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=bConstructive 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_hitDirect 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
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)
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–15
03Separate the logical casesL16–21
04Establish hcL22–25
05Separate the logical casesL26–26
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L26
cases hc
06Calculate and transport equalitiesL27–29
07Use earlier factsL30–33
08Fix variables and assumptionsL34–38
09Establish hnL39–42
10Separate the logical casesL43–43
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L43
cases hn
11Use earlier factsL44–44
Instantiate or apply named facts and discharge the corresponding proof obligations.
- 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.
- L45
- L46
specialize signed_support_incidence_nonzero_source_image (A) - L47
specialize signed_support_incidence_nonzero_source_image (r) - L48
specialize signed_support_incidence_nonzero_source_image (s) - L49
specialize signed_support_incidence_nonzero_source_image (i) - L50
specialize signed_support_incidence_nonzero_source_image (j) - L51
specialize signed_support_incidence_nonzero_source_image (v) - L52
apply signed_support_incidence_nonzero_source_image - L53
specialize signed_support_incidence_column_lookup (A) - L54
specialize signed_support_incidence_column_lookup (r)
13Use earlier factsL55–64
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L55
specialize signed_support_incidence_column_lookup (s) - L56
specialize signed_support_incidence_column_lookup (L) - L57
specialize signed_support_incidence_column_lookup (M) - L58
specialize signed_support_incidence_column_lookup (T) - L59
specialize signed_support_incidence_column_lookup (x) - L60
specialize signed_support_incidence_column_lookup (i) - L61
specialize signed_support_incidence_column_lookup (j) - L62
specialize signed_support_incidence_column_lookup (v) - L63
apply signed_support_incidence_column_lookup - L64
exact hg
14Use earlier factsL65–69
15Separate the logical casesL70–70
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- 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.
17Separate the logical casesL78–80
18Establish heL81–90
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply beta at unique.
19Calculate and transport equalitiesL91–93
20Use earlier factsL94–101
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L94
specialize divisor_signed_table_at_functional (B) - L95
specialize divisor_signed_table_at_functional (j) - L96
specialize divisor_signed_table_at_functional (v) - L97
specialize divisor_signed_table_at_functional (0) - L98
apply divisor_signed_table_at_functional - L99
exact hm_witness_right_right - L100
exact hb - 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.
22Separate the logical casesL109–111
23Use earlier factsL112–117
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L112
specialize signed_prefix_sum_point_spike_value (x) - L113
specialize signed_prefix_sum_point_spike_value (L) - L114
specialize signed_prefix_sum_point_spike_value (x1) - L115
specialize signed_prefix_sum_point_spike_value (b) - L116
specialize signed_prefix_sum_point_spike_value (z) - L117
apply signed_prefix_sum_point_spike_value
24Separate the logical casesL118–119
25Use earlier factsL120–125
Instantiate or apply named facts and discharge the corresponding proof obligations.
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.
27Separate the logical casesL131–132
28Use earlier factsL133–133
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L133
exact hs_witness_left_right_left
29Separate the logical casesL134–134
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- 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.
- L135
have he : x2=b - L136
specialize signed_support_incidence_entry_functional (A) - L137
specialize signed_support_incidence_entry_functional (r) - L138
specialize signed_support_incidence_entry_functional (s) - L139
specialize signed_support_incidence_entry_functional (x1) - L140
specialize signed_support_incidence_entry_functional (j) - L141
specialize signed_support_incidence_entry_functional (x2) - L142
specialize signed_support_incidence_entry_functional (b) - L143
apply signed_support_incidence_entry_functional - L144
specialize signed_support_incidence_column_lookup (A)
31Use earlier factsL145–154
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L145
specialize signed_support_incidence_column_lookup (r) - L146
specialize signed_support_incidence_column_lookup (s) - L147
specialize signed_support_incidence_column_lookup (L) - L148
specialize signed_support_incidence_column_lookup (M) - L149
specialize signed_support_incidence_column_lookup (T) - L150
specialize signed_support_incidence_column_lookup (x) - L151
specialize signed_support_incidence_column_lookup (x1) - L152
specialize signed_support_incidence_column_lookup (j) - L153
specialize signed_support_incidence_column_lookup (x2) - L154
apply signed_support_incidence_column_lookup
32Use earlier factsL155–164
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L155
exact hg - L156
exact hs_witness_left - L157
exact hm_witness_left - L158
exact hj - L159
exact hv_witness - L160
specialize signed_support_incidence_entry_hit (A) - L161
specialize signed_support_incidence_entry_hit (r) - L162
specialize signed_support_incidence_entry_hit (s) - L163
specialize signed_support_incidence_entry_hit (x1) - L164
specialize signed_support_incidence_entry_hit (j)
33Use earlier factsL165–168
34Calculate and transport equalitiesL169–170
35Use earlier factsL171–171
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L171
exact hv_witness
36Fix variables and assumptionsL172–176
37Establish hnL177–180
38Separate the logical casesL181–181
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L181
cases hn
39Use earlier factsL182–182
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L182
exact hn_left
40Separate the logical casesL183–183
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L183
exfalso
41Use earlier factsL184–184
Instantiate or apply named facts and discharge the corresponding proof obligations.
- 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.
- L185
- L186
specialize signed_support_incidence_nonzero_source_image (A) - L187
specialize signed_support_incidence_nonzero_source_image (r) - L188
specialize signed_support_incidence_nonzero_source_image (s) - L189
specialize signed_support_incidence_nonzero_source_image (i) - L190
specialize signed_support_incidence_nonzero_source_image (j) - L191
specialize signed_support_incidence_nonzero_source_image (v) - L192
apply signed_support_incidence_nonzero_source_image - L193
specialize signed_support_incidence_column_lookup (A) - L194
specialize signed_support_incidence_column_lookup (r)
43Use earlier factsL195–204
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L195
specialize signed_support_incidence_column_lookup (s) - L196
specialize signed_support_incidence_column_lookup (L) - L197
specialize signed_support_incidence_column_lookup (M) - L198
specialize signed_support_incidence_column_lookup (T) - L199
specialize signed_support_incidence_column_lookup (x) - L200
specialize signed_support_incidence_column_lookup (i) - L201
specialize signed_support_incidence_column_lookup (j) - L202
specialize signed_support_incidence_column_lookup (v) - L203
apply signed_support_incidence_column_lookup - L204
exact hg
44Use earlier factsL205–209
45Separate the logical casesL210–210
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L210
cases hsource
46Use earlier factsL211–220
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L211
specialize hp_right_right_right_left (i) - L212
specialize hp_right_right_right_left (x1) - L213
specialize hp_right_right_right_left (j) - L214
specialize hp_right_right_right_left (v) - L215
specialize hp_right_right_right_left (b) - L216
apply hp_right_right_right_left - L217
exact hi - L218
exact hm_witness_left - L219
exact hsource_left - L220
exact hn_right
Original exact command ledger · 225 lines
- 0001
intro A - 0002
intro B - 0003
intro r - 0004
intro s - 0005
intro L - 0006
intro M - 0007
intro T - 0008
intro j - 0009
intro b - 0010
intro z - 0011
intro hp - 0012
intro hg - 0013
intro hj - 0014
intro hb - 0015
intro hs - 0016
cases hp - 0017
cases hp_right - 0018
cases hp_right_right - 0019
cases hp_right_right_right - 0020
cases hs - 0021
cases hs_witness - 0022
have hc : b=0 \/ ~(b=0) - 0023
specialize eq_decidable (b) - 0024
specialize eq_decidable (0) - 0025
apply eq_decidable - 0026
cases hc - 0027
rewrite hc_left at hb - 0028
rewrite hc_left at hb - 0029
rewrite hc_left - 0030
specialize signed_prefix_sum_zero_value (x) - 0031
specialize signed_prefix_sum_zero_value (L) - 0032
specialize signed_prefix_sum_zero_value (z) - 0033
apply signed_prefix_sum_zero_value - 0034
intro i - 0035
intro v - 0036
intro h0i - 0037
intro hi - 0038
intro hv - 0039
have hn : v=0 \/ ~(v=0) - 0040
specialize eq_decidable (v) - 0041
specialize eq_decidable (0) - 0042
apply eq_decidable - 0043
cases hn - 0044
exact hn_left - 0045
have 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)))) - 0046
specialize signed_support_incidence_nonzero_source_image (A) - 0047
specialize signed_support_incidence_nonzero_source_image (r) - 0048
specialize signed_support_incidence_nonzero_source_image (s) - 0049
specialize signed_support_incidence_nonzero_source_image (i) - 0050
specialize signed_support_incidence_nonzero_source_image (j) - 0051
specialize signed_support_incidence_nonzero_source_image (v) - 0052
apply signed_support_incidence_nonzero_source_image - 0053
specialize signed_support_incidence_column_lookup (A) - 0054
specialize signed_support_incidence_column_lookup (r) - 0055
specialize signed_support_incidence_column_lookup (s) - 0056
specialize signed_support_incidence_column_lookup (L) - 0057
specialize signed_support_incidence_column_lookup (M) - 0058
specialize signed_support_incidence_column_lookup (T) - 0059
specialize signed_support_incidence_column_lookup (x) - 0060
specialize signed_support_incidence_column_lookup (i) - 0061
specialize signed_support_incidence_column_lookup (j) - 0062
specialize signed_support_incidence_column_lookup (v) - 0063
apply signed_support_incidence_column_lookup - 0064
exact hg - 0065
exact hs_witness_left - 0066
exact hi - 0067
exact hj - 0068
exact hv - 0069
exact hn_right - 0070
cases hsource - 0071
have 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))))))))))))) - 0072
specialize hp_right_right_left (i) - 0073
specialize hp_right_right_left (v) - 0074
apply hp_right_right_left - 0075
exact hi - 0076
exact hsource_left - 0077
exact hn_right - 0078
cases hm - 0079
cases hm_witness - 0080
cases hm_witness_right - 0081
have he : x1=j - 0082
specialize beta_at_unique (r) - 0083
specialize beta_at_unique (s) - 0084
specialize beta_at_unique (i) - 0085
specialize beta_at_unique (x1) - 0086
specialize beta_at_unique (j) - 0087
apply beta_at_unique - 0088
exact hm_witness_left - 0089
exact hsource_right - 0090
rewrite he at hm_witness_right_right - 0091
rewrite he at hm_witness_right_right - 0092
rewrite he at hm_witness_right_right - 0093
rewrite he at hm_witness_right_right - 0094
specialize divisor_signed_table_at_functional (B) - 0095
specialize divisor_signed_table_at_functional (j) - 0096
specialize divisor_signed_table_at_functional (v) - 0097
specialize divisor_signed_table_at_functional (0) - 0098
apply divisor_signed_table_at_functional - 0099
exact hm_witness_right_right - 0100
exact hb - 0101
exact hs_witness_right - 0102
have 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))))))))))))) - 0103
specialize hp_right_right_right_right (j) - 0104
specialize hp_right_right_right_right (b) - 0105
apply hp_right_right_right_right - 0106
exact hj - 0107
exact hb - 0108
exact hc_right - 0109
cases hm - 0110
cases hm_witness - 0111
cases hm_witness_right - 0112
specialize signed_prefix_sum_point_spike_value (x) - 0113
specialize signed_prefix_sum_point_spike_value (L) - 0114
specialize signed_prefix_sum_point_spike_value (x1) - 0115
specialize signed_prefix_sum_point_spike_value (b) - 0116
specialize signed_prefix_sum_point_spike_value (z) - 0117
apply signed_prefix_sum_point_spike_value - 0118
cases hs_witness_left - 0119
cases hs_witness_left_right - 0120
specialize signed_table_domain_resize (L) - 0121
specialize signed_table_domain_resize (0) - 0122
specialize signed_table_domain_resize (x) - 0123
apply signed_table_domain_resize - 0124
exact hs_witness_left_right_left - 0125
exact hm_witness_left - 0126
have 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))))))))) - 0127
specialize signed_table_lookup_any (L) - 0128
specialize signed_table_lookup_any (x) - 0129
specialize signed_table_lookup_any (x1) - 0130
apply signed_table_lookup_any - 0131
cases hs_witness_left - 0132
cases hs_witness_left_right - 0133
exact hs_witness_left_right_left - 0134
cases hv - 0135
have he : x2=b - 0136
specialize signed_support_incidence_entry_functional (A) - 0137
specialize signed_support_incidence_entry_functional (r) - 0138
specialize signed_support_incidence_entry_functional (s) - 0139
specialize signed_support_incidence_entry_functional (x1) - 0140
specialize signed_support_incidence_entry_functional (j) - 0141
specialize signed_support_incidence_entry_functional (x2) - 0142
specialize signed_support_incidence_entry_functional (b) - 0143
apply signed_support_incidence_entry_functional - 0144
specialize signed_support_incidence_column_lookup (A) - 0145
specialize signed_support_incidence_column_lookup (r) - 0146
specialize signed_support_incidence_column_lookup (s) - 0147
specialize signed_support_incidence_column_lookup (L) - 0148
specialize signed_support_incidence_column_lookup (M) - 0149
specialize signed_support_incidence_column_lookup (T) - 0150
specialize signed_support_incidence_column_lookup (x) - 0151
specialize signed_support_incidence_column_lookup (x1) - 0152
specialize signed_support_incidence_column_lookup (j) - 0153
specialize signed_support_incidence_column_lookup (x2) - 0154
apply signed_support_incidence_column_lookup - 0155
exact hg - 0156
exact hs_witness_left - 0157
exact hm_witness_left - 0158
exact hj - 0159
exact hv_witness - 0160
specialize signed_support_incidence_entry_hit (A) - 0161
specialize signed_support_incidence_entry_hit (r) - 0162
specialize signed_support_incidence_entry_hit (s) - 0163
specialize signed_support_incidence_entry_hit (x1) - 0164
specialize signed_support_incidence_entry_hit (j) - 0165
specialize signed_support_incidence_entry_hit (b) - 0166
apply signed_support_incidence_entry_hit - 0167
exact hm_witness_right_right - 0168
exact hm_witness_right_left - 0169
rewrite he at hv_witness - 0170
rewrite he at hv_witness - 0171
exact hv_witness - 0172
intro i - 0173
intro v - 0174
intro hi - 0175
intro hne - 0176
intro hv - 0177
have hn : v=0 \/ ~(v=0) - 0178
specialize eq_decidable (v) - 0179
specialize eq_decidable (0) - 0180
apply eq_decidable - 0181
cases hn - 0182
exact hn_left - 0183
exfalso - 0184
apply hne - 0185
have 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)))) - 0186
specialize signed_support_incidence_nonzero_source_image (A) - 0187
specialize signed_support_incidence_nonzero_source_image (r) - 0188
specialize signed_support_incidence_nonzero_source_image (s) - 0189
specialize signed_support_incidence_nonzero_source_image (i) - 0190
specialize signed_support_incidence_nonzero_source_image (j) - 0191
specialize signed_support_incidence_nonzero_source_image (v) - 0192
apply signed_support_incidence_nonzero_source_image - 0193
specialize signed_support_incidence_column_lookup (A) - 0194
specialize signed_support_incidence_column_lookup (r) - 0195
specialize signed_support_incidence_column_lookup (s) - 0196
specialize signed_support_incidence_column_lookup (L) - 0197
specialize signed_support_incidence_column_lookup (M) - 0198
specialize signed_support_incidence_column_lookup (T) - 0199
specialize signed_support_incidence_column_lookup (x) - 0200
specialize signed_support_incidence_column_lookup (i) - 0201
specialize signed_support_incidence_column_lookup (j) - 0202
specialize signed_support_incidence_column_lookup (v) - 0203
apply signed_support_incidence_column_lookup - 0204
exact hg - 0205
exact hs_witness_left - 0206
exact hi - 0207
exact hj - 0208
exact hv - 0209
exact hn_right - 0210
cases hsource - 0211
specialize hp_right_right_right_left (i) - 0212
specialize hp_right_right_right_left (x1) - 0213
specialize hp_right_right_right_left (j) - 0214
specialize hp_right_right_right_left (v) - 0215
specialize hp_right_right_right_left (b) - 0216
apply hp_right_right_right_left - 0217
exact hi - 0218
exact hm_witness_left - 0219
exact hsource_left - 0220
exact hn_right - 0221
exact hm_witness_right_right - 0222
exact hc_right - 0223
exact hsource_right - 0224
exact hm_witness_right_left - 0225
exact hs_witness_right