MX0046

signed_support_incidence_row_sum_value

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

Each actual incidence row is zero or one genuinely bounded spike, so its actual sum is the actual source value.

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 i a z. (((exists dst_positive_code_row_value_supportsource_table dst_positive_scale_row_value_supportsource_table dst_negative_code_row_value_supportsource_table dst_negative_scale_row_value_supportsource_table. (((A) = (((((dst_positive_code_row_value_supportsource_table) + (dst_positive_scale_row_value_supportsource_table)) * S ((dst_positive_code_row_value_supportsource_table) + (dst_positive_scale_row_value_supportsource_table)) + ((dst_positive_scale_row_value_supportsource_table) + (dst_positive_scale_row_value_supportsource_table))) + (((dst_negative_code_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)) * S ((dst_negative_code_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)) + ((dst_negative_scale_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)))) * S ((((dst_positive_code_row_value_supportsource_table) + (dst_positive_scale_row_value_supportsource_table)) * S ((dst_positive_code_row_value_supportsource_table) + (dst_positive_scale_row_value_supportsource_table)) + ((dst_positive_scale_row_value_supportsource_table) + (dst_positive_scale_row_value_supportsource_table))) + (((dst_negative_code_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)) * S ((dst_negative_code_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)) + ((dst_negative_scale_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)))) + ((((dst_negative_code_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)) * S ((dst_negative_code_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)) + ((dst_negative_scale_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table))) + (((dst_negative_code_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)) * S ((dst_negative_code_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)) + ((dst_negative_scale_row_value_supportsource_table) + (dst_negative_scale_row_value_supportsource_table)))))) /\ (forall dst_index_row_value_supportsource_table. (exists pvs_le_gap_row_value_supportsource_tabledomain. pvs_le_gap_row_value_supportsource_tabledomain + (dst_index_row_value_supportsource_table) = (0)) -> exists dst_positive_row_value_supportsource_table dst_negative_row_value_supportsource_table dst_value_row_value_supportsource_table. ((((exists ff_h_pvs_row_value_supportsource_tableentrypositive. ff_h_pvs_row_value_supportsource_tableentrypositive + S (dst_positive_row_value_supportsource_table) = S ((S (dst_index_row_value_supportsource_table)) * dst_positive_scale_row_value_supportsource_table)) /\ exists ff_q_pvs_row_value_supportsource_tableentrypositive. dst_positive_code_row_value_supportsource_table = ff_q_pvs_row_value_supportsource_tableentrypositive * S ((S (dst_index_row_value_supportsource_table)) * dst_positive_scale_row_value_supportsource_table) + (dst_positive_row_value_supportsource_table))) /\ (((((exists ff_h_pvs_row_value_supportsource_tableentrynegative. ff_h_pvs_row_value_supportsource_tableentrynegative + S (dst_negative_row_value_supportsource_table) = S ((S (dst_index_row_value_supportsource_table)) * dst_negative_scale_row_value_supportsource_table)) /\ exists ff_q_pvs_row_value_supportsource_tableentrynegative. dst_negative_code_row_value_supportsource_table = ff_q_pvs_row_value_supportsource_tableentrynegative * S ((S (dst_index_row_value_supportsource_table)) * dst_negative_scale_row_value_supportsource_table) + (dst_negative_row_value_supportsource_table))) /\ (exists ge_balance_positive_row_value_supportsource_tableentryvalue ge_balance_negative_row_value_supportsource_tableentryvalue. (((((dst_value_row_value_supportsource_table) = 2 * (ge_balance_positive_row_value_supportsource_tableentryvalue) /\ (ge_balance_negative_row_value_supportsource_tableentryvalue) = 0) \/ exists ge_signed_half_row_value_supportsource_tableentryvaluedecode. (((dst_value_row_value_supportsource_table) = 2 * ge_signed_half_row_value_supportsource_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_value_supportsource_tableentryvalue) = 0) /\ (ge_balance_negative_row_value_supportsource_tableentryvalue) = S ge_signed_half_row_value_supportsource_tableentryvaluedecode))) /\ ((dst_positive_row_value_supportsource_table) + ge_balance_negative_row_value_supportsource_tableentryvalue = (dst_negative_row_value_supportsource_table) + ge_balance_positive_row_value_supportsource_tableentryvalue))))))))) /\ (((exists dst_positive_code_row_value_supporttarget_table dst_positive_scale_row_value_supporttarget_table dst_negative_code_row_value_supporttarget_table dst_negative_scale_row_value_supporttarget_table. (((B) = (((((dst_positive_code_row_value_supporttarget_table) + (dst_positive_scale_row_value_supporttarget_table)) * S ((dst_positive_code_row_value_supporttarget_table) + (dst_positive_scale_row_value_supporttarget_table)) + ((dst_positive_scale_row_value_supporttarget_table) + (dst_positive_scale_row_value_supporttarget_table))) + (((dst_negative_code_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)) * S ((dst_negative_code_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)) + ((dst_negative_scale_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)))) * S ((((dst_positive_code_row_value_supporttarget_table) + (dst_positive_scale_row_value_supporttarget_table)) * S ((dst_positive_code_row_value_supporttarget_table) + (dst_positive_scale_row_value_supporttarget_table)) + ((dst_positive_scale_row_value_supporttarget_table) + (dst_positive_scale_row_value_supporttarget_table))) + (((dst_negative_code_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)) * S ((dst_negative_code_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)) + ((dst_negative_scale_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)))) + ((((dst_negative_code_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)) * S ((dst_negative_code_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)) + ((dst_negative_scale_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table))) + (((dst_negative_code_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)) * S ((dst_negative_code_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)) + ((dst_negative_scale_row_value_supporttarget_table) + (dst_negative_scale_row_value_supporttarget_table)))))) /\ (forall dst_index_row_value_supporttarget_table. (exists pvs_le_gap_row_value_supporttarget_tabledomain. pvs_le_gap_row_value_supporttarget_tabledomain + (dst_index_row_value_supporttarget_table) = (0)) -> exists dst_positive_row_value_supporttarget_table dst_negative_row_value_supporttarget_table dst_value_row_value_supporttarget_table. ((((exists ff_h_pvs_row_value_supporttarget_tableentrypositive. ff_h_pvs_row_value_supporttarget_tableentrypositive + S (dst_positive_row_value_supporttarget_table) = S ((S (dst_index_row_value_supporttarget_table)) * dst_positive_scale_row_value_supporttarget_table)) /\ exists ff_q_pvs_row_value_supporttarget_tableentrypositive. dst_positive_code_row_value_supporttarget_table = ff_q_pvs_row_value_supporttarget_tableentrypositive * S ((S (dst_index_row_value_supporttarget_table)) * dst_positive_scale_row_value_supporttarget_table) + (dst_positive_row_value_supporttarget_table))) /\ (((((exists ff_h_pvs_row_value_supporttarget_tableentrynegative. ff_h_pvs_row_value_supporttarget_tableentrynegative + S (dst_negative_row_value_supporttarget_table) = S ((S (dst_index_row_value_supporttarget_table)) * dst_negative_scale_row_value_supporttarget_table)) /\ exists ff_q_pvs_row_value_supporttarget_tableentrynegative. dst_negative_code_row_value_supporttarget_table = ff_q_pvs_row_value_supporttarget_tableentrynegative * S ((S (dst_index_row_value_supporttarget_table)) * dst_negative_scale_row_value_supporttarget_table) + (dst_negative_row_value_supporttarget_table))) /\ (exists ge_balance_positive_row_value_supporttarget_tableentryvalue ge_balance_negative_row_value_supporttarget_tableentryvalue. (((((dst_value_row_value_supporttarget_table) = 2 * (ge_balance_positive_row_value_supporttarget_tableentryvalue) /\ (ge_balance_negative_row_value_supporttarget_tableentryvalue) = 0) \/ exists ge_signed_half_row_value_supporttarget_tableentryvaluedecode. (((dst_value_row_value_supporttarget_table) = 2 * ge_signed_half_row_value_supporttarget_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_value_supporttarget_tableentryvalue) = 0) /\ (ge_balance_negative_row_value_supporttarget_tableentryvalue) = S ge_signed_half_row_value_supporttarget_tableentryvaluedecode))) /\ ((dst_positive_row_value_supporttarget_table) + ge_balance_negative_row_value_supporttarget_tableentryvalue = (dst_negative_row_value_supporttarget_table) + ge_balance_positive_row_value_supporttarget_tableentryvalue))))))))) /\ (((forall ssr_source_row_value_supportpreserve ssr_value_row_value_supportpreserve. (exists pvs_gap_row_value_supportpreservesource_bound. pvs_gap_row_value_supportpreservesource_bound + S (ssr_source_row_value_supportpreserve) = (L)) -> (exists dst_positive_code_row_value_supportpreservesource_value dst_positive_scale_row_value_supportpreservesource_value dst_negative_code_row_value_supportpreservesource_value dst_negative_scale_row_value_supportpreservesource_value dst_positive_row_value_supportpreservesource_value dst_negative_row_value_supportpreservesource_value. (((A) = (((((dst_positive_code_row_value_supportpreservesource_value) + (dst_positive_scale_row_value_supportpreservesource_value)) * S ((dst_positive_code_row_value_supportpreservesource_value) + (dst_positive_scale_row_value_supportpreservesource_value)) + ((dst_positive_scale_row_value_supportpreservesource_value) + (dst_positive_scale_row_value_supportpreservesource_value))) + (((dst_negative_code_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)) * S ((dst_negative_code_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)) + ((dst_negative_scale_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)))) * S ((((dst_positive_code_row_value_supportpreservesource_value) + (dst_positive_scale_row_value_supportpreservesource_value)) * S ((dst_positive_code_row_value_supportpreservesource_value) + (dst_positive_scale_row_value_supportpreservesource_value)) + ((dst_positive_scale_row_value_supportpreservesource_value) + (dst_positive_scale_row_value_supportpreservesource_value))) + (((dst_negative_code_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)) * S ((dst_negative_code_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)) + ((dst_negative_scale_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)))) + ((((dst_negative_code_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)) * S ((dst_negative_code_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)) + ((dst_negative_scale_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value))) + (((dst_negative_code_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)) * S ((dst_negative_code_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)) + ((dst_negative_scale_row_value_supportpreservesource_value) + (dst_negative_scale_row_value_supportpreservesource_value)))))) /\ (((((exists ff_h_pvs_row_value_supportpreservesource_valuepositive. ff_h_pvs_row_value_supportpreservesource_valuepositive + S (dst_positive_row_value_supportpreservesource_value) = S ((S (ssr_source_row_value_supportpreserve)) * dst_positive_scale_row_value_supportpreservesource_value)) /\ exists ff_q_pvs_row_value_supportpreservesource_valuepositive. dst_positive_code_row_value_supportpreservesource_value = ff_q_pvs_row_value_supportpreservesource_valuepositive * S ((S (ssr_source_row_value_supportpreserve)) * dst_positive_scale_row_value_supportpreservesource_value) + (dst_positive_row_value_supportpreservesource_value))) /\ (((((exists ff_h_pvs_row_value_supportpreservesource_valuenegative. ff_h_pvs_row_value_supportpreservesource_valuenegative + S (dst_negative_row_value_supportpreservesource_value) = S ((S (ssr_source_row_value_supportpreserve)) * dst_negative_scale_row_value_supportpreservesource_value)) /\ exists ff_q_pvs_row_value_supportpreservesource_valuenegative. dst_negative_code_row_value_supportpreservesource_value = ff_q_pvs_row_value_supportpreservesource_valuenegative * S ((S (ssr_source_row_value_supportpreserve)) * dst_negative_scale_row_value_supportpreservesource_value) + (dst_negative_row_value_supportpreservesource_value))) /\ (exists ge_balance_positive_row_value_supportpreservesource_valuevalue ge_balance_negative_row_value_supportpreservesource_valuevalue. (((((ssr_value_row_value_supportpreserve) = 2 * (ge_balance_positive_row_value_supportpreservesource_valuevalue) /\ (ge_balance_negative_row_value_supportpreservesource_valuevalue) = 0) \/ exists ge_signed_half_row_value_supportpreservesource_valuevaluedecode. (((ssr_value_row_value_supportpreserve) = 2 * ge_signed_half_row_value_supportpreservesource_valuevaluedecode + 1 /\ (ge_balance_positive_row_value_supportpreservesource_valuevalue) = 0) /\ (ge_balance_negative_row_value_supportpreservesource_valuevalue) = S ge_signed_half_row_value_supportpreservesource_valuevaluedecode))) /\ ((dst_positive_row_value_supportpreservesource_value) + ge_balance_negative_row_value_supportpreservesource_valuevalue = (dst_negative_row_value_supportpreservesource_value) + ge_balance_positive_row_value_supportpreservesource_valuevalue))))))))) -> ~(ssr_value_row_value_supportpreserve=0) -> exists ssr_target_row_value_supportpreserve. ((((exists ff_h_pvs_row_value_supportpreservemap. ff_h_pvs_row_value_supportpreservemap + S (ssr_target_row_value_supportpreserve) = S ((S (ssr_source_row_value_supportpreserve)) * s)) /\ exists ff_q_pvs_row_value_supportpreservemap. r = ff_q_pvs_row_value_supportpreservemap * S ((S (ssr_source_row_value_supportpreserve)) * s) + (ssr_target_row_value_supportpreserve))) /\ (((exists pvs_gap_row_value_supportpreservetarget_bound. pvs_gap_row_value_supportpreservetarget_bound + S (ssr_target_row_value_supportpreserve) = (M)) /\ (exists dst_positive_code_row_value_supportpreservetarget_value dst_positive_scale_row_value_supportpreservetarget_value dst_negative_code_row_value_supportpreservetarget_value dst_negative_scale_row_value_supportpreservetarget_value dst_positive_row_value_supportpreservetarget_value dst_negative_row_value_supportpreservetarget_value. (((B) = (((((dst_positive_code_row_value_supportpreservetarget_value) + (dst_positive_scale_row_value_supportpreservetarget_value)) * S ((dst_positive_code_row_value_supportpreservetarget_value) + (dst_positive_scale_row_value_supportpreservetarget_value)) + ((dst_positive_scale_row_value_supportpreservetarget_value) + (dst_positive_scale_row_value_supportpreservetarget_value))) + (((dst_negative_code_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)) * S ((dst_negative_code_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)) + ((dst_negative_scale_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)))) * S ((((dst_positive_code_row_value_supportpreservetarget_value) + (dst_positive_scale_row_value_supportpreservetarget_value)) * S ((dst_positive_code_row_value_supportpreservetarget_value) + (dst_positive_scale_row_value_supportpreservetarget_value)) + ((dst_positive_scale_row_value_supportpreservetarget_value) + (dst_positive_scale_row_value_supportpreservetarget_value))) + (((dst_negative_code_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)) * S ((dst_negative_code_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)) + ((dst_negative_scale_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)))) + ((((dst_negative_code_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)) * S ((dst_negative_code_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)) + ((dst_negative_scale_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value))) + (((dst_negative_code_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)) * S ((dst_negative_code_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)) + ((dst_negative_scale_row_value_supportpreservetarget_value) + (dst_negative_scale_row_value_supportpreservetarget_value)))))) /\ (((((exists ff_h_pvs_row_value_supportpreservetarget_valuepositive. ff_h_pvs_row_value_supportpreservetarget_valuepositive + S (dst_positive_row_value_supportpreservetarget_value) = S ((S (ssr_target_row_value_supportpreserve)) * dst_positive_scale_row_value_supportpreservetarget_value)) /\ exists ff_q_pvs_row_value_supportpreservetarget_valuepositive. dst_positive_code_row_value_supportpreservetarget_value = ff_q_pvs_row_value_supportpreservetarget_valuepositive * S ((S (ssr_target_row_value_supportpreserve)) * dst_positive_scale_row_value_supportpreservetarget_value) + (dst_positive_row_value_supportpreservetarget_value))) /\ (((((exists ff_h_pvs_row_value_supportpreservetarget_valuenegative. ff_h_pvs_row_value_supportpreservetarget_valuenegative + S (dst_negative_row_value_supportpreservetarget_value) = S ((S (ssr_target_row_value_supportpreserve)) * dst_negative_scale_row_value_supportpreservetarget_value)) /\ exists ff_q_pvs_row_value_supportpreservetarget_valuenegative. dst_negative_code_row_value_supportpreservetarget_value = ff_q_pvs_row_value_supportpreservetarget_valuenegative * S ((S (ssr_target_row_value_supportpreserve)) * dst_negative_scale_row_value_supportpreservetarget_value) + (dst_negative_row_value_supportpreservetarget_value))) /\ (exists ge_balance_positive_row_value_supportpreservetarget_valuevalue ge_balance_negative_row_value_supportpreservetarget_valuevalue. (((((ssr_value_row_value_supportpreserve) = 2 * (ge_balance_positive_row_value_supportpreservetarget_valuevalue) /\ (ge_balance_negative_row_value_supportpreservetarget_valuevalue) = 0) \/ exists ge_signed_half_row_value_supportpreservetarget_valuevaluedecode. (((ssr_value_row_value_supportpreserve) = 2 * ge_signed_half_row_value_supportpreservetarget_valuevaluedecode + 1 /\ (ge_balance_positive_row_value_supportpreservetarget_valuevalue) = 0) /\ (ge_balance_negative_row_value_supportpreservetarget_valuevalue) = S ge_signed_half_row_value_supportpreservetarget_valuevaluedecode))) /\ ((dst_positive_row_value_supportpreservetarget_value) + ge_balance_negative_row_value_supportpreservetarget_valuevalue = (dst_negative_row_value_supportpreservetarget_value) + ge_balance_positive_row_value_supportpreservetarget_valuevalue))))))))))))) /\ (((forall ssr_first_row_value_supportinjective ssr_second_row_value_supportinjective ssr_image_row_value_supportinjective ssr_a_row_value_supportinjective ssr_b_row_value_supportinjective. (exists pvs_gap_row_value_supportinjectivefirst_bound. pvs_gap_row_value_supportinjectivefirst_bound + S (ssr_first_row_value_supportinjective) = (L)) -> (exists pvs_gap_row_value_supportinjectivesecond_bound. pvs_gap_row_value_supportinjectivesecond_bound + S (ssr_second_row_value_supportinjective) = (L)) -> (exists dst_positive_code_row_value_supportinjectivefirst_value dst_positive_scale_row_value_supportinjectivefirst_value dst_negative_code_row_value_supportinjectivefirst_value dst_negative_scale_row_value_supportinjectivefirst_value dst_positive_row_value_supportinjectivefirst_value dst_negative_row_value_supportinjectivefirst_value. (((A) = (((((dst_positive_code_row_value_supportinjectivefirst_value) + (dst_positive_scale_row_value_supportinjectivefirst_value)) * S ((dst_positive_code_row_value_supportinjectivefirst_value) + (dst_positive_scale_row_value_supportinjectivefirst_value)) + ((dst_positive_scale_row_value_supportinjectivefirst_value) + (dst_positive_scale_row_value_supportinjectivefirst_value))) + (((dst_negative_code_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)) * S ((dst_negative_code_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)) + ((dst_negative_scale_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)))) * S ((((dst_positive_code_row_value_supportinjectivefirst_value) + (dst_positive_scale_row_value_supportinjectivefirst_value)) * S ((dst_positive_code_row_value_supportinjectivefirst_value) + (dst_positive_scale_row_value_supportinjectivefirst_value)) + ((dst_positive_scale_row_value_supportinjectivefirst_value) + (dst_positive_scale_row_value_supportinjectivefirst_value))) + (((dst_negative_code_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)) * S ((dst_negative_code_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)) + ((dst_negative_scale_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)))) + ((((dst_negative_code_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)) * S ((dst_negative_code_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)) + ((dst_negative_scale_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value))) + (((dst_negative_code_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)) * S ((dst_negative_code_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)) + ((dst_negative_scale_row_value_supportinjectivefirst_value) + (dst_negative_scale_row_value_supportinjectivefirst_value)))))) /\ (((((exists ff_h_pvs_row_value_supportinjectivefirst_valuepositive. ff_h_pvs_row_value_supportinjectivefirst_valuepositive + S (dst_positive_row_value_supportinjectivefirst_value) = S ((S (ssr_first_row_value_supportinjective)) * dst_positive_scale_row_value_supportinjectivefirst_value)) /\ exists ff_q_pvs_row_value_supportinjectivefirst_valuepositive. dst_positive_code_row_value_supportinjectivefirst_value = ff_q_pvs_row_value_supportinjectivefirst_valuepositive * S ((S (ssr_first_row_value_supportinjective)) * dst_positive_scale_row_value_supportinjectivefirst_value) + (dst_positive_row_value_supportinjectivefirst_value))) /\ (((((exists ff_h_pvs_row_value_supportinjectivefirst_valuenegative. ff_h_pvs_row_value_supportinjectivefirst_valuenegative + S (dst_negative_row_value_supportinjectivefirst_value) = S ((S (ssr_first_row_value_supportinjective)) * dst_negative_scale_row_value_supportinjectivefirst_value)) /\ exists ff_q_pvs_row_value_supportinjectivefirst_valuenegative. dst_negative_code_row_value_supportinjectivefirst_value = ff_q_pvs_row_value_supportinjectivefirst_valuenegative * S ((S (ssr_first_row_value_supportinjective)) * dst_negative_scale_row_value_supportinjectivefirst_value) + (dst_negative_row_value_supportinjectivefirst_value))) /\ (exists ge_balance_positive_row_value_supportinjectivefirst_valuevalue ge_balance_negative_row_value_supportinjectivefirst_valuevalue. (((((ssr_a_row_value_supportinjective) = 2 * (ge_balance_positive_row_value_supportinjectivefirst_valuevalue) /\ (ge_balance_negative_row_value_supportinjectivefirst_valuevalue) = 0) \/ exists ge_signed_half_row_value_supportinjectivefirst_valuevaluedecode. (((ssr_a_row_value_supportinjective) = 2 * ge_signed_half_row_value_supportinjectivefirst_valuevaluedecode + 1 /\ (ge_balance_positive_row_value_supportinjectivefirst_valuevalue) = 0) /\ (ge_balance_negative_row_value_supportinjectivefirst_valuevalue) = S ge_signed_half_row_value_supportinjectivefirst_valuevaluedecode))) /\ ((dst_positive_row_value_supportinjectivefirst_value) + ge_balance_negative_row_value_supportinjectivefirst_valuevalue = (dst_negative_row_value_supportinjectivefirst_value) + ge_balance_positive_row_value_supportinjectivefirst_valuevalue))))))))) -> ~(ssr_a_row_value_supportinjective=0) -> (exists dst_positive_code_row_value_supportinjectivesecond_value dst_positive_scale_row_value_supportinjectivesecond_value dst_negative_code_row_value_supportinjectivesecond_value dst_negative_scale_row_value_supportinjectivesecond_value dst_positive_row_value_supportinjectivesecond_value dst_negative_row_value_supportinjectivesecond_value. (((A) = (((((dst_positive_code_row_value_supportinjectivesecond_value) + (dst_positive_scale_row_value_supportinjectivesecond_value)) * S ((dst_positive_code_row_value_supportinjectivesecond_value) + (dst_positive_scale_row_value_supportinjectivesecond_value)) + ((dst_positive_scale_row_value_supportinjectivesecond_value) + (dst_positive_scale_row_value_supportinjectivesecond_value))) + (((dst_negative_code_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)) * S ((dst_negative_code_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)) + ((dst_negative_scale_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)))) * S ((((dst_positive_code_row_value_supportinjectivesecond_value) + (dst_positive_scale_row_value_supportinjectivesecond_value)) * S ((dst_positive_code_row_value_supportinjectivesecond_value) + (dst_positive_scale_row_value_supportinjectivesecond_value)) + ((dst_positive_scale_row_value_supportinjectivesecond_value) + (dst_positive_scale_row_value_supportinjectivesecond_value))) + (((dst_negative_code_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)) * S ((dst_negative_code_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)) + ((dst_negative_scale_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)))) + ((((dst_negative_code_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)) * S ((dst_negative_code_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)) + ((dst_negative_scale_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value))) + (((dst_negative_code_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)) * S ((dst_negative_code_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)) + ((dst_negative_scale_row_value_supportinjectivesecond_value) + (dst_negative_scale_row_value_supportinjectivesecond_value)))))) /\ (((((exists ff_h_pvs_row_value_supportinjectivesecond_valuepositive. ff_h_pvs_row_value_supportinjectivesecond_valuepositive + S (dst_positive_row_value_supportinjectivesecond_value) = S ((S (ssr_second_row_value_supportinjective)) * dst_positive_scale_row_value_supportinjectivesecond_value)) /\ exists ff_q_pvs_row_value_supportinjectivesecond_valuepositive. dst_positive_code_row_value_supportinjectivesecond_value = ff_q_pvs_row_value_supportinjectivesecond_valuepositive * S ((S (ssr_second_row_value_supportinjective)) * dst_positive_scale_row_value_supportinjectivesecond_value) + (dst_positive_row_value_supportinjectivesecond_value))) /\ (((((exists ff_h_pvs_row_value_supportinjectivesecond_valuenegative. ff_h_pvs_row_value_supportinjectivesecond_valuenegative + S (dst_negative_row_value_supportinjectivesecond_value) = S ((S (ssr_second_row_value_supportinjective)) * dst_negative_scale_row_value_supportinjectivesecond_value)) /\ exists ff_q_pvs_row_value_supportinjectivesecond_valuenegative. dst_negative_code_row_value_supportinjectivesecond_value = ff_q_pvs_row_value_supportinjectivesecond_valuenegative * S ((S (ssr_second_row_value_supportinjective)) * dst_negative_scale_row_value_supportinjectivesecond_value) + (dst_negative_row_value_supportinjectivesecond_value))) /\ (exists ge_balance_positive_row_value_supportinjectivesecond_valuevalue ge_balance_negative_row_value_supportinjectivesecond_valuevalue. (((((ssr_b_row_value_supportinjective) = 2 * (ge_balance_positive_row_value_supportinjectivesecond_valuevalue) /\ (ge_balance_negative_row_value_supportinjectivesecond_valuevalue) = 0) \/ exists ge_signed_half_row_value_supportinjectivesecond_valuevaluedecode. (((ssr_b_row_value_supportinjective) = 2 * ge_signed_half_row_value_supportinjectivesecond_valuevaluedecode + 1 /\ (ge_balance_positive_row_value_supportinjectivesecond_valuevalue) = 0) /\ (ge_balance_negative_row_value_supportinjectivesecond_valuevalue) = S ge_signed_half_row_value_supportinjectivesecond_valuevaluedecode))) /\ ((dst_positive_row_value_supportinjectivesecond_value) + ge_balance_negative_row_value_supportinjectivesecond_valuevalue = (dst_negative_row_value_supportinjectivesecond_value) + ge_balance_positive_row_value_supportinjectivesecond_valuevalue))))))))) -> ~(ssr_b_row_value_supportinjective=0) -> (((exists ff_h_pvs_row_value_supportinjectivefirst_map. ff_h_pvs_row_value_supportinjectivefirst_map + S (ssr_image_row_value_supportinjective) = S ((S (ssr_first_row_value_supportinjective)) * s)) /\ exists ff_q_pvs_row_value_supportinjectivefirst_map. r = ff_q_pvs_row_value_supportinjectivefirst_map * S ((S (ssr_first_row_value_supportinjective)) * s) + (ssr_image_row_value_supportinjective))) -> (((exists ff_h_pvs_row_value_supportinjectivesecond_map. ff_h_pvs_row_value_supportinjectivesecond_map + S (ssr_image_row_value_supportinjective) = S ((S (ssr_second_row_value_supportinjective)) * s)) /\ exists ff_q_pvs_row_value_supportinjectivesecond_map. r = ff_q_pvs_row_value_supportinjectivesecond_map * S ((S (ssr_second_row_value_supportinjective)) * s) + (ssr_image_row_value_supportinjective))) -> ssr_first_row_value_supportinjective=ssr_second_row_value_supportinjective) /\ (forall ssr_target_row_value_supportcover ssr_value_row_value_supportcover. (exists pvs_gap_row_value_supportcovertarget_bound. pvs_gap_row_value_supportcovertarget_bound + S (ssr_target_row_value_supportcover) = (M)) -> (exists dst_positive_code_row_value_supportcovertarget_value dst_positive_scale_row_value_supportcovertarget_value dst_negative_code_row_value_supportcovertarget_value dst_negative_scale_row_value_supportcovertarget_value dst_positive_row_value_supportcovertarget_value dst_negative_row_value_supportcovertarget_value. (((B) = (((((dst_positive_code_row_value_supportcovertarget_value) + (dst_positive_scale_row_value_supportcovertarget_value)) * S ((dst_positive_code_row_value_supportcovertarget_value) + (dst_positive_scale_row_value_supportcovertarget_value)) + ((dst_positive_scale_row_value_supportcovertarget_value) + (dst_positive_scale_row_value_supportcovertarget_value))) + (((dst_negative_code_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)) * S ((dst_negative_code_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)) + ((dst_negative_scale_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)))) * S ((((dst_positive_code_row_value_supportcovertarget_value) + (dst_positive_scale_row_value_supportcovertarget_value)) * S ((dst_positive_code_row_value_supportcovertarget_value) + (dst_positive_scale_row_value_supportcovertarget_value)) + ((dst_positive_scale_row_value_supportcovertarget_value) + (dst_positive_scale_row_value_supportcovertarget_value))) + (((dst_negative_code_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)) * S ((dst_negative_code_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)) + ((dst_negative_scale_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)))) + ((((dst_negative_code_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)) * S ((dst_negative_code_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)) + ((dst_negative_scale_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value))) + (((dst_negative_code_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)) * S ((dst_negative_code_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)) + ((dst_negative_scale_row_value_supportcovertarget_value) + (dst_negative_scale_row_value_supportcovertarget_value)))))) /\ (((((exists ff_h_pvs_row_value_supportcovertarget_valuepositive. ff_h_pvs_row_value_supportcovertarget_valuepositive + S (dst_positive_row_value_supportcovertarget_value) = S ((S (ssr_target_row_value_supportcover)) * dst_positive_scale_row_value_supportcovertarget_value)) /\ exists ff_q_pvs_row_value_supportcovertarget_valuepositive. dst_positive_code_row_value_supportcovertarget_value = ff_q_pvs_row_value_supportcovertarget_valuepositive * S ((S (ssr_target_row_value_supportcover)) * dst_positive_scale_row_value_supportcovertarget_value) + (dst_positive_row_value_supportcovertarget_value))) /\ (((((exists ff_h_pvs_row_value_supportcovertarget_valuenegative. ff_h_pvs_row_value_supportcovertarget_valuenegative + S (dst_negative_row_value_supportcovertarget_value) = S ((S (ssr_target_row_value_supportcover)) * dst_negative_scale_row_value_supportcovertarget_value)) /\ exists ff_q_pvs_row_value_supportcovertarget_valuenegative. dst_negative_code_row_value_supportcovertarget_value = ff_q_pvs_row_value_supportcovertarget_valuenegative * S ((S (ssr_target_row_value_supportcover)) * dst_negative_scale_row_value_supportcovertarget_value) + (dst_negative_row_value_supportcovertarget_value))) /\ (exists ge_balance_positive_row_value_supportcovertarget_valuevalue ge_balance_negative_row_value_supportcovertarget_valuevalue. (((((ssr_value_row_value_supportcover) = 2 * (ge_balance_positive_row_value_supportcovertarget_valuevalue) /\ (ge_balance_negative_row_value_supportcovertarget_valuevalue) = 0) \/ exists ge_signed_half_row_value_supportcovertarget_valuevaluedecode. (((ssr_value_row_value_supportcover) = 2 * ge_signed_half_row_value_supportcovertarget_valuevaluedecode + 1 /\ (ge_balance_positive_row_value_supportcovertarget_valuevalue) = 0) /\ (ge_balance_negative_row_value_supportcovertarget_valuevalue) = S ge_signed_half_row_value_supportcovertarget_valuevaluedecode))) /\ ((dst_positive_row_value_supportcovertarget_value) + ge_balance_negative_row_value_supportcovertarget_valuevalue = (dst_negative_row_value_supportcovertarget_value) + ge_balance_positive_row_value_supportcovertarget_valuevalue))))))))) -> ~(ssr_value_row_value_supportcover=0) -> exists ssr_source_row_value_supportcover. ((exists pvs_gap_row_value_supportcoversource_bound. pvs_gap_row_value_supportcoversource_bound + S (ssr_source_row_value_supportcover) = (L)) /\ (((((exists ff_h_pvs_row_value_supportcovermap. ff_h_pvs_row_value_supportcovermap + S (ssr_target_row_value_supportcover) = S ((S (ssr_source_row_value_supportcover)) * s)) /\ exists ff_q_pvs_row_value_supportcovermap. r = ff_q_pvs_row_value_supportcovermap * S ((S (ssr_source_row_value_supportcover)) * s) + (ssr_target_row_value_supportcover))) /\ (exists dst_positive_code_row_value_supportcoversource_value dst_positive_scale_row_value_supportcoversource_value dst_negative_code_row_value_supportcoversource_value dst_negative_scale_row_value_supportcoversource_value dst_positive_row_value_supportcoversource_value dst_negative_row_value_supportcoversource_value. (((A) = (((((dst_positive_code_row_value_supportcoversource_value) + (dst_positive_scale_row_value_supportcoversource_value)) * S ((dst_positive_code_row_value_supportcoversource_value) + (dst_positive_scale_row_value_supportcoversource_value)) + ((dst_positive_scale_row_value_supportcoversource_value) + (dst_positive_scale_row_value_supportcoversource_value))) + (((dst_negative_code_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)) * S ((dst_negative_code_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)) + ((dst_negative_scale_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)))) * S ((((dst_positive_code_row_value_supportcoversource_value) + (dst_positive_scale_row_value_supportcoversource_value)) * S ((dst_positive_code_row_value_supportcoversource_value) + (dst_positive_scale_row_value_supportcoversource_value)) + ((dst_positive_scale_row_value_supportcoversource_value) + (dst_positive_scale_row_value_supportcoversource_value))) + (((dst_negative_code_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)) * S ((dst_negative_code_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)) + ((dst_negative_scale_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)))) + ((((dst_negative_code_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)) * S ((dst_negative_code_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)) + ((dst_negative_scale_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value))) + (((dst_negative_code_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)) * S ((dst_negative_code_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)) + ((dst_negative_scale_row_value_supportcoversource_value) + (dst_negative_scale_row_value_supportcoversource_value)))))) /\ (((((exists ff_h_pvs_row_value_supportcoversource_valuepositive. ff_h_pvs_row_value_supportcoversource_valuepositive + S (dst_positive_row_value_supportcoversource_value) = S ((S (ssr_source_row_value_supportcover)) * dst_positive_scale_row_value_supportcoversource_value)) /\ exists ff_q_pvs_row_value_supportcoversource_valuepositive. dst_positive_code_row_value_supportcoversource_value = ff_q_pvs_row_value_supportcoversource_valuepositive * S ((S (ssr_source_row_value_supportcover)) * dst_positive_scale_row_value_supportcoversource_value) + (dst_positive_row_value_supportcoversource_value))) /\ (((((exists ff_h_pvs_row_value_supportcoversource_valuenegative. ff_h_pvs_row_value_supportcoversource_valuenegative + S (dst_negative_row_value_supportcoversource_value) = S ((S (ssr_source_row_value_supportcover)) * dst_negative_scale_row_value_supportcoversource_value)) /\ exists ff_q_pvs_row_value_supportcoversource_valuenegative. dst_negative_code_row_value_supportcoversource_value = ff_q_pvs_row_value_supportcoversource_valuenegative * S ((S (ssr_source_row_value_supportcover)) * dst_negative_scale_row_value_supportcoversource_value) + (dst_negative_row_value_supportcoversource_value))) /\ (exists ge_balance_positive_row_value_supportcoversource_valuevalue ge_balance_negative_row_value_supportcoversource_valuevalue. (((((ssr_value_row_value_supportcover) = 2 * (ge_balance_positive_row_value_supportcoversource_valuevalue) /\ (ge_balance_negative_row_value_supportcoversource_valuevalue) = 0) \/ exists ge_signed_half_row_value_supportcoversource_valuevaluedecode. (((ssr_value_row_value_supportcover) = 2 * ge_signed_half_row_value_supportcoversource_valuevaluedecode + 1 /\ (ge_balance_positive_row_value_supportcoversource_valuevalue) = 0) /\ (ge_balance_negative_row_value_supportcoversource_valuevalue) = S ge_signed_half_row_value_supportcoversource_valuevaluedecode))) /\ ((dst_positive_row_value_supportcoversource_value) + ge_balance_negative_row_value_supportcoversource_valuevalue = (dst_negative_row_value_supportcoversource_value) + ge_balance_positive_row_value_supportcoversource_valuevalue))))))))))))))))))))) -> (((exists dst_positive_code_row_value_gridsource dst_positive_scale_row_value_gridsource dst_negative_code_row_value_gridsource dst_negative_scale_row_value_gridsource. (((A) = (((((dst_positive_code_row_value_gridsource) + (dst_positive_scale_row_value_gridsource)) * S ((dst_positive_code_row_value_gridsource) + (dst_positive_scale_row_value_gridsource)) + ((dst_positive_scale_row_value_gridsource) + (dst_positive_scale_row_value_gridsource))) + (((dst_negative_code_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)) * S ((dst_negative_code_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)) + ((dst_negative_scale_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)))) * S ((((dst_positive_code_row_value_gridsource) + (dst_positive_scale_row_value_gridsource)) * S ((dst_positive_code_row_value_gridsource) + (dst_positive_scale_row_value_gridsource)) + ((dst_positive_scale_row_value_gridsource) + (dst_positive_scale_row_value_gridsource))) + (((dst_negative_code_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)) * S ((dst_negative_code_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)) + ((dst_negative_scale_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)))) + ((((dst_negative_code_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)) * S ((dst_negative_code_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)) + ((dst_negative_scale_row_value_gridsource) + (dst_negative_scale_row_value_gridsource))) + (((dst_negative_code_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)) * S ((dst_negative_code_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)) + ((dst_negative_scale_row_value_gridsource) + (dst_negative_scale_row_value_gridsource)))))) /\ (forall dst_index_row_value_gridsource. (exists pvs_le_gap_row_value_gridsourcedomain. pvs_le_gap_row_value_gridsourcedomain + (dst_index_row_value_gridsource) = (0)) -> exists dst_positive_row_value_gridsource dst_negative_row_value_gridsource dst_value_row_value_gridsource. ((((exists ff_h_pvs_row_value_gridsourceentrypositive. ff_h_pvs_row_value_gridsourceentrypositive + S (dst_positive_row_value_gridsource) = S ((S (dst_index_row_value_gridsource)) * dst_positive_scale_row_value_gridsource)) /\ exists ff_q_pvs_row_value_gridsourceentrypositive. dst_positive_code_row_value_gridsource = ff_q_pvs_row_value_gridsourceentrypositive * S ((S (dst_index_row_value_gridsource)) * dst_positive_scale_row_value_gridsource) + (dst_positive_row_value_gridsource))) /\ (((((exists ff_h_pvs_row_value_gridsourceentrynegative. ff_h_pvs_row_value_gridsourceentrynegative + S (dst_negative_row_value_gridsource) = S ((S (dst_index_row_value_gridsource)) * dst_negative_scale_row_value_gridsource)) /\ exists ff_q_pvs_row_value_gridsourceentrynegative. dst_negative_code_row_value_gridsource = ff_q_pvs_row_value_gridsourceentrynegative * S ((S (dst_index_row_value_gridsource)) * dst_negative_scale_row_value_gridsource) + (dst_negative_row_value_gridsource))) /\ (exists ge_balance_positive_row_value_gridsourceentryvalue ge_balance_negative_row_value_gridsourceentryvalue. (((((dst_value_row_value_gridsource) = 2 * (ge_balance_positive_row_value_gridsourceentryvalue) /\ (ge_balance_negative_row_value_gridsourceentryvalue) = 0) \/ exists ge_signed_half_row_value_gridsourceentryvaluedecode. (((dst_value_row_value_gridsource) = 2 * ge_signed_half_row_value_gridsourceentryvaluedecode + 1 /\ (ge_balance_positive_row_value_gridsourceentryvalue) = 0) /\ (ge_balance_negative_row_value_gridsourceentryvalue) = S ge_signed_half_row_value_gridsourceentryvaluedecode))) /\ ((dst_positive_row_value_gridsource) + ge_balance_negative_row_value_gridsourceentryvalue = (dst_negative_row_value_gridsource) + ge_balance_positive_row_value_gridsourceentryvalue))))))))) /\ (((exists dst_positive_code_row_value_gridtable dst_positive_scale_row_value_gridtable dst_negative_code_row_value_gridtable dst_negative_scale_row_value_gridtable. (((T) = (((((dst_positive_code_row_value_gridtable) + (dst_positive_scale_row_value_gridtable)) * S ((dst_positive_code_row_value_gridtable) + (dst_positive_scale_row_value_gridtable)) + ((dst_positive_scale_row_value_gridtable) + (dst_positive_scale_row_value_gridtable))) + (((dst_negative_code_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)) * S ((dst_negative_code_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)) + ((dst_negative_scale_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)))) * S ((((dst_positive_code_row_value_gridtable) + (dst_positive_scale_row_value_gridtable)) * S ((dst_positive_code_row_value_gridtable) + (dst_positive_scale_row_value_gridtable)) + ((dst_positive_scale_row_value_gridtable) + (dst_positive_scale_row_value_gridtable))) + (((dst_negative_code_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)) * S ((dst_negative_code_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)) + ((dst_negative_scale_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)))) + ((((dst_negative_code_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)) * S ((dst_negative_code_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)) + ((dst_negative_scale_row_value_gridtable) + (dst_negative_scale_row_value_gridtable))) + (((dst_negative_code_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)) * S ((dst_negative_code_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)) + ((dst_negative_scale_row_value_gridtable) + (dst_negative_scale_row_value_gridtable)))))) /\ (forall dst_index_row_value_gridtable. (exists pvs_le_gap_row_value_gridtabledomain. pvs_le_gap_row_value_gridtabledomain + (dst_index_row_value_gridtable) = ((L)*(S (M)))) -> exists dst_positive_row_value_gridtable dst_negative_row_value_gridtable dst_value_row_value_gridtable. ((((exists ff_h_pvs_row_value_gridtableentrypositive. ff_h_pvs_row_value_gridtableentrypositive + S (dst_positive_row_value_gridtable) = S ((S (dst_index_row_value_gridtable)) * dst_positive_scale_row_value_gridtable)) /\ exists ff_q_pvs_row_value_gridtableentrypositive. dst_positive_code_row_value_gridtable = ff_q_pvs_row_value_gridtableentrypositive * S ((S (dst_index_row_value_gridtable)) * dst_positive_scale_row_value_gridtable) + (dst_positive_row_value_gridtable))) /\ (((((exists ff_h_pvs_row_value_gridtableentrynegative. ff_h_pvs_row_value_gridtableentrynegative + S (dst_negative_row_value_gridtable) = S ((S (dst_index_row_value_gridtable)) * dst_negative_scale_row_value_gridtable)) /\ exists ff_q_pvs_row_value_gridtableentrynegative. dst_negative_code_row_value_gridtable = ff_q_pvs_row_value_gridtableentrynegative * S ((S (dst_index_row_value_gridtable)) * dst_negative_scale_row_value_gridtable) + (dst_negative_row_value_gridtable))) /\ (exists ge_balance_positive_row_value_gridtableentryvalue ge_balance_negative_row_value_gridtableentryvalue. (((((dst_value_row_value_gridtable) = 2 * (ge_balance_positive_row_value_gridtableentryvalue) /\ (ge_balance_negative_row_value_gridtableentryvalue) = 0) \/ exists ge_signed_half_row_value_gridtableentryvaluedecode. (((dst_value_row_value_gridtable) = 2 * ge_signed_half_row_value_gridtableentryvaluedecode + 1 /\ (ge_balance_positive_row_value_gridtableentryvalue) = 0) /\ (ge_balance_negative_row_value_gridtableentryvalue) = S ge_signed_half_row_value_gridtableentryvaluedecode))) /\ ((dst_positive_row_value_gridtable) + ge_balance_negative_row_value_gridtableentryvalue = (dst_negative_row_value_gridtable) + ge_balance_positive_row_value_gridtableentryvalue))))))))) /\ (forall ssr_grid_row_row_value_grid ssr_grid_column_row_value_grid ssr_grid_value_row_value_grid. (exists pvs_gap_row_value_gridrow_bound. pvs_gap_row_value_gridrow_bound + S (ssr_grid_row_row_value_grid) = (L)) -> (exists pvs_gap_row_value_gridcolumn_bound. pvs_gap_row_value_gridcolumn_bound + S (ssr_grid_column_row_value_grid) = (M)) -> (exists dst_positive_code_row_value_gridlookup dst_positive_scale_row_value_gridlookup dst_negative_code_row_value_gridlookup dst_negative_scale_row_value_gridlookup dst_positive_row_value_gridlookup dst_negative_row_value_gridlookup. (((T) = (((((dst_positive_code_row_value_gridlookup) + (dst_positive_scale_row_value_gridlookup)) * S ((dst_positive_code_row_value_gridlookup) + (dst_positive_scale_row_value_gridlookup)) + ((dst_positive_scale_row_value_gridlookup) + (dst_positive_scale_row_value_gridlookup))) + (((dst_negative_code_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)) * S ((dst_negative_code_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)) + ((dst_negative_scale_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)))) * S ((((dst_positive_code_row_value_gridlookup) + (dst_positive_scale_row_value_gridlookup)) * S ((dst_positive_code_row_value_gridlookup) + (dst_positive_scale_row_value_gridlookup)) + ((dst_positive_scale_row_value_gridlookup) + (dst_positive_scale_row_value_gridlookup))) + (((dst_negative_code_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)) * S ((dst_negative_code_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)) + ((dst_negative_scale_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)))) + ((((dst_negative_code_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)) * S ((dst_negative_code_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)) + ((dst_negative_scale_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup))) + (((dst_negative_code_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)) * S ((dst_negative_code_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)) + ((dst_negative_scale_row_value_gridlookup) + (dst_negative_scale_row_value_gridlookup)))))) /\ (((((exists ff_h_pvs_row_value_gridlookuppositive. ff_h_pvs_row_value_gridlookuppositive + S (dst_positive_row_value_gridlookup) = S ((S (((S (M))*(ssr_grid_row_row_value_grid)+(ssr_grid_column_row_value_grid)))) * dst_positive_scale_row_value_gridlookup)) /\ exists ff_q_pvs_row_value_gridlookuppositive. dst_positive_code_row_value_gridlookup = ff_q_pvs_row_value_gridlookuppositive * S ((S (((S (M))*(ssr_grid_row_row_value_grid)+(ssr_grid_column_row_value_grid)))) * dst_positive_scale_row_value_gridlookup) + (dst_positive_row_value_gridlookup))) /\ (((((exists ff_h_pvs_row_value_gridlookupnegative. ff_h_pvs_row_value_gridlookupnegative + S (dst_negative_row_value_gridlookup) = S ((S (((S (M))*(ssr_grid_row_row_value_grid)+(ssr_grid_column_row_value_grid)))) * dst_negative_scale_row_value_gridlookup)) /\ exists ff_q_pvs_row_value_gridlookupnegative. dst_negative_code_row_value_gridlookup = ff_q_pvs_row_value_gridlookupnegative * S ((S (((S (M))*(ssr_grid_row_row_value_grid)+(ssr_grid_column_row_value_grid)))) * dst_negative_scale_row_value_gridlookup) + (dst_negative_row_value_gridlookup))) /\ (exists ge_balance_positive_row_value_gridlookupvalue ge_balance_negative_row_value_gridlookupvalue. (((((ssr_grid_value_row_value_grid) = 2 * (ge_balance_positive_row_value_gridlookupvalue) /\ (ge_balance_negative_row_value_gridlookupvalue) = 0) \/ exists ge_signed_half_row_value_gridlookupvaluedecode. (((ssr_grid_value_row_value_grid) = 2 * ge_signed_half_row_value_gridlookupvaluedecode + 1 /\ (ge_balance_positive_row_value_gridlookupvalue) = 0) /\ (ge_balance_negative_row_value_gridlookupvalue) = S ge_signed_half_row_value_gridlookupvaluedecode))) /\ ((dst_positive_row_value_gridlookup) + ge_balance_negative_row_value_gridlookupvalue = (dst_negative_row_value_gridlookup) + ge_balance_positive_row_value_gridlookupvalue))))))))) -> (exists ssr_entry_value_row_value_gridentry ssr_entry_image_row_value_gridentry. ((exists dst_positive_code_row_value_gridentrysource dst_positive_scale_row_value_gridentrysource dst_negative_code_row_value_gridentrysource dst_negative_scale_row_value_gridentrysource dst_positive_row_value_gridentrysource dst_negative_row_value_gridentrysource. (((A) = (((((dst_positive_code_row_value_gridentrysource) + (dst_positive_scale_row_value_gridentrysource)) * S ((dst_positive_code_row_value_gridentrysource) + (dst_positive_scale_row_value_gridentrysource)) + ((dst_positive_scale_row_value_gridentrysource) + (dst_positive_scale_row_value_gridentrysource))) + (((dst_negative_code_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)) * S ((dst_negative_code_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)) + ((dst_negative_scale_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)))) * S ((((dst_positive_code_row_value_gridentrysource) + (dst_positive_scale_row_value_gridentrysource)) * S ((dst_positive_code_row_value_gridentrysource) + (dst_positive_scale_row_value_gridentrysource)) + ((dst_positive_scale_row_value_gridentrysource) + (dst_positive_scale_row_value_gridentrysource))) + (((dst_negative_code_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)) * S ((dst_negative_code_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)) + ((dst_negative_scale_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)))) + ((((dst_negative_code_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)) * S ((dst_negative_code_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)) + ((dst_negative_scale_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource))) + (((dst_negative_code_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)) * S ((dst_negative_code_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)) + ((dst_negative_scale_row_value_gridentrysource) + (dst_negative_scale_row_value_gridentrysource)))))) /\ (((((exists ff_h_pvs_row_value_gridentrysourcepositive. ff_h_pvs_row_value_gridentrysourcepositive + S (dst_positive_row_value_gridentrysource) = S ((S (ssr_grid_row_row_value_grid)) * dst_positive_scale_row_value_gridentrysource)) /\ exists ff_q_pvs_row_value_gridentrysourcepositive. dst_positive_code_row_value_gridentrysource = ff_q_pvs_row_value_gridentrysourcepositive * S ((S (ssr_grid_row_row_value_grid)) * dst_positive_scale_row_value_gridentrysource) + (dst_positive_row_value_gridentrysource))) /\ (((((exists ff_h_pvs_row_value_gridentrysourcenegative. ff_h_pvs_row_value_gridentrysourcenegative + S (dst_negative_row_value_gridentrysource) = S ((S (ssr_grid_row_row_value_grid)) * dst_negative_scale_row_value_gridentrysource)) /\ exists ff_q_pvs_row_value_gridentrysourcenegative. dst_negative_code_row_value_gridentrysource = ff_q_pvs_row_value_gridentrysourcenegative * S ((S (ssr_grid_row_row_value_grid)) * dst_negative_scale_row_value_gridentrysource) + (dst_negative_row_value_gridentrysource))) /\ (exists ge_balance_positive_row_value_gridentrysourcevalue ge_balance_negative_row_value_gridentrysourcevalue. (((((ssr_entry_value_row_value_gridentry) = 2 * (ge_balance_positive_row_value_gridentrysourcevalue) /\ (ge_balance_negative_row_value_gridentrysourcevalue) = 0) \/ exists ge_signed_half_row_value_gridentrysourcevaluedecode. (((ssr_entry_value_row_value_gridentry) = 2 * ge_signed_half_row_value_gridentrysourcevaluedecode + 1 /\ (ge_balance_positive_row_value_gridentrysourcevalue) = 0) /\ (ge_balance_negative_row_value_gridentrysourcevalue) = S ge_signed_half_row_value_gridentrysourcevaluedecode))) /\ ((dst_positive_row_value_gridentrysource) + ge_balance_negative_row_value_gridentrysourcevalue = (dst_negative_row_value_gridentrysource) + ge_balance_positive_row_value_gridentrysourcevalue))))))))) /\ (((((exists ff_h_pvs_row_value_gridentrymap. ff_h_pvs_row_value_gridentrymap + S (ssr_entry_image_row_value_gridentry) = S ((S (ssr_grid_row_row_value_grid)) * s)) /\ exists ff_q_pvs_row_value_gridentrymap. r = ff_q_pvs_row_value_gridentrymap * S ((S (ssr_grid_row_row_value_grid)) * s) + (ssr_entry_image_row_value_gridentry))) /\ (((((ssr_grid_column_row_value_grid)=(ssr_entry_image_row_value_gridentry)) /\ ((ssr_grid_value_row_value_grid)=(ssr_entry_value_row_value_gridentry)))) \/ (((~((ssr_grid_column_row_value_grid)=(ssr_entry_image_row_value_gridentry))) /\ ((ssr_grid_value_row_value_grid)=0))))))))))))) -> (exists pvs_gap_row_value_bound. pvs_gap_row_value_bound + S (i) = (L)) -> (exists dst_positive_code_row_value_source dst_positive_scale_row_value_source dst_negative_code_row_value_source dst_negative_scale_row_value_source dst_positive_row_value_source dst_negative_row_value_source. (((A) = (((((dst_positive_code_row_value_source) + (dst_positive_scale_row_value_source)) * S ((dst_positive_code_row_value_source) + (dst_positive_scale_row_value_source)) + ((dst_positive_scale_row_value_source) + (dst_positive_scale_row_value_source))) + (((dst_negative_code_row_value_source) + (dst_negative_scale_row_value_source)) * S ((dst_negative_code_row_value_source) + (dst_negative_scale_row_value_source)) + ((dst_negative_scale_row_value_source) + (dst_negative_scale_row_value_source)))) * S ((((dst_positive_code_row_value_source) + (dst_positive_scale_row_value_source)) * S ((dst_positive_code_row_value_source) + (dst_positive_scale_row_value_source)) + ((dst_positive_scale_row_value_source) + (dst_positive_scale_row_value_source))) + (((dst_negative_code_row_value_source) + (dst_negative_scale_row_value_source)) * S ((dst_negative_code_row_value_source) + (dst_negative_scale_row_value_source)) + ((dst_negative_scale_row_value_source) + (dst_negative_scale_row_value_source)))) + ((((dst_negative_code_row_value_source) + (dst_negative_scale_row_value_source)) * S ((dst_negative_code_row_value_source) + (dst_negative_scale_row_value_source)) + ((dst_negative_scale_row_value_source) + (dst_negative_scale_row_value_source))) + (((dst_negative_code_row_value_source) + (dst_negative_scale_row_value_source)) * S ((dst_negative_code_row_value_source) + (dst_negative_scale_row_value_source)) + ((dst_negative_scale_row_value_source) + (dst_negative_scale_row_value_source)))))) /\ (((((exists ff_h_pvs_row_value_sourcepositive. ff_h_pvs_row_value_sourcepositive + S (dst_positive_row_value_source) = S ((S (i)) * dst_positive_scale_row_value_source)) /\ exists ff_q_pvs_row_value_sourcepositive. dst_positive_code_row_value_source = ff_q_pvs_row_value_sourcepositive * S ((S (i)) * dst_positive_scale_row_value_source) + (dst_positive_row_value_source))) /\ (((((exists ff_h_pvs_row_value_sourcenegative. ff_h_pvs_row_value_sourcenegative + S (dst_negative_row_value_source) = S ((S (i)) * dst_negative_scale_row_value_source)) /\ exists ff_q_pvs_row_value_sourcenegative. dst_negative_code_row_value_source = ff_q_pvs_row_value_sourcenegative * S ((S (i)) * dst_negative_scale_row_value_source) + (dst_negative_row_value_source))) /\ (exists ge_balance_positive_row_value_sourcevalue ge_balance_negative_row_value_sourcevalue. (((((a) = 2 * (ge_balance_positive_row_value_sourcevalue) /\ (ge_balance_negative_row_value_sourcevalue) = 0) \/ exists ge_signed_half_row_value_sourcevaluedecode. (((a) = 2 * ge_signed_half_row_value_sourcevaluedecode + 1 /\ (ge_balance_positive_row_value_sourcevalue) = 0) /\ (ge_balance_negative_row_value_sourcevalue) = S ge_signed_half_row_value_sourcevaluedecode))) /\ ((dst_positive_row_value_source) + ge_balance_negative_row_value_sourcevalue = (dst_negative_row_value_source) + ge_balance_positive_row_value_sourcevalue))))))))) -> (exists srs_slice_row_value_sum. ((((exists dst_positive_code_row_value_sumslicesource_table dst_positive_scale_row_value_sumslicesource_table dst_negative_code_row_value_sumslicesource_table dst_negative_scale_row_value_sumslicesource_table. (((T) = (((((dst_positive_code_row_value_sumslicesource_table) + (dst_positive_scale_row_value_sumslicesource_table)) * S ((dst_positive_code_row_value_sumslicesource_table) + (dst_positive_scale_row_value_sumslicesource_table)) + ((dst_positive_scale_row_value_sumslicesource_table) + (dst_positive_scale_row_value_sumslicesource_table))) + (((dst_negative_code_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)) * S ((dst_negative_code_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)) + ((dst_negative_scale_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)))) * S ((((dst_positive_code_row_value_sumslicesource_table) + (dst_positive_scale_row_value_sumslicesource_table)) * S ((dst_positive_code_row_value_sumslicesource_table) + (dst_positive_scale_row_value_sumslicesource_table)) + ((dst_positive_scale_row_value_sumslicesource_table) + (dst_positive_scale_row_value_sumslicesource_table))) + (((dst_negative_code_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)) * S ((dst_negative_code_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)) + ((dst_negative_scale_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)))) + ((((dst_negative_code_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)) * S ((dst_negative_code_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)) + ((dst_negative_scale_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table))) + (((dst_negative_code_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)) * S ((dst_negative_code_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)) + ((dst_negative_scale_row_value_sumslicesource_table) + (dst_negative_scale_row_value_sumslicesource_table)))))) /\ (forall dst_index_row_value_sumslicesource_table. (exists pvs_le_gap_row_value_sumslicesource_tabledomain. pvs_le_gap_row_value_sumslicesource_tabledomain + (dst_index_row_value_sumslicesource_table) = (0)) -> exists dst_positive_row_value_sumslicesource_table dst_negative_row_value_sumslicesource_table dst_value_row_value_sumslicesource_table. ((((exists ff_h_pvs_row_value_sumslicesource_tableentrypositive. ff_h_pvs_row_value_sumslicesource_tableentrypositive + S (dst_positive_row_value_sumslicesource_table) = S ((S (dst_index_row_value_sumslicesource_table)) * dst_positive_scale_row_value_sumslicesource_table)) /\ exists ff_q_pvs_row_value_sumslicesource_tableentrypositive. dst_positive_code_row_value_sumslicesource_table = ff_q_pvs_row_value_sumslicesource_tableentrypositive * S ((S (dst_index_row_value_sumslicesource_table)) * dst_positive_scale_row_value_sumslicesource_table) + (dst_positive_row_value_sumslicesource_table))) /\ (((((exists ff_h_pvs_row_value_sumslicesource_tableentrynegative. ff_h_pvs_row_value_sumslicesource_tableentrynegative + S (dst_negative_row_value_sumslicesource_table) = S ((S (dst_index_row_value_sumslicesource_table)) * dst_negative_scale_row_value_sumslicesource_table)) /\ exists ff_q_pvs_row_value_sumslicesource_tableentrynegative. dst_negative_code_row_value_sumslicesource_table = ff_q_pvs_row_value_sumslicesource_tableentrynegative * S ((S (dst_index_row_value_sumslicesource_table)) * dst_negative_scale_row_value_sumslicesource_table) + (dst_negative_row_value_sumslicesource_table))) /\ (exists ge_balance_positive_row_value_sumslicesource_tableentryvalue ge_balance_negative_row_value_sumslicesource_tableentryvalue. (((((dst_value_row_value_sumslicesource_table) = 2 * (ge_balance_positive_row_value_sumslicesource_tableentryvalue) /\ (ge_balance_negative_row_value_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_row_value_sumslicesource_tableentryvaluedecode. (((dst_value_row_value_sumslicesource_table) = 2 * ge_signed_half_row_value_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_value_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_row_value_sumslicesource_tableentryvalue) = S ge_signed_half_row_value_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_row_value_sumslicesource_table) + ge_balance_negative_row_value_sumslicesource_tableentryvalue = (dst_negative_row_value_sumslicesource_table) + ge_balance_positive_row_value_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_row_value_sumsliceoutput_table dst_positive_scale_row_value_sumsliceoutput_table dst_negative_code_row_value_sumsliceoutput_table dst_negative_scale_row_value_sumsliceoutput_table. (((srs_slice_row_value_sum) = (((((dst_positive_code_row_value_sumsliceoutput_table) + (dst_positive_scale_row_value_sumsliceoutput_table)) * S ((dst_positive_code_row_value_sumsliceoutput_table) + (dst_positive_scale_row_value_sumsliceoutput_table)) + ((dst_positive_scale_row_value_sumsliceoutput_table) + (dst_positive_scale_row_value_sumsliceoutput_table))) + (((dst_negative_code_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)) * S ((dst_negative_code_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)) + ((dst_negative_scale_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)))) * S ((((dst_positive_code_row_value_sumsliceoutput_table) + (dst_positive_scale_row_value_sumsliceoutput_table)) * S ((dst_positive_code_row_value_sumsliceoutput_table) + (dst_positive_scale_row_value_sumsliceoutput_table)) + ((dst_positive_scale_row_value_sumsliceoutput_table) + (dst_positive_scale_row_value_sumsliceoutput_table))) + (((dst_negative_code_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)) * S ((dst_negative_code_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)) + ((dst_negative_scale_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)))) + ((((dst_negative_code_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)) * S ((dst_negative_code_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)) + ((dst_negative_scale_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table))) + (((dst_negative_code_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)) * S ((dst_negative_code_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)) + ((dst_negative_scale_row_value_sumsliceoutput_table) + (dst_negative_scale_row_value_sumsliceoutput_table)))))) /\ (forall dst_index_row_value_sumsliceoutput_table. (exists pvs_le_gap_row_value_sumsliceoutput_tabledomain. pvs_le_gap_row_value_sumsliceoutput_tabledomain + (dst_index_row_value_sumsliceoutput_table) = (M)) -> exists dst_positive_row_value_sumsliceoutput_table dst_negative_row_value_sumsliceoutput_table dst_value_row_value_sumsliceoutput_table. ((((exists ff_h_pvs_row_value_sumsliceoutput_tableentrypositive. ff_h_pvs_row_value_sumsliceoutput_tableentrypositive + S (dst_positive_row_value_sumsliceoutput_table) = S ((S (dst_index_row_value_sumsliceoutput_table)) * dst_positive_scale_row_value_sumsliceoutput_table)) /\ exists ff_q_pvs_row_value_sumsliceoutput_tableentrypositive. dst_positive_code_row_value_sumsliceoutput_table = ff_q_pvs_row_value_sumsliceoutput_tableentrypositive * S ((S (dst_index_row_value_sumsliceoutput_table)) * dst_positive_scale_row_value_sumsliceoutput_table) + (dst_positive_row_value_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_row_value_sumsliceoutput_tableentrynegative. ff_h_pvs_row_value_sumsliceoutput_tableentrynegative + S (dst_negative_row_value_sumsliceoutput_table) = S ((S (dst_index_row_value_sumsliceoutput_table)) * dst_negative_scale_row_value_sumsliceoutput_table)) /\ exists ff_q_pvs_row_value_sumsliceoutput_tableentrynegative. dst_negative_code_row_value_sumsliceoutput_table = ff_q_pvs_row_value_sumsliceoutput_tableentrynegative * S ((S (dst_index_row_value_sumsliceoutput_table)) * dst_negative_scale_row_value_sumsliceoutput_table) + (dst_negative_row_value_sumsliceoutput_table))) /\ (exists ge_balance_positive_row_value_sumsliceoutput_tableentryvalue ge_balance_negative_row_value_sumsliceoutput_tableentryvalue. (((((dst_value_row_value_sumsliceoutput_table) = 2 * (ge_balance_positive_row_value_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_row_value_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_row_value_sumsliceoutput_tableentryvaluedecode. (((dst_value_row_value_sumsliceoutput_table) = 2 * ge_signed_half_row_value_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_value_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_row_value_sumsliceoutput_tableentryvalue) = S ge_signed_half_row_value_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_row_value_sumsliceoutput_table) + ge_balance_negative_row_value_sumsliceoutput_tableentryvalue = (dst_negative_row_value_sumsliceoutput_table) + ge_balance_positive_row_value_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_row_value_sumslice. (exists pvs_gap_row_value_sumslicebound. pvs_gap_row_value_sumslicebound + S (srs_index_row_value_sumslice) = (M)) -> exists srs_value_row_value_sumslice. (((exists dst_positive_code_row_value_sumsliceentrysource dst_positive_scale_row_value_sumsliceentrysource dst_negative_code_row_value_sumsliceentrysource dst_negative_scale_row_value_sumsliceentrysource dst_positive_row_value_sumsliceentrysource dst_negative_row_value_sumsliceentrysource. (((T) = (((((dst_positive_code_row_value_sumsliceentrysource) + (dst_positive_scale_row_value_sumsliceentrysource)) * S ((dst_positive_code_row_value_sumsliceentrysource) + (dst_positive_scale_row_value_sumsliceentrysource)) + ((dst_positive_scale_row_value_sumsliceentrysource) + (dst_positive_scale_row_value_sumsliceentrysource))) + (((dst_negative_code_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)) * S ((dst_negative_code_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)) + ((dst_negative_scale_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)))) * S ((((dst_positive_code_row_value_sumsliceentrysource) + (dst_positive_scale_row_value_sumsliceentrysource)) * S ((dst_positive_code_row_value_sumsliceentrysource) + (dst_positive_scale_row_value_sumsliceentrysource)) + ((dst_positive_scale_row_value_sumsliceentrysource) + (dst_positive_scale_row_value_sumsliceentrysource))) + (((dst_negative_code_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)) * S ((dst_negative_code_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)) + ((dst_negative_scale_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)))) + ((((dst_negative_code_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)) * S ((dst_negative_code_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)) + ((dst_negative_scale_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource))) + (((dst_negative_code_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)) * S ((dst_negative_code_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)) + ((dst_negative_scale_row_value_sumsliceentrysource) + (dst_negative_scale_row_value_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_row_value_sumsliceentrysourcepositive. ff_h_pvs_row_value_sumsliceentrysourcepositive + S (dst_positive_row_value_sumsliceentrysource) = S ((S (((((0) + ((S M) * (i)))) + ((1) * (srs_index_row_value_sumslice))))) * dst_positive_scale_row_value_sumsliceentrysource)) /\ exists ff_q_pvs_row_value_sumsliceentrysourcepositive. dst_positive_code_row_value_sumsliceentrysource = ff_q_pvs_row_value_sumsliceentrysourcepositive * S ((S (((((0) + ((S M) * (i)))) + ((1) * (srs_index_row_value_sumslice))))) * dst_positive_scale_row_value_sumsliceentrysource) + (dst_positive_row_value_sumsliceentrysource))) /\ (((((exists ff_h_pvs_row_value_sumsliceentrysourcenegative. ff_h_pvs_row_value_sumsliceentrysourcenegative + S (dst_negative_row_value_sumsliceentrysource) = S ((S (((((0) + ((S M) * (i)))) + ((1) * (srs_index_row_value_sumslice))))) * dst_negative_scale_row_value_sumsliceentrysource)) /\ exists ff_q_pvs_row_value_sumsliceentrysourcenegative. dst_negative_code_row_value_sumsliceentrysource = ff_q_pvs_row_value_sumsliceentrysourcenegative * S ((S (((((0) + ((S M) * (i)))) + ((1) * (srs_index_row_value_sumslice))))) * dst_negative_scale_row_value_sumsliceentrysource) + (dst_negative_row_value_sumsliceentrysource))) /\ (exists ge_balance_positive_row_value_sumsliceentrysourcevalue ge_balance_negative_row_value_sumsliceentrysourcevalue. (((((srs_value_row_value_sumslice) = 2 * (ge_balance_positive_row_value_sumsliceentrysourcevalue) /\ (ge_balance_negative_row_value_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_row_value_sumsliceentrysourcevaluedecode. (((srs_value_row_value_sumslice) = 2 * ge_signed_half_row_value_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_row_value_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_row_value_sumsliceentrysourcevalue) = S ge_signed_half_row_value_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_row_value_sumsliceentrysource) + ge_balance_negative_row_value_sumsliceentrysourcevalue = (dst_negative_row_value_sumsliceentrysource) + ge_balance_positive_row_value_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_row_value_sumsliceentryoutput dst_positive_scale_row_value_sumsliceentryoutput dst_negative_code_row_value_sumsliceentryoutput dst_negative_scale_row_value_sumsliceentryoutput dst_positive_row_value_sumsliceentryoutput dst_negative_row_value_sumsliceentryoutput. (((srs_slice_row_value_sum) = (((((dst_positive_code_row_value_sumsliceentryoutput) + (dst_positive_scale_row_value_sumsliceentryoutput)) * S ((dst_positive_code_row_value_sumsliceentryoutput) + (dst_positive_scale_row_value_sumsliceentryoutput)) + ((dst_positive_scale_row_value_sumsliceentryoutput) + (dst_positive_scale_row_value_sumsliceentryoutput))) + (((dst_negative_code_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)) * S ((dst_negative_code_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)) + ((dst_negative_scale_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)))) * S ((((dst_positive_code_row_value_sumsliceentryoutput) + (dst_positive_scale_row_value_sumsliceentryoutput)) * S ((dst_positive_code_row_value_sumsliceentryoutput) + (dst_positive_scale_row_value_sumsliceentryoutput)) + ((dst_positive_scale_row_value_sumsliceentryoutput) + (dst_positive_scale_row_value_sumsliceentryoutput))) + (((dst_negative_code_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)) * S ((dst_negative_code_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)) + ((dst_negative_scale_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)))) + ((((dst_negative_code_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)) * S ((dst_negative_code_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)) + ((dst_negative_scale_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput))) + (((dst_negative_code_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)) * S ((dst_negative_code_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)) + ((dst_negative_scale_row_value_sumsliceentryoutput) + (dst_negative_scale_row_value_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_row_value_sumsliceentryoutputpositive. ff_h_pvs_row_value_sumsliceentryoutputpositive + S (dst_positive_row_value_sumsliceentryoutput) = S ((S (srs_index_row_value_sumslice)) * dst_positive_scale_row_value_sumsliceentryoutput)) /\ exists ff_q_pvs_row_value_sumsliceentryoutputpositive. dst_positive_code_row_value_sumsliceentryoutput = ff_q_pvs_row_value_sumsliceentryoutputpositive * S ((S (srs_index_row_value_sumslice)) * dst_positive_scale_row_value_sumsliceentryoutput) + (dst_positive_row_value_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_row_value_sumsliceentryoutputnegative. ff_h_pvs_row_value_sumsliceentryoutputnegative + S (dst_negative_row_value_sumsliceentryoutput) = S ((S (srs_index_row_value_sumslice)) * dst_negative_scale_row_value_sumsliceentryoutput)) /\ exists ff_q_pvs_row_value_sumsliceentryoutputnegative. dst_negative_code_row_value_sumsliceentryoutput = ff_q_pvs_row_value_sumsliceentryoutputnegative * S ((S (srs_index_row_value_sumslice)) * dst_negative_scale_row_value_sumsliceentryoutput) + (dst_negative_row_value_sumsliceentryoutput))) /\ (exists ge_balance_positive_row_value_sumsliceentryoutputvalue ge_balance_negative_row_value_sumsliceentryoutputvalue. (((((srs_value_row_value_sumslice) = 2 * (ge_balance_positive_row_value_sumsliceentryoutputvalue) /\ (ge_balance_negative_row_value_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_row_value_sumsliceentryoutputvaluedecode. (((srs_value_row_value_sumslice) = 2 * ge_signed_half_row_value_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_row_value_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_row_value_sumsliceentryoutputvalue) = S ge_signed_half_row_value_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_row_value_sumsliceentryoutput) + ge_balance_negative_row_value_sumsliceentryoutputvalue = (dst_negative_row_value_sumsliceentryoutput) + ge_balance_positive_row_value_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_row_value_sumsum dst_positive_scale_row_value_sumsum dst_negative_code_row_value_sumsum dst_negative_scale_row_value_sumsum dst_positive_sum_row_value_sumsum dst_negative_sum_row_value_sumsum. (((srs_slice_row_value_sum) = (((((dst_positive_code_row_value_sumsum) + (dst_positive_scale_row_value_sumsum)) * S ((dst_positive_code_row_value_sumsum) + (dst_positive_scale_row_value_sumsum)) + ((dst_positive_scale_row_value_sumsum) + (dst_positive_scale_row_value_sumsum))) + (((dst_negative_code_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)) * S ((dst_negative_code_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)) + ((dst_negative_scale_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)))) * S ((((dst_positive_code_row_value_sumsum) + (dst_positive_scale_row_value_sumsum)) * S ((dst_positive_code_row_value_sumsum) + (dst_positive_scale_row_value_sumsum)) + ((dst_positive_scale_row_value_sumsum) + (dst_positive_scale_row_value_sumsum))) + (((dst_negative_code_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)) * S ((dst_negative_code_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)) + ((dst_negative_scale_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)))) + ((((dst_negative_code_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)) * S ((dst_negative_code_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)) + ((dst_negative_scale_row_value_sumsum) + (dst_negative_scale_row_value_sumsum))) + (((dst_negative_code_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)) * S ((dst_negative_code_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)) + ((dst_negative_scale_row_value_sumsum) + (dst_negative_scale_row_value_sumsum)))))) /\ (((exists fs_u_dst_row_value_sumsumpositive fs_v_dst_row_value_sumsumpositive. ((((exists fs_h_dst_row_value_sumsumpositive_body_start. fs_h_dst_row_value_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_row_value_sumsumpositive)) /\ exists fs_q_dst_row_value_sumsumpositive_body_start. fs_u_dst_row_value_sumsumpositive = fs_q_dst_row_value_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_row_value_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_row_value_sumsumpositive_body_terminal. fs_h_dst_row_value_sumsumpositive_body_terminal + S (dst_positive_sum_row_value_sumsum) = S ((S (M)) * fs_v_dst_row_value_sumsumpositive)) /\ exists fs_q_dst_row_value_sumsumpositive_body_terminal. fs_u_dst_row_value_sumsumpositive = fs_q_dst_row_value_sumsumpositive_body_terminal * S ((S (M)) * fs_v_dst_row_value_sumsumpositive) + (dst_positive_sum_row_value_sumsum))) /\ forall fs_i_dst_row_value_sumsumpositive_body_steps. (exists fs_lt_dst_row_value_sumsumpositive_body_steps_bound. fs_lt_dst_row_value_sumsumpositive_body_steps_bound + S fs_i_dst_row_value_sumsumpositive_body_steps = M) -> exists fs_a_dst_row_value_sumsumpositive_body_steps fs_r_dst_row_value_sumsumpositive_body_steps fs_s_dst_row_value_sumsumpositive_body_steps. ((((exists fs_h_dst_row_value_sumsumpositive_body_steps_summand. fs_h_dst_row_value_sumsumpositive_body_steps_summand + S (fs_a_dst_row_value_sumsumpositive_body_steps) = S ((S (fs_i_dst_row_value_sumsumpositive_body_steps)) * dst_positive_scale_row_value_sumsum)) /\ exists fs_q_dst_row_value_sumsumpositive_body_steps_summand. dst_positive_code_row_value_sumsum = fs_q_dst_row_value_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_row_value_sumsumpositive_body_steps)) * dst_positive_scale_row_value_sumsum) + (fs_a_dst_row_value_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_row_value_sumsumpositive_body_steps_partial. fs_h_dst_row_value_sumsumpositive_body_steps_partial + S (fs_r_dst_row_value_sumsumpositive_body_steps) = S ((S (fs_i_dst_row_value_sumsumpositive_body_steps)) * fs_v_dst_row_value_sumsumpositive)) /\ exists fs_q_dst_row_value_sumsumpositive_body_steps_partial. fs_u_dst_row_value_sumsumpositive = fs_q_dst_row_value_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_row_value_sumsumpositive_body_steps)) * fs_v_dst_row_value_sumsumpositive) + (fs_r_dst_row_value_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_row_value_sumsumpositive_body_steps_successor. fs_h_dst_row_value_sumsumpositive_body_steps_successor + S (fs_s_dst_row_value_sumsumpositive_body_steps) = S ((S (S fs_i_dst_row_value_sumsumpositive_body_steps)) * fs_v_dst_row_value_sumsumpositive)) /\ exists fs_q_dst_row_value_sumsumpositive_body_steps_successor. fs_u_dst_row_value_sumsumpositive = fs_q_dst_row_value_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_row_value_sumsumpositive_body_steps)) * fs_v_dst_row_value_sumsumpositive) + (fs_s_dst_row_value_sumsumpositive_body_steps))) /\ fs_s_dst_row_value_sumsumpositive_body_steps = fs_r_dst_row_value_sumsumpositive_body_steps + fs_a_dst_row_value_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_row_value_sumsumnegative fs_v_dst_row_value_sumsumnegative. ((((exists fs_h_dst_row_value_sumsumnegative_body_start. fs_h_dst_row_value_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_row_value_sumsumnegative)) /\ exists fs_q_dst_row_value_sumsumnegative_body_start. fs_u_dst_row_value_sumsumnegative = fs_q_dst_row_value_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_row_value_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_row_value_sumsumnegative_body_terminal. fs_h_dst_row_value_sumsumnegative_body_terminal + S (dst_negative_sum_row_value_sumsum) = S ((S (M)) * fs_v_dst_row_value_sumsumnegative)) /\ exists fs_q_dst_row_value_sumsumnegative_body_terminal. fs_u_dst_row_value_sumsumnegative = fs_q_dst_row_value_sumsumnegative_body_terminal * S ((S (M)) * fs_v_dst_row_value_sumsumnegative) + (dst_negative_sum_row_value_sumsum))) /\ forall fs_i_dst_row_value_sumsumnegative_body_steps. (exists fs_lt_dst_row_value_sumsumnegative_body_steps_bound. fs_lt_dst_row_value_sumsumnegative_body_steps_bound + S fs_i_dst_row_value_sumsumnegative_body_steps = M) -> exists fs_a_dst_row_value_sumsumnegative_body_steps fs_r_dst_row_value_sumsumnegative_body_steps fs_s_dst_row_value_sumsumnegative_body_steps. ((((exists fs_h_dst_row_value_sumsumnegative_body_steps_summand. fs_h_dst_row_value_sumsumnegative_body_steps_summand + S (fs_a_dst_row_value_sumsumnegative_body_steps) = S ((S (fs_i_dst_row_value_sumsumnegative_body_steps)) * dst_negative_scale_row_value_sumsum)) /\ exists fs_q_dst_row_value_sumsumnegative_body_steps_summand. dst_negative_code_row_value_sumsum = fs_q_dst_row_value_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_row_value_sumsumnegative_body_steps)) * dst_negative_scale_row_value_sumsum) + (fs_a_dst_row_value_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_row_value_sumsumnegative_body_steps_partial. fs_h_dst_row_value_sumsumnegative_body_steps_partial + S (fs_r_dst_row_value_sumsumnegative_body_steps) = S ((S (fs_i_dst_row_value_sumsumnegative_body_steps)) * fs_v_dst_row_value_sumsumnegative)) /\ exists fs_q_dst_row_value_sumsumnegative_body_steps_partial. fs_u_dst_row_value_sumsumnegative = fs_q_dst_row_value_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_row_value_sumsumnegative_body_steps)) * fs_v_dst_row_value_sumsumnegative) + (fs_r_dst_row_value_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_row_value_sumsumnegative_body_steps_successor. fs_h_dst_row_value_sumsumnegative_body_steps_successor + S (fs_s_dst_row_value_sumsumnegative_body_steps) = S ((S (S fs_i_dst_row_value_sumsumnegative_body_steps)) * fs_v_dst_row_value_sumsumnegative)) /\ exists fs_q_dst_row_value_sumsumnegative_body_steps_successor. fs_u_dst_row_value_sumsumnegative = fs_q_dst_row_value_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_row_value_sumsumnegative_body_steps)) * fs_v_dst_row_value_sumsumnegative) + (fs_s_dst_row_value_sumsumnegative_body_steps))) /\ fs_s_dst_row_value_sumsumnegative_body_steps = fs_r_dst_row_value_sumsumnegative_body_steps + fs_a_dst_row_value_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_row_value_sumsumresult ge_balance_negative_row_value_sumsumresult. (((((z) = 2 * (ge_balance_positive_row_value_sumsumresult) /\ (ge_balance_negative_row_value_sumsumresult) = 0) \/ exists ge_signed_half_row_value_sumsumresultdecode. (((z) = 2 * ge_signed_half_row_value_sumsumresultdecode + 1 /\ (ge_balance_positive_row_value_sumsumresult) = 0) /\ (ge_balance_negative_row_value_sumsumresult) = S ge_signed_half_row_value_sumsumresultdecode))) /\ ((dst_positive_sum_row_value_sumsum) + ge_balance_negative_row_value_sumsumresult = (dst_negative_sum_row_value_sumsum) + ge_balance_positive_row_value_sumsumresult))))))))))) -> z=a

Constructive proof overview

Generated structural guide

Each actual incidence row is zero or one genuinely bounded spike, so its actual sum is the actual source value.

The unchanged tactic script uses 10 declared prerequisites and contains 174 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 MX003B signed_support_incidence_zero_source_value MX0044 signed_support_incidence_row_lookup MX0035 signed_prefix_sum_point_spike_value signed_table_domain_resize Alpha theorem; checked-use authorized signed_table_lookup_any Alpha theorem; checked-use authorized MX0039 signed_support_incidence_entry_functional MX0036 signed_support_incidence_entry_hit MX0037 signed_support_incidence_entry_miss

Direct dependents

Formal native tactic body

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

Read the argument

Proof checkpoints

174 script commands · 31 reading checkpoints · 4 local claims

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

Named ingredients (6)

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

01Fix variables and assumptionsL1–10

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

  1. L1
    intro A
  2. L2
    intro B
  3. L3
    intro r
  4. L4
    intro s
  5. L5
    intro L
  6. L6
    intro M
  7. L7
    intro T
  8. L8
    intro i
  9. L9
    intro a
  10. L10
    intro z
02Fix variables and assumptionsL11–15

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

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

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

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

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

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

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

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

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

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

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

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

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

  1. L34
    intro j
  2. L35
    intro v
  3. L36
    intro h0j
  4. L37
    intro hj
  5. L38
    intro hv
09Use earlier factsL39–48

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

  1. L39
    specialize signed_support_incidence_zero_source_value (A)
  2. L40
    specialize signed_support_incidence_zero_source_value (r)
  3. L41
    specialize signed_support_incidence_zero_source_value (s)
  4. L42
    specialize signed_support_incidence_zero_source_value (i)
  5. L43
    specialize signed_support_incidence_zero_source_value (j)
  6. L44
    specialize signed_support_incidence_zero_source_value (v)
  7. L45
    apply signed_support_incidence_zero_source_value
  8. L46
    exact ha
  9. L47
    specialize signed_support_incidence_row_lookup (A)
  10. L48
    specialize signed_support_incidence_row_lookup (r)
10Use earlier factsL49–58

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

  1. L49
    specialize signed_support_incidence_row_lookup (s)
  2. L50
    specialize signed_support_incidence_row_lookup (L)
  3. L51
    specialize signed_support_incidence_row_lookup (M)
  4. L52
    specialize signed_support_incidence_row_lookup (T)
  5. L53
    specialize signed_support_incidence_row_lookup (x)
  6. L54
    specialize signed_support_incidence_row_lookup (i)
  7. L55
    specialize signed_support_incidence_row_lookup (j)
  8. L56
    specialize signed_support_incidence_row_lookup (v)
  9. L57
    apply signed_support_incidence_row_lookup
  10. L58
    exact hg
11Use earlier factsL59–63

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

  1. L59
    exact hs_witness_left
  2. L60
    exact hi
  3. L61
    exact hj
  4. L62
    exact hv
  5. L63
    exact hs_witness_right
12Establish hmL64–70

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

  1. L64
    have hm : ∃ j. BetaAt(r,s,i,j) ∧ (Lt(j,M) ∧ ArithAt(B,j,a))Definitions: ArithAtLtBetaAt
  2. L65
    specialize hp_right_right_left (i)
  3. L66
    specialize hp_right_right_left (a)
  4. L67
    apply hp_right_right_left
  5. L68
    exact hi
  6. L69
    exact ha
  7. L70
    exact hc_right
13Separate the logical casesL71–73

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

  1. L71
    cases hm
  2. L72
    cases hm_witness
  3. L73
    cases hm_witness_right
14Use earlier factsL74–79

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

  1. L74
    specialize signed_prefix_sum_point_spike_value (x)
  2. L75
    specialize signed_prefix_sum_point_spike_value (M)
  3. L76
    specialize signed_prefix_sum_point_spike_value (x1)
  4. L77
    specialize signed_prefix_sum_point_spike_value (a)
  5. L78
    specialize signed_prefix_sum_point_spike_value (z)
  6. L79
    apply signed_prefix_sum_point_spike_value
15Separate the logical casesL80–81

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

  1. L80
    cases hs_witness_left
  2. L81
    cases hs_witness_left_right
16Use earlier factsL82–87

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

  1. L82
    specialize signed_table_domain_resize (M)
  2. L83
    specialize signed_table_domain_resize (0)
  3. L84
    specialize signed_table_domain_resize (x)
  4. L85
    apply signed_table_domain_resize
  5. L86
    exact hs_witness_left_right_left
  6. L87
    exact hm_witness_right_left
17Establish hvL88–92

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

  1. L88
    have hv : ∃ v. ArithAt(x,x1,v)Definitions: ArithAt
  2. L89
    specialize signed_table_lookup_any (M)
  3. L90
    specialize signed_table_lookup_any (x)
  4. L91
    specialize signed_table_lookup_any (x1)
  5. L92
    apply signed_table_lookup_any
18Separate the logical casesL93–94

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

  1. L93
    cases hs_witness_left
  2. L94
    cases hs_witness_left_right
19Use earlier factsL95–95

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

  1. L95
    exact hs_witness_left_right_left
20Separate the logical casesL96–96

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

  1. L96
    cases hv
21Establish heL97–106

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

  1. L97
    have he : x2=a
  2. L98
    specialize signed_support_incidence_entry_functional (A)
  3. L99
    specialize signed_support_incidence_entry_functional (r)
  4. L100
    specialize signed_support_incidence_entry_functional (s)
  5. L101
    specialize signed_support_incidence_entry_functional (i)
  6. L102
    specialize signed_support_incidence_entry_functional (x1)
  7. L103
    specialize signed_support_incidence_entry_functional (x2)
  8. L104
    specialize signed_support_incidence_entry_functional (a)
  9. L105
    apply signed_support_incidence_entry_functional
  10. L106
    specialize signed_support_incidence_row_lookup (A)
22Use earlier factsL107–116

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

  1. L107
    specialize signed_support_incidence_row_lookup (r)
  2. L108
    specialize signed_support_incidence_row_lookup (s)
  3. L109
    specialize signed_support_incidence_row_lookup (L)
  4. L110
    specialize signed_support_incidence_row_lookup (M)
  5. L111
    specialize signed_support_incidence_row_lookup (T)
  6. L112
    specialize signed_support_incidence_row_lookup (x)
  7. L113
    specialize signed_support_incidence_row_lookup (i)
  8. L114
    specialize signed_support_incidence_row_lookup (x1)
  9. L115
    specialize signed_support_incidence_row_lookup (x2)
  10. L116
    apply signed_support_incidence_row_lookup
23Use earlier factsL117–126

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

  1. L117
    exact hg
  2. L118
    exact hs_witness_left
  3. L119
    exact hi
  4. L120
    exact hm_witness_right_left
  5. L121
    exact hv_witness
  6. L122
    specialize signed_support_incidence_entry_hit (A)
  7. L123
    specialize signed_support_incidence_entry_hit (r)
  8. L124
    specialize signed_support_incidence_entry_hit (s)
  9. L125
    specialize signed_support_incidence_entry_hit (i)
  10. L126
    specialize signed_support_incidence_entry_hit (x1)
24Use earlier factsL127–130

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

  1. L127
    specialize signed_support_incidence_entry_hit (a)
  2. L128
    apply signed_support_incidence_entry_hit
  3. L129
    exact ha
  4. L130
    exact hm_witness_left
25Calculate and transport equalitiesL131–132

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

  1. L131
    rewrite he at hv_witness
  2. L132
    rewrite he at hv_witness
26Use earlier factsL133–133

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

  1. L133
    exact hv_witness
27Fix variables and assumptionsL134–138

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

  1. L134
    intro j
  2. L135
    intro v
  3. L136
    intro hj
  4. L137
    intro hne
  5. L138
    intro hv
28Use earlier factsL139–148

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

  1. L139
    specialize signed_support_incidence_entry_functional (A)
  2. L140
    specialize signed_support_incidence_entry_functional (r)
  3. L141
    specialize signed_support_incidence_entry_functional (s)
  4. L142
    specialize signed_support_incidence_entry_functional (i)
  5. L143
    specialize signed_support_incidence_entry_functional (j)
  6. L144
    specialize signed_support_incidence_entry_functional (v)
  7. L145
    specialize signed_support_incidence_entry_functional (0)
  8. L146
    apply signed_support_incidence_entry_functional
  9. L147
    specialize signed_support_incidence_row_lookup (A)
  10. L148
    specialize signed_support_incidence_row_lookup (r)
29Use earlier factsL149–158

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

  1. L149
    specialize signed_support_incidence_row_lookup (s)
  2. L150
    specialize signed_support_incidence_row_lookup (L)
  3. L151
    specialize signed_support_incidence_row_lookup (M)
  4. L152
    specialize signed_support_incidence_row_lookup (T)
  5. L153
    specialize signed_support_incidence_row_lookup (x)
  6. L154
    specialize signed_support_incidence_row_lookup (i)
  7. L155
    specialize signed_support_incidence_row_lookup (j)
  8. L156
    specialize signed_support_incidence_row_lookup (v)
  9. L157
    apply signed_support_incidence_row_lookup
  10. L158
    exact hg
30Use earlier factsL159–168

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

  1. L159
    exact hs_witness_left
  2. L160
    exact hi
  3. L161
    exact hj
  4. L162
    exact hv
  5. L163
    specialize signed_support_incidence_entry_miss (A)
  6. L164
    specialize signed_support_incidence_entry_miss (r)
  7. L165
    specialize signed_support_incidence_entry_miss (s)
  8. L166
    specialize signed_support_incidence_entry_miss (i)
  9. L167
    specialize signed_support_incidence_entry_miss (j)
  10. L168
    specialize signed_support_incidence_entry_miss (x1)
31Use earlier factsL169–174

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

  1. L169
    specialize signed_support_incidence_entry_miss (a)
  2. L170
    apply signed_support_incidence_entry_miss
  3. L171
    exact ha
  4. L172
    exact hm_witness_left
  5. L173
    exact hne
  6. L174
    exact hs_witness_right

Library-wide reading audit

Original exact command ledger · 174 lines
  1. 0001intro A
  2. 0002intro B
  3. 0003intro r
  4. 0004intro s
  5. 0005intro L
  6. 0006intro M
  7. 0007intro T
  8. 0008intro i
  9. 0009intro a
  10. 0010intro z
  11. 0011intro hp
  12. 0012intro hg
  13. 0013intro hi
  14. 0014intro ha
  15. 0015intro hs
  16. 0016cases hp
  17. 0017cases hp_right
  18. 0018cases hp_right_right
  19. 0019cases hp_right_right_right
  20. 0020cases hs
  21. 0021cases hs_witness
  22. 0022have hc : a=0 \/ ~(a=0)
  23. 0023specialize eq_decidable (a)
  24. 0024specialize eq_decidable (0)
  25. 0025apply eq_decidable
  26. 0026cases hc
  27. 0027rewrite hc_left at ha
  28. 0028rewrite hc_left at ha
  29. 0029rewrite hc_left
  30. 0030specialize signed_prefix_sum_zero_value (x)
  31. 0031specialize signed_prefix_sum_zero_value (M)
  32. 0032specialize signed_prefix_sum_zero_value (z)
  33. 0033apply signed_prefix_sum_zero_value
  34. 0034intro j
  35. 0035intro v
  36. 0036intro h0j
  37. 0037intro hj
  38. 0038intro hv
  39. 0039specialize signed_support_incidence_zero_source_value (A)
  40. 0040specialize signed_support_incidence_zero_source_value (r)
  41. 0041specialize signed_support_incidence_zero_source_value (s)
  42. 0042specialize signed_support_incidence_zero_source_value (i)
  43. 0043specialize signed_support_incidence_zero_source_value (j)
  44. 0044specialize signed_support_incidence_zero_source_value (v)
  45. 0045apply signed_support_incidence_zero_source_value
  46. 0046exact ha
  47. 0047specialize signed_support_incidence_row_lookup (A)
  48. 0048specialize signed_support_incidence_row_lookup (r)
  49. 0049specialize signed_support_incidence_row_lookup (s)
  50. 0050specialize signed_support_incidence_row_lookup (L)
  51. 0051specialize signed_support_incidence_row_lookup (M)
  52. 0052specialize signed_support_incidence_row_lookup (T)
  53. 0053specialize signed_support_incidence_row_lookup (x)
  54. 0054specialize signed_support_incidence_row_lookup (i)
  55. 0055specialize signed_support_incidence_row_lookup (j)
  56. 0056specialize signed_support_incidence_row_lookup (v)
  57. 0057apply signed_support_incidence_row_lookup
  58. 0058exact hg
  59. 0059exact hs_witness_left
  60. 0060exact hi
  61. 0061exact hj
  62. 0062exact hv
  63. 0063exact hs_witness_right
  64. 0064have hm : exists j. (((((exists ff_h_pvs_row_active_map. ff_h_pvs_row_active_map + S (j) = S ((S (i)) * s)) /\ exists ff_q_pvs_row_active_map. r = ff_q_pvs_row_active_map * S ((S (i)) * s) + (j))) /\ (((exists pvs_gap_row_active_bound. pvs_gap_row_active_bound + S (j) = (M)) /\ (exists dst_positive_code_row_active_value dst_positive_scale_row_active_value dst_negative_code_row_active_value dst_negative_scale_row_active_value dst_positive_row_active_value dst_negative_row_active_value. (((B) = (((((dst_positive_code_row_active_value) + (dst_positive_scale_row_active_value)) * S ((dst_positive_code_row_active_value) + (dst_positive_scale_row_active_value)) + ((dst_positive_scale_row_active_value) + (dst_positive_scale_row_active_value))) + (((dst_negative_code_row_active_value) + (dst_negative_scale_row_active_value)) * S ((dst_negative_code_row_active_value) + (dst_negative_scale_row_active_value)) + ((dst_negative_scale_row_active_value) + (dst_negative_scale_row_active_value)))) * S ((((dst_positive_code_row_active_value) + (dst_positive_scale_row_active_value)) * S ((dst_positive_code_row_active_value) + (dst_positive_scale_row_active_value)) + ((dst_positive_scale_row_active_value) + (dst_positive_scale_row_active_value))) + (((dst_negative_code_row_active_value) + (dst_negative_scale_row_active_value)) * S ((dst_negative_code_row_active_value) + (dst_negative_scale_row_active_value)) + ((dst_negative_scale_row_active_value) + (dst_negative_scale_row_active_value)))) + ((((dst_negative_code_row_active_value) + (dst_negative_scale_row_active_value)) * S ((dst_negative_code_row_active_value) + (dst_negative_scale_row_active_value)) + ((dst_negative_scale_row_active_value) + (dst_negative_scale_row_active_value))) + (((dst_negative_code_row_active_value) + (dst_negative_scale_row_active_value)) * S ((dst_negative_code_row_active_value) + (dst_negative_scale_row_active_value)) + ((dst_negative_scale_row_active_value) + (dst_negative_scale_row_active_value)))))) /\ (((((exists ff_h_pvs_row_active_valuepositive. ff_h_pvs_row_active_valuepositive + S (dst_positive_row_active_value) = S ((S (j)) * dst_positive_scale_row_active_value)) /\ exists ff_q_pvs_row_active_valuepositive. dst_positive_code_row_active_value = ff_q_pvs_row_active_valuepositive * S ((S (j)) * dst_positive_scale_row_active_value) + (dst_positive_row_active_value))) /\ (((((exists ff_h_pvs_row_active_valuenegative. ff_h_pvs_row_active_valuenegative + S (dst_negative_row_active_value) = S ((S (j)) * dst_negative_scale_row_active_value)) /\ exists ff_q_pvs_row_active_valuenegative. dst_negative_code_row_active_value = ff_q_pvs_row_active_valuenegative * S ((S (j)) * dst_negative_scale_row_active_value) + (dst_negative_row_active_value))) /\ (exists ge_balance_positive_row_active_valuevalue ge_balance_negative_row_active_valuevalue. (((((a) = 2 * (ge_balance_positive_row_active_valuevalue) /\ (ge_balance_negative_row_active_valuevalue) = 0) \/ exists ge_signed_half_row_active_valuevaluedecode. (((a) = 2 * ge_signed_half_row_active_valuevaluedecode + 1 /\ (ge_balance_positive_row_active_valuevalue) = 0) /\ (ge_balance_negative_row_active_valuevalue) = S ge_signed_half_row_active_valuevaluedecode))) /\ ((dst_positive_row_active_value) + ge_balance_negative_row_active_valuevalue = (dst_negative_row_active_value) + ge_balance_positive_row_active_valuevalue)))))))))))))
  65. 0065specialize hp_right_right_left (i)
  66. 0066specialize hp_right_right_left (a)
  67. 0067apply hp_right_right_left
  68. 0068exact hi
  69. 0069exact ha
  70. 0070exact hc_right
  71. 0071cases hm
  72. 0072cases hm_witness
  73. 0073cases hm_witness_right
  74. 0074specialize signed_prefix_sum_point_spike_value (x)
  75. 0075specialize signed_prefix_sum_point_spike_value (M)
  76. 0076specialize signed_prefix_sum_point_spike_value (x1)
  77. 0077specialize signed_prefix_sum_point_spike_value (a)
  78. 0078specialize signed_prefix_sum_point_spike_value (z)
  79. 0079apply signed_prefix_sum_point_spike_value
  80. 0080cases hs_witness_left
  81. 0081cases hs_witness_left_right
  82. 0082specialize signed_table_domain_resize (M)
  83. 0083specialize signed_table_domain_resize (0)
  84. 0084specialize signed_table_domain_resize (x)
  85. 0085apply signed_table_domain_resize
  86. 0086exact hs_witness_left_right_left
  87. 0087exact hm_witness_right_left
  88. 0088have hv : exists v. (exists dst_positive_code_row_spike_actual_lookup dst_positive_scale_row_spike_actual_lookup dst_negative_code_row_spike_actual_lookup dst_negative_scale_row_spike_actual_lookup dst_positive_row_spike_actual_lookup dst_negative_row_spike_actual_lookup. (((x) = (((((dst_positive_code_row_spike_actual_lookup) + (dst_positive_scale_row_spike_actual_lookup)) * S ((dst_positive_code_row_spike_actual_lookup) + (dst_positive_scale_row_spike_actual_lookup)) + ((dst_positive_scale_row_spike_actual_lookup) + (dst_positive_scale_row_spike_actual_lookup))) + (((dst_negative_code_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)) * S ((dst_negative_code_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)) + ((dst_negative_scale_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)))) * S ((((dst_positive_code_row_spike_actual_lookup) + (dst_positive_scale_row_spike_actual_lookup)) * S ((dst_positive_code_row_spike_actual_lookup) + (dst_positive_scale_row_spike_actual_lookup)) + ((dst_positive_scale_row_spike_actual_lookup) + (dst_positive_scale_row_spike_actual_lookup))) + (((dst_negative_code_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)) * S ((dst_negative_code_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)) + ((dst_negative_scale_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)))) + ((((dst_negative_code_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)) * S ((dst_negative_code_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)) + ((dst_negative_scale_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup))) + (((dst_negative_code_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)) * S ((dst_negative_code_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)) + ((dst_negative_scale_row_spike_actual_lookup) + (dst_negative_scale_row_spike_actual_lookup)))))) /\ (((((exists ff_h_pvs_row_spike_actual_lookuppositive. ff_h_pvs_row_spike_actual_lookuppositive + S (dst_positive_row_spike_actual_lookup) = S ((S (x1)) * dst_positive_scale_row_spike_actual_lookup)) /\ exists ff_q_pvs_row_spike_actual_lookuppositive. dst_positive_code_row_spike_actual_lookup = ff_q_pvs_row_spike_actual_lookuppositive * S ((S (x1)) * dst_positive_scale_row_spike_actual_lookup) + (dst_positive_row_spike_actual_lookup))) /\ (((((exists ff_h_pvs_row_spike_actual_lookupnegative. ff_h_pvs_row_spike_actual_lookupnegative + S (dst_negative_row_spike_actual_lookup) = S ((S (x1)) * dst_negative_scale_row_spike_actual_lookup)) /\ exists ff_q_pvs_row_spike_actual_lookupnegative. dst_negative_code_row_spike_actual_lookup = ff_q_pvs_row_spike_actual_lookupnegative * S ((S (x1)) * dst_negative_scale_row_spike_actual_lookup) + (dst_negative_row_spike_actual_lookup))) /\ (exists ge_balance_positive_row_spike_actual_lookupvalue ge_balance_negative_row_spike_actual_lookupvalue. (((((v) = 2 * (ge_balance_positive_row_spike_actual_lookupvalue) /\ (ge_balance_negative_row_spike_actual_lookupvalue) = 0) \/ exists ge_signed_half_row_spike_actual_lookupvaluedecode. (((v) = 2 * ge_signed_half_row_spike_actual_lookupvaluedecode + 1 /\ (ge_balance_positive_row_spike_actual_lookupvalue) = 0) /\ (ge_balance_negative_row_spike_actual_lookupvalue) = S ge_signed_half_row_spike_actual_lookupvaluedecode))) /\ ((dst_positive_row_spike_actual_lookup) + ge_balance_negative_row_spike_actual_lookupvalue = (dst_negative_row_spike_actual_lookup) + ge_balance_positive_row_spike_actual_lookupvalue)))))))))
  89. 0089specialize signed_table_lookup_any (M)
  90. 0090specialize signed_table_lookup_any (x)
  91. 0091specialize signed_table_lookup_any (x1)
  92. 0092apply signed_table_lookup_any
  93. 0093cases hs_witness_left
  94. 0094cases hs_witness_left_right
  95. 0095exact hs_witness_left_right_left
  96. 0096cases hv
  97. 0097have he : x2=a
  98. 0098specialize signed_support_incidence_entry_functional (A)
  99. 0099specialize signed_support_incidence_entry_functional (r)
  100. 0100specialize signed_support_incidence_entry_functional (s)
  101. 0101specialize signed_support_incidence_entry_functional (i)
  102. 0102specialize signed_support_incidence_entry_functional (x1)
  103. 0103specialize signed_support_incidence_entry_functional (x2)
  104. 0104specialize signed_support_incidence_entry_functional (a)
  105. 0105apply signed_support_incidence_entry_functional
  106. 0106specialize signed_support_incidence_row_lookup (A)
  107. 0107specialize signed_support_incidence_row_lookup (r)
  108. 0108specialize signed_support_incidence_row_lookup (s)
  109. 0109specialize signed_support_incidence_row_lookup (L)
  110. 0110specialize signed_support_incidence_row_lookup (M)
  111. 0111specialize signed_support_incidence_row_lookup (T)
  112. 0112specialize signed_support_incidence_row_lookup (x)
  113. 0113specialize signed_support_incidence_row_lookup (i)
  114. 0114specialize signed_support_incidence_row_lookup (x1)
  115. 0115specialize signed_support_incidence_row_lookup (x2)
  116. 0116apply signed_support_incidence_row_lookup
  117. 0117exact hg
  118. 0118exact hs_witness_left
  119. 0119exact hi
  120. 0120exact hm_witness_right_left
  121. 0121exact hv_witness
  122. 0122specialize signed_support_incidence_entry_hit (A)
  123. 0123specialize signed_support_incidence_entry_hit (r)
  124. 0124specialize signed_support_incidence_entry_hit (s)
  125. 0125specialize signed_support_incidence_entry_hit (i)
  126. 0126specialize signed_support_incidence_entry_hit (x1)
  127. 0127specialize signed_support_incidence_entry_hit (a)
  128. 0128apply signed_support_incidence_entry_hit
  129. 0129exact ha
  130. 0130exact hm_witness_left
  131. 0131rewrite he at hv_witness
  132. 0132rewrite he at hv_witness
  133. 0133exact hv_witness
  134. 0134intro j
  135. 0135intro v
  136. 0136intro hj
  137. 0137intro hne
  138. 0138intro hv
  139. 0139specialize signed_support_incidence_entry_functional (A)
  140. 0140specialize signed_support_incidence_entry_functional (r)
  141. 0141specialize signed_support_incidence_entry_functional (s)
  142. 0142specialize signed_support_incidence_entry_functional (i)
  143. 0143specialize signed_support_incidence_entry_functional (j)
  144. 0144specialize signed_support_incidence_entry_functional (v)
  145. 0145specialize signed_support_incidence_entry_functional (0)
  146. 0146apply signed_support_incidence_entry_functional
  147. 0147specialize signed_support_incidence_row_lookup (A)
  148. 0148specialize signed_support_incidence_row_lookup (r)
  149. 0149specialize signed_support_incidence_row_lookup (s)
  150. 0150specialize signed_support_incidence_row_lookup (L)
  151. 0151specialize signed_support_incidence_row_lookup (M)
  152. 0152specialize signed_support_incidence_row_lookup (T)
  153. 0153specialize signed_support_incidence_row_lookup (x)
  154. 0154specialize signed_support_incidence_row_lookup (i)
  155. 0155specialize signed_support_incidence_row_lookup (j)
  156. 0156specialize signed_support_incidence_row_lookup (v)
  157. 0157apply signed_support_incidence_row_lookup
  158. 0158exact hg
  159. 0159exact hs_witness_left
  160. 0160exact hi
  161. 0161exact hj
  162. 0162exact hv
  163. 0163specialize signed_support_incidence_entry_miss (A)
  164. 0164specialize signed_support_incidence_entry_miss (r)
  165. 0165specialize signed_support_incidence_entry_miss (s)
  166. 0166specialize signed_support_incidence_entry_miss (i)
  167. 0167specialize signed_support_incidence_entry_miss (j)
  168. 0168specialize signed_support_incidence_entry_miss (x1)
  169. 0169specialize signed_support_incidence_entry_miss (a)
  170. 0170apply signed_support_incidence_entry_miss
  171. 0171exact ha
  172. 0172exact hm_witness_left
  173. 0173exact hne
  174. 0174exact hs_witness_right