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. ∀ o. ∀ s. ∀ t. ∀ m. ∀ z. SignedRectangularSum(F,o,s,t,m,0,z) → z = 0
Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Original expanded first-order statement
forall F o s t m z. (exists srt_rows_zero_inner_input. ((((exists dst_positive_code_zero_inner_inputrowssource_table dst_positive_scale_zero_inner_inputrowssource_table dst_negative_code_zero_inner_inputrowssource_table dst_negative_scale_zero_inner_inputrowssource_table. (((F) = (((((dst_positive_code_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table)) * S ((dst_positive_code_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table)) + ((dst_positive_scale_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table))) + (((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) * S ((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) + ((dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)))) * S ((((dst_positive_code_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table)) * S ((dst_positive_code_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table)) + ((dst_positive_scale_zero_inner_inputrowssource_table) + (dst_positive_scale_zero_inner_inputrowssource_table))) + (((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) * S ((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) + ((dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)))) + ((((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) * S ((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) + ((dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table))) + (((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) * S ((dst_negative_code_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)) + ((dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_scale_zero_inner_inputrowssource_table)))))) /\ (forall dst_index_zero_inner_inputrowssource_table. (exists pvs_le_gap_zero_inner_inputrowssource_tabledomain. pvs_le_gap_zero_inner_inputrowssource_tabledomain + (dst_index_zero_inner_inputrowssource_table) = (0)) -> exists dst_positive_zero_inner_inputrowssource_table dst_negative_zero_inner_inputrowssource_table dst_value_zero_inner_inputrowssource_table. ((((exists ff_h_pvs_zero_inner_inputrowssource_tableentrypositive. ff_h_pvs_zero_inner_inputrowssource_tableentrypositive + S (dst_positive_zero_inner_inputrowssource_table) = S ((S (dst_index_zero_inner_inputrowssource_table)) * dst_positive_scale_zero_inner_inputrowssource_table)) /\ exists ff_q_pvs_zero_inner_inputrowssource_tableentrypositive. dst_positive_code_zero_inner_inputrowssource_table = ff_q_pvs_zero_inner_inputrowssource_tableentrypositive * S ((S (dst_index_zero_inner_inputrowssource_table)) * dst_positive_scale_zero_inner_inputrowssource_table) + (dst_positive_zero_inner_inputrowssource_table))) /\ (((((exists ff_h_pvs_zero_inner_inputrowssource_tableentrynegative. ff_h_pvs_zero_inner_inputrowssource_tableentrynegative + S (dst_negative_zero_inner_inputrowssource_table) = S ((S (dst_index_zero_inner_inputrowssource_table)) * dst_negative_scale_zero_inner_inputrowssource_table)) /\ exists ff_q_pvs_zero_inner_inputrowssource_tableentrynegative. dst_negative_code_zero_inner_inputrowssource_table = ff_q_pvs_zero_inner_inputrowssource_tableentrynegative * S ((S (dst_index_zero_inner_inputrowssource_table)) * dst_negative_scale_zero_inner_inputrowssource_table) + (dst_negative_zero_inner_inputrowssource_table))) /\ (exists ge_balance_positive_zero_inner_inputrowssource_tableentryvalue ge_balance_negative_zero_inner_inputrowssource_tableentryvalue. (((((dst_value_zero_inner_inputrowssource_table) = 2 * (ge_balance_positive_zero_inner_inputrowssource_tableentryvalue) /\ (ge_balance_negative_zero_inner_inputrowssource_tableentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowssource_tableentryvaluedecode. (((dst_value_zero_inner_inputrowssource_table) = 2 * ge_signed_half_zero_inner_inputrowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowssource_tableentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowssource_tableentryvalue) = S ge_signed_half_zero_inner_inputrowssource_tableentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowssource_table) + ge_balance_negative_zero_inner_inputrowssource_tableentryvalue = (dst_negative_zero_inner_inputrowssource_table) + ge_balance_positive_zero_inner_inputrowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_zero_inner_inputrowsrow_table dst_positive_scale_zero_inner_inputrowsrow_table dst_negative_code_zero_inner_inputrowsrow_table dst_negative_scale_zero_inner_inputrowsrow_table. (((srt_rows_zero_inner_input) = (((((dst_positive_code_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table)) * S ((dst_positive_code_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table)) + ((dst_positive_scale_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table))) + (((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) * S ((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) + ((dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)))) * S ((((dst_positive_code_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table)) * S ((dst_positive_code_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table)) + ((dst_positive_scale_zero_inner_inputrowsrow_table) + (dst_positive_scale_zero_inner_inputrowsrow_table))) + (((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) * S ((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) + ((dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)))) + ((((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) * S ((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) + ((dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table))) + (((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) * S ((dst_negative_code_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)) + ((dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_scale_zero_inner_inputrowsrow_table)))))) /\ (forall dst_index_zero_inner_inputrowsrow_table. (exists pvs_le_gap_zero_inner_inputrowsrow_tabledomain. pvs_le_gap_zero_inner_inputrowsrow_tabledomain + (dst_index_zero_inner_inputrowsrow_table) = (m)) -> exists dst_positive_zero_inner_inputrowsrow_table dst_negative_zero_inner_inputrowsrow_table dst_value_zero_inner_inputrowsrow_table. ((((exists ff_h_pvs_zero_inner_inputrowsrow_tableentrypositive. ff_h_pvs_zero_inner_inputrowsrow_tableentrypositive + S (dst_positive_zero_inner_inputrowsrow_table) = S ((S (dst_index_zero_inner_inputrowsrow_table)) * dst_positive_scale_zero_inner_inputrowsrow_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrow_tableentrypositive. dst_positive_code_zero_inner_inputrowsrow_table = ff_q_pvs_zero_inner_inputrowsrow_tableentrypositive * S ((S (dst_index_zero_inner_inputrowsrow_table)) * dst_positive_scale_zero_inner_inputrowsrow_table) + (dst_positive_zero_inner_inputrowsrow_table))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrow_tableentrynegative. ff_h_pvs_zero_inner_inputrowsrow_tableentrynegative + S (dst_negative_zero_inner_inputrowsrow_table) = S ((S (dst_index_zero_inner_inputrowsrow_table)) * dst_negative_scale_zero_inner_inputrowsrow_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrow_tableentrynegative. dst_negative_code_zero_inner_inputrowsrow_table = ff_q_pvs_zero_inner_inputrowsrow_tableentrynegative * S ((S (dst_index_zero_inner_inputrowsrow_table)) * dst_negative_scale_zero_inner_inputrowsrow_table) + (dst_negative_zero_inner_inputrowsrow_table))) /\ (exists ge_balance_positive_zero_inner_inputrowsrow_tableentryvalue ge_balance_negative_zero_inner_inputrowsrow_tableentryvalue. (((((dst_value_zero_inner_inputrowsrow_table) = 2 * (ge_balance_positive_zero_inner_inputrowsrow_tableentryvalue) /\ (ge_balance_negative_zero_inner_inputrowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrow_tableentryvaluedecode. (((dst_value_zero_inner_inputrowsrow_table) = 2 * ge_signed_half_zero_inner_inputrowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrow_tableentryvalue) = S ge_signed_half_zero_inner_inputrowsrow_tableentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrow_table) + ge_balance_negative_zero_inner_inputrowsrow_tableentryvalue = (dst_negative_zero_inner_inputrowsrow_table) + ge_balance_positive_zero_inner_inputrowsrow_tableentryvalue))))))))) /\ (forall srt_index_zero_inner_inputrows. (exists pvs_gap_zero_inner_inputrowsbound. pvs_gap_zero_inner_inputrowsbound + S (srt_index_zero_inner_inputrows) = (m)) -> exists srt_value_zero_inner_inputrows. (((exists dst_positive_code_zero_inner_inputrowsrowentry dst_positive_scale_zero_inner_inputrowsrowentry dst_negative_code_zero_inner_inputrowsrowentry dst_negative_scale_zero_inner_inputrowsrowentry dst_positive_zero_inner_inputrowsrowentry dst_negative_zero_inner_inputrowsrowentry. (((srt_rows_zero_inner_input) = (((((dst_positive_code_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry)) * S ((dst_positive_code_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry)) + ((dst_positive_scale_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry))) + (((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) * S ((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) + ((dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)))) * S ((((dst_positive_code_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry)) * S ((dst_positive_code_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry)) + ((dst_positive_scale_zero_inner_inputrowsrowentry) + (dst_positive_scale_zero_inner_inputrowsrowentry))) + (((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) * S ((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) + ((dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)))) + ((((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) * S ((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) + ((dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry))) + (((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) * S ((dst_negative_code_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)) + ((dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_scale_zero_inner_inputrowsrowentry)))))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowentrypositive. ff_h_pvs_zero_inner_inputrowsrowentrypositive + S (dst_positive_zero_inner_inputrowsrowentry) = S ((S (srt_index_zero_inner_inputrows)) * dst_positive_scale_zero_inner_inputrowsrowentry)) /\ exists ff_q_pvs_zero_inner_inputrowsrowentrypositive. dst_positive_code_zero_inner_inputrowsrowentry = ff_q_pvs_zero_inner_inputrowsrowentrypositive * S ((S (srt_index_zero_inner_inputrows)) * dst_positive_scale_zero_inner_inputrowsrowentry) + (dst_positive_zero_inner_inputrowsrowentry))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowentrynegative. ff_h_pvs_zero_inner_inputrowsrowentrynegative + S (dst_negative_zero_inner_inputrowsrowentry) = S ((S (srt_index_zero_inner_inputrows)) * dst_negative_scale_zero_inner_inputrowsrowentry)) /\ exists ff_q_pvs_zero_inner_inputrowsrowentrynegative. dst_negative_code_zero_inner_inputrowsrowentry = ff_q_pvs_zero_inner_inputrowsrowentrynegative * S ((S (srt_index_zero_inner_inputrows)) * dst_negative_scale_zero_inner_inputrowsrowentry) + (dst_negative_zero_inner_inputrowsrowentry))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowentryvalue ge_balance_negative_zero_inner_inputrowsrowentryvalue. (((((srt_value_zero_inner_inputrows) = 2 * (ge_balance_positive_zero_inner_inputrowsrowentryvalue) /\ (ge_balance_negative_zero_inner_inputrowsrowentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowentryvaluedecode. (((srt_value_zero_inner_inputrows) = 2 * ge_signed_half_zero_inner_inputrowsrowentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowentryvalue) = S ge_signed_half_zero_inner_inputrowsrowentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowentry) + ge_balance_negative_zero_inner_inputrowsrowentryvalue = (dst_negative_zero_inner_inputrowsrowentry) + ge_balance_positive_zero_inner_inputrowsrowentryvalue))))))))) /\ (exists srs_slice_zero_inner_inputrowsrowrow_sum. ((((exists dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_zero_inner_inputrowsrowrow_sumslicesource_table. (exists pvs_le_gap_zero_inner_inputrowsrowrow_sumslicesource_tabledomain. pvs_le_gap_zero_inner_inputrowsrowrow_sumslicesource_tabledomain + (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_zero_inner_inputrowsrowrow_sumslicesource_table dst_negative_zero_inner_inputrowsrowrow_sumslicesource_table dst_value_zero_inner_inputrowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_zero_inner_inputrowsrowrow_sumslicesource_table) = S ((S (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_zero_inner_inputrowsrowrow_sumslicesource_table = ff_q_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_positive_zero_inner_inputrowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_zero_inner_inputrowsrowrow_sumslicesource_table) = S ((S (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_zero_inner_inputrowsrowrow_sumslicesource_table = ff_q_pvs_zero_inner_inputrowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_zero_inner_inputrowsrowrow_sumslicesource_table)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumslicesource_table) + (dst_negative_zero_inner_inputrowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_zero_inner_inputrowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_zero_inner_inputrowsrowrow_sumslicesource_table) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_zero_inner_inputrowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowrow_sumslicesource_table) + ge_balance_negative_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue = (dst_negative_zero_inner_inputrowsrowrow_sumslicesource_table) + ge_balance_positive_zero_inner_inputrowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table. (((srs_slice_zero_inner_inputrowsrowrow_sum) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_zero_inner_inputrowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_zero_inner_inputrowsrowrow_sumsliceoutput_tabledomain + (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table) = (0)) -> exists dst_positive_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_negative_zero_inner_inputrowsrowrow_sumsliceoutput_table dst_value_zero_inner_inputrowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_zero_inner_inputrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_zero_inner_inputrowsrowrow_sumsliceoutput_table = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_positive_zero_inner_inputrowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_zero_inner_inputrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_zero_inner_inputrowsrowrow_sumsliceoutput_table = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_zero_inner_inputrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceoutput_table) + (dst_negative_zero_inner_inputrowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_zero_inner_inputrowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_zero_inner_inputrowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowrow_sumsliceoutput_table) + ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_zero_inner_inputrowsrowrow_sumsliceoutput_table) + ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_zero_inner_inputrowsrowrow_sumslice. (exists pvs_gap_zero_inner_inputrowsrowrow_sumslicebound. pvs_gap_zero_inner_inputrowsrowrow_sumslicebound + S (srs_index_zero_inner_inputrowsrowrow_sumslice) = (0)) -> exists srs_value_zero_inner_inputrowsrowrow_sumslice. (((exists dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource dst_positive_zero_inner_inputrowsrowrow_sumsliceentrysource dst_negative_zero_inner_inputrowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcepositive + S (dst_positive_zero_inner_inputrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_zero_inner_inputrows)))) + ((t) * (srs_index_zero_inner_inputrowsrowrow_sumslice))))) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcepositive. dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentrysource = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_zero_inner_inputrows)))) + ((t) * (srs_index_zero_inner_inputrowsrowrow_sumslice))))) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_positive_zero_inner_inputrowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcenegative + S (dst_negative_zero_inner_inputrowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_zero_inner_inputrows)))) + ((t) * (srs_index_zero_inner_inputrowsrowrow_sumslice))))) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcenegative. dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentrysource = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_zero_inner_inputrows)))) + ((t) * (srs_index_zero_inner_inputrowsrowrow_sumslice))))) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentrysource) + (dst_negative_zero_inner_inputrowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue. (((((srs_value_zero_inner_inputrowsrowrow_sumslice) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_zero_inner_inputrowsrowrow_sumslice) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowrow_sumsliceentrysource) + ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue = (dst_negative_zero_inner_inputrowsrowrow_sumsliceentrysource) + ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_positive_zero_inner_inputrowsrowrow_sumsliceentryoutput dst_negative_zero_inner_inputrowsrowrow_sumsliceentryoutput. (((srs_slice_zero_inner_inputrowsrowrow_sum) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputpositive + S (dst_positive_zero_inner_inputrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_zero_inner_inputrowsrowrow_sumslice)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputpositive. dst_positive_code_zero_inner_inputrowsrowrow_sumsliceentryoutput = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_zero_inner_inputrowsrowrow_sumslice)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_positive_zero_inner_inputrowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputnegative + S (dst_negative_zero_inner_inputrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_zero_inner_inputrowsrowrow_sumslice)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputnegative. dst_negative_code_zero_inner_inputrowsrowrow_sumsliceentryoutput = ff_q_pvs_zero_inner_inputrowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_zero_inner_inputrowsrowrow_sumslice)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsliceentryoutput) + (dst_negative_zero_inner_inputrowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue. (((((srs_value_zero_inner_inputrowsrowrow_sumslice) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_zero_inner_inputrowsrowrow_sumslice) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_zero_inner_inputrowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_zero_inner_inputrowsrowrow_sumsliceentryoutput) + ge_balance_negative_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue = (dst_negative_zero_inner_inputrowsrowrow_sumsliceentryoutput) + ge_balance_positive_zero_inner_inputrowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_zero_inner_inputrowsrowrow_sumsum dst_positive_scale_zero_inner_inputrowsrowrow_sumsum dst_negative_code_zero_inner_inputrowsrowrow_sumsum dst_negative_scale_zero_inner_inputrowsrowrow_sumsum dst_positive_sum_zero_inner_inputrowsrowrow_sumsum dst_negative_sum_zero_inner_inputrowsrowrow_sumsum. (((srs_slice_zero_inner_inputrowsrowrow_sum) = (((((dst_positive_code_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)))) * S ((((dst_positive_code_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_positive_code_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_positive_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_positive_scale_zero_inner_inputrowsrowrow_sumsum))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)))) + ((((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum))) + (((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) * S ((dst_negative_code_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) + ((dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive. ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_start. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_start. fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_terminal. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_zero_inner_inputrowsrowrow_sumsum) = S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_terminal. fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_terminal * S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive) + (dst_positive_sum_zero_inner_inputrowsrowrow_sumsum))) /\ forall fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps = 0) -> exists fs_a_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps fs_r_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps fs_s_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsum)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_zero_inner_inputrowsrowrow_sumsum = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_zero_inner_inputrowsrowrow_sumsum) + (fs_a_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive) + (fs_r_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_zero_inner_inputrowsrowrow_sumsumpositive = fs_q_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumpositive) + (fs_s_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps = fs_r_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps + fs_a_dst_zero_inner_inputrowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative. ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_start. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_start. fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_terminal. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_zero_inner_inputrowsrowrow_sumsum) = S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_terminal. fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_terminal * S ((S (0)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative) + (dst_negative_sum_zero_inner_inputrowsrowrow_sumsum))) /\ forall fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps = 0) -> exists fs_a_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps fs_r_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps fs_s_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsum)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_zero_inner_inputrowsrowrow_sumsum = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_zero_inner_inputrowsrowrow_sumsum) + (fs_a_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative) + (fs_r_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_zero_inner_inputrowsrowrow_sumsumnegative = fs_q_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_zero_inner_inputrowsrowrow_sumsumnegative) + (fs_s_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps = fs_r_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps + fs_a_dst_zero_inner_inputrowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_zero_inner_inputrowsrowrow_sumsumresult ge_balance_negative_zero_inner_inputrowsrowrow_sumsumresult. (((((srt_value_zero_inner_inputrows) = 2 * (ge_balance_positive_zero_inner_inputrowsrowrow_sumsumresult) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_zero_inner_inputrowsrowrow_sumsumresultdecode. (((srt_value_zero_inner_inputrows) = 2 * ge_signed_half_zero_inner_inputrowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_zero_inner_inputrowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_zero_inner_inputrowsrowrow_sumsumresult) = S ge_signed_half_zero_inner_inputrowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_zero_inner_inputrowsrowrow_sumsum) + ge_balance_negative_zero_inner_inputrowsrowrow_sumsumresult = (dst_negative_sum_zero_inner_inputrowsrowrow_sumsum) + ge_balance_positive_zero_inner_inputrowsrowrow_sumsumresult)))))))))))))))))) /\ (exists dst_positive_code_zero_inner_inputtotal dst_positive_scale_zero_inner_inputtotal dst_negative_code_zero_inner_inputtotal dst_negative_scale_zero_inner_inputtotal dst_positive_sum_zero_inner_inputtotal dst_negative_sum_zero_inner_inputtotal. (((srt_rows_zero_inner_input) = (((((dst_positive_code_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal)) * S ((dst_positive_code_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal)) + ((dst_positive_scale_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal))) + (((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) * S ((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) + ((dst_negative_scale_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)))) * S ((((dst_positive_code_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal)) * S ((dst_positive_code_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal)) + ((dst_positive_scale_zero_inner_inputtotal) + (dst_positive_scale_zero_inner_inputtotal))) + (((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) * S ((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) + ((dst_negative_scale_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)))) + ((((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) * S ((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) + ((dst_negative_scale_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal))) + (((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) * S ((dst_negative_code_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)) + ((dst_negative_scale_zero_inner_inputtotal) + (dst_negative_scale_zero_inner_inputtotal)))))) /\ (((exists fs_u_dst_zero_inner_inputtotalpositive fs_v_dst_zero_inner_inputtotalpositive. ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_start. fs_h_dst_zero_inner_inputtotalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_inner_inputtotalpositive)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_start. fs_u_dst_zero_inner_inputtotalpositive = fs_q_dst_zero_inner_inputtotalpositive_body_start * S ((S (0)) * fs_v_dst_zero_inner_inputtotalpositive) + (0))) /\ ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_terminal. fs_h_dst_zero_inner_inputtotalpositive_body_terminal + S (dst_positive_sum_zero_inner_inputtotal) = S ((S (m)) * fs_v_dst_zero_inner_inputtotalpositive)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_terminal. fs_u_dst_zero_inner_inputtotalpositive = fs_q_dst_zero_inner_inputtotalpositive_body_terminal * S ((S (m)) * fs_v_dst_zero_inner_inputtotalpositive) + (dst_positive_sum_zero_inner_inputtotal))) /\ forall fs_i_dst_zero_inner_inputtotalpositive_body_steps. (exists fs_lt_dst_zero_inner_inputtotalpositive_body_steps_bound. fs_lt_dst_zero_inner_inputtotalpositive_body_steps_bound + S fs_i_dst_zero_inner_inputtotalpositive_body_steps = m) -> exists fs_a_dst_zero_inner_inputtotalpositive_body_steps fs_r_dst_zero_inner_inputtotalpositive_body_steps fs_s_dst_zero_inner_inputtotalpositive_body_steps. ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_steps_summand. fs_h_dst_zero_inner_inputtotalpositive_body_steps_summand + S (fs_a_dst_zero_inner_inputtotalpositive_body_steps) = S ((S (fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * dst_positive_scale_zero_inner_inputtotal)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_steps_summand. dst_positive_code_zero_inner_inputtotal = fs_q_dst_zero_inner_inputtotalpositive_body_steps_summand * S ((S (fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * dst_positive_scale_zero_inner_inputtotal) + (fs_a_dst_zero_inner_inputtotalpositive_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_steps_partial. fs_h_dst_zero_inner_inputtotalpositive_body_steps_partial + S (fs_r_dst_zero_inner_inputtotalpositive_body_steps) = S ((S (fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * fs_v_dst_zero_inner_inputtotalpositive)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_steps_partial. fs_u_dst_zero_inner_inputtotalpositive = fs_q_dst_zero_inner_inputtotalpositive_body_steps_partial * S ((S (fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * fs_v_dst_zero_inner_inputtotalpositive) + (fs_r_dst_zero_inner_inputtotalpositive_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputtotalpositive_body_steps_successor. fs_h_dst_zero_inner_inputtotalpositive_body_steps_successor + S (fs_s_dst_zero_inner_inputtotalpositive_body_steps) = S ((S (S fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * fs_v_dst_zero_inner_inputtotalpositive)) /\ exists fs_q_dst_zero_inner_inputtotalpositive_body_steps_successor. fs_u_dst_zero_inner_inputtotalpositive = fs_q_dst_zero_inner_inputtotalpositive_body_steps_successor * S ((S (S fs_i_dst_zero_inner_inputtotalpositive_body_steps)) * fs_v_dst_zero_inner_inputtotalpositive) + (fs_s_dst_zero_inner_inputtotalpositive_body_steps))) /\ fs_s_dst_zero_inner_inputtotalpositive_body_steps = fs_r_dst_zero_inner_inputtotalpositive_body_steps + fs_a_dst_zero_inner_inputtotalpositive_body_steps)))))) /\ (((exists fs_u_dst_zero_inner_inputtotalnegative fs_v_dst_zero_inner_inputtotalnegative. ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_start. fs_h_dst_zero_inner_inputtotalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_inner_inputtotalnegative)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_start. fs_u_dst_zero_inner_inputtotalnegative = fs_q_dst_zero_inner_inputtotalnegative_body_start * S ((S (0)) * fs_v_dst_zero_inner_inputtotalnegative) + (0))) /\ ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_terminal. fs_h_dst_zero_inner_inputtotalnegative_body_terminal + S (dst_negative_sum_zero_inner_inputtotal) = S ((S (m)) * fs_v_dst_zero_inner_inputtotalnegative)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_terminal. fs_u_dst_zero_inner_inputtotalnegative = fs_q_dst_zero_inner_inputtotalnegative_body_terminal * S ((S (m)) * fs_v_dst_zero_inner_inputtotalnegative) + (dst_negative_sum_zero_inner_inputtotal))) /\ forall fs_i_dst_zero_inner_inputtotalnegative_body_steps. (exists fs_lt_dst_zero_inner_inputtotalnegative_body_steps_bound. fs_lt_dst_zero_inner_inputtotalnegative_body_steps_bound + S fs_i_dst_zero_inner_inputtotalnegative_body_steps = m) -> exists fs_a_dst_zero_inner_inputtotalnegative_body_steps fs_r_dst_zero_inner_inputtotalnegative_body_steps fs_s_dst_zero_inner_inputtotalnegative_body_steps. ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_steps_summand. fs_h_dst_zero_inner_inputtotalnegative_body_steps_summand + S (fs_a_dst_zero_inner_inputtotalnegative_body_steps) = S ((S (fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * dst_negative_scale_zero_inner_inputtotal)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_steps_summand. dst_negative_code_zero_inner_inputtotal = fs_q_dst_zero_inner_inputtotalnegative_body_steps_summand * S ((S (fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * dst_negative_scale_zero_inner_inputtotal) + (fs_a_dst_zero_inner_inputtotalnegative_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_steps_partial. fs_h_dst_zero_inner_inputtotalnegative_body_steps_partial + S (fs_r_dst_zero_inner_inputtotalnegative_body_steps) = S ((S (fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * fs_v_dst_zero_inner_inputtotalnegative)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_steps_partial. fs_u_dst_zero_inner_inputtotalnegative = fs_q_dst_zero_inner_inputtotalnegative_body_steps_partial * S ((S (fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * fs_v_dst_zero_inner_inputtotalnegative) + (fs_r_dst_zero_inner_inputtotalnegative_body_steps))) /\ ((((exists fs_h_dst_zero_inner_inputtotalnegative_body_steps_successor. fs_h_dst_zero_inner_inputtotalnegative_body_steps_successor + S (fs_s_dst_zero_inner_inputtotalnegative_body_steps) = S ((S (S fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * fs_v_dst_zero_inner_inputtotalnegative)) /\ exists fs_q_dst_zero_inner_inputtotalnegative_body_steps_successor. fs_u_dst_zero_inner_inputtotalnegative = fs_q_dst_zero_inner_inputtotalnegative_body_steps_successor * S ((S (S fs_i_dst_zero_inner_inputtotalnegative_body_steps)) * fs_v_dst_zero_inner_inputtotalnegative) + (fs_s_dst_zero_inner_inputtotalnegative_body_steps))) /\ fs_s_dst_zero_inner_inputtotalnegative_body_steps = fs_r_dst_zero_inner_inputtotalnegative_body_steps + fs_a_dst_zero_inner_inputtotalnegative_body_steps)))))) /\ (exists ge_balance_positive_zero_inner_inputtotalresult ge_balance_negative_zero_inner_inputtotalresult. (((((z) = 2 * (ge_balance_positive_zero_inner_inputtotalresult) /\ (ge_balance_negative_zero_inner_inputtotalresult) = 0) \/ exists ge_signed_half_zero_inner_inputtotalresultdecode. (((z) = 2 * ge_signed_half_zero_inner_inputtotalresultdecode + 1 /\ (ge_balance_positive_zero_inner_inputtotalresult) = 0) /\ (ge_balance_negative_zero_inner_inputtotalresult) = S ge_signed_half_zero_inner_inputtotalresultdecode))) /\ ((dst_positive_sum_zero_inner_inputtotal) + ge_balance_negative_zero_inner_inputtotalresult = (dst_negative_sum_zero_inner_inputtotal) + ge_balance_positive_zero_inner_inputtotalresult))))))))))) -> z=0Complete tactic proof in conservative notation
All 19 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
19 script commands · 3 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 (1)
01Fix variables and assumptionsL1–7
02Separate the logical casesL8–9
03Use earlier factsL10–19
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L10
specialize signed_rectangular_row_sums_zero_inner (m) - L11
specialize signed_rectangular_row_sums_zero_inner (F) - L12
specialize signed_rectangular_row_sums_zero_inner (x) - L13
specialize signed_rectangular_row_sums_zero_inner (o) - L14
specialize signed_rectangular_row_sums_zero_inner (s) - L15
specialize signed_rectangular_row_sums_zero_inner (t) - L16
specialize signed_rectangular_row_sums_zero_inner (z) - L17
apply signed_rectangular_row_sums_zero_inner - L18
exact hz_witness_left - L19
exact hz_witness_right
Original defined command ledger · 19 lines
- 0001
intro F - 0002
intro o - 0003
intro s - 0004
intro t - 0005
intro m - 0006
intro z - 0007
intro hz - 0008
cases hz - 0009
cases hz_witness - 0010
specialize signed_rectangular_row_sums_zero_inner (m) - 0011
specialize signed_rectangular_row_sums_zero_inner (F) - 0012
specialize signed_rectangular_row_sums_zero_inner (x) - 0013
specialize signed_rectangular_row_sums_zero_inner (o) - 0014
specialize signed_rectangular_row_sums_zero_inner (s) - 0015
specialize signed_rectangular_row_sums_zero_inner (t) - 0016
specialize signed_rectangular_row_sums_zero_inner (z) - 0017
apply signed_rectangular_row_sums_zero_inner - 0018
exact hz_witness_left - 0019
exact hz_witness_right