RS0013

signed_rectangular_row_sums_extensional_unique

All genuine row-sum tables agree entrywise in canonical signed values, without identifying arbitrary beta encodings.

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

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.

Every slice, row table, column table and signed sum is an actual beta-coded witness. Entries are F((o+s*i)+t*j), for i<m and j<n. Zero dimensions and zero strides are allowed; separately certified endpoints are unused. Table uniqueness concerns values, not codes. No infinite-sum assertion is made.

Exact theorem in conservative defined notation

∀ F. ∀ R. ∀ Q. ∀ o. ∀ s. ∀ t. ∀ m. ∀ n. ArithRowSums(F,R,o,s,t,m,n)ArithRowSums(F,Q,o,s,t,m,n)ArithTableEqual(R,Q,m)

Every linked abbreviation expands hygienically to the identical original native formula.

Definition DAG

Actual proof prerequisites

Original expanded first-order statement
forall F R Q o s t m n. (((exists dst_positive_code_unique_firstsource_table dst_positive_scale_unique_firstsource_table dst_negative_code_unique_firstsource_table dst_negative_scale_unique_firstsource_table. (((F) = (((((dst_positive_code_unique_firstsource_table) + (dst_positive_scale_unique_firstsource_table)) * S ((dst_positive_code_unique_firstsource_table) + (dst_positive_scale_unique_firstsource_table)) + ((dst_positive_scale_unique_firstsource_table) + (dst_positive_scale_unique_firstsource_table))) + (((dst_negative_code_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)) * S ((dst_negative_code_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)) + ((dst_negative_scale_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)))) * S ((((dst_positive_code_unique_firstsource_table) + (dst_positive_scale_unique_firstsource_table)) * S ((dst_positive_code_unique_firstsource_table) + (dst_positive_scale_unique_firstsource_table)) + ((dst_positive_scale_unique_firstsource_table) + (dst_positive_scale_unique_firstsource_table))) + (((dst_negative_code_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)) * S ((dst_negative_code_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)) + ((dst_negative_scale_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)))) + ((((dst_negative_code_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)) * S ((dst_negative_code_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)) + ((dst_negative_scale_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table))) + (((dst_negative_code_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)) * S ((dst_negative_code_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)) + ((dst_negative_scale_unique_firstsource_table) + (dst_negative_scale_unique_firstsource_table)))))) /\ (forall dst_index_unique_firstsource_table. (exists pvs_le_gap_unique_firstsource_tabledomain. pvs_le_gap_unique_firstsource_tabledomain + (dst_index_unique_firstsource_table) = (0)) -> exists dst_positive_unique_firstsource_table dst_negative_unique_firstsource_table dst_value_unique_firstsource_table. ((((exists ff_h_pvs_unique_firstsource_tableentrypositive. ff_h_pvs_unique_firstsource_tableentrypositive + S (dst_positive_unique_firstsource_table) = S ((S (dst_index_unique_firstsource_table)) * dst_positive_scale_unique_firstsource_table)) /\ exists ff_q_pvs_unique_firstsource_tableentrypositive. dst_positive_code_unique_firstsource_table = ff_q_pvs_unique_firstsource_tableentrypositive * S ((S (dst_index_unique_firstsource_table)) * dst_positive_scale_unique_firstsource_table) + (dst_positive_unique_firstsource_table))) /\ (((((exists ff_h_pvs_unique_firstsource_tableentrynegative. ff_h_pvs_unique_firstsource_tableentrynegative + S (dst_negative_unique_firstsource_table) = S ((S (dst_index_unique_firstsource_table)) * dst_negative_scale_unique_firstsource_table)) /\ exists ff_q_pvs_unique_firstsource_tableentrynegative. dst_negative_code_unique_firstsource_table = ff_q_pvs_unique_firstsource_tableentrynegative * S ((S (dst_index_unique_firstsource_table)) * dst_negative_scale_unique_firstsource_table) + (dst_negative_unique_firstsource_table))) /\ (exists ge_balance_positive_unique_firstsource_tableentryvalue ge_balance_negative_unique_firstsource_tableentryvalue. (((((dst_value_unique_firstsource_table) = 2 * (ge_balance_positive_unique_firstsource_tableentryvalue) /\ (ge_balance_negative_unique_firstsource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_firstsource_tableentryvaluedecode. (((dst_value_unique_firstsource_table) = 2 * ge_signed_half_unique_firstsource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_firstsource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_firstsource_tableentryvalue) = S ge_signed_half_unique_firstsource_tableentryvaluedecode))) /\ ((dst_positive_unique_firstsource_table) + ge_balance_negative_unique_firstsource_tableentryvalue = (dst_negative_unique_firstsource_table) + ge_balance_positive_unique_firstsource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_firstrow_table dst_positive_scale_unique_firstrow_table dst_negative_code_unique_firstrow_table dst_negative_scale_unique_firstrow_table. (((R) = (((((dst_positive_code_unique_firstrow_table) + (dst_positive_scale_unique_firstrow_table)) * S ((dst_positive_code_unique_firstrow_table) + (dst_positive_scale_unique_firstrow_table)) + ((dst_positive_scale_unique_firstrow_table) + (dst_positive_scale_unique_firstrow_table))) + (((dst_negative_code_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)) * S ((dst_negative_code_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)) + ((dst_negative_scale_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)))) * S ((((dst_positive_code_unique_firstrow_table) + (dst_positive_scale_unique_firstrow_table)) * S ((dst_positive_code_unique_firstrow_table) + (dst_positive_scale_unique_firstrow_table)) + ((dst_positive_scale_unique_firstrow_table) + (dst_positive_scale_unique_firstrow_table))) + (((dst_negative_code_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)) * S ((dst_negative_code_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)) + ((dst_negative_scale_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)))) + ((((dst_negative_code_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)) * S ((dst_negative_code_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)) + ((dst_negative_scale_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table))) + (((dst_negative_code_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)) * S ((dst_negative_code_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)) + ((dst_negative_scale_unique_firstrow_table) + (dst_negative_scale_unique_firstrow_table)))))) /\ (forall dst_index_unique_firstrow_table. (exists pvs_le_gap_unique_firstrow_tabledomain. pvs_le_gap_unique_firstrow_tabledomain + (dst_index_unique_firstrow_table) = (m)) -> exists dst_positive_unique_firstrow_table dst_negative_unique_firstrow_table dst_value_unique_firstrow_table. ((((exists ff_h_pvs_unique_firstrow_tableentrypositive. ff_h_pvs_unique_firstrow_tableentrypositive + S (dst_positive_unique_firstrow_table) = S ((S (dst_index_unique_firstrow_table)) * dst_positive_scale_unique_firstrow_table)) /\ exists ff_q_pvs_unique_firstrow_tableentrypositive. dst_positive_code_unique_firstrow_table = ff_q_pvs_unique_firstrow_tableentrypositive * S ((S (dst_index_unique_firstrow_table)) * dst_positive_scale_unique_firstrow_table) + (dst_positive_unique_firstrow_table))) /\ (((((exists ff_h_pvs_unique_firstrow_tableentrynegative. ff_h_pvs_unique_firstrow_tableentrynegative + S (dst_negative_unique_firstrow_table) = S ((S (dst_index_unique_firstrow_table)) * dst_negative_scale_unique_firstrow_table)) /\ exists ff_q_pvs_unique_firstrow_tableentrynegative. dst_negative_code_unique_firstrow_table = ff_q_pvs_unique_firstrow_tableentrynegative * S ((S (dst_index_unique_firstrow_table)) * dst_negative_scale_unique_firstrow_table) + (dst_negative_unique_firstrow_table))) /\ (exists ge_balance_positive_unique_firstrow_tableentryvalue ge_balance_negative_unique_firstrow_tableentryvalue. (((((dst_value_unique_firstrow_table) = 2 * (ge_balance_positive_unique_firstrow_tableentryvalue) /\ (ge_balance_negative_unique_firstrow_tableentryvalue) = 0) \/ exists ge_signed_half_unique_firstrow_tableentryvaluedecode. (((dst_value_unique_firstrow_table) = 2 * ge_signed_half_unique_firstrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_firstrow_tableentryvalue) = 0) /\ (ge_balance_negative_unique_firstrow_tableentryvalue) = S ge_signed_half_unique_firstrow_tableentryvaluedecode))) /\ ((dst_positive_unique_firstrow_table) + ge_balance_negative_unique_firstrow_tableentryvalue = (dst_negative_unique_firstrow_table) + ge_balance_positive_unique_firstrow_tableentryvalue))))))))) /\ (forall srt_index_unique_first. (exists pvs_gap_unique_firstbound. pvs_gap_unique_firstbound + S (srt_index_unique_first) = (m)) -> exists srt_value_unique_first. (((exists dst_positive_code_unique_firstrowentry dst_positive_scale_unique_firstrowentry dst_negative_code_unique_firstrowentry dst_negative_scale_unique_firstrowentry dst_positive_unique_firstrowentry dst_negative_unique_firstrowentry. (((R) = (((((dst_positive_code_unique_firstrowentry) + (dst_positive_scale_unique_firstrowentry)) * S ((dst_positive_code_unique_firstrowentry) + (dst_positive_scale_unique_firstrowentry)) + ((dst_positive_scale_unique_firstrowentry) + (dst_positive_scale_unique_firstrowentry))) + (((dst_negative_code_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)) * S ((dst_negative_code_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)) + ((dst_negative_scale_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)))) * S ((((dst_positive_code_unique_firstrowentry) + (dst_positive_scale_unique_firstrowentry)) * S ((dst_positive_code_unique_firstrowentry) + (dst_positive_scale_unique_firstrowentry)) + ((dst_positive_scale_unique_firstrowentry) + (dst_positive_scale_unique_firstrowentry))) + (((dst_negative_code_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)) * S ((dst_negative_code_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)) + ((dst_negative_scale_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)))) + ((((dst_negative_code_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)) * S ((dst_negative_code_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)) + ((dst_negative_scale_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry))) + (((dst_negative_code_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)) * S ((dst_negative_code_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)) + ((dst_negative_scale_unique_firstrowentry) + (dst_negative_scale_unique_firstrowentry)))))) /\ (((((exists ff_h_pvs_unique_firstrowentrypositive. ff_h_pvs_unique_firstrowentrypositive + S (dst_positive_unique_firstrowentry) = S ((S (srt_index_unique_first)) * dst_positive_scale_unique_firstrowentry)) /\ exists ff_q_pvs_unique_firstrowentrypositive. dst_positive_code_unique_firstrowentry = ff_q_pvs_unique_firstrowentrypositive * S ((S (srt_index_unique_first)) * dst_positive_scale_unique_firstrowentry) + (dst_positive_unique_firstrowentry))) /\ (((((exists ff_h_pvs_unique_firstrowentrynegative. ff_h_pvs_unique_firstrowentrynegative + S (dst_negative_unique_firstrowentry) = S ((S (srt_index_unique_first)) * dst_negative_scale_unique_firstrowentry)) /\ exists ff_q_pvs_unique_firstrowentrynegative. dst_negative_code_unique_firstrowentry = ff_q_pvs_unique_firstrowentrynegative * S ((S (srt_index_unique_first)) * dst_negative_scale_unique_firstrowentry) + (dst_negative_unique_firstrowentry))) /\ (exists ge_balance_positive_unique_firstrowentryvalue ge_balance_negative_unique_firstrowentryvalue. (((((srt_value_unique_first) = 2 * (ge_balance_positive_unique_firstrowentryvalue) /\ (ge_balance_negative_unique_firstrowentryvalue) = 0) \/ exists ge_signed_half_unique_firstrowentryvaluedecode. (((srt_value_unique_first) = 2 * ge_signed_half_unique_firstrowentryvaluedecode + 1 /\ (ge_balance_positive_unique_firstrowentryvalue) = 0) /\ (ge_balance_negative_unique_firstrowentryvalue) = S ge_signed_half_unique_firstrowentryvaluedecode))) /\ ((dst_positive_unique_firstrowentry) + ge_balance_negative_unique_firstrowentryvalue = (dst_negative_unique_firstrowentry) + ge_balance_positive_unique_firstrowentryvalue))))))))) /\ (exists srs_slice_unique_firstrowrow_sum. ((((exists dst_positive_code_unique_firstrowrow_sumslicesource_table dst_positive_scale_unique_firstrowrow_sumslicesource_table dst_negative_code_unique_firstrowrow_sumslicesource_table dst_negative_scale_unique_firstrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_unique_firstrowrow_sumslicesource_table) + (dst_positive_scale_unique_firstrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_firstrowrow_sumslicesource_table) + (dst_positive_scale_unique_firstrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_firstrowrow_sumslicesource_table) + (dst_positive_scale_unique_firstrowrow_sumslicesource_table))) + (((dst_negative_code_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)))) * S ((((dst_positive_code_unique_firstrowrow_sumslicesource_table) + (dst_positive_scale_unique_firstrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_firstrowrow_sumslicesource_table) + (dst_positive_scale_unique_firstrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_firstrowrow_sumslicesource_table) + (dst_positive_scale_unique_firstrowrow_sumslicesource_table))) + (((dst_negative_code_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)))) + ((((dst_negative_code_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table))) + (((dst_negative_code_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_firstrowrow_sumslicesource_table) + (dst_negative_scale_unique_firstrowrow_sumslicesource_table)))))) /\ (forall dst_index_unique_firstrowrow_sumslicesource_table. (exists pvs_le_gap_unique_firstrowrow_sumslicesource_tabledomain. pvs_le_gap_unique_firstrowrow_sumslicesource_tabledomain + (dst_index_unique_firstrowrow_sumslicesource_table) = (0)) -> exists dst_positive_unique_firstrowrow_sumslicesource_table dst_negative_unique_firstrowrow_sumslicesource_table dst_value_unique_firstrowrow_sumslicesource_table. ((((exists ff_h_pvs_unique_firstrowrow_sumslicesource_tableentrypositive. ff_h_pvs_unique_firstrowrow_sumslicesource_tableentrypositive + S (dst_positive_unique_firstrowrow_sumslicesource_table) = S ((S (dst_index_unique_firstrowrow_sumslicesource_table)) * dst_positive_scale_unique_firstrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_firstrowrow_sumslicesource_tableentrypositive. dst_positive_code_unique_firstrowrow_sumslicesource_table = ff_q_pvs_unique_firstrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_unique_firstrowrow_sumslicesource_table)) * dst_positive_scale_unique_firstrowrow_sumslicesource_table) + (dst_positive_unique_firstrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_unique_firstrowrow_sumslicesource_tableentrynegative. ff_h_pvs_unique_firstrowrow_sumslicesource_tableentrynegative + S (dst_negative_unique_firstrowrow_sumslicesource_table) = S ((S (dst_index_unique_firstrowrow_sumslicesource_table)) * dst_negative_scale_unique_firstrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_firstrowrow_sumslicesource_tableentrynegative. dst_negative_code_unique_firstrowrow_sumslicesource_table = ff_q_pvs_unique_firstrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_unique_firstrowrow_sumslicesource_table)) * dst_negative_scale_unique_firstrowrow_sumslicesource_table) + (dst_negative_unique_firstrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_unique_firstrowrow_sumslicesource_tableentryvalue ge_balance_negative_unique_firstrowrow_sumslicesource_tableentryvalue. (((((dst_value_unique_firstrowrow_sumslicesource_table) = 2 * (ge_balance_positive_unique_firstrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_unique_firstrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_firstrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_unique_firstrowrow_sumslicesource_table) = 2 * ge_signed_half_unique_firstrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_firstrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_firstrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_unique_firstrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_unique_firstrowrow_sumslicesource_table) + ge_balance_negative_unique_firstrowrow_sumslicesource_tableentryvalue = (dst_negative_unique_firstrowrow_sumslicesource_table) + ge_balance_positive_unique_firstrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_firstrowrow_sumsliceoutput_table dst_positive_scale_unique_firstrowrow_sumsliceoutput_table dst_negative_code_unique_firstrowrow_sumsliceoutput_table dst_negative_scale_unique_firstrowrow_sumsliceoutput_table. (((srs_slice_unique_firstrowrow_sum) = (((((dst_positive_code_unique_firstrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_firstrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_firstrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_firstrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_firstrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_firstrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_unique_firstrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_firstrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_firstrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_firstrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_firstrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_firstrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_unique_firstrowrow_sumsliceoutput_table. (exists pvs_le_gap_unique_firstrowrow_sumsliceoutput_tabledomain. pvs_le_gap_unique_firstrowrow_sumsliceoutput_tabledomain + (dst_index_unique_firstrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_unique_firstrowrow_sumsliceoutput_table dst_negative_unique_firstrowrow_sumsliceoutput_table dst_value_unique_firstrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_unique_firstrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_unique_firstrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_unique_firstrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_firstrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_firstrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_firstrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_unique_firstrowrow_sumsliceoutput_table = ff_q_pvs_unique_firstrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_unique_firstrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_firstrowrow_sumsliceoutput_table) + (dst_positive_unique_firstrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_unique_firstrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_unique_firstrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_unique_firstrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_firstrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_firstrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_firstrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_unique_firstrowrow_sumsliceoutput_table = ff_q_pvs_unique_firstrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_unique_firstrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_firstrowrow_sumsliceoutput_table) + (dst_negative_unique_firstrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_unique_firstrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_unique_firstrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_unique_firstrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_unique_firstrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_unique_firstrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_unique_firstrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_unique_firstrowrow_sumsliceoutput_table) = 2 * ge_signed_half_unique_firstrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_firstrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_unique_firstrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_unique_firstrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_unique_firstrowrow_sumsliceoutput_table) + ge_balance_negative_unique_firstrowrow_sumsliceoutput_tableentryvalue = (dst_negative_unique_firstrowrow_sumsliceoutput_table) + ge_balance_positive_unique_firstrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_unique_firstrowrow_sumslice. (exists pvs_gap_unique_firstrowrow_sumslicebound. pvs_gap_unique_firstrowrow_sumslicebound + S (srs_index_unique_firstrowrow_sumslice) = (n)) -> exists srs_value_unique_firstrowrow_sumslice. (((exists dst_positive_code_unique_firstrowrow_sumsliceentrysource dst_positive_scale_unique_firstrowrow_sumsliceentrysource dst_negative_code_unique_firstrowrow_sumsliceentrysource dst_negative_scale_unique_firstrowrow_sumsliceentrysource dst_positive_unique_firstrowrow_sumsliceentrysource dst_negative_unique_firstrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_unique_firstrowrow_sumsliceentrysource) + (dst_positive_scale_unique_firstrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_firstrowrow_sumsliceentrysource) + (dst_positive_scale_unique_firstrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_firstrowrow_sumsliceentrysource) + (dst_positive_scale_unique_firstrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_unique_firstrowrow_sumsliceentrysource) + (dst_positive_scale_unique_firstrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_firstrowrow_sumsliceentrysource) + (dst_positive_scale_unique_firstrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_firstrowrow_sumsliceentrysource) + (dst_positive_scale_unique_firstrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)))) + ((((dst_negative_code_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_firstrowrow_sumsliceentrysource) + (dst_negative_scale_unique_firstrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_unique_firstrowrow_sumsliceentrysourcepositive. ff_h_pvs_unique_firstrowrow_sumsliceentrysourcepositive + S (dst_positive_unique_firstrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_first)))) + ((t) * (srs_index_unique_firstrowrow_sumslice))))) * dst_positive_scale_unique_firstrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_firstrowrow_sumsliceentrysourcepositive. dst_positive_code_unique_firstrowrow_sumsliceentrysource = ff_q_pvs_unique_firstrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_unique_first)))) + ((t) * (srs_index_unique_firstrowrow_sumslice))))) * dst_positive_scale_unique_firstrowrow_sumsliceentrysource) + (dst_positive_unique_firstrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_unique_firstrowrow_sumsliceentrysourcenegative. ff_h_pvs_unique_firstrowrow_sumsliceentrysourcenegative + S (dst_negative_unique_firstrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_first)))) + ((t) * (srs_index_unique_firstrowrow_sumslice))))) * dst_negative_scale_unique_firstrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_firstrowrow_sumsliceentrysourcenegative. dst_negative_code_unique_firstrowrow_sumsliceentrysource = ff_q_pvs_unique_firstrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_unique_first)))) + ((t) * (srs_index_unique_firstrowrow_sumslice))))) * dst_negative_scale_unique_firstrowrow_sumsliceentrysource) + (dst_negative_unique_firstrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_unique_firstrowrow_sumsliceentrysourcevalue ge_balance_negative_unique_firstrowrow_sumsliceentrysourcevalue. (((((srs_value_unique_firstrowrow_sumslice) = 2 * (ge_balance_positive_unique_firstrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_unique_firstrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_unique_firstrowrow_sumsliceentrysourcevaluedecode. (((srs_value_unique_firstrowrow_sumslice) = 2 * ge_signed_half_unique_firstrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_unique_firstrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_unique_firstrowrow_sumsliceentrysourcevalue) = S ge_signed_half_unique_firstrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_unique_firstrowrow_sumsliceentrysource) + ge_balance_negative_unique_firstrowrow_sumsliceentrysourcevalue = (dst_negative_unique_firstrowrow_sumsliceentrysource) + ge_balance_positive_unique_firstrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_unique_firstrowrow_sumsliceentryoutput dst_positive_scale_unique_firstrowrow_sumsliceentryoutput dst_negative_code_unique_firstrowrow_sumsliceentryoutput dst_negative_scale_unique_firstrowrow_sumsliceentryoutput dst_positive_unique_firstrowrow_sumsliceentryoutput dst_negative_unique_firstrowrow_sumsliceentryoutput. (((srs_slice_unique_firstrowrow_sum) = (((((dst_positive_code_unique_firstrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_firstrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_firstrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_firstrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_firstrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_firstrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_unique_firstrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_firstrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_firstrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_firstrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_firstrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_firstrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_unique_firstrowrow_sumsliceentryoutputpositive. ff_h_pvs_unique_firstrowrow_sumsliceentryoutputpositive + S (dst_positive_unique_firstrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_firstrowrow_sumslice)) * dst_positive_scale_unique_firstrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_firstrowrow_sumsliceentryoutputpositive. dst_positive_code_unique_firstrowrow_sumsliceentryoutput = ff_q_pvs_unique_firstrowrow_sumsliceentryoutputpositive * S ((S (srs_index_unique_firstrowrow_sumslice)) * dst_positive_scale_unique_firstrowrow_sumsliceentryoutput) + (dst_positive_unique_firstrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_unique_firstrowrow_sumsliceentryoutputnegative. ff_h_pvs_unique_firstrowrow_sumsliceentryoutputnegative + S (dst_negative_unique_firstrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_firstrowrow_sumslice)) * dst_negative_scale_unique_firstrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_firstrowrow_sumsliceentryoutputnegative. dst_negative_code_unique_firstrowrow_sumsliceentryoutput = ff_q_pvs_unique_firstrowrow_sumsliceentryoutputnegative * S ((S (srs_index_unique_firstrowrow_sumslice)) * dst_negative_scale_unique_firstrowrow_sumsliceentryoutput) + (dst_negative_unique_firstrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_unique_firstrowrow_sumsliceentryoutputvalue ge_balance_negative_unique_firstrowrow_sumsliceentryoutputvalue. (((((srs_value_unique_firstrowrow_sumslice) = 2 * (ge_balance_positive_unique_firstrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_unique_firstrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_unique_firstrowrow_sumsliceentryoutputvaluedecode. (((srs_value_unique_firstrowrow_sumslice) = 2 * ge_signed_half_unique_firstrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_unique_firstrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_unique_firstrowrow_sumsliceentryoutputvalue) = S ge_signed_half_unique_firstrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_unique_firstrowrow_sumsliceentryoutput) + ge_balance_negative_unique_firstrowrow_sumsliceentryoutputvalue = (dst_negative_unique_firstrowrow_sumsliceentryoutput) + ge_balance_positive_unique_firstrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_unique_firstrowrow_sumsum dst_positive_scale_unique_firstrowrow_sumsum dst_negative_code_unique_firstrowrow_sumsum dst_negative_scale_unique_firstrowrow_sumsum dst_positive_sum_unique_firstrowrow_sumsum dst_negative_sum_unique_firstrowrow_sumsum. (((srs_slice_unique_firstrowrow_sum) = (((((dst_positive_code_unique_firstrowrow_sumsum) + (dst_positive_scale_unique_firstrowrow_sumsum)) * S ((dst_positive_code_unique_firstrowrow_sumsum) + (dst_positive_scale_unique_firstrowrow_sumsum)) + ((dst_positive_scale_unique_firstrowrow_sumsum) + (dst_positive_scale_unique_firstrowrow_sumsum))) + (((dst_negative_code_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)) * S ((dst_negative_code_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)) + ((dst_negative_scale_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)))) * S ((((dst_positive_code_unique_firstrowrow_sumsum) + (dst_positive_scale_unique_firstrowrow_sumsum)) * S ((dst_positive_code_unique_firstrowrow_sumsum) + (dst_positive_scale_unique_firstrowrow_sumsum)) + ((dst_positive_scale_unique_firstrowrow_sumsum) + (dst_positive_scale_unique_firstrowrow_sumsum))) + (((dst_negative_code_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)) * S ((dst_negative_code_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)) + ((dst_negative_scale_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)))) + ((((dst_negative_code_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)) * S ((dst_negative_code_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)) + ((dst_negative_scale_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum))) + (((dst_negative_code_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)) * S ((dst_negative_code_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)) + ((dst_negative_scale_unique_firstrowrow_sumsum) + (dst_negative_scale_unique_firstrowrow_sumsum)))))) /\ (((exists fs_u_dst_unique_firstrowrow_sumsumpositive fs_v_dst_unique_firstrowrow_sumsumpositive. ((((exists fs_h_dst_unique_firstrowrow_sumsumpositive_body_start. fs_h_dst_unique_firstrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_firstrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_firstrowrow_sumsumpositive_body_start. fs_u_dst_unique_firstrowrow_sumsumpositive = fs_q_dst_unique_firstrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_unique_firstrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_unique_firstrowrow_sumsumpositive_body_terminal. fs_h_dst_unique_firstrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_unique_firstrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_firstrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_firstrowrow_sumsumpositive_body_terminal. fs_u_dst_unique_firstrowrow_sumsumpositive = fs_q_dst_unique_firstrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_unique_firstrowrow_sumsumpositive) + (dst_positive_sum_unique_firstrowrow_sumsum))) /\ forall fs_i_dst_unique_firstrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_unique_firstrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_unique_firstrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_unique_firstrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_unique_firstrowrow_sumsumpositive_body_steps fs_r_dst_unique_firstrowrow_sumsumpositive_body_steps fs_s_dst_unique_firstrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_unique_firstrowrow_sumsumpositive_body_steps_summand. fs_h_dst_unique_firstrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_unique_firstrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_firstrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_firstrowrow_sumsum)) /\ exists fs_q_dst_unique_firstrowrow_sumsumpositive_body_steps_summand. dst_positive_code_unique_firstrowrow_sumsum = fs_q_dst_unique_firstrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_unique_firstrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_firstrowrow_sumsum) + (fs_a_dst_unique_firstrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_firstrowrow_sumsumpositive_body_steps_partial. fs_h_dst_unique_firstrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_unique_firstrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_firstrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_firstrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_firstrowrow_sumsumpositive_body_steps_partial. fs_u_dst_unique_firstrowrow_sumsumpositive = fs_q_dst_unique_firstrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_unique_firstrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_firstrowrow_sumsumpositive) + (fs_r_dst_unique_firstrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_firstrowrow_sumsumpositive_body_steps_successor. fs_h_dst_unique_firstrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_unique_firstrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_unique_firstrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_firstrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_firstrowrow_sumsumpositive_body_steps_successor. fs_u_dst_unique_firstrowrow_sumsumpositive = fs_q_dst_unique_firstrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_unique_firstrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_firstrowrow_sumsumpositive) + (fs_s_dst_unique_firstrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_unique_firstrowrow_sumsumpositive_body_steps = fs_r_dst_unique_firstrowrow_sumsumpositive_body_steps + fs_a_dst_unique_firstrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_unique_firstrowrow_sumsumnegative fs_v_dst_unique_firstrowrow_sumsumnegative. ((((exists fs_h_dst_unique_firstrowrow_sumsumnegative_body_start. fs_h_dst_unique_firstrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_firstrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_firstrowrow_sumsumnegative_body_start. fs_u_dst_unique_firstrowrow_sumsumnegative = fs_q_dst_unique_firstrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_unique_firstrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_unique_firstrowrow_sumsumnegative_body_terminal. fs_h_dst_unique_firstrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_unique_firstrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_firstrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_firstrowrow_sumsumnegative_body_terminal. fs_u_dst_unique_firstrowrow_sumsumnegative = fs_q_dst_unique_firstrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_unique_firstrowrow_sumsumnegative) + (dst_negative_sum_unique_firstrowrow_sumsum))) /\ forall fs_i_dst_unique_firstrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_unique_firstrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_unique_firstrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_unique_firstrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_unique_firstrowrow_sumsumnegative_body_steps fs_r_dst_unique_firstrowrow_sumsumnegative_body_steps fs_s_dst_unique_firstrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_unique_firstrowrow_sumsumnegative_body_steps_summand. fs_h_dst_unique_firstrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_unique_firstrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_firstrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_firstrowrow_sumsum)) /\ exists fs_q_dst_unique_firstrowrow_sumsumnegative_body_steps_summand. dst_negative_code_unique_firstrowrow_sumsum = fs_q_dst_unique_firstrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_unique_firstrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_firstrowrow_sumsum) + (fs_a_dst_unique_firstrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_firstrowrow_sumsumnegative_body_steps_partial. fs_h_dst_unique_firstrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_unique_firstrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_firstrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_firstrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_firstrowrow_sumsumnegative_body_steps_partial. fs_u_dst_unique_firstrowrow_sumsumnegative = fs_q_dst_unique_firstrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_unique_firstrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_firstrowrow_sumsumnegative) + (fs_r_dst_unique_firstrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_firstrowrow_sumsumnegative_body_steps_successor. fs_h_dst_unique_firstrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_unique_firstrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_unique_firstrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_firstrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_firstrowrow_sumsumnegative_body_steps_successor. fs_u_dst_unique_firstrowrow_sumsumnegative = fs_q_dst_unique_firstrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_unique_firstrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_firstrowrow_sumsumnegative) + (fs_s_dst_unique_firstrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_unique_firstrowrow_sumsumnegative_body_steps = fs_r_dst_unique_firstrowrow_sumsumnegative_body_steps + fs_a_dst_unique_firstrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_unique_firstrowrow_sumsumresult ge_balance_negative_unique_firstrowrow_sumsumresult. (((((srt_value_unique_first) = 2 * (ge_balance_positive_unique_firstrowrow_sumsumresult) /\ (ge_balance_negative_unique_firstrowrow_sumsumresult) = 0) \/ exists ge_signed_half_unique_firstrowrow_sumsumresultdecode. (((srt_value_unique_first) = 2 * ge_signed_half_unique_firstrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_unique_firstrowrow_sumsumresult) = 0) /\ (ge_balance_negative_unique_firstrowrow_sumsumresult) = S ge_signed_half_unique_firstrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_unique_firstrowrow_sumsum) + ge_balance_negative_unique_firstrowrow_sumsumresult = (dst_negative_sum_unique_firstrowrow_sumsum) + ge_balance_positive_unique_firstrowrow_sumsumresult)))))))))))))))))) -> (((exists dst_positive_code_unique_secondsource_table dst_positive_scale_unique_secondsource_table dst_negative_code_unique_secondsource_table dst_negative_scale_unique_secondsource_table. (((F) = (((((dst_positive_code_unique_secondsource_table) + (dst_positive_scale_unique_secondsource_table)) * S ((dst_positive_code_unique_secondsource_table) + (dst_positive_scale_unique_secondsource_table)) + ((dst_positive_scale_unique_secondsource_table) + (dst_positive_scale_unique_secondsource_table))) + (((dst_negative_code_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)) * S ((dst_negative_code_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)) + ((dst_negative_scale_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)))) * S ((((dst_positive_code_unique_secondsource_table) + (dst_positive_scale_unique_secondsource_table)) * S ((dst_positive_code_unique_secondsource_table) + (dst_positive_scale_unique_secondsource_table)) + ((dst_positive_scale_unique_secondsource_table) + (dst_positive_scale_unique_secondsource_table))) + (((dst_negative_code_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)) * S ((dst_negative_code_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)) + ((dst_negative_scale_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)))) + ((((dst_negative_code_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)) * S ((dst_negative_code_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)) + ((dst_negative_scale_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table))) + (((dst_negative_code_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)) * S ((dst_negative_code_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)) + ((dst_negative_scale_unique_secondsource_table) + (dst_negative_scale_unique_secondsource_table)))))) /\ (forall dst_index_unique_secondsource_table. (exists pvs_le_gap_unique_secondsource_tabledomain. pvs_le_gap_unique_secondsource_tabledomain + (dst_index_unique_secondsource_table) = (0)) -> exists dst_positive_unique_secondsource_table dst_negative_unique_secondsource_table dst_value_unique_secondsource_table. ((((exists ff_h_pvs_unique_secondsource_tableentrypositive. ff_h_pvs_unique_secondsource_tableentrypositive + S (dst_positive_unique_secondsource_table) = S ((S (dst_index_unique_secondsource_table)) * dst_positive_scale_unique_secondsource_table)) /\ exists ff_q_pvs_unique_secondsource_tableentrypositive. dst_positive_code_unique_secondsource_table = ff_q_pvs_unique_secondsource_tableentrypositive * S ((S (dst_index_unique_secondsource_table)) * dst_positive_scale_unique_secondsource_table) + (dst_positive_unique_secondsource_table))) /\ (((((exists ff_h_pvs_unique_secondsource_tableentrynegative. ff_h_pvs_unique_secondsource_tableentrynegative + S (dst_negative_unique_secondsource_table) = S ((S (dst_index_unique_secondsource_table)) * dst_negative_scale_unique_secondsource_table)) /\ exists ff_q_pvs_unique_secondsource_tableentrynegative. dst_negative_code_unique_secondsource_table = ff_q_pvs_unique_secondsource_tableentrynegative * S ((S (dst_index_unique_secondsource_table)) * dst_negative_scale_unique_secondsource_table) + (dst_negative_unique_secondsource_table))) /\ (exists ge_balance_positive_unique_secondsource_tableentryvalue ge_balance_negative_unique_secondsource_tableentryvalue. (((((dst_value_unique_secondsource_table) = 2 * (ge_balance_positive_unique_secondsource_tableentryvalue) /\ (ge_balance_negative_unique_secondsource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_secondsource_tableentryvaluedecode. (((dst_value_unique_secondsource_table) = 2 * ge_signed_half_unique_secondsource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_secondsource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_secondsource_tableentryvalue) = S ge_signed_half_unique_secondsource_tableentryvaluedecode))) /\ ((dst_positive_unique_secondsource_table) + ge_balance_negative_unique_secondsource_tableentryvalue = (dst_negative_unique_secondsource_table) + ge_balance_positive_unique_secondsource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_secondrow_table dst_positive_scale_unique_secondrow_table dst_negative_code_unique_secondrow_table dst_negative_scale_unique_secondrow_table. (((Q) = (((((dst_positive_code_unique_secondrow_table) + (dst_positive_scale_unique_secondrow_table)) * S ((dst_positive_code_unique_secondrow_table) + (dst_positive_scale_unique_secondrow_table)) + ((dst_positive_scale_unique_secondrow_table) + (dst_positive_scale_unique_secondrow_table))) + (((dst_negative_code_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)) * S ((dst_negative_code_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)) + ((dst_negative_scale_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)))) * S ((((dst_positive_code_unique_secondrow_table) + (dst_positive_scale_unique_secondrow_table)) * S ((dst_positive_code_unique_secondrow_table) + (dst_positive_scale_unique_secondrow_table)) + ((dst_positive_scale_unique_secondrow_table) + (dst_positive_scale_unique_secondrow_table))) + (((dst_negative_code_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)) * S ((dst_negative_code_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)) + ((dst_negative_scale_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)))) + ((((dst_negative_code_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)) * S ((dst_negative_code_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)) + ((dst_negative_scale_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table))) + (((dst_negative_code_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)) * S ((dst_negative_code_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)) + ((dst_negative_scale_unique_secondrow_table) + (dst_negative_scale_unique_secondrow_table)))))) /\ (forall dst_index_unique_secondrow_table. (exists pvs_le_gap_unique_secondrow_tabledomain. pvs_le_gap_unique_secondrow_tabledomain + (dst_index_unique_secondrow_table) = (m)) -> exists dst_positive_unique_secondrow_table dst_negative_unique_secondrow_table dst_value_unique_secondrow_table. ((((exists ff_h_pvs_unique_secondrow_tableentrypositive. ff_h_pvs_unique_secondrow_tableentrypositive + S (dst_positive_unique_secondrow_table) = S ((S (dst_index_unique_secondrow_table)) * dst_positive_scale_unique_secondrow_table)) /\ exists ff_q_pvs_unique_secondrow_tableentrypositive. dst_positive_code_unique_secondrow_table = ff_q_pvs_unique_secondrow_tableentrypositive * S ((S (dst_index_unique_secondrow_table)) * dst_positive_scale_unique_secondrow_table) + (dst_positive_unique_secondrow_table))) /\ (((((exists ff_h_pvs_unique_secondrow_tableentrynegative. ff_h_pvs_unique_secondrow_tableentrynegative + S (dst_negative_unique_secondrow_table) = S ((S (dst_index_unique_secondrow_table)) * dst_negative_scale_unique_secondrow_table)) /\ exists ff_q_pvs_unique_secondrow_tableentrynegative. dst_negative_code_unique_secondrow_table = ff_q_pvs_unique_secondrow_tableentrynegative * S ((S (dst_index_unique_secondrow_table)) * dst_negative_scale_unique_secondrow_table) + (dst_negative_unique_secondrow_table))) /\ (exists ge_balance_positive_unique_secondrow_tableentryvalue ge_balance_negative_unique_secondrow_tableentryvalue. (((((dst_value_unique_secondrow_table) = 2 * (ge_balance_positive_unique_secondrow_tableentryvalue) /\ (ge_balance_negative_unique_secondrow_tableentryvalue) = 0) \/ exists ge_signed_half_unique_secondrow_tableentryvaluedecode. (((dst_value_unique_secondrow_table) = 2 * ge_signed_half_unique_secondrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_secondrow_tableentryvalue) = 0) /\ (ge_balance_negative_unique_secondrow_tableentryvalue) = S ge_signed_half_unique_secondrow_tableentryvaluedecode))) /\ ((dst_positive_unique_secondrow_table) + ge_balance_negative_unique_secondrow_tableentryvalue = (dst_negative_unique_secondrow_table) + ge_balance_positive_unique_secondrow_tableentryvalue))))))))) /\ (forall srt_index_unique_second. (exists pvs_gap_unique_secondbound. pvs_gap_unique_secondbound + S (srt_index_unique_second) = (m)) -> exists srt_value_unique_second. (((exists dst_positive_code_unique_secondrowentry dst_positive_scale_unique_secondrowentry dst_negative_code_unique_secondrowentry dst_negative_scale_unique_secondrowentry dst_positive_unique_secondrowentry dst_negative_unique_secondrowentry. (((Q) = (((((dst_positive_code_unique_secondrowentry) + (dst_positive_scale_unique_secondrowentry)) * S ((dst_positive_code_unique_secondrowentry) + (dst_positive_scale_unique_secondrowentry)) + ((dst_positive_scale_unique_secondrowentry) + (dst_positive_scale_unique_secondrowentry))) + (((dst_negative_code_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)) * S ((dst_negative_code_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)) + ((dst_negative_scale_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)))) * S ((((dst_positive_code_unique_secondrowentry) + (dst_positive_scale_unique_secondrowentry)) * S ((dst_positive_code_unique_secondrowentry) + (dst_positive_scale_unique_secondrowentry)) + ((dst_positive_scale_unique_secondrowentry) + (dst_positive_scale_unique_secondrowentry))) + (((dst_negative_code_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)) * S ((dst_negative_code_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)) + ((dst_negative_scale_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)))) + ((((dst_negative_code_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)) * S ((dst_negative_code_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)) + ((dst_negative_scale_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry))) + (((dst_negative_code_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)) * S ((dst_negative_code_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)) + ((dst_negative_scale_unique_secondrowentry) + (dst_negative_scale_unique_secondrowentry)))))) /\ (((((exists ff_h_pvs_unique_secondrowentrypositive. ff_h_pvs_unique_secondrowentrypositive + S (dst_positive_unique_secondrowentry) = S ((S (srt_index_unique_second)) * dst_positive_scale_unique_secondrowentry)) /\ exists ff_q_pvs_unique_secondrowentrypositive. dst_positive_code_unique_secondrowentry = ff_q_pvs_unique_secondrowentrypositive * S ((S (srt_index_unique_second)) * dst_positive_scale_unique_secondrowentry) + (dst_positive_unique_secondrowentry))) /\ (((((exists ff_h_pvs_unique_secondrowentrynegative. ff_h_pvs_unique_secondrowentrynegative + S (dst_negative_unique_secondrowentry) = S ((S (srt_index_unique_second)) * dst_negative_scale_unique_secondrowentry)) /\ exists ff_q_pvs_unique_secondrowentrynegative. dst_negative_code_unique_secondrowentry = ff_q_pvs_unique_secondrowentrynegative * S ((S (srt_index_unique_second)) * dst_negative_scale_unique_secondrowentry) + (dst_negative_unique_secondrowentry))) /\ (exists ge_balance_positive_unique_secondrowentryvalue ge_balance_negative_unique_secondrowentryvalue. (((((srt_value_unique_second) = 2 * (ge_balance_positive_unique_secondrowentryvalue) /\ (ge_balance_negative_unique_secondrowentryvalue) = 0) \/ exists ge_signed_half_unique_secondrowentryvaluedecode. (((srt_value_unique_second) = 2 * ge_signed_half_unique_secondrowentryvaluedecode + 1 /\ (ge_balance_positive_unique_secondrowentryvalue) = 0) /\ (ge_balance_negative_unique_secondrowentryvalue) = S ge_signed_half_unique_secondrowentryvaluedecode))) /\ ((dst_positive_unique_secondrowentry) + ge_balance_negative_unique_secondrowentryvalue = (dst_negative_unique_secondrowentry) + ge_balance_positive_unique_secondrowentryvalue))))))))) /\ (exists srs_slice_unique_secondrowrow_sum. ((((exists dst_positive_code_unique_secondrowrow_sumslicesource_table dst_positive_scale_unique_secondrowrow_sumslicesource_table dst_negative_code_unique_secondrowrow_sumslicesource_table dst_negative_scale_unique_secondrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_unique_secondrowrow_sumslicesource_table) + (dst_positive_scale_unique_secondrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_secondrowrow_sumslicesource_table) + (dst_positive_scale_unique_secondrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_secondrowrow_sumslicesource_table) + (dst_positive_scale_unique_secondrowrow_sumslicesource_table))) + (((dst_negative_code_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)))) * S ((((dst_positive_code_unique_secondrowrow_sumslicesource_table) + (dst_positive_scale_unique_secondrowrow_sumslicesource_table)) * S ((dst_positive_code_unique_secondrowrow_sumslicesource_table) + (dst_positive_scale_unique_secondrowrow_sumslicesource_table)) + ((dst_positive_scale_unique_secondrowrow_sumslicesource_table) + (dst_positive_scale_unique_secondrowrow_sumslicesource_table))) + (((dst_negative_code_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)))) + ((((dst_negative_code_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table))) + (((dst_negative_code_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)) * S ((dst_negative_code_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)) + ((dst_negative_scale_unique_secondrowrow_sumslicesource_table) + (dst_negative_scale_unique_secondrowrow_sumslicesource_table)))))) /\ (forall dst_index_unique_secondrowrow_sumslicesource_table. (exists pvs_le_gap_unique_secondrowrow_sumslicesource_tabledomain. pvs_le_gap_unique_secondrowrow_sumslicesource_tabledomain + (dst_index_unique_secondrowrow_sumslicesource_table) = (0)) -> exists dst_positive_unique_secondrowrow_sumslicesource_table dst_negative_unique_secondrowrow_sumslicesource_table dst_value_unique_secondrowrow_sumslicesource_table. ((((exists ff_h_pvs_unique_secondrowrow_sumslicesource_tableentrypositive. ff_h_pvs_unique_secondrowrow_sumslicesource_tableentrypositive + S (dst_positive_unique_secondrowrow_sumslicesource_table) = S ((S (dst_index_unique_secondrowrow_sumslicesource_table)) * dst_positive_scale_unique_secondrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_secondrowrow_sumslicesource_tableentrypositive. dst_positive_code_unique_secondrowrow_sumslicesource_table = ff_q_pvs_unique_secondrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_unique_secondrowrow_sumslicesource_table)) * dst_positive_scale_unique_secondrowrow_sumslicesource_table) + (dst_positive_unique_secondrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_unique_secondrowrow_sumslicesource_tableentrynegative. ff_h_pvs_unique_secondrowrow_sumslicesource_tableentrynegative + S (dst_negative_unique_secondrowrow_sumslicesource_table) = S ((S (dst_index_unique_secondrowrow_sumslicesource_table)) * dst_negative_scale_unique_secondrowrow_sumslicesource_table)) /\ exists ff_q_pvs_unique_secondrowrow_sumslicesource_tableentrynegative. dst_negative_code_unique_secondrowrow_sumslicesource_table = ff_q_pvs_unique_secondrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_unique_secondrowrow_sumslicesource_table)) * dst_negative_scale_unique_secondrowrow_sumslicesource_table) + (dst_negative_unique_secondrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_unique_secondrowrow_sumslicesource_tableentryvalue ge_balance_negative_unique_secondrowrow_sumslicesource_tableentryvalue. (((((dst_value_unique_secondrowrow_sumslicesource_table) = 2 * (ge_balance_positive_unique_secondrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_unique_secondrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_unique_secondrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_unique_secondrowrow_sumslicesource_table) = 2 * ge_signed_half_unique_secondrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_secondrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_unique_secondrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_unique_secondrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_unique_secondrowrow_sumslicesource_table) + ge_balance_negative_unique_secondrowrow_sumslicesource_tableentryvalue = (dst_negative_unique_secondrowrow_sumslicesource_table) + ge_balance_positive_unique_secondrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_unique_secondrowrow_sumsliceoutput_table dst_positive_scale_unique_secondrowrow_sumsliceoutput_table dst_negative_code_unique_secondrowrow_sumsliceoutput_table dst_negative_scale_unique_secondrowrow_sumsliceoutput_table. (((srs_slice_unique_secondrowrow_sum) = (((((dst_positive_code_unique_secondrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_secondrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_secondrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_secondrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_secondrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_secondrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_unique_secondrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_secondrowrow_sumsliceoutput_table)) * S ((dst_positive_code_unique_secondrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_secondrowrow_sumsliceoutput_table)) + ((dst_positive_scale_unique_secondrowrow_sumsliceoutput_table) + (dst_positive_scale_unique_secondrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table))) + (((dst_negative_code_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)) * S ((dst_negative_code_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)) + ((dst_negative_scale_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_unique_secondrowrow_sumsliceoutput_table. (exists pvs_le_gap_unique_secondrowrow_sumsliceoutput_tabledomain. pvs_le_gap_unique_secondrowrow_sumsliceoutput_tabledomain + (dst_index_unique_secondrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_unique_secondrowrow_sumsliceoutput_table dst_negative_unique_secondrowrow_sumsliceoutput_table dst_value_unique_secondrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_unique_secondrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_unique_secondrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_unique_secondrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_secondrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_secondrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_secondrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_unique_secondrowrow_sumsliceoutput_table = ff_q_pvs_unique_secondrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_unique_secondrowrow_sumsliceoutput_table)) * dst_positive_scale_unique_secondrowrow_sumsliceoutput_table) + (dst_positive_unique_secondrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_unique_secondrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_unique_secondrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_unique_secondrowrow_sumsliceoutput_table) = S ((S (dst_index_unique_secondrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_secondrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_unique_secondrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_unique_secondrowrow_sumsliceoutput_table = ff_q_pvs_unique_secondrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_unique_secondrowrow_sumsliceoutput_table)) * dst_negative_scale_unique_secondrowrow_sumsliceoutput_table) + (dst_negative_unique_secondrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_unique_secondrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_unique_secondrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_unique_secondrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_unique_secondrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_unique_secondrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_unique_secondrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_unique_secondrowrow_sumsliceoutput_table) = 2 * ge_signed_half_unique_secondrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_unique_secondrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_unique_secondrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_unique_secondrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_unique_secondrowrow_sumsliceoutput_table) + ge_balance_negative_unique_secondrowrow_sumsliceoutput_tableentryvalue = (dst_negative_unique_secondrowrow_sumsliceoutput_table) + ge_balance_positive_unique_secondrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_unique_secondrowrow_sumslice. (exists pvs_gap_unique_secondrowrow_sumslicebound. pvs_gap_unique_secondrowrow_sumslicebound + S (srs_index_unique_secondrowrow_sumslice) = (n)) -> exists srs_value_unique_secondrowrow_sumslice. (((exists dst_positive_code_unique_secondrowrow_sumsliceentrysource dst_positive_scale_unique_secondrowrow_sumsliceentrysource dst_negative_code_unique_secondrowrow_sumsliceentrysource dst_negative_scale_unique_secondrowrow_sumsliceentrysource dst_positive_unique_secondrowrow_sumsliceentrysource dst_negative_unique_secondrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_unique_secondrowrow_sumsliceentrysource) + (dst_positive_scale_unique_secondrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_secondrowrow_sumsliceentrysource) + (dst_positive_scale_unique_secondrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_secondrowrow_sumsliceentrysource) + (dst_positive_scale_unique_secondrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_unique_secondrowrow_sumsliceentrysource) + (dst_positive_scale_unique_secondrowrow_sumsliceentrysource)) * S ((dst_positive_code_unique_secondrowrow_sumsliceentrysource) + (dst_positive_scale_unique_secondrowrow_sumsliceentrysource)) + ((dst_positive_scale_unique_secondrowrow_sumsliceentrysource) + (dst_positive_scale_unique_secondrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)))) + ((((dst_negative_code_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource))) + (((dst_negative_code_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)) * S ((dst_negative_code_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)) + ((dst_negative_scale_unique_secondrowrow_sumsliceentrysource) + (dst_negative_scale_unique_secondrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_unique_secondrowrow_sumsliceentrysourcepositive. ff_h_pvs_unique_secondrowrow_sumsliceentrysourcepositive + S (dst_positive_unique_secondrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_second)))) + ((t) * (srs_index_unique_secondrowrow_sumslice))))) * dst_positive_scale_unique_secondrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_secondrowrow_sumsliceentrysourcepositive. dst_positive_code_unique_secondrowrow_sumsliceentrysource = ff_q_pvs_unique_secondrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_unique_second)))) + ((t) * (srs_index_unique_secondrowrow_sumslice))))) * dst_positive_scale_unique_secondrowrow_sumsliceentrysource) + (dst_positive_unique_secondrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_unique_secondrowrow_sumsliceentrysourcenegative. ff_h_pvs_unique_secondrowrow_sumsliceentrysourcenegative + S (dst_negative_unique_secondrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_unique_second)))) + ((t) * (srs_index_unique_secondrowrow_sumslice))))) * dst_negative_scale_unique_secondrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_unique_secondrowrow_sumsliceentrysourcenegative. dst_negative_code_unique_secondrowrow_sumsliceentrysource = ff_q_pvs_unique_secondrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_unique_second)))) + ((t) * (srs_index_unique_secondrowrow_sumslice))))) * dst_negative_scale_unique_secondrowrow_sumsliceentrysource) + (dst_negative_unique_secondrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_unique_secondrowrow_sumsliceentrysourcevalue ge_balance_negative_unique_secondrowrow_sumsliceentrysourcevalue. (((((srs_value_unique_secondrowrow_sumslice) = 2 * (ge_balance_positive_unique_secondrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_unique_secondrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_unique_secondrowrow_sumsliceentrysourcevaluedecode. (((srs_value_unique_secondrowrow_sumslice) = 2 * ge_signed_half_unique_secondrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_unique_secondrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_unique_secondrowrow_sumsliceentrysourcevalue) = S ge_signed_half_unique_secondrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_unique_secondrowrow_sumsliceentrysource) + ge_balance_negative_unique_secondrowrow_sumsliceentrysourcevalue = (dst_negative_unique_secondrowrow_sumsliceentrysource) + ge_balance_positive_unique_secondrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_unique_secondrowrow_sumsliceentryoutput dst_positive_scale_unique_secondrowrow_sumsliceentryoutput dst_negative_code_unique_secondrowrow_sumsliceentryoutput dst_negative_scale_unique_secondrowrow_sumsliceentryoutput dst_positive_unique_secondrowrow_sumsliceentryoutput dst_negative_unique_secondrowrow_sumsliceentryoutput. (((srs_slice_unique_secondrowrow_sum) = (((((dst_positive_code_unique_secondrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_secondrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_secondrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_secondrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_secondrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_secondrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_unique_secondrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_secondrowrow_sumsliceentryoutput)) * S ((dst_positive_code_unique_secondrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_secondrowrow_sumsliceentryoutput)) + ((dst_positive_scale_unique_secondrowrow_sumsliceentryoutput) + (dst_positive_scale_unique_secondrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput))) + (((dst_negative_code_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)) * S ((dst_negative_code_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)) + ((dst_negative_scale_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_unique_secondrowrow_sumsliceentryoutputpositive. ff_h_pvs_unique_secondrowrow_sumsliceentryoutputpositive + S (dst_positive_unique_secondrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_secondrowrow_sumslice)) * dst_positive_scale_unique_secondrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_secondrowrow_sumsliceentryoutputpositive. dst_positive_code_unique_secondrowrow_sumsliceentryoutput = ff_q_pvs_unique_secondrowrow_sumsliceentryoutputpositive * S ((S (srs_index_unique_secondrowrow_sumslice)) * dst_positive_scale_unique_secondrowrow_sumsliceentryoutput) + (dst_positive_unique_secondrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_unique_secondrowrow_sumsliceentryoutputnegative. ff_h_pvs_unique_secondrowrow_sumsliceentryoutputnegative + S (dst_negative_unique_secondrowrow_sumsliceentryoutput) = S ((S (srs_index_unique_secondrowrow_sumslice)) * dst_negative_scale_unique_secondrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_unique_secondrowrow_sumsliceentryoutputnegative. dst_negative_code_unique_secondrowrow_sumsliceentryoutput = ff_q_pvs_unique_secondrowrow_sumsliceentryoutputnegative * S ((S (srs_index_unique_secondrowrow_sumslice)) * dst_negative_scale_unique_secondrowrow_sumsliceentryoutput) + (dst_negative_unique_secondrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_unique_secondrowrow_sumsliceentryoutputvalue ge_balance_negative_unique_secondrowrow_sumsliceentryoutputvalue. (((((srs_value_unique_secondrowrow_sumslice) = 2 * (ge_balance_positive_unique_secondrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_unique_secondrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_unique_secondrowrow_sumsliceentryoutputvaluedecode. (((srs_value_unique_secondrowrow_sumslice) = 2 * ge_signed_half_unique_secondrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_unique_secondrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_unique_secondrowrow_sumsliceentryoutputvalue) = S ge_signed_half_unique_secondrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_unique_secondrowrow_sumsliceentryoutput) + ge_balance_negative_unique_secondrowrow_sumsliceentryoutputvalue = (dst_negative_unique_secondrowrow_sumsliceentryoutput) + ge_balance_positive_unique_secondrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_unique_secondrowrow_sumsum dst_positive_scale_unique_secondrowrow_sumsum dst_negative_code_unique_secondrowrow_sumsum dst_negative_scale_unique_secondrowrow_sumsum dst_positive_sum_unique_secondrowrow_sumsum dst_negative_sum_unique_secondrowrow_sumsum. (((srs_slice_unique_secondrowrow_sum) = (((((dst_positive_code_unique_secondrowrow_sumsum) + (dst_positive_scale_unique_secondrowrow_sumsum)) * S ((dst_positive_code_unique_secondrowrow_sumsum) + (dst_positive_scale_unique_secondrowrow_sumsum)) + ((dst_positive_scale_unique_secondrowrow_sumsum) + (dst_positive_scale_unique_secondrowrow_sumsum))) + (((dst_negative_code_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)) * S ((dst_negative_code_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)) + ((dst_negative_scale_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)))) * S ((((dst_positive_code_unique_secondrowrow_sumsum) + (dst_positive_scale_unique_secondrowrow_sumsum)) * S ((dst_positive_code_unique_secondrowrow_sumsum) + (dst_positive_scale_unique_secondrowrow_sumsum)) + ((dst_positive_scale_unique_secondrowrow_sumsum) + (dst_positive_scale_unique_secondrowrow_sumsum))) + (((dst_negative_code_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)) * S ((dst_negative_code_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)) + ((dst_negative_scale_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)))) + ((((dst_negative_code_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)) * S ((dst_negative_code_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)) + ((dst_negative_scale_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum))) + (((dst_negative_code_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)) * S ((dst_negative_code_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)) + ((dst_negative_scale_unique_secondrowrow_sumsum) + (dst_negative_scale_unique_secondrowrow_sumsum)))))) /\ (((exists fs_u_dst_unique_secondrowrow_sumsumpositive fs_v_dst_unique_secondrowrow_sumsumpositive. ((((exists fs_h_dst_unique_secondrowrow_sumsumpositive_body_start. fs_h_dst_unique_secondrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_secondrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_secondrowrow_sumsumpositive_body_start. fs_u_dst_unique_secondrowrow_sumsumpositive = fs_q_dst_unique_secondrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_unique_secondrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_unique_secondrowrow_sumsumpositive_body_terminal. fs_h_dst_unique_secondrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_unique_secondrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_secondrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_secondrowrow_sumsumpositive_body_terminal. fs_u_dst_unique_secondrowrow_sumsumpositive = fs_q_dst_unique_secondrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_unique_secondrowrow_sumsumpositive) + (dst_positive_sum_unique_secondrowrow_sumsum))) /\ forall fs_i_dst_unique_secondrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_unique_secondrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_unique_secondrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_unique_secondrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_unique_secondrowrow_sumsumpositive_body_steps fs_r_dst_unique_secondrowrow_sumsumpositive_body_steps fs_s_dst_unique_secondrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_unique_secondrowrow_sumsumpositive_body_steps_summand. fs_h_dst_unique_secondrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_unique_secondrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_secondrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_secondrowrow_sumsum)) /\ exists fs_q_dst_unique_secondrowrow_sumsumpositive_body_steps_summand. dst_positive_code_unique_secondrowrow_sumsum = fs_q_dst_unique_secondrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_unique_secondrowrow_sumsumpositive_body_steps)) * dst_positive_scale_unique_secondrowrow_sumsum) + (fs_a_dst_unique_secondrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_secondrowrow_sumsumpositive_body_steps_partial. fs_h_dst_unique_secondrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_unique_secondrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_unique_secondrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_secondrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_secondrowrow_sumsumpositive_body_steps_partial. fs_u_dst_unique_secondrowrow_sumsumpositive = fs_q_dst_unique_secondrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_unique_secondrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_secondrowrow_sumsumpositive) + (fs_r_dst_unique_secondrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_unique_secondrowrow_sumsumpositive_body_steps_successor. fs_h_dst_unique_secondrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_unique_secondrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_unique_secondrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_secondrowrow_sumsumpositive)) /\ exists fs_q_dst_unique_secondrowrow_sumsumpositive_body_steps_successor. fs_u_dst_unique_secondrowrow_sumsumpositive = fs_q_dst_unique_secondrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_unique_secondrowrow_sumsumpositive_body_steps)) * fs_v_dst_unique_secondrowrow_sumsumpositive) + (fs_s_dst_unique_secondrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_unique_secondrowrow_sumsumpositive_body_steps = fs_r_dst_unique_secondrowrow_sumsumpositive_body_steps + fs_a_dst_unique_secondrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_unique_secondrowrow_sumsumnegative fs_v_dst_unique_secondrowrow_sumsumnegative. ((((exists fs_h_dst_unique_secondrowrow_sumsumnegative_body_start. fs_h_dst_unique_secondrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_unique_secondrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_secondrowrow_sumsumnegative_body_start. fs_u_dst_unique_secondrowrow_sumsumnegative = fs_q_dst_unique_secondrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_unique_secondrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_unique_secondrowrow_sumsumnegative_body_terminal. fs_h_dst_unique_secondrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_unique_secondrowrow_sumsum) = S ((S (n)) * fs_v_dst_unique_secondrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_secondrowrow_sumsumnegative_body_terminal. fs_u_dst_unique_secondrowrow_sumsumnegative = fs_q_dst_unique_secondrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_unique_secondrowrow_sumsumnegative) + (dst_negative_sum_unique_secondrowrow_sumsum))) /\ forall fs_i_dst_unique_secondrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_unique_secondrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_unique_secondrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_unique_secondrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_unique_secondrowrow_sumsumnegative_body_steps fs_r_dst_unique_secondrowrow_sumsumnegative_body_steps fs_s_dst_unique_secondrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_unique_secondrowrow_sumsumnegative_body_steps_summand. fs_h_dst_unique_secondrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_unique_secondrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_secondrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_secondrowrow_sumsum)) /\ exists fs_q_dst_unique_secondrowrow_sumsumnegative_body_steps_summand. dst_negative_code_unique_secondrowrow_sumsum = fs_q_dst_unique_secondrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_unique_secondrowrow_sumsumnegative_body_steps)) * dst_negative_scale_unique_secondrowrow_sumsum) + (fs_a_dst_unique_secondrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_secondrowrow_sumsumnegative_body_steps_partial. fs_h_dst_unique_secondrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_unique_secondrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_unique_secondrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_secondrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_secondrowrow_sumsumnegative_body_steps_partial. fs_u_dst_unique_secondrowrow_sumsumnegative = fs_q_dst_unique_secondrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_unique_secondrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_secondrowrow_sumsumnegative) + (fs_r_dst_unique_secondrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_unique_secondrowrow_sumsumnegative_body_steps_successor. fs_h_dst_unique_secondrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_unique_secondrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_unique_secondrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_secondrowrow_sumsumnegative)) /\ exists fs_q_dst_unique_secondrowrow_sumsumnegative_body_steps_successor. fs_u_dst_unique_secondrowrow_sumsumnegative = fs_q_dst_unique_secondrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_unique_secondrowrow_sumsumnegative_body_steps)) * fs_v_dst_unique_secondrowrow_sumsumnegative) + (fs_s_dst_unique_secondrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_unique_secondrowrow_sumsumnegative_body_steps = fs_r_dst_unique_secondrowrow_sumsumnegative_body_steps + fs_a_dst_unique_secondrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_unique_secondrowrow_sumsumresult ge_balance_negative_unique_secondrowrow_sumsumresult. (((((srt_value_unique_second) = 2 * (ge_balance_positive_unique_secondrowrow_sumsumresult) /\ (ge_balance_negative_unique_secondrowrow_sumsumresult) = 0) \/ exists ge_signed_half_unique_secondrowrow_sumsumresultdecode. (((srt_value_unique_second) = 2 * ge_signed_half_unique_secondrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_unique_secondrowrow_sumsumresult) = 0) /\ (ge_balance_negative_unique_secondrowrow_sumsumresult) = S ge_signed_half_unique_secondrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_unique_secondrowrow_sumsum) + ge_balance_negative_unique_secondrowrow_sumsumresult = (dst_negative_sum_unique_secondrowrow_sumsum) + ge_balance_positive_unique_secondrowrow_sumsumresult)))))))))))))))))) -> (forall dst_index_unique_equal dst_first_unique_equal dst_second_unique_equal. (exists pvs_gap_unique_equalbound. pvs_gap_unique_equalbound + S (dst_index_unique_equal) = (m)) -> (exists dst_positive_code_unique_equalfirst dst_positive_scale_unique_equalfirst dst_negative_code_unique_equalfirst dst_negative_scale_unique_equalfirst dst_positive_unique_equalfirst dst_negative_unique_equalfirst. (((R) = (((((dst_positive_code_unique_equalfirst) + (dst_positive_scale_unique_equalfirst)) * S ((dst_positive_code_unique_equalfirst) + (dst_positive_scale_unique_equalfirst)) + ((dst_positive_scale_unique_equalfirst) + (dst_positive_scale_unique_equalfirst))) + (((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) * S ((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) + ((dst_negative_scale_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)))) * S ((((dst_positive_code_unique_equalfirst) + (dst_positive_scale_unique_equalfirst)) * S ((dst_positive_code_unique_equalfirst) + (dst_positive_scale_unique_equalfirst)) + ((dst_positive_scale_unique_equalfirst) + (dst_positive_scale_unique_equalfirst))) + (((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) * S ((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) + ((dst_negative_scale_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)))) + ((((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) * S ((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) + ((dst_negative_scale_unique_equalfirst) + (dst_negative_scale_unique_equalfirst))) + (((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) * S ((dst_negative_code_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)) + ((dst_negative_scale_unique_equalfirst) + (dst_negative_scale_unique_equalfirst)))))) /\ (((((exists ff_h_pvs_unique_equalfirstpositive. ff_h_pvs_unique_equalfirstpositive + S (dst_positive_unique_equalfirst) = S ((S (dst_index_unique_equal)) * dst_positive_scale_unique_equalfirst)) /\ exists ff_q_pvs_unique_equalfirstpositive. dst_positive_code_unique_equalfirst = ff_q_pvs_unique_equalfirstpositive * S ((S (dst_index_unique_equal)) * dst_positive_scale_unique_equalfirst) + (dst_positive_unique_equalfirst))) /\ (((((exists ff_h_pvs_unique_equalfirstnegative. ff_h_pvs_unique_equalfirstnegative + S (dst_negative_unique_equalfirst) = S ((S (dst_index_unique_equal)) * dst_negative_scale_unique_equalfirst)) /\ exists ff_q_pvs_unique_equalfirstnegative. dst_negative_code_unique_equalfirst = ff_q_pvs_unique_equalfirstnegative * S ((S (dst_index_unique_equal)) * dst_negative_scale_unique_equalfirst) + (dst_negative_unique_equalfirst))) /\ (exists ge_balance_positive_unique_equalfirstvalue ge_balance_negative_unique_equalfirstvalue. (((((dst_first_unique_equal) = 2 * (ge_balance_positive_unique_equalfirstvalue) /\ (ge_balance_negative_unique_equalfirstvalue) = 0) \/ exists ge_signed_half_unique_equalfirstvaluedecode. (((dst_first_unique_equal) = 2 * ge_signed_half_unique_equalfirstvaluedecode + 1 /\ (ge_balance_positive_unique_equalfirstvalue) = 0) /\ (ge_balance_negative_unique_equalfirstvalue) = S ge_signed_half_unique_equalfirstvaluedecode))) /\ ((dst_positive_unique_equalfirst) + ge_balance_negative_unique_equalfirstvalue = (dst_negative_unique_equalfirst) + ge_balance_positive_unique_equalfirstvalue))))))))) -> (exists dst_positive_code_unique_equalsecond dst_positive_scale_unique_equalsecond dst_negative_code_unique_equalsecond dst_negative_scale_unique_equalsecond dst_positive_unique_equalsecond dst_negative_unique_equalsecond. (((Q) = (((((dst_positive_code_unique_equalsecond) + (dst_positive_scale_unique_equalsecond)) * S ((dst_positive_code_unique_equalsecond) + (dst_positive_scale_unique_equalsecond)) + ((dst_positive_scale_unique_equalsecond) + (dst_positive_scale_unique_equalsecond))) + (((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) * S ((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) + ((dst_negative_scale_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)))) * S ((((dst_positive_code_unique_equalsecond) + (dst_positive_scale_unique_equalsecond)) * S ((dst_positive_code_unique_equalsecond) + (dst_positive_scale_unique_equalsecond)) + ((dst_positive_scale_unique_equalsecond) + (dst_positive_scale_unique_equalsecond))) + (((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) * S ((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) + ((dst_negative_scale_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)))) + ((((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) * S ((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) + ((dst_negative_scale_unique_equalsecond) + (dst_negative_scale_unique_equalsecond))) + (((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) * S ((dst_negative_code_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)) + ((dst_negative_scale_unique_equalsecond) + (dst_negative_scale_unique_equalsecond)))))) /\ (((((exists ff_h_pvs_unique_equalsecondpositive. ff_h_pvs_unique_equalsecondpositive + S (dst_positive_unique_equalsecond) = S ((S (dst_index_unique_equal)) * dst_positive_scale_unique_equalsecond)) /\ exists ff_q_pvs_unique_equalsecondpositive. dst_positive_code_unique_equalsecond = ff_q_pvs_unique_equalsecondpositive * S ((S (dst_index_unique_equal)) * dst_positive_scale_unique_equalsecond) + (dst_positive_unique_equalsecond))) /\ (((((exists ff_h_pvs_unique_equalsecondnegative. ff_h_pvs_unique_equalsecondnegative + S (dst_negative_unique_equalsecond) = S ((S (dst_index_unique_equal)) * dst_negative_scale_unique_equalsecond)) /\ exists ff_q_pvs_unique_equalsecondnegative. dst_negative_code_unique_equalsecond = ff_q_pvs_unique_equalsecondnegative * S ((S (dst_index_unique_equal)) * dst_negative_scale_unique_equalsecond) + (dst_negative_unique_equalsecond))) /\ (exists ge_balance_positive_unique_equalsecondvalue ge_balance_negative_unique_equalsecondvalue. (((((dst_second_unique_equal) = 2 * (ge_balance_positive_unique_equalsecondvalue) /\ (ge_balance_negative_unique_equalsecondvalue) = 0) \/ exists ge_signed_half_unique_equalsecondvaluedecode. (((dst_second_unique_equal) = 2 * ge_signed_half_unique_equalsecondvaluedecode + 1 /\ (ge_balance_positive_unique_equalsecondvalue) = 0) /\ (ge_balance_negative_unique_equalsecondvalue) = S ge_signed_half_unique_equalsecondvaluedecode))) /\ ((dst_positive_unique_equalsecond) + ge_balance_negative_unique_equalsecondvalue = (dst_negative_unique_equalsecond) + ge_balance_positive_unique_equalsecondvalue))))))))) -> dst_first_unique_equal = dst_second_unique_equal)

Complete tactic proof in conservative notation

All 49 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay script.

Read the argument

Proof checkpoints

49 script commands · 6 reading checkpoints · 0 local claims

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

Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.

Named ingredients (2)
01Fix variables and assumptionsL1–10

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

  1. L1
    intro F
  2. L2
    intro R
  3. L3
    intro Q
  4. L4
    intro o
  5. L5
    intro s
  6. L6
    intro t
  7. L7
    intro m
  8. L8
    intro n
  9. L9
    intro hR
  10. L10
    intro hQ
02Fix variables and assumptionsL11–16

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

  1. L11
    intro i
  2. L12
    intro a
  3. L13
    intro b
  4. L14
    intro hi
  5. L15
    intro ha
  6. L16
    intro hb
03Use earlier factsL17–26

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

  1. L17
    specialize signed_rectangular_slice_sum_functional (F)
  2. L18
    specialize signed_rectangular_slice_sum_functional (((o) + ((s) * (i))))
  3. L19
    specialize signed_rectangular_slice_sum_functional (t)
  4. L20
    specialize signed_rectangular_slice_sum_functional (n)
  5. L21
    specialize signed_rectangular_slice_sum_functional (a)
  6. L22
    specialize signed_rectangular_slice_sum_functional (b)
  7. L23
    apply signed_rectangular_slice_sum_functional
  8. L24
    specialize signed_rectangular_row_sums_lookup (F)
  9. L25
    specialize signed_rectangular_row_sums_lookup (R)
  10. L26
    specialize signed_rectangular_row_sums_lookup (o)
04Use earlier factsL27–36

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

  1. L27
    specialize signed_rectangular_row_sums_lookup (s)
  2. L28
    specialize signed_rectangular_row_sums_lookup (t)
  3. L29
    specialize signed_rectangular_row_sums_lookup (m)
  4. L30
    specialize signed_rectangular_row_sums_lookup (n)
  5. L31
    specialize signed_rectangular_row_sums_lookup (i)
  6. L32
    specialize signed_rectangular_row_sums_lookup (a)
  7. L33
    apply signed_rectangular_row_sums_lookup
  8. L34
    exact hR
  9. L35
    exact hi
  10. L36
    exact ha
05Use earlier factsL37–46

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

  1. L37
    specialize signed_rectangular_row_sums_lookup (F)
  2. L38
    specialize signed_rectangular_row_sums_lookup (Q)
  3. L39
    specialize signed_rectangular_row_sums_lookup (o)
  4. L40
    specialize signed_rectangular_row_sums_lookup (s)
  5. L41
    specialize signed_rectangular_row_sums_lookup (t)
  6. L42
    specialize signed_rectangular_row_sums_lookup (m)
  7. L43
    specialize signed_rectangular_row_sums_lookup (n)
  8. L44
    specialize signed_rectangular_row_sums_lookup (i)
  9. L45
    specialize signed_rectangular_row_sums_lookup (b)
  10. L46
    apply signed_rectangular_row_sums_lookup
06Use earlier factsL47–49

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

  1. L47
    exact hQ
  2. L48
    exact hi
  3. L49
    exact hb

Library-wide reading audit

Original defined command ledger · 49 lines
  1. 0001intro F
  2. 0002intro R
  3. 0003intro Q
  4. 0004intro o
  5. 0005intro s
  6. 0006intro t
  7. 0007intro m
  8. 0008intro n
  9. 0009intro hR
  10. 0010intro hQ
  11. 0011intro i
  12. 0012intro a
  13. 0013intro b
  14. 0014intro hi
  15. 0015intro ha
  16. 0016intro hb
  17. 0017specialize signed_rectangular_slice_sum_functional (F)
  18. 0018specialize signed_rectangular_slice_sum_functional (((o) + ((s) * (i))))
  19. 0019specialize signed_rectangular_slice_sum_functional (t)
  20. 0020specialize signed_rectangular_slice_sum_functional (n)
  21. 0021specialize signed_rectangular_slice_sum_functional (a)
  22. 0022specialize signed_rectangular_slice_sum_functional (b)
  23. 0023apply signed_rectangular_slice_sum_functional
  24. 0024specialize signed_rectangular_row_sums_lookup (F)
  25. 0025specialize signed_rectangular_row_sums_lookup (R)
  26. 0026specialize signed_rectangular_row_sums_lookup (o)
  27. 0027specialize signed_rectangular_row_sums_lookup (s)
  28. 0028specialize signed_rectangular_row_sums_lookup (t)
  29. 0029specialize signed_rectangular_row_sums_lookup (m)
  30. 0030specialize signed_rectangular_row_sums_lookup (n)
  31. 0031specialize signed_rectangular_row_sums_lookup (i)
  32. 0032specialize signed_rectangular_row_sums_lookup (a)
  33. 0033apply signed_rectangular_row_sums_lookup
  34. 0034exact hR
  35. 0035exact hi
  36. 0036exact ha
  37. 0037specialize signed_rectangular_row_sums_lookup (F)
  38. 0038specialize signed_rectangular_row_sums_lookup (Q)
  39. 0039specialize signed_rectangular_row_sums_lookup (o)
  40. 0040specialize signed_rectangular_row_sums_lookup (s)
  41. 0041specialize signed_rectangular_row_sums_lookup (t)
  42. 0042specialize signed_rectangular_row_sums_lookup (m)
  43. 0043specialize signed_rectangular_row_sums_lookup (n)
  44. 0044specialize signed_rectangular_row_sums_lookup (i)
  45. 0045specialize signed_rectangular_row_sums_lookup (b)
  46. 0046apply signed_rectangular_row_sums_lookup
  47. 0047exact hQ
  48. 0048exact hi
  49. 0049exact hb