual_lookup) + ge_balance_negative_column_spike_actual_lookupvalue = (dst_negative_column_spike_actual_lookup) + ge_balance_positive_column_spike_actual_lookupvalue)))))))))
  127. 0127specialize signed_table_lookup_any (L)
  128. 0128specialize signed_table_lookup_any (x)
  129. 0129specialize signed_table_lookup_any (x1)
  130. 0130apply signed_table_lookup_any
  131. 0131cases hs_witness_left
  132. 0132cases hs_witness_left_right
  133. 0133exact hs_witness_left_right_left
  134. 0134cases hv
  135. 0135have he : x2=b
  136. 0136specialize signed_support_incidence_entry_functional (A)
  137. 0137specialize signed_support_incidence_entry_functional (r)
  138. 0138specialize signed_support_incidence_entry_functional (s)
  139. 0139specialize signed_support_incidence_entry_functional (x1)
  140. 0140specialize signed_support_incidence_entry_functional (j)
  141. 0141specialize signed_support_incidence_entry_functional (x2)
  142. 0142specialize signed_support_incidence_entry_functional (b)
  143. 0143apply signed_support_incidence_entry_functional
  144. 0144specialize signed_support_incidence_column_lookup (A)
  145. 0145specialize signed_support_incidence_column_lookup (r)
  146. 0146specialize signed_support_incidence_column_lookup (s)
  147. 0147specialize signed_support_incidence_column_lookup (L)
  148. 0148specialize signed_support_incidence_column_lookup (M)
  149. 0149specialize signed_support_incidence_column_lookup (T)
  150. 0150specialize signed_support_incidence_column_lookup (x)
  151. 0151specialize signed_support_incidence_column_lookup (x1)
  152. 0152specialize signed_support_incidence_column_lookup (j)
  153. 0153specialize signed_support_incidence_column_lookup (x2)
  154. 0154apply signed_support_incidence_column_lookup
  155. 0155exact hg
  156. 0156exact hs_witness_left
  157. 0157exact hm_witness_left
  158. 0158exact hj
  159. 0159exact hv_witness
  160. 0160specialize signed_support_incidence_entry_hit (A)
  161. 0161specialize signed_support_incidence_entry_hit (r)
  162. 0162specialize signed_support_incidence_entry_hit (s)
  163. 0163specialize signed_support_incidence_entry_hit (x1)
  164. 0164specialize signed_support_incidence_entry_hit (j)
  165. 0165specialize signed_support_incidence_entry_hit (b)
  166. 0166apply signed_support_incidence_entry_hit
  167. 0167exact hm_witness_right_right
  168. 0168exact hm_witness_right_left
  169. 0169rewrite he at hv_witness
  170. 0170rewrite he at hv_witness
  171. 0171exact hv_witness
  172. 0172intro i
  173. 0173intro v
  174. 0174intro hi
  175. 0175intro hne
  176. 0176intro hv
  177. 0177have hn : v=0 \/ ~(v=0)
  178. 0178specialize eq_decidable (v)
  179. 0179specialize eq_decidable (0)
  180. 0180apply eq_decidable
  181. 0181cases hn
  182. 0182exact hn_left
  183. 0183exfalso
  184. 0184apply hne
  185. 0185have hsource : ((exists dst_positive_code_column_other_source dst_positive_scale_column_other_source dst_negative_code_column_other_source dst_negative_scale_column_other_source dst_positive_column_other_source dst_negative_column_other_source. (((A) = (((((dst_positive_code_column_other_source) + (dst_positive_scale_column_other_source)) * S ((dst_positive_code_column_other_source) + (dst_positive_scale_column_other_source)) + ((dst_positive_scale_column_other_source) + (dst_positive_scale_column_other_source))) + (((dst_negative_code_column_other_source) + (dst_negative_scale_column_other_source)) * S ((dst_negative_code_column_other_source) + (dst_negative_scale_column_other_source)) + ((dst_negative_scale_column_other_source) + (dst_negative_scale_column_other_source)))) * S ((((dst_positive_code_column_other_source) + (dst_positive_scale_column_other_source)) * S ((dst_positive_code_column_other_source) + (dst_positive_scale_column_other_source)) + ((dst_positive_scale_column_other_source) + (dst_positive_scale_column_other_source))) + (((dst_negative_code_column_other_source) + (dst_negative_scale_column_other_source)) * S ((dst_negative_code_column_other_source) + (dst_negative_scale_column_other_source)) + ((dst_negative_scale_column_other_source) + (dst_negative_scale_column_other_source)))) + ((((dst_negative_code_column_other_source) + (dst_negative_scale_column_other_source)) * S ((dst_negative_code_column_other_source) + (dst_negative_scale_column_other_source)) + ((dst_negative_scale_column_other_source) + (dst_negative_scale_column_other_source))) + (((dst_negative_code_column_other_source) + (dst_negative_scale_column_other_source)) * S ((dst_negative_code_column_other_source) + (dst_negative_scale_column_other_source)) + ((dst_negative_scale_column_other_source) + (dst_negative_scale_column_other_source)))))) /\ (((((exists ff_h_pvs_column_other_sourcepositive. ff_h_pvs_column_other_sourcepositive + S (dst_positive_column_other_source) = S ((S (i)) * dst_positive_scale_column_other_source)) /\ exists ff_q_pvs_column_other_sourcepositive. dst_positive_code_column_other_source = ff_q_pvs_column_other_sourcepositive * S ((S (i)) * dst_positive_scale_column_other_source) + (dst_positive_column_other_source))) /\ (((((exists ff_h_pvs_column_other_sourcenegative. ff_h_pvs_column_other_sourcenegative + S (dst_negative_column_other_source) = S ((S (i)) * dst_negative_scale_column_other_source)) /\ exists ff_q_pvs_column_other_sourcenegative. dst_negative_code_column_other_source = ff_q_pvs_column_other_sourcenegative * S ((S (i)) * dst_negative_scale_column_other_source) + (dst_negative_column_other_source))) /\ (exists ge_balance_positive_column_other_sourcevalue ge_balance_negative_column_other_sourcevalue. (((((v) = 2 * (ge_balance_positive_column_other_sourcevalue) /\ (ge_balance_negative_column_other_sourcevalue) = 0) \/ exists ge_signed_half_column_other_sourcevaluedecode. (((v) = 2 * ge_signed_half_column_other_sourcevaluedecode + 1 /\ (ge_balance_positive_column_other_sourcevalue) = 0) /\ (ge_balance_negative_column_other_sourcevalue) = S ge_signed_half_column_other_sourcevaluedecode))) /\ ((dst_positive_column_other_source) + ge_balance_negative_column_other_sourcevalue = (dst_negative_column_other_source) + ge_balance_positive_column_other_sourcevalue))))))))) /\ (((exists ff_h_pvs_column_other_map. ff_h_pvs_column_other_map + S (j) = S ((S (i)) * s)) /\ exists ff_q_pvs_column_other_map. r = ff_q_pvs_column_other_map * S ((S (i)) * s) + (j))))
  186. 0186specialize signed_support_incidence_nonzero_source_image (A)
  187. 0187specialize signed_support_incidence_nonzero_source_image (r)
  188. 0188specialize signed_support_incidence_nonzero_source_image (s)
  189. 0189specialize signed_support_incidence_nonzero_source_image (i)
  190. 0190specialize signed_support_incidence_nonzero_source_image (j)
  191. 0191specialize signed_support_incidence_nonzero_source_image (v)
  192. 0192apply signed_support_incidence_nonzero_source_image
  193. 0193specialize signed_support_incidence_column_lookup (A)
  194. 0194specialize signed_support_incidence_column_lookup (r)
  195. 0195specialize signed_support_incidence_column_lookup (s)
  196. 0196specialize signed_support_incidence_column_lookup (L)
  197. 0197specialize signed_support_incidence_column_lookup (M)
  198. 0198specialize signed_support_incidence_column_lookup (T)
  199. 0199specialize signed_support_incidence_column_lookup (x)
  200. 0200specialize signed_support_incidence_column_lookup (i)
  201. 0201specialize signed_support_incidence_column_lookup (j)
  202. 0202specialize signed_support_incidence_column_lookup (v)
  203. 0203apply signed_support_incidence_column_lookup
  204. 0204exact hg
  205. 0205exact hs_witness_left
  206. 0206exact hi
  207. 0207exact hj
  208. 0208exact hv
  209. 0209exact hn_right
  210. 0210cases hsource
  211. 0211specialize hp_right_right_right_left (i)
  212. 0212specialize hp_right_right_right_left (x1)
  213. 0213specialize hp_right_right_right_left (j)
  214. 0214specialize hp_right_right_right_left (v)
  215. 0215specialize hp_right_right_right_left (b)
  216. 0216apply hp_right_right_right_left
  217. 0217exact hi
  218. 0218exact hm_witness_left
  219. 0219exact hsource_left
  220. 0220exact hn_right
  221. 0221exact hm_witness_right_right
  222. 0222exact hc_right
  223. 0223exact hsource_right
  224. 0224exact hm_witness_right_left
  225. 0225exact hs_witness_right