Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Exact expanded first-order arithmetic statement
forall F m n z. (exists dst_positive_code_flat_source dst_positive_scale_flat_source dst_negative_code_flat_source dst_negative_scale_flat_source. (((F) = (((((dst_positive_code_flat_source) + (dst_positive_scale_flat_source)) * S ((dst_positive_code_flat_source) + (dst_positive_scale_flat_source)) + ((dst_positive_scale_flat_source) + (dst_positive_scale_flat_source))) + (((dst_negative_code_flat_source) + (dst_negative_scale_flat_source)) * S ((dst_negative_code_flat_source) + (dst_negative_scale_flat_source)) + ((dst_negative_scale_flat_source) + (dst_negative_scale_flat_source)))) * S ((((dst_positive_code_flat_source) + (dst_positive_scale_flat_source)) * S ((dst_positive_code_flat_source) + (dst_positive_scale_flat_source)) + ((dst_positive_scale_flat_source) + (dst_positive_scale_flat_source))) + (((dst_negative_code_flat_source) + (dst_negative_scale_flat_source)) * S ((dst_negative_code_flat_source) + (dst_negative_scale_flat_source)) + ((dst_negative_scale_flat_source) + (dst_negative_scale_flat_source)))) + ((((dst_negative_code_flat_source) + (dst_negative_scale_flat_source)) * S ((dst_negative_code_flat_source) + (dst_negative_scale_flat_source)) + ((dst_negative_scale_flat_source) + (dst_negative_scale_flat_source))) + (((dst_negative_code_flat_source) + (dst_negative_scale_flat_source)) * S ((dst_negative_code_flat_source) + (dst_negative_scale_flat_source)) + ((dst_negative_scale_flat_source) + (dst_negative_scale_flat_source)))))) /\ (forall dst_index_flat_source. (exists pvs_le_gap_flat_sourcedomain. pvs_le_gap_flat_sourcedomain + (dst_index_flat_source) = (0)) -> exists dst_positive_flat_source dst_negative_flat_source dst_value_flat_source. ((((exists ff_h_pvs_flat_sourceentrypositive. ff_h_pvs_flat_sourceentrypositive + S (dst_positive_flat_source) = S ((S (dst_index_flat_source)) * dst_positive_scale_flat_source)) /\ exists ff_q_pvs_flat_sourceentrypositive. dst_positive_code_flat_source = ff_q_pvs_flat_sourceentrypositive * S ((S (dst_index_flat_source)) * dst_positive_scale_flat_source) + (dst_positive_flat_source))) /\ (((((exists ff_h_pvs_flat_sourceentrynegative. ff_h_pvs_flat_sourceentrynegative + S (dst_negative_flat_source) = S ((S (dst_index_flat_source)) * dst_negative_scale_flat_source)) /\ exists ff_q_pvs_flat_sourceentrynegative. dst_negative_code_flat_source = ff_q_pvs_flat_sourceentrynegative * S ((S (dst_index_flat_source)) * dst_negative_scale_flat_source) + (dst_negative_flat_source))) /\ (exists ge_balance_positive_flat_sourceentryvalue ge_balance_negative_flat_sourceentryvalue. (((((dst_value_flat_source) = 2 * (ge_balance_positive_flat_sourceentryvalue) /\ (ge_balance_negative_flat_sourceentryvalue) = 0) \/ exists ge_signed_half_flat_sourceentryvaluedecode. (((dst_value_flat_source) = 2 * ge_signed_half_flat_sourceentryvaluedecode + 1 /\ (ge_balance_positive_flat_sourceentryvalue) = 0) /\ (ge_balance_negative_flat_sourceentryvalue) = S ge_signed_half_flat_sourceentryvaluedecode))) /\ ((dst_positive_flat_source) + ge_balance_negative_flat_sourceentryvalue = (dst_negative_flat_source) + ge_balance_positive_flat_sourceentryvalue))))))))) -> (((exists dst_positive_code_flat_prefix dst_positive_scale_flat_prefix dst_negative_code_flat_prefix dst_negative_scale_flat_prefix dst_positive_sum_flat_prefix dst_negative_sum_flat_prefix. (((F) = (((((dst_positive_code_flat_prefix) + (dst_positive_scale_flat_prefix)) * S ((dst_positive_code_flat_prefix) + (dst_positive_scale_flat_prefix)) + ((dst_positive_scale_flat_prefix) + (dst_positive_scale_flat_prefix))) + (((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) * S ((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) + ((dst_negative_scale_flat_prefix) + (dst_negative_scale_flat_prefix)))) * S ((((dst_positive_code_flat_prefix) + (dst_positive_scale_flat_prefix)) * S ((dst_positive_code_flat_prefix) + (dst_positive_scale_flat_prefix)) + ((dst_positive_scale_flat_prefix) + (dst_positive_scale_flat_prefix))) + (((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) * S ((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) + ((dst_negative_scale_flat_prefix) + (dst_negative_scale_flat_prefix)))) + ((((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) * S ((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) + ((dst_negative_scale_flat_prefix) + (dst_negative_scale_flat_prefix))) + (((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) * S ((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) + ((dst_negative_scale_flat_prefix) + (dst_negative_scale_flat_prefix)))))) /\ (((exists fs_u_dst_flat_prefixpositive fs_v_dst_flat_prefixpositive. ((((exists fs_h_dst_flat_prefixpositive_body_start. fs_h_dst_flat_prefixpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_prefixpositive)) /\ exists fs_q_dst_flat_prefixpositive_body_start. fs_u_dst_flat_prefixpositive = fs_q_dst_flat_prefixpositive_body_start * S ((S (0)) * fs_v_dst_flat_prefixpositive) + (0))) /\ ((((exists fs_h_dst_flat_prefixpositive_body_terminal. fs_h_dst_flat_prefixpositive_body_terminal + S (dst_positive_sum_flat_prefix) = S ((S (m*n)) * fs_v_dst_flat_prefixpositive)) /\ exists fs_q_dst_flat_prefixpositive_body_terminal. fs_u_dst_flat_prefixpositive = fs_q_dst_flat_prefixpositive_body_terminal * S ((S (m*n)) * fs_v_dst_flat_prefixpositive) + (dst_positive_sum_flat_prefix))) /\ forall fs_i_dst_flat_prefixpositive_body_steps. (exists fs_lt_dst_flat_prefixpositive_body_steps_bound. fs_lt_dst_flat_prefixpositive_body_steps_bound + S fs_i_dst_flat_prefixpositive_body_steps = m*n) -> exists fs_a_dst_flat_prefixpositive_body_steps fs_r_dst_flat_prefixpositive_body_steps fs_s_dst_flat_prefixpositive_body_steps. ((((exists fs_h_dst_flat_prefixpositive_body_steps_summand. fs_h_dst_flat_prefixpositive_body_steps_summand + S (fs_a_dst_flat_prefixpositive_body_steps) = S ((S (fs_i_dst_flat_prefixpositive_body_steps)) * dst_positive_scale_flat_prefix)) /\ exists fs_q_dst_flat_prefixpositive_body_steps_summand. dst_positive_code_flat_prefix = fs_q_dst_flat_prefixpositive_body_steps_summand * S ((S (fs_i_dst_flat_prefixpositive_body_steps)) * dst_positive_scale_flat_prefix) + (fs_a_dst_flat_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_flat_prefixpositive_body_steps_partial. fs_h_dst_flat_prefixpositive_body_steps_partial + S (fs_r_dst_flat_prefixpositive_body_steps) = S ((S (fs_i_dst_flat_prefixpositive_body_steps)) * fs_v_dst_flat_prefixpositive)) /\ exists fs_q_dst_flat_prefixpositive_body_steps_partial. fs_u_dst_flat_prefixpositive = fs_q_dst_flat_prefixpositive_body_steps_partial * S ((S (fs_i_dst_flat_prefixpositive_body_steps)) * fs_v_dst_flat_prefixpositive) + (fs_r_dst_flat_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_flat_prefixpositive_body_steps_successor. fs_h_dst_flat_prefixpositive_body_steps_successor + S (fs_s_dst_flat_prefixpositive_body_steps) = S ((S (S fs_i_dst_flat_prefixpositive_body_steps)) * fs_v_dst_flat_prefixpositive)) /\ exists fs_q_dst_flat_prefixpositive_body_steps_successor. fs_u_dst_flat_prefixpositive = fs_q_dst_flat_prefixpositive_body_steps_successor * S ((S (S fs_i_dst_flat_prefixpositive_body_steps)) * fs_v_dst_flat_prefixpositive) + (fs_s_dst_flat_prefixpositive_body_steps))) /\ fs_s_dst_flat_prefixpositive_body_steps = fs_r_dst_flat_prefixpositive_body_steps + fs_a_dst_flat_prefixpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_prefixnegative fs_v_dst_flat_prefixnegative. ((((exists fs_h_dst_flat_prefixnegative_body_start. fs_h_dst_flat_prefixnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_prefixnegative)) /\ exists fs_q_dst_flat_prefixnegative_body_start. fs_u_dst_flat_prefixnegative = fs_q_dst_flat_prefixnegative_body_start * S ((S (0)) * fs_v_dst_flat_prefixnegative) + (0))) /\ ((((exists fs_h_dst_flat_prefixnegative_body_terminal. fs_h_dst_flat_prefixnegative_body_terminal + S (dst_negative_sum_flat_prefix) = S ((S (m*n)) * fs_v_dst_flat_prefixnegative)) /\ exists fs_q_dst_flat_prefixnegative_body_terminal. fs_u_dst_flat_prefixnegative = fs_q_dst_flat_prefixnegative_body_terminal * S ((S (m*n)) * fs_v_dst_flat_prefixnegative) + (dst_negative_sum_flat_prefix))) /\ forall fs_i_dst_flat_prefixnegative_body_steps. (exists fs_lt_dst_flat_prefixnegative_body_steps_bound. fs_lt_dst_flat_prefixnegative_body_steps_bound + S fs_i_dst_flat_prefixnegative_body_steps = m*n) -> exists fs_a_dst_flat_prefixnegative_body_steps fs_r_dst_flat_prefixnegative_body_steps fs_s_dst_flat_prefixnegative_body_steps. ((((exists fs_h_dst_flat_prefixnegative_body_steps_summand. fs_h_dst_flat_prefixnegative_body_steps_summand + S (fs_a_dst_flat_prefixnegative_body_steps) = S ((S (fs_i_dst_flat_prefixnegative_body_steps)) * dst_negative_scale_flat_prefix)) /\ exists fs_q_dst_flat_prefixnegative_body_steps_summand. dst_negative_code_flat_prefix = fs_q_dst_flat_prefixnegative_body_steps_summand * S ((S (fs_i_dst_flat_prefixnegative_body_steps)) * dst_negative_scale_flat_prefix) + (fs_a_dst_flat_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_flat_prefixnegative_body_steps_partial. fs_h_dst_flat_prefixnegative_body_steps_partial + S (fs_r_dst_flat_prefixnegative_body_steps) = S ((S (fs_i_dst_flat_prefixnegative_body_steps)) * fs_v_dst_flat_prefixnegative)) /\ exists fs_q_dst_flat_prefixnegative_body_steps_partial. fs_u_dst_flat_prefixnegative = fs_q_dst_flat_prefixnegative_body_steps_partial * S ((S (fs_i_dst_flat_prefixnegative_body_steps)) * fs_v_dst_flat_prefixnegative) + (fs_r_dst_flat_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_flat_prefixnegative_body_steps_successor. fs_h_dst_flat_prefixnegative_body_steps_successor + S (fs_s_dst_flat_prefixnegative_body_steps) = S ((S (S fs_i_dst_flat_prefixnegative_body_steps)) * fs_v_dst_flat_prefixnegative)) /\ exists fs_q_dst_flat_prefixnegative_body_steps_successor. fs_u_dst_flat_prefixnegative = fs_q_dst_flat_prefixnegative_body_steps_successor * S ((S (S fs_i_dst_flat_prefixnegative_body_steps)) * fs_v_dst_flat_prefixnegative) + (fs_s_dst_flat_prefixnegative_body_steps))) /\ fs_s_dst_flat_prefixnegative_body_steps = fs_r_dst_flat_prefixnegative_body_steps + fs_a_dst_flat_prefixnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_prefixresult ge_balance_negative_flat_prefixresult. (((((z) = 2 * (ge_balance_positive_flat_prefixresult) /\ (ge_balance_negative_flat_prefixresult) = 0) \/ exists ge_signed_half_flat_prefixresultdecode. (((z) = 2 * ge_signed_half_flat_prefixresultdecode + 1 /\ (ge_balance_positive_flat_prefixresult) = 0) /\ (ge_balance_negative_flat_prefixresult) = S ge_signed_half_flat_prefixresultdecode))) /\ ((dst_positive_sum_flat_prefix) + ge_balance_negative_flat_prefixresult = (dst_negative_sum_flat_prefix) + ge_balance_positive_flat_prefixresult))))))))) -> (exists srt_rows_flat_rectangle. ((((exists dst_positive_code_flat_rectanglerowssource_table dst_positive_scale_flat_rectanglerowssource_table dst_negative_code_flat_rectanglerowssource_table dst_negative_scale_flat_rectanglerowssource_table. (((F) = (((((dst_positive_code_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table)) * S ((dst_positive_code_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table)) + ((dst_positive_scale_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table))) + (((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) * S ((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) + ((dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)))) * S ((((dst_positive_code_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table)) * S ((dst_positive_code_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table)) + ((dst_positive_scale_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table))) + (((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) * S ((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) + ((dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)))) + ((((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) * S ((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) + ((dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table))) + (((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) * S ((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) + ((dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)))))) /\ (forall dst_index_flat_rectanglerowssource_table. (exists pvs_le_gap_flat_rectanglerowssource_tabledomain. pvs_le_gap_flat_rectanglerowssource_tabledomain + (dst_index_flat_rectanglerowssource_table) = (0)) -> exists dst_positive_flat_rectanglerowssource_table dst_negative_flat_rectanglerowssource_table dst_value_flat_rectanglerowssource_table. ((((exists ff_h_pvs_flat_rectanglerowssource_tableentrypositive. ff_h_pvs_flat_rectanglerowssource_tableentrypositive + S (dst_positive_flat_rectanglerowssource_table) = S ((S (dst_index_flat_rectanglerowssource_table)) * dst_positive_scale_flat_rectanglerowssource_table)) /\ exists ff_q_pvs_flat_rectanglerowssource_tableentrypositive. dst_positive_code_flat_rectanglerowssource_table = ff_q_pvs_flat_rectanglerowssource_tableentrypositive * S ((S (dst_index_flat_rectanglerowssource_table)) * dst_positive_scale_flat_rectanglerowssource_table) + (dst_positive_flat_rectanglerowssource_table))) /\ (((((exists ff_h_pvs_flat_rectanglerowssource_tableentrynegative. ff_h_pvs_flat_rectanglerowssource_tableentrynegative + S (dst_negative_flat_rectanglerowssource_table) = S ((S (dst_index_flat_rectanglerowssource_table)) * dst_negative_scale_flat_rectanglerowssource_table)) /\ exists ff_q_pvs_flat_rectanglerowssource_tableentrynegative. dst_negative_code_flat_rectanglerowssource_table = ff_q_pvs_flat_rectanglerowssource_tableentrynegative * S ((S (dst_index_flat_rectanglerowssource_table)) * dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_flat_rectanglerowssource_table))) /\ (exists ge_balance_positive_flat_rectanglerowssource_tableentryvalue ge_balance_negative_flat_rectanglerowssource_tableentryvalue. (((((dst_value_flat_rectanglerowssource_table) = 2 * (ge_balance_positive_flat_rectanglerowssource_tableentryvalue) /\ (ge_balance_negative_flat_rectanglerowssource_tableentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowssource_tableentryvaluedecode. (((dst_value_flat_rectanglerowssource_table) = 2 * ge_signed_half_flat_rectanglerowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowssource_tableentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowssource_tableentryvalue) = S ge_signed_half_flat_rectanglerowssource_tableentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowssource_table) + ge_balance_negative_flat_rectanglerowssource_tableentryvalue = (dst_negative_flat_rectanglerowssource_table) + ge_balance_positive_flat_rectanglerowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_flat_rectanglerowsrow_table dst_positive_scale_flat_rectanglerowsrow_table dst_negative_code_flat_rectanglerowsrow_table dst_negative_scale_flat_rectanglerowsrow_table. (((srt_rows_flat_rectangle) = (((((dst_positive_code_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table)) * S ((dst_positive_code_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table)) + ((dst_positive_scale_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table))) + (((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) * S ((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) + ((dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)))) * S ((((dst_positive_code_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table)) * S ((dst_positive_code_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table)) + ((dst_positive_scale_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table))) + (((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) * S ((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) + ((dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)))) + ((((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) * S ((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) + ((dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table))) + (((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) * S ((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) + ((dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)))))) /\ (forall dst_index_flat_rectanglerowsrow_table. (exists pvs_le_gap_flat_rectanglerowsrow_tabledomain. pvs_le_gap_flat_rectanglerowsrow_tabledomain + (dst_index_flat_rectanglerowsrow_table) = (m)) -> exists dst_positive_flat_rectanglerowsrow_table dst_negative_flat_rectanglerowsrow_table dst_value_flat_rectanglerowsrow_table. ((((exists ff_h_pvs_flat_rectanglerowsrow_tableentrypositive. ff_h_pvs_flat_rectanglerowsrow_tableentrypositive + S (dst_positive_flat_rectanglerowsrow_table) = S ((S (dst_index_flat_rectanglerowsrow_table)) * dst_positive_scale_flat_rectanglerowsrow_table)) /\ exists ff_q_pvs_flat_rectanglerowsrow_tableentrypositive. dst_positive_code_flat_rectanglerowsrow_table = ff_q_pvs_flat_rectanglerowsrow_tableentrypositive * S ((S (dst_index_flat_rectanglerowsrow_table)) * dst_positive_scale_flat_rectanglerowsrow_table) + (dst_positive_flat_rectanglerowsrow_table))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrow_tableentrynegative. ff_h_pvs_flat_rectanglerowsrow_tableentrynegative + S (dst_negative_flat_rectanglerowsrow_table) = S ((S (dst_index_flat_rectanglerowsrow_table)) * dst_negative_scale_flat_rectanglerowsrow_table)) /\ exists ff_q_pvs_flat_rectanglerowsrow_tableentrynegative. dst_negative_code_flat_rectanglerowsrow_table = ff_q_pvs_flat_rectanglerowsrow_tableentrynegative * S ((S (dst_index_flat_rectanglerowsrow_table)) * dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_flat_rectanglerowsrow_table))) /\ (exists ge_balance_positive_flat_rectanglerowsrow_tableentryvalue ge_balance_negative_flat_rectanglerowsrow_tableentryvalue. (((((dst_value_flat_rectanglerowsrow_table) = 2 * (ge_balance_positive_flat_rectanglerowsrow_tableentryvalue) /\ (ge_balance_negative_flat_rectanglerowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrow_tableentryvaluedecode. (((dst_value_flat_rectanglerowsrow_table) = 2 * ge_signed_half_flat_rectanglerowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrow_tableentryvalue) = S ge_signed_half_flat_rectanglerowsrow_tableentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrow_table) + ge_balance_negative_flat_rectanglerowsrow_tableentryvalue = (dst_negative_flat_rectanglerowsrow_table) + ge_balance_positive_flat_rectanglerowsrow_tableentryvalue))))))))) /\ (forall srt_index_flat_rectanglerows. (exists pvs_gap_flat_rectanglerowsbound. pvs_gap_flat_rectanglerowsbound + S (srt_index_flat_rectanglerows) = (m)) -> exists srt_value_flat_rectanglerows. (((exists dst_positive_code_flat_rectanglerowsrowentry dst_positive_scale_flat_rectanglerowsrowentry dst_negative_code_flat_rectanglerowsrowentry dst_negative_scale_flat_rectanglerowsrowentry dst_positive_flat_rectanglerowsrowentry dst_negative_flat_rectanglerowsrowentry. (((srt_rows_flat_rectangle) = (((((dst_positive_code_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry)) * S ((dst_positive_code_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry)) + ((dst_positive_scale_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry))) + (((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) * S ((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) + ((dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)))) * S ((((dst_positive_code_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry)) * S ((dst_positive_code_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry)) + ((dst_positive_scale_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry))) + (((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) * S ((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) + ((dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)))) + ((((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) * S ((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) + ((dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry))) + (((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) * S ((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) + ((dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)))))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowentrypositive. ff_h_pvs_flat_rectanglerowsrowentrypositive + S (dst_positive_flat_rectanglerowsrowentry) = S ((S (srt_index_flat_rectanglerows)) * dst_positive_scale_flat_rectanglerowsrowentry)) /\ exists ff_q_pvs_flat_rectanglerowsrowentrypositive. dst_positive_code_flat_rectanglerowsrowentry = ff_q_pvs_flat_rectanglerowsrowentrypositive * S ((S (srt_index_flat_rectanglerows)) * dst_positive_scale_flat_rectanglerowsrowentry) + (dst_positive_flat_rectanglerowsrowentry))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowentrynegative. ff_h_pvs_flat_rectanglerowsrowentrynegative + S (dst_negative_flat_rectanglerowsrowentry) = S ((S (srt_index_flat_rectanglerows)) * dst_negative_scale_flat_rectanglerowsrowentry)) /\ exists ff_q_pvs_flat_rectanglerowsrowentrynegative. dst_negative_code_flat_rectanglerowsrowentry = ff_q_pvs_flat_rectanglerowsrowentrynegative * S ((S (srt_index_flat_rectanglerows)) * dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_flat_rectanglerowsrowentry))) /\ (exists ge_balance_positive_flat_rectanglerowsrowentryvalue ge_balance_negative_flat_rectanglerowsrowentryvalue. (((((srt_value_flat_rectanglerows) = 2 * (ge_balance_positive_flat_rectanglerowsrowentryvalue) /\ (ge_balance_negative_flat_rectanglerowsrowentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowentryvaluedecode. (((srt_value_flat_rectanglerows) = 2 * ge_signed_half_flat_rectanglerowsrowentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowentryvalue) = S ge_signed_half_flat_rectanglerowsrowentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowentry) + ge_balance_negative_flat_rectanglerowsrowentryvalue = (dst_negative_flat_rectanglerowsrowentry) + ge_balance_positive_flat_rectanglerowsrowentryvalue))))))))) /\ (exists srs_slice_flat_rectanglerowsrowrow_sum. ((((exists dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_flat_rectanglerowsrowrow_sumslicesource_table. (exists pvs_le_gap_flat_rectanglerowsrowrow_sumslicesource_tabledomain. pvs_le_gap_flat_rectanglerowsrowrow_sumslicesource_tabledomain + (dst_index_flat_rectanglerowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_flat_rectanglerowsrowrow_sumslicesource_table dst_negative_flat_rectanglerowsrowrow_sumslicesource_table dst_value_flat_rectanglerowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_flat_rectanglerowsrowrow_sumslicesource_table) = S ((S (dst_index_flat_rectanglerowsrowrow_sumslicesource_table)) * dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table = ff_q_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_flat_rectanglerowsrowrow_sumslicesource_table)) * dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_flat_rectanglerowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_flat_rectanglerowsrowrow_sumslicesource_table) = S ((S (dst_index_flat_rectanglerowsrowrow_sumslicesource_table)) * dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table = ff_q_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_flat_rectanglerowsrowrow_sumslicesource_table)) * dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_flat_rectanglerowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_flat_rectanglerowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_flat_rectanglerowsrowrow_sumslicesource_table) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_flat_rectanglerowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowrow_sumslicesource_table) + ge_balance_negative_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue = (dst_negative_flat_rectanglerowsrowrow_sumslicesource_table) + ge_balance_positive_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table. (((srs_slice_flat_rectanglerowsrowrow_sum) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_flat_rectanglerowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_flat_rectanglerowsrowrow_sumsliceoutput_tabledomain + (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_flat_rectanglerowsrowrow_sumsliceoutput_table dst_negative_flat_rectanglerowsrowrow_sumsliceoutput_table dst_value_flat_rectanglerowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_flat_rectanglerowsrowrow_sumsliceoutput_table) = S ((S (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_flat_rectanglerowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_flat_rectanglerowsrowrow_sumsliceoutput_table) = S ((S (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_flat_rectanglerowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_flat_rectanglerowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_flat_rectanglerowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowrow_sumsliceoutput_table) + ge_balance_negative_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_flat_rectanglerowsrowrow_sumsliceoutput_table) + ge_balance_positive_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_flat_rectanglerowsrowrow_sumslice. (exists pvs_gap_flat_rectanglerowsrowrow_sumslicebound. pvs_gap_flat_rectanglerowsrowrow_sumslicebound + S (srs_index_flat_rectanglerowsrowrow_sumslice) = (n)) -> exists srs_value_flat_rectanglerowsrowrow_sumslice. (((exists dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource dst_positive_flat_rectanglerowsrowrow_sumsliceentrysource dst_negative_flat_rectanglerowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcepositive + S (dst_positive_flat_rectanglerowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((n) * (srt_index_flat_rectanglerows)))) + ((1) * (srs_index_flat_rectanglerowsrowrow_sumslice))))) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcepositive. dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcepositive * S ((S (((((0) + ((n) * (srt_index_flat_rectanglerows)))) + ((1) * (srs_index_flat_rectanglerowsrowrow_sumslice))))) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_flat_rectanglerowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcenegative + S (dst_negative_flat_rectanglerowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((n) * (srt_index_flat_rectanglerows)))) + ((1) * (srs_index_flat_rectanglerowsrowrow_sumslice))))) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcenegative. dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcenegative * S ((S (((((0) + ((n) * (srt_index_flat_rectanglerows)))) + ((1) * (srs_index_flat_rectanglerowsrowrow_sumslice))))) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_flat_rectanglerowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentrysourcevalue ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentrysourcevalue. (((((srs_value_flat_rectanglerowsrowrow_sumslice) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_flat_rectanglerowsrowrow_sumslice) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_flat_rectanglerowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowrow_sumsliceentrysource) + ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentrysourcevalue = (dst_negative_flat_rectanglerowsrowrow_sumsliceentrysource) + ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput dst_positive_flat_rectanglerowsrowrow_sumsliceentryoutput dst_negative_flat_rectanglerowsrowrow_sumsliceentryoutput. (((srs_slice_flat_rectanglerowsrowrow_sum) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputpositive + S (dst_positive_flat_rectanglerowsrowrow_sumsliceentryoutput) = S ((S (srs_index_flat_rectanglerowsrowrow_sumslice)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputpositive. dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_flat_rectanglerowsrowrow_sumslice)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_flat_rectanglerowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputnegative + S (dst_negative_flat_rectanglerowsrowrow_sumsliceentryoutput) = S ((S (srs_index_flat_rectanglerowsrowrow_sumslice)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputnegative. dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_flat_rectanglerowsrowrow_sumslice)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_flat_rectanglerowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentryoutputvalue ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentryoutputvalue. (((((srs_value_flat_rectanglerowsrowrow_sumslice) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_flat_rectanglerowsrowrow_sumslice) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_flat_rectanglerowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowrow_sumsliceentryoutput) + ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentryoutputvalue = (dst_negative_flat_rectanglerowsrowrow_sumsliceentryoutput) + ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_flat_rectanglerowsrowrow_sumsum dst_positive_scale_flat_rectanglerowsrowrow_sumsum dst_negative_code_flat_rectanglerowsrowrow_sumsum dst_negative_scale_flat_rectanglerowsrowrow_sumsum dst_positive_sum_flat_rectanglerowsrowrow_sumsum dst_negative_sum_flat_rectanglerowsrowrow_sumsum. (((srs_slice_flat_rectanglerowsrowrow_sum) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive. ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_start. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_start. fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_terminal. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_flat_rectanglerowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_terminal. fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive) + (dst_positive_sum_flat_rectanglerowsrowrow_sumsum))) /\ forall fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps fs_r_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps fs_s_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_flat_rectanglerowsrowrow_sumsum = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsum) + (fs_a_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive) + (fs_r_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive) + (fs_s_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps = fs_r_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps + fs_a_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative. ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_start. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_start. fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_terminal. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_flat_rectanglerowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_terminal. fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative) + (dst_negative_sum_flat_rectanglerowsrowrow_sumsum))) /\ forall fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps fs_r_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps fs_s_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_flat_rectanglerowsrowrow_sumsum = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (fs_a_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative) + (fs_r_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative) + (fs_s_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps = fs_r_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps + fs_a_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumsumresult ge_balance_negative_flat_rectanglerowsrowrow_sumsumresult. (((((srt_value_flat_rectanglerows) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumsumresult) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumsumresultdecode. (((srt_value_flat_rectanglerows) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsumresult) = S ge_signed_half_flat_rectanglerowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_flat_rectanglerowsrowrow_sumsum) + ge_balance_negative_flat_rectanglerowsrowrow_sumsumresult = (dst_negative_sum_flat_rectanglerowsrowrow_sumsum) + ge_balance_positive_flat_rectanglerowsrowrow_sumsumresult)))))))))))))))))) /\ (exists dst_positive_code_flat_rectangletotal dst_positive_scale_flat_rectangletotal dst_negative_code_flat_rectangletotal dst_negative_scale_flat_rectangletotal dst_positive_sum_flat_rectangletotal dst_negative_sum_flat_rectangletotal. (((srt_rows_flat_rectangle) = (((((dst_positive_code_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal)) * S ((dst_positive_code_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal)) + ((dst_positive_scale_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal))) + (((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) * S ((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) + ((dst_negative_scale_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)))) * S ((((dst_positive_code_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal)) * S ((dst_positive_code_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal)) + ((dst_positive_scale_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal))) + (((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) * S ((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) + ((dst_negative_scale_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)))) + ((((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) * S ((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) + ((dst_negative_scale_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal))) + (((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) * S ((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) + ((dst_negative_scale_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)))))) /\ (((exists fs_u_dst_flat_rectangletotalpositive fs_v_dst_flat_rectangletotalpositive. ((((exists fs_h_dst_flat_rectangletotalpositive_body_start. fs_h_dst_flat_rectangletotalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_rectangletotalpositive)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_start. fs_u_dst_flat_rectangletotalpositive = fs_q_dst_flat_rectangletotalpositive_body_start * S ((S (0)) * fs_v_dst_flat_rectangletotalpositive) + (0))) /\ ((((exists fs_h_dst_flat_rectangletotalpositive_body_terminal. fs_h_dst_flat_rectangletotalpositive_body_terminal + S (dst_positive_sum_flat_rectangletotal) = S ((S (m)) * fs_v_dst_flat_rectangletotalpositive)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_terminal. fs_u_dst_flat_rectangletotalpositive = fs_q_dst_flat_rectangletotalpositive_body_terminal * S ((S (m)) * fs_v_dst_flat_rectangletotalpositive) + (dst_positive_sum_flat_rectangletotal))) /\ forall fs_i_dst_flat_rectangletotalpositive_body_steps. (exists fs_lt_dst_flat_rectangletotalpositive_body_steps_bound. fs_lt_dst_flat_rectangletotalpositive_body_steps_bound + S fs_i_dst_flat_rectangletotalpositive_body_steps = m) -> exists fs_a_dst_flat_rectangletotalpositive_body_steps fs_r_dst_flat_rectangletotalpositive_body_steps fs_s_dst_flat_rectangletotalpositive_body_steps. ((((exists fs_h_dst_flat_rectangletotalpositive_body_steps_summand. fs_h_dst_flat_rectangletotalpositive_body_steps_summand + S (fs_a_dst_flat_rectangletotalpositive_body_steps) = S ((S (fs_i_dst_flat_rectangletotalpositive_body_steps)) * dst_positive_scale_flat_rectangletotal)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_steps_summand. dst_positive_code_flat_rectangletotal = fs_q_dst_flat_rectangletotalpositive_body_steps_summand * S ((S (fs_i_dst_flat_rectangletotalpositive_body_steps)) * dst_positive_scale_flat_rectangletotal) + (fs_a_dst_flat_rectangletotalpositive_body_steps))) /\ ((((exists fs_h_dst_flat_rectangletotalpositive_body_steps_partial. fs_h_dst_flat_rectangletotalpositive_body_steps_partial + S (fs_r_dst_flat_rectangletotalpositive_body_steps) = S ((S (fs_i_dst_flat_rectangletotalpositive_body_steps)) * fs_v_dst_flat_rectangletotalpositive)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_steps_partial. fs_u_dst_flat_rectangletotalpositive = fs_q_dst_flat_rectangletotalpositive_body_steps_partial * S ((S (fs_i_dst_flat_rectangletotalpositive_body_steps)) * fs_v_dst_flat_rectangletotalpositive) + (fs_r_dst_flat_rectangletotalpositive_body_steps))) /\ ((((exists fs_h_dst_flat_rectangletotalpositive_body_steps_successor. fs_h_dst_flat_rectangletotalpositive_body_steps_successor + S (fs_s_dst_flat_rectangletotalpositive_body_steps) = S ((S (S fs_i_dst_flat_rectangletotalpositive_body_steps)) * fs_v_dst_flat_rectangletotalpositive)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_steps_successor. fs_u_dst_flat_rectangletotalpositive = fs_q_dst_flat_rectangletotalpositive_body_steps_successor * S ((S (S fs_i_dst_flat_rectangletotalpositive_body_steps)) * fs_v_dst_flat_rectangletotalpositive) + (fs_s_dst_flat_rectangletotalpositive_body_steps))) /\ fs_s_dst_flat_rectangletotalpositive_body_steps = fs_r_dst_flat_rectangletotalpositive_body_steps + fs_a_dst_flat_rectangletotalpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_rectangletotalnegative fs_v_dst_flat_rectangletotalnegative. ((((exists fs_h_dst_flat_rectangletotalnegative_body_start. fs_h_dst_flat_rectangletotalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_rectangletotalnegative)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_start. fs_u_dst_flat_rectangletotalnegative = fs_q_dst_flat_rectangletotalnegative_body_start * S ((S (0)) * fs_v_dst_flat_rectangletotalnegative) + (0))) /\ ((((exists fs_h_dst_flat_rectangletotalnegative_body_terminal. fs_h_dst_flat_rectangletotalnegative_body_terminal + S (dst_negative_sum_flat_rectangletotal) = S ((S (m)) * fs_v_dst_flat_rectangletotalnegative)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_terminal. fs_u_dst_flat_rectangletotalnegative = fs_q_dst_flat_rectangletotalnegative_body_terminal * S ((S (m)) * fs_v_dst_flat_rectangletotalnegative) + (dst_negative_sum_flat_rectangletotal))) /\ forall fs_i_dst_flat_rectangletotalnegative_body_steps. (exists fs_lt_dst_flat_rectangletotalnegative_body_steps_bound. fs_lt_dst_flat_rectangletotalnegative_body_steps_bound + S fs_i_dst_flat_rectangletotalnegative_body_steps = m) -> exists fs_a_dst_flat_rectangletotalnegative_body_steps fs_r_dst_flat_rectangletotalnegative_body_steps fs_s_dst_flat_rectangletotalnegative_body_steps. ((((exists fs_h_dst_flat_rectangletotalnegative_body_steps_summand. fs_h_dst_flat_rectangletotalnegative_body_steps_summand + S (fs_a_dst_flat_rectangletotalnegative_body_steps) = S ((S (fs_i_dst_flat_rectangletotalnegative_body_steps)) * dst_negative_scale_flat_rectangletotal)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_steps_summand. dst_negative_code_flat_rectangletotal = fs_q_dst_flat_rectangletotalnegative_body_steps_summand * S ((S (fs_i_dst_flat_rectangletotalnegative_body_steps)) * dst_negative_scale_flat_rectangletotal) + (fs_a_dst_flat_rectangletotalnegative_body_steps))) /\ ((((exists fs_h_dst_flat_rectangletotalnegative_body_steps_partial. fs_h_dst_flat_rectangletotalnegative_body_steps_partial + S (fs_r_dst_flat_rectangletotalnegative_body_steps) = S ((S (fs_i_dst_flat_rectangletotalnegative_body_steps)) * fs_v_dst_flat_rectangletotalnegative)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_steps_partial. fs_u_dst_flat_rectangletotalnegative = fs_q_dst_flat_rectangletotalnegative_body_steps_partial * S ((S (fs_i_dst_flat_rectangletotalnegative_body_steps)) * fs_v_dst_flat_rectangletotalnegative) + (fs_r_dst_flat_rectangletotalnegative_body_steps))) /\ ((((exists fs_h_dst_flat_rectangletotalnegative_body_steps_successor. fs_h_dst_flat_rectangletotalnegative_body_steps_successor + S (fs_s_dst_flat_rectangletotalnegative_body_steps) = S ((S (S fs_i_dst_flat_rectangletotalnegative_body_steps)) * fs_v_dst_flat_rectangletotalnegative)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_steps_successor. fs_u_dst_flat_rectangletotalnegative = fs_q_dst_flat_rectangletotalnegative_body_steps_successor * S ((S (S fs_i_dst_flat_rectangletotalnegative_body_steps)) * fs_v_dst_flat_rectangletotalnegative) + (fs_s_dst_flat_rectangletotalnegative_body_steps))) /\ fs_s_dst_flat_rectangletotalnegative_body_steps = fs_r_dst_flat_rectangletotalnegative_body_steps + fs_a_dst_flat_rectangletotalnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_rectangletotalresult ge_balance_negative_flat_rectangletotalresult. (((((z) = 2 * (ge_balance_positive_flat_rectangletotalresult) /\ (ge_balance_negative_flat_rectangletotalresult) = 0) \/ exists ge_signed_half_flat_rectangletotalresultdecode. (((z) = 2 * ge_signed_half_flat_rectangletotalresultdecode + 1 /\ (ge_balance_positive_flat_rectangletotalresult) = 0) /\ (ge_balance_negative_flat_rectangletotalresult) = S ge_signed_half_flat_rectangletotalresultdecode))) /\ ((dst_positive_sum_flat_rectangletotal) + ge_balance_negative_flat_rectangletotalresult = (dst_negative_sum_flat_rectangletotal) + ge_balance_positive_flat_rectangletotalresult)))))))))))) /\ ((exists srt_rows_flat_rectangle. ((((exists dst_positive_code_flat_rectanglerowssource_table dst_positive_scale_flat_rectanglerowssource_table dst_negative_code_flat_rectanglerowssource_table dst_negative_scale_flat_rectanglerowssource_table. (((F) = (((((dst_positive_code_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table)) * S ((dst_positive_code_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table)) + ((dst_positive_scale_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table))) + (((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) * S ((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) + ((dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)))) * S ((((dst_positive_code_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table)) * S ((dst_positive_code_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table)) + ((dst_positive_scale_flat_rectanglerowssource_table) + (dst_positive_scale_flat_rectanglerowssource_table))) + (((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) * S ((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) + ((dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)))) + ((((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) * S ((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) + ((dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table))) + (((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) * S ((dst_negative_code_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)) + ((dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_scale_flat_rectanglerowssource_table)))))) /\ (forall dst_index_flat_rectanglerowssource_table. (exists pvs_le_gap_flat_rectanglerowssource_tabledomain. pvs_le_gap_flat_rectanglerowssource_tabledomain + (dst_index_flat_rectanglerowssource_table) = (0)) -> exists dst_positive_flat_rectanglerowssource_table dst_negative_flat_rectanglerowssource_table dst_value_flat_rectanglerowssource_table. ((((exists ff_h_pvs_flat_rectanglerowssource_tableentrypositive. ff_h_pvs_flat_rectanglerowssource_tableentrypositive + S (dst_positive_flat_rectanglerowssource_table) = S ((S (dst_index_flat_rectanglerowssource_table)) * dst_positive_scale_flat_rectanglerowssource_table)) /\ exists ff_q_pvs_flat_rectanglerowssource_tableentrypositive. dst_positive_code_flat_rectanglerowssource_table = ff_q_pvs_flat_rectanglerowssource_tableentrypositive * S ((S (dst_index_flat_rectanglerowssource_table)) * dst_positive_scale_flat_rectanglerowssource_table) + (dst_positive_flat_rectanglerowssource_table))) /\ (((((exists ff_h_pvs_flat_rectanglerowssource_tableentrynegative. ff_h_pvs_flat_rectanglerowssource_tableentrynegative + S (dst_negative_flat_rectanglerowssource_table) = S ((S (dst_index_flat_rectanglerowssource_table)) * dst_negative_scale_flat_rectanglerowssource_table)) /\ exists ff_q_pvs_flat_rectanglerowssource_tableentrynegative. dst_negative_code_flat_rectanglerowssource_table = ff_q_pvs_flat_rectanglerowssource_tableentrynegative * S ((S (dst_index_flat_rectanglerowssource_table)) * dst_negative_scale_flat_rectanglerowssource_table) + (dst_negative_flat_rectanglerowssource_table))) /\ (exists ge_balance_positive_flat_rectanglerowssource_tableentryvalue ge_balance_negative_flat_rectanglerowssource_tableentryvalue. (((((dst_value_flat_rectanglerowssource_table) = 2 * (ge_balance_positive_flat_rectanglerowssource_tableentryvalue) /\ (ge_balance_negative_flat_rectanglerowssource_tableentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowssource_tableentryvaluedecode. (((dst_value_flat_rectanglerowssource_table) = 2 * ge_signed_half_flat_rectanglerowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowssource_tableentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowssource_tableentryvalue) = S ge_signed_half_flat_rectanglerowssource_tableentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowssource_table) + ge_balance_negative_flat_rectanglerowssource_tableentryvalue = (dst_negative_flat_rectanglerowssource_table) + ge_balance_positive_flat_rectanglerowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_flat_rectanglerowsrow_table dst_positive_scale_flat_rectanglerowsrow_table dst_negative_code_flat_rectanglerowsrow_table dst_negative_scale_flat_rectanglerowsrow_table. (((srt_rows_flat_rectangle) = (((((dst_positive_code_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table)) * S ((dst_positive_code_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table)) + ((dst_positive_scale_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table))) + (((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) * S ((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) + ((dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)))) * S ((((dst_positive_code_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table)) * S ((dst_positive_code_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table)) + ((dst_positive_scale_flat_rectanglerowsrow_table) + (dst_positive_scale_flat_rectanglerowsrow_table))) + (((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) * S ((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) + ((dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)))) + ((((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) * S ((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) + ((dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table))) + (((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) * S ((dst_negative_code_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)) + ((dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_scale_flat_rectanglerowsrow_table)))))) /\ (forall dst_index_flat_rectanglerowsrow_table. (exists pvs_le_gap_flat_rectanglerowsrow_tabledomain. pvs_le_gap_flat_rectanglerowsrow_tabledomain + (dst_index_flat_rectanglerowsrow_table) = (m)) -> exists dst_positive_flat_rectanglerowsrow_table dst_negative_flat_rectanglerowsrow_table dst_value_flat_rectanglerowsrow_table. ((((exists ff_h_pvs_flat_rectanglerowsrow_tableentrypositive. ff_h_pvs_flat_rectanglerowsrow_tableentrypositive + S (dst_positive_flat_rectanglerowsrow_table) = S ((S (dst_index_flat_rectanglerowsrow_table)) * dst_positive_scale_flat_rectanglerowsrow_table)) /\ exists ff_q_pvs_flat_rectanglerowsrow_tableentrypositive. dst_positive_code_flat_rectanglerowsrow_table = ff_q_pvs_flat_rectanglerowsrow_tableentrypositive * S ((S (dst_index_flat_rectanglerowsrow_table)) * dst_positive_scale_flat_rectanglerowsrow_table) + (dst_positive_flat_rectanglerowsrow_table))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrow_tableentrynegative. ff_h_pvs_flat_rectanglerowsrow_tableentrynegative + S (dst_negative_flat_rectanglerowsrow_table) = S ((S (dst_index_flat_rectanglerowsrow_table)) * dst_negative_scale_flat_rectanglerowsrow_table)) /\ exists ff_q_pvs_flat_rectanglerowsrow_tableentrynegative. dst_negative_code_flat_rectanglerowsrow_table = ff_q_pvs_flat_rectanglerowsrow_tableentrynegative * S ((S (dst_index_flat_rectanglerowsrow_table)) * dst_negative_scale_flat_rectanglerowsrow_table) + (dst_negative_flat_rectanglerowsrow_table))) /\ (exists ge_balance_positive_flat_rectanglerowsrow_tableentryvalue ge_balance_negative_flat_rectanglerowsrow_tableentryvalue. (((((dst_value_flat_rectanglerowsrow_table) = 2 * (ge_balance_positive_flat_rectanglerowsrow_tableentryvalue) /\ (ge_balance_negative_flat_rectanglerowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrow_tableentryvaluedecode. (((dst_value_flat_rectanglerowsrow_table) = 2 * ge_signed_half_flat_rectanglerowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrow_tableentryvalue) = S ge_signed_half_flat_rectanglerowsrow_tableentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrow_table) + ge_balance_negative_flat_rectanglerowsrow_tableentryvalue = (dst_negative_flat_rectanglerowsrow_table) + ge_balance_positive_flat_rectanglerowsrow_tableentryvalue))))))))) /\ (forall srt_index_flat_rectanglerows. (exists pvs_gap_flat_rectanglerowsbound. pvs_gap_flat_rectanglerowsbound + S (srt_index_flat_rectanglerows) = (m)) -> exists srt_value_flat_rectanglerows. (((exists dst_positive_code_flat_rectanglerowsrowentry dst_positive_scale_flat_rectanglerowsrowentry dst_negative_code_flat_rectanglerowsrowentry dst_negative_scale_flat_rectanglerowsrowentry dst_positive_flat_rectanglerowsrowentry dst_negative_flat_rectanglerowsrowentry. (((srt_rows_flat_rectangle) = (((((dst_positive_code_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry)) * S ((dst_positive_code_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry)) + ((dst_positive_scale_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry))) + (((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) * S ((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) + ((dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)))) * S ((((dst_positive_code_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry)) * S ((dst_positive_code_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry)) + ((dst_positive_scale_flat_rectanglerowsrowentry) + (dst_positive_scale_flat_rectanglerowsrowentry))) + (((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) * S ((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) + ((dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)))) + ((((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) * S ((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) + ((dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry))) + (((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) * S ((dst_negative_code_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)) + ((dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_scale_flat_rectanglerowsrowentry)))))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowentrypositive. ff_h_pvs_flat_rectanglerowsrowentrypositive + S (dst_positive_flat_rectanglerowsrowentry) = S ((S (srt_index_flat_rectanglerows)) * dst_positive_scale_flat_rectanglerowsrowentry)) /\ exists ff_q_pvs_flat_rectanglerowsrowentrypositive. dst_positive_code_flat_rectanglerowsrowentry = ff_q_pvs_flat_rectanglerowsrowentrypositive * S ((S (srt_index_flat_rectanglerows)) * dst_positive_scale_flat_rectanglerowsrowentry) + (dst_positive_flat_rectanglerowsrowentry))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowentrynegative. ff_h_pvs_flat_rectanglerowsrowentrynegative + S (dst_negative_flat_rectanglerowsrowentry) = S ((S (srt_index_flat_rectanglerows)) * dst_negative_scale_flat_rectanglerowsrowentry)) /\ exists ff_q_pvs_flat_rectanglerowsrowentrynegative. dst_negative_code_flat_rectanglerowsrowentry = ff_q_pvs_flat_rectanglerowsrowentrynegative * S ((S (srt_index_flat_rectanglerows)) * dst_negative_scale_flat_rectanglerowsrowentry) + (dst_negative_flat_rectanglerowsrowentry))) /\ (exists ge_balance_positive_flat_rectanglerowsrowentryvalue ge_balance_negative_flat_rectanglerowsrowentryvalue. (((((srt_value_flat_rectanglerows) = 2 * (ge_balance_positive_flat_rectanglerowsrowentryvalue) /\ (ge_balance_negative_flat_rectanglerowsrowentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowentryvaluedecode. (((srt_value_flat_rectanglerows) = 2 * ge_signed_half_flat_rectanglerowsrowentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowentryvalue) = S ge_signed_half_flat_rectanglerowsrowentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowentry) + ge_balance_negative_flat_rectanglerowsrowentryvalue = (dst_negative_flat_rectanglerowsrowentry) + ge_balance_positive_flat_rectanglerowsrowentryvalue))))))))) /\ (exists srs_slice_flat_rectanglerowsrowrow_sum. ((((exists dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_flat_rectanglerowsrowrow_sumslicesource_table. (exists pvs_le_gap_flat_rectanglerowsrowrow_sumslicesource_tabledomain. pvs_le_gap_flat_rectanglerowsrowrow_sumslicesource_tabledomain + (dst_index_flat_rectanglerowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_flat_rectanglerowsrowrow_sumslicesource_table dst_negative_flat_rectanglerowsrowrow_sumslicesource_table dst_value_flat_rectanglerowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_flat_rectanglerowsrowrow_sumslicesource_table) = S ((S (dst_index_flat_rectanglerowsrowrow_sumslicesource_table)) * dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_flat_rectanglerowsrowrow_sumslicesource_table = ff_q_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_flat_rectanglerowsrowrow_sumslicesource_table)) * dst_positive_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_positive_flat_rectanglerowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_flat_rectanglerowsrowrow_sumslicesource_table) = S ((S (dst_index_flat_rectanglerowsrowrow_sumslicesource_table)) * dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_flat_rectanglerowsrowrow_sumslicesource_table = ff_q_pvs_flat_rectanglerowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_flat_rectanglerowsrowrow_sumslicesource_table)) * dst_negative_scale_flat_rectanglerowsrowrow_sumslicesource_table) + (dst_negative_flat_rectanglerowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_flat_rectanglerowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_flat_rectanglerowsrowrow_sumslicesource_table) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_flat_rectanglerowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowrow_sumslicesource_table) + ge_balance_negative_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue = (dst_negative_flat_rectanglerowsrowrow_sumslicesource_table) + ge_balance_positive_flat_rectanglerowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table. (((srs_slice_flat_rectanglerowsrowrow_sum) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_flat_rectanglerowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_flat_rectanglerowsrowrow_sumsliceoutput_tabledomain + (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_flat_rectanglerowsrowrow_sumsliceoutput_table dst_negative_flat_rectanglerowsrowrow_sumsliceoutput_table dst_value_flat_rectanglerowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_flat_rectanglerowsrowrow_sumsliceoutput_table) = S ((S (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_flat_rectanglerowsrowrow_sumsliceoutput_table = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_positive_flat_rectanglerowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_flat_rectanglerowsrowrow_sumsliceoutput_table) = S ((S (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_flat_rectanglerowsrowrow_sumsliceoutput_table = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_flat_rectanglerowsrowrow_sumsliceoutput_table)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceoutput_table) + (dst_negative_flat_rectanglerowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_flat_rectanglerowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_flat_rectanglerowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowrow_sumsliceoutput_table) + ge_balance_negative_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_flat_rectanglerowsrowrow_sumsliceoutput_table) + ge_balance_positive_flat_rectanglerowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_flat_rectanglerowsrowrow_sumslice. (exists pvs_gap_flat_rectanglerowsrowrow_sumslicebound. pvs_gap_flat_rectanglerowsrowrow_sumslicebound + S (srs_index_flat_rectanglerowsrowrow_sumslice) = (n)) -> exists srs_value_flat_rectanglerowsrowrow_sumslice. (((exists dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource dst_positive_flat_rectanglerowsrowrow_sumsliceentrysource dst_negative_flat_rectanglerowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcepositive + S (dst_positive_flat_rectanglerowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((n) * (srt_index_flat_rectanglerows)))) + ((1) * (srs_index_flat_rectanglerowsrowrow_sumslice))))) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcepositive. dst_positive_code_flat_rectanglerowsrowrow_sumsliceentrysource = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcepositive * S ((S (((((0) + ((n) * (srt_index_flat_rectanglerows)))) + ((1) * (srs_index_flat_rectanglerowsrowrow_sumslice))))) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_positive_flat_rectanglerowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcenegative + S (dst_negative_flat_rectanglerowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((n) * (srt_index_flat_rectanglerows)))) + ((1) * (srs_index_flat_rectanglerowsrowrow_sumslice))))) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcenegative. dst_negative_code_flat_rectanglerowsrowrow_sumsliceentrysource = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentrysourcenegative * S ((S (((((0) + ((n) * (srt_index_flat_rectanglerows)))) + ((1) * (srs_index_flat_rectanglerowsrowrow_sumslice))))) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentrysource) + (dst_negative_flat_rectanglerowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentrysourcevalue ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentrysourcevalue. (((((srs_value_flat_rectanglerowsrowrow_sumslice) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_flat_rectanglerowsrowrow_sumslice) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_flat_rectanglerowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowrow_sumsliceentrysource) + ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentrysourcevalue = (dst_negative_flat_rectanglerowsrowrow_sumsliceentrysource) + ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput dst_positive_flat_rectanglerowsrowrow_sumsliceentryoutput dst_negative_flat_rectanglerowsrowrow_sumsliceentryoutput. (((srs_slice_flat_rectanglerowsrowrow_sum) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputpositive + S (dst_positive_flat_rectanglerowsrowrow_sumsliceentryoutput) = S ((S (srs_index_flat_rectanglerowsrowrow_sumslice)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputpositive. dst_positive_code_flat_rectanglerowsrowrow_sumsliceentryoutput = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_flat_rectanglerowsrowrow_sumslice)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_positive_flat_rectanglerowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputnegative + S (dst_negative_flat_rectanglerowsrowrow_sumsliceentryoutput) = S ((S (srs_index_flat_rectanglerowsrowrow_sumslice)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputnegative. dst_negative_code_flat_rectanglerowsrowrow_sumsliceentryoutput = ff_q_pvs_flat_rectanglerowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_flat_rectanglerowsrowrow_sumslice)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsliceentryoutput) + (dst_negative_flat_rectanglerowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentryoutputvalue ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentryoutputvalue. (((((srs_value_flat_rectanglerowsrowrow_sumslice) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_flat_rectanglerowsrowrow_sumslice) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_flat_rectanglerowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_flat_rectanglerowsrowrow_sumsliceentryoutput) + ge_balance_negative_flat_rectanglerowsrowrow_sumsliceentryoutputvalue = (dst_negative_flat_rectanglerowsrowrow_sumsliceentryoutput) + ge_balance_positive_flat_rectanglerowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_flat_rectanglerowsrowrow_sumsum dst_positive_scale_flat_rectanglerowsrowrow_sumsum dst_negative_code_flat_rectanglerowsrowrow_sumsum dst_negative_scale_flat_rectanglerowsrowrow_sumsum dst_positive_sum_flat_rectanglerowsrowrow_sumsum dst_negative_sum_flat_rectanglerowsrowrow_sumsum. (((srs_slice_flat_rectanglerowsrowrow_sum) = (((((dst_positive_code_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)))) * S ((((dst_positive_code_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_positive_code_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_positive_scale_flat_rectanglerowsrowrow_sumsum) + (dst_positive_scale_flat_rectanglerowsrowrow_sumsum))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)))) + ((((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum))) + (((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) * S ((dst_negative_code_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) + ((dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (dst_negative_scale_flat_rectanglerowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive. ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_start. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_start. fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_terminal. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_flat_rectanglerowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_terminal. fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive) + (dst_positive_sum_flat_rectanglerowsrowrow_sumsum))) /\ forall fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps fs_r_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps fs_s_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsum)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_flat_rectanglerowsrowrow_sumsum = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_flat_rectanglerowsrowrow_sumsum) + (fs_a_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive) + (fs_r_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_flat_rectanglerowsrowrow_sumsumpositive = fs_q_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumpositive) + (fs_s_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps = fs_r_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps + fs_a_dst_flat_rectanglerowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative. ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_start. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_start. fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_terminal. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_flat_rectanglerowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_terminal. fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative) + (dst_negative_sum_flat_rectanglerowsrowrow_sumsum))) /\ forall fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps fs_r_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps fs_s_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsum)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_flat_rectanglerowsrowrow_sumsum = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_flat_rectanglerowsrowrow_sumsum) + (fs_a_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative) + (fs_r_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_flat_rectanglerowsrowrow_sumsumnegative = fs_q_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_rectanglerowsrowrow_sumsumnegative) + (fs_s_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps = fs_r_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps + fs_a_dst_flat_rectanglerowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_rectanglerowsrowrow_sumsumresult ge_balance_negative_flat_rectanglerowsrowrow_sumsumresult. (((((srt_value_flat_rectanglerows) = 2 * (ge_balance_positive_flat_rectanglerowsrowrow_sumsumresult) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_flat_rectanglerowsrowrow_sumsumresultdecode. (((srt_value_flat_rectanglerows) = 2 * ge_signed_half_flat_rectanglerowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_flat_rectanglerowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_flat_rectanglerowsrowrow_sumsumresult) = S ge_signed_half_flat_rectanglerowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_flat_rectanglerowsrowrow_sumsum) + ge_balance_negative_flat_rectanglerowsrowrow_sumsumresult = (dst_negative_sum_flat_rectanglerowsrowrow_sumsum) + ge_balance_positive_flat_rectanglerowsrowrow_sumsumresult)))))))))))))))))) /\ (exists dst_positive_code_flat_rectangletotal dst_positive_scale_flat_rectangletotal dst_negative_code_flat_rectangletotal dst_negative_scale_flat_rectangletotal dst_positive_sum_flat_rectangletotal dst_negative_sum_flat_rectangletotal. (((srt_rows_flat_rectangle) = (((((dst_positive_code_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal)) * S ((dst_positive_code_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal)) + ((dst_positive_scale_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal))) + (((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) * S ((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) + ((dst_negative_scale_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)))) * S ((((dst_positive_code_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal)) * S ((dst_positive_code_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal)) + ((dst_positive_scale_flat_rectangletotal) + (dst_positive_scale_flat_rectangletotal))) + (((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) * S ((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) + ((dst_negative_scale_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)))) + ((((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) * S ((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) + ((dst_negative_scale_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal))) + (((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) * S ((dst_negative_code_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)) + ((dst_negative_scale_flat_rectangletotal) + (dst_negative_scale_flat_rectangletotal)))))) /\ (((exists fs_u_dst_flat_rectangletotalpositive fs_v_dst_flat_rectangletotalpositive. ((((exists fs_h_dst_flat_rectangletotalpositive_body_start. fs_h_dst_flat_rectangletotalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_rectangletotalpositive)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_start. fs_u_dst_flat_rectangletotalpositive = fs_q_dst_flat_rectangletotalpositive_body_start * S ((S (0)) * fs_v_dst_flat_rectangletotalpositive) + (0))) /\ ((((exists fs_h_dst_flat_rectangletotalpositive_body_terminal. fs_h_dst_flat_rectangletotalpositive_body_terminal + S (dst_positive_sum_flat_rectangletotal) = S ((S (m)) * fs_v_dst_flat_rectangletotalpositive)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_terminal. fs_u_dst_flat_rectangletotalpositive = fs_q_dst_flat_rectangletotalpositive_body_terminal * S ((S (m)) * fs_v_dst_flat_rectangletotalpositive) + (dst_positive_sum_flat_rectangletotal))) /\ forall fs_i_dst_flat_rectangletotalpositive_body_steps. (exists fs_lt_dst_flat_rectangletotalpositive_body_steps_bound. fs_lt_dst_flat_rectangletotalpositive_body_steps_bound + S fs_i_dst_flat_rectangletotalpositive_body_steps = m) -> exists fs_a_dst_flat_rectangletotalpositive_body_steps fs_r_dst_flat_rectangletotalpositive_body_steps fs_s_dst_flat_rectangletotalpositive_body_steps. ((((exists fs_h_dst_flat_rectangletotalpositive_body_steps_summand. fs_h_dst_flat_rectangletotalpositive_body_steps_summand + S (fs_a_dst_flat_rectangletotalpositive_body_steps) = S ((S (fs_i_dst_flat_rectangletotalpositive_body_steps)) * dst_positive_scale_flat_rectangletotal)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_steps_summand. dst_positive_code_flat_rectangletotal = fs_q_dst_flat_rectangletotalpositive_body_steps_summand * S ((S (fs_i_dst_flat_rectangletotalpositive_body_steps)) * dst_positive_scale_flat_rectangletotal) + (fs_a_dst_flat_rectangletotalpositive_body_steps))) /\ ((((exists fs_h_dst_flat_rectangletotalpositive_body_steps_partial. fs_h_dst_flat_rectangletotalpositive_body_steps_partial + S (fs_r_dst_flat_rectangletotalpositive_body_steps) = S ((S (fs_i_dst_flat_rectangletotalpositive_body_steps)) * fs_v_dst_flat_rectangletotalpositive)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_steps_partial. fs_u_dst_flat_rectangletotalpositive = fs_q_dst_flat_rectangletotalpositive_body_steps_partial * S ((S (fs_i_dst_flat_rectangletotalpositive_body_steps)) * fs_v_dst_flat_rectangletotalpositive) + (fs_r_dst_flat_rectangletotalpositive_body_steps))) /\ ((((exists fs_h_dst_flat_rectangletotalpositive_body_steps_successor. fs_h_dst_flat_rectangletotalpositive_body_steps_successor + S (fs_s_dst_flat_rectangletotalpositive_body_steps) = S ((S (S fs_i_dst_flat_rectangletotalpositive_body_steps)) * fs_v_dst_flat_rectangletotalpositive)) /\ exists fs_q_dst_flat_rectangletotalpositive_body_steps_successor. fs_u_dst_flat_rectangletotalpositive = fs_q_dst_flat_rectangletotalpositive_body_steps_successor * S ((S (S fs_i_dst_flat_rectangletotalpositive_body_steps)) * fs_v_dst_flat_rectangletotalpositive) + (fs_s_dst_flat_rectangletotalpositive_body_steps))) /\ fs_s_dst_flat_rectangletotalpositive_body_steps = fs_r_dst_flat_rectangletotalpositive_body_steps + fs_a_dst_flat_rectangletotalpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_rectangletotalnegative fs_v_dst_flat_rectangletotalnegative. ((((exists fs_h_dst_flat_rectangletotalnegative_body_start. fs_h_dst_flat_rectangletotalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_rectangletotalnegative)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_start. fs_u_dst_flat_rectangletotalnegative = fs_q_dst_flat_rectangletotalnegative_body_start * S ((S (0)) * fs_v_dst_flat_rectangletotalnegative) + (0))) /\ ((((exists fs_h_dst_flat_rectangletotalnegative_body_terminal. fs_h_dst_flat_rectangletotalnegative_body_terminal + S (dst_negative_sum_flat_rectangletotal) = S ((S (m)) * fs_v_dst_flat_rectangletotalnegative)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_terminal. fs_u_dst_flat_rectangletotalnegative = fs_q_dst_flat_rectangletotalnegative_body_terminal * S ((S (m)) * fs_v_dst_flat_rectangletotalnegative) + (dst_negative_sum_flat_rectangletotal))) /\ forall fs_i_dst_flat_rectangletotalnegative_body_steps. (exists fs_lt_dst_flat_rectangletotalnegative_body_steps_bound. fs_lt_dst_flat_rectangletotalnegative_body_steps_bound + S fs_i_dst_flat_rectangletotalnegative_body_steps = m) -> exists fs_a_dst_flat_rectangletotalnegative_body_steps fs_r_dst_flat_rectangletotalnegative_body_steps fs_s_dst_flat_rectangletotalnegative_body_steps. ((((exists fs_h_dst_flat_rectangletotalnegative_body_steps_summand. fs_h_dst_flat_rectangletotalnegative_body_steps_summand + S (fs_a_dst_flat_rectangletotalnegative_body_steps) = S ((S (fs_i_dst_flat_rectangletotalnegative_body_steps)) * dst_negative_scale_flat_rectangletotal)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_steps_summand. dst_negative_code_flat_rectangletotal = fs_q_dst_flat_rectangletotalnegative_body_steps_summand * S ((S (fs_i_dst_flat_rectangletotalnegative_body_steps)) * dst_negative_scale_flat_rectangletotal) + (fs_a_dst_flat_rectangletotalnegative_body_steps))) /\ ((((exists fs_h_dst_flat_rectangletotalnegative_body_steps_partial. fs_h_dst_flat_rectangletotalnegative_body_steps_partial + S (fs_r_dst_flat_rectangletotalnegative_body_steps) = S ((S (fs_i_dst_flat_rectangletotalnegative_body_steps)) * fs_v_dst_flat_rectangletotalnegative)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_steps_partial. fs_u_dst_flat_rectangletotalnegative = fs_q_dst_flat_rectangletotalnegative_body_steps_partial * S ((S (fs_i_dst_flat_rectangletotalnegative_body_steps)) * fs_v_dst_flat_rectangletotalnegative) + (fs_r_dst_flat_rectangletotalnegative_body_steps))) /\ ((((exists fs_h_dst_flat_rectangletotalnegative_body_steps_successor. fs_h_dst_flat_rectangletotalnegative_body_steps_successor + S (fs_s_dst_flat_rectangletotalnegative_body_steps) = S ((S (S fs_i_dst_flat_rectangletotalnegative_body_steps)) * fs_v_dst_flat_rectangletotalnegative)) /\ exists fs_q_dst_flat_rectangletotalnegative_body_steps_successor. fs_u_dst_flat_rectangletotalnegative = fs_q_dst_flat_rectangletotalnegative_body_steps_successor * S ((S (S fs_i_dst_flat_rectangletotalnegative_body_steps)) * fs_v_dst_flat_rectangletotalnegative) + (fs_s_dst_flat_rectangletotalnegative_body_steps))) /\ fs_s_dst_flat_rectangletotalnegative_body_steps = fs_r_dst_flat_rectangletotalnegative_body_steps + fs_a_dst_flat_rectangletotalnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_rectangletotalresult ge_balance_negative_flat_rectangletotalresult. (((((z) = 2 * (ge_balance_positive_flat_rectangletotalresult) /\ (ge_balance_negative_flat_rectangletotalresult) = 0) \/ exists ge_signed_half_flat_rectangletotalresultdecode. (((z) = 2 * ge_signed_half_flat_rectangletotalresultdecode + 1 /\ (ge_balance_positive_flat_rectangletotalresult) = 0) /\ (ge_balance_negative_flat_rectangletotalresult) = S ge_signed_half_flat_rectangletotalresultdecode))) /\ ((dst_positive_sum_flat_rectangletotal) + ge_balance_negative_flat_rectangletotalresult = (dst_negative_sum_flat_rectangletotal) + ge_balance_positive_flat_rectangletotalresult))))))))))) -> (exists dst_positive_code_flat_prefix dst_positive_scale_flat_prefix dst_negative_code_flat_prefix dst_negative_scale_flat_prefix dst_positive_sum_flat_prefix dst_negative_sum_flat_prefix. (((F) = (((((dst_positive_code_flat_prefix) + (dst_positive_scale_flat_prefix)) * S ((dst_positive_code_flat_prefix) + (dst_positive_scale_flat_prefix)) + ((dst_positive_scale_flat_prefix) + (dst_positive_scale_flat_prefix))) + (((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) * S ((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) + ((dst_negative_scale_flat_prefix) + (dst_negative_scale_flat_prefix)))) * S ((((dst_positive_code_flat_prefix) + (dst_positive_scale_flat_prefix)) * S ((dst_positive_code_flat_prefix) + (dst_positive_scale_flat_prefix)) + ((dst_positive_scale_flat_prefix) + (dst_positive_scale_flat_prefix))) + (((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) * S ((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) + ((dst_negative_scale_flat_prefix) + (dst_negative_scale_flat_prefix)))) + ((((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) * S ((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) + ((dst_negative_scale_flat_prefix) + (dst_negative_scale_flat_prefix))) + (((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) * S ((dst_negative_code_flat_prefix) + (dst_negative_scale_flat_prefix)) + ((dst_negative_scale_flat_prefix) + (dst_negative_scale_flat_prefix)))))) /\ (((exists fs_u_dst_flat_prefixpositive fs_v_dst_flat_prefixpositive. ((((exists fs_h_dst_flat_prefixpositive_body_start. fs_h_dst_flat_prefixpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_prefixpositive)) /\ exists fs_q_dst_flat_prefixpositive_body_start. fs_u_dst_flat_prefixpositive = fs_q_dst_flat_prefixpositive_body_start * S ((S (0)) * fs_v_dst_flat_prefixpositive) + (0))) /\ ((((exists fs_h_dst_flat_prefixpositive_body_terminal. fs_h_dst_flat_prefixpositive_body_terminal + S (dst_positive_sum_flat_prefix) = S ((S (m*n)) * fs_v_dst_flat_prefixpositive)) /\ exists fs_q_dst_flat_prefixpositive_body_terminal. fs_u_dst_flat_prefixpositive = fs_q_dst_flat_prefixpositive_body_terminal * S ((S (m*n)) * fs_v_dst_flat_prefixpositive) + (dst_positive_sum_flat_prefix))) /\ forall fs_i_dst_flat_prefixpositive_body_steps. (exists fs_lt_dst_flat_prefixpositive_body_steps_bound. fs_lt_dst_flat_prefixpositive_body_steps_bound + S fs_i_dst_flat_prefixpositive_body_steps = m*n) -> exists fs_a_dst_flat_prefixpositive_body_steps fs_r_dst_flat_prefixpositive_body_steps fs_s_dst_flat_prefixpositive_body_steps. ((((exists fs_h_dst_flat_prefixpositive_body_steps_summand. fs_h_dst_flat_prefixpositive_body_steps_summand + S (fs_a_dst_flat_prefixpositive_body_steps) = S ((S (fs_i_dst_flat_prefixpositive_body_steps)) * dst_positive_scale_flat_prefix)) /\ exists fs_q_dst_flat_prefixpositive_body_steps_summand. dst_positive_code_flat_prefix = fs_q_dst_flat_prefixpositive_body_steps_summand * S ((S (fs_i_dst_flat_prefixpositive_body_steps)) * dst_positive_scale_flat_prefix) + (fs_a_dst_flat_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_flat_prefixpositive_body_steps_partial. fs_h_dst_flat_prefixpositive_body_steps_partial + S (fs_r_dst_flat_prefixpositive_body_steps) = S ((S (fs_i_dst_flat_prefixpositive_body_steps)) * fs_v_dst_flat_prefixpositive)) /\ exists fs_q_dst_flat_prefixpositive_body_steps_partial. fs_u_dst_flat_prefixpositive = fs_q_dst_flat_prefixpositive_body_steps_partial * S ((S (fs_i_dst_flat_prefixpositive_body_steps)) * fs_v_dst_flat_prefixpositive) + (fs_r_dst_flat_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_flat_prefixpositive_body_steps_successor. fs_h_dst_flat_prefixpositive_body_steps_successor + S (fs_s_dst_flat_prefixpositive_body_steps) = S ((S (S fs_i_dst_flat_prefixpositive_body_steps)) * fs_v_dst_flat_prefixpositive)) /\ exists fs_q_dst_flat_prefixpositive_body_steps_successor. fs_u_dst_flat_prefixpositive = fs_q_dst_flat_prefixpositive_body_steps_successor * S ((S (S fs_i_dst_flat_prefixpositive_body_steps)) * fs_v_dst_flat_prefixpositive) + (fs_s_dst_flat_prefixpositive_body_steps))) /\ fs_s_dst_flat_prefixpositive_body_steps = fs_r_dst_flat_prefixpositive_body_steps + fs_a_dst_flat_prefixpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_prefixnegative fs_v_dst_flat_prefixnegative. ((((exists fs_h_dst_flat_prefixnegative_body_start. fs_h_dst_flat_prefixnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_prefixnegative)) /\ exists fs_q_dst_flat_prefixnegative_body_start. fs_u_dst_flat_prefixnegative = fs_q_dst_flat_prefixnegative_body_start * S ((S (0)) * fs_v_dst_flat_prefixnegative) + (0))) /\ ((((exists fs_h_dst_flat_prefixnegative_body_terminal. fs_h_dst_flat_prefixnegative_body_terminal + S (dst_negative_sum_flat_prefix) = S ((S (m*n)) * fs_v_dst_flat_prefixnegative)) /\ exists fs_q_dst_flat_prefixnegative_body_terminal. fs_u_dst_flat_prefixnegative = fs_q_dst_flat_prefixnegative_body_terminal * S ((S (m*n)) * fs_v_dst_flat_prefixnegative) + (dst_negative_sum_flat_prefix))) /\ forall fs_i_dst_flat_prefixnegative_body_steps. (exists fs_lt_dst_flat_prefixnegative_body_steps_bound. fs_lt_dst_flat_prefixnegative_body_steps_bound + S fs_i_dst_flat_prefixnegative_body_steps = m*n) -> exists fs_a_dst_flat_prefixnegative_body_steps fs_r_dst_flat_prefixnegative_body_steps fs_s_dst_flat_prefixnegative_body_steps. ((((exists fs_h_dst_flat_prefixnegative_body_steps_summand. fs_h_dst_flat_prefixnegative_body_steps_summand + S (fs_a_dst_flat_prefixnegative_body_steps) = S ((S (fs_i_dst_flat_prefixnegative_body_steps)) * dst_negative_scale_flat_prefix)) /\ exists fs_q_dst_flat_prefixnegative_body_steps_summand. dst_negative_code_flat_prefix = fs_q_dst_flat_prefixnegative_body_steps_summand * S ((S (fs_i_dst_flat_prefixnegative_body_steps)) * dst_negative_scale_flat_prefix) + (fs_a_dst_flat_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_flat_prefixnegative_body_steps_partial. fs_h_dst_flat_prefixnegative_body_steps_partial + S (fs_r_dst_flat_prefixnegative_body_steps) = S ((S (fs_i_dst_flat_prefixnegative_body_steps)) * fs_v_dst_flat_prefixnegative)) /\ exists fs_q_dst_flat_prefixnegative_body_steps_partial. fs_u_dst_flat_prefixnegative = fs_q_dst_flat_prefixnegative_body_steps_partial * S ((S (fs_i_dst_flat_prefixnegative_body_steps)) * fs_v_dst_flat_prefixnegative) + (fs_r_dst_flat_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_flat_prefixnegative_body_steps_successor. fs_h_dst_flat_prefixnegative_body_steps_successor + S (fs_s_dst_flat_prefixnegative_body_steps) = S ((S (S fs_i_dst_flat_prefixnegative_body_steps)) * fs_v_dst_flat_prefixnegative)) /\ exists fs_q_dst_flat_prefixnegative_body_steps_successor. fs_u_dst_flat_prefixnegative = fs_q_dst_flat_prefixnegative_body_steps_successor * S ((S (S fs_i_dst_flat_prefixnegative_body_steps)) * fs_v_dst_flat_prefixnegative) + (fs_s_dst_flat_prefixnegative_body_steps))) /\ fs_s_dst_flat_prefixnegative_body_steps = fs_r_dst_flat_prefixnegative_body_steps + fs_a_dst_flat_prefixnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_prefixresult ge_balance_negative_flat_prefixresult. (((((z) = 2 * (ge_balance_positive_flat_prefixresult) /\ (ge_balance_negative_flat_prefixresult) = 0) \/ exists ge_signed_half_flat_prefixresultdecode. (((z) = 2 * ge_signed_half_flat_prefixresultdecode + 1 /\ (ge_balance_positive_flat_prefixresult) = 0) /\ (ge_balance_negative_flat_prefixresult) = S ge_signed_half_flat_prefixresultdecode))) /\ ((dst_positive_sum_flat_prefix) + ge_balance_negative_flat_prefixresult = (dst_negative_sum_flat_prefix) + ge_balance_positive_flat_prefixresult)))))))))))Constructive proof overview
Generated structural guide
The actual flattened signed prefix and actual row-major rectangle are equivalent, not merely two transposed rectangular folds.
The unchanged tactic script uses 5 declared prerequisites and contains 71 exact native proof lines.
Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
MX0019 signed_slice_sum_unit_prefix_iff signed_rectangular_row_sums_exists Alpha theorem; checked-use authorized arithmetic_signed_sum_exists Alpha theorem; checked-use authorized MX001C signed_row_sums_flatten signed_rectangular_slice_sum_functional Alpha theorem; checked-use authorizedDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Named ingredients (2)
01Fix variables and assumptionsL1–5
02Establish hiL6–11
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed slice sum unit prefix iff.
- L6
have hi : (SignedSliceSum(F,0,1,m · n,z) → SignedPrefixSum(F,m · n,z)) ∧ (SignedPrefixSum(F,m · n,z) → SignedSliceSum(F,0,1,m · n,z))Definitions: SignedPrefixSumSignedSliceSum - L7
specialize signed_slice_sum_unit_prefix_iff (F) - L8
specialize signed_slice_sum_unit_prefix_iff (m*n) - L9
specialize signed_slice_sum_unit_prefix_iff (z) - L10
apply signed_slice_sum_unit_prefix_iff - L11
exact hF
03Separate the logical casesL12–13
04Fix variables and assumptionsL14–14
Work with arbitrary variables or the premises of the current implication.
- L14
intro hs
05Establish hrL15–23
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed rectangular row sums exists.
- L15
have hr : ∃ R. ArithRowSums(F,R,0,n,1,m,n)Definitions: ArithRowSums - L16
specialize signed_rectangular_row_sums_exists (m) - L17
specialize signed_rectangular_row_sums_exists (F) - L18
specialize signed_rectangular_row_sums_exists (0) - L19
specialize signed_rectangular_row_sums_exists (n) - L20
specialize signed_rectangular_row_sums_exists (1) - L21
specialize signed_rectangular_row_sums_exists (n) - L22
apply signed_rectangular_row_sums_exists - L23
exact hF
06Separate the logical casesL24–24
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L24
cases hr
07Establish hvL25–29
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply arithmetic signed sum exists.
08Separate the logical casesL30–31
09Use earlier factsL32–32
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L32
exact hr_witness_right_left
10Separate the logical casesL33–33
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L33
cases hv
11Establish hflatL34–42
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed row sums flatten.
- L34
have hflat : SignedSliceSum(F,0,1,m · n,x1)Definitions: SignedSliceSum - L35
specialize signed_row_sums_flatten (m) - L36
specialize signed_row_sums_flatten (F) - L37
specialize signed_row_sums_flatten (x) - L38
specialize signed_row_sums_flatten (n) - L39
specialize signed_row_sums_flatten (x1) - L40
apply signed_row_sums_flatten - L41
exact hr_witness - L42
exact hv_witness
12Establish heqL43–52
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed rectangular slice sum functional.
- L43
have heq : x1=z - L44
specialize signed_rectangular_slice_sum_functional (F) - L45
specialize signed_rectangular_slice_sum_functional (0) - L46
specialize signed_rectangular_slice_sum_functional (1) - L47
specialize signed_rectangular_slice_sum_functional (m*n) - L48
specialize signed_rectangular_slice_sum_functional (x1) - L49
specialize signed_rectangular_slice_sum_functional (z) - L50
apply signed_rectangular_slice_sum_functional - L51
exact hflat - L52
apply hi_right
13Use earlier factsL53–53
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L53
exact hs
14Calculate and transport equalitiesL54–55
15Construct an explicit witnessL56–56
Supply the displayed value, then prove that it has the required property.
- L56
exists x
16Separate the logical casesL57–57
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L57
split
17Use earlier factsL58–59
18Fix variables and assumptionsL60–60
Work with arbitrary variables or the premises of the current implication.
- L60
intro hr
19Separate the logical casesL61–62
20Use earlier factsL63–71
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L63
apply hi_left - L64
specialize signed_row_sums_flatten (m) - L65
specialize signed_row_sums_flatten (F) - L66
specialize signed_row_sums_flatten (x) - L67
specialize signed_row_sums_flatten (n) - L68
specialize signed_row_sums_flatten (z) - L69
apply signed_row_sums_flatten - L70
exact hr_witness_left - L71
exact hr_witness_right
Original exact command ledger · 71 lines
- 0001
intro F - 0002
intro m - 0003
intro n - 0004
intro z - 0005
intro hF - 0006
have hi : (((exists srs_slice_flat_unit_slice. ((((exists dst_positive_code_flat_unit_sliceslicesource_table dst_positive_scale_flat_unit_sliceslicesource_table dst_negative_code_flat_unit_sliceslicesource_table dst_negative_scale_flat_unit_sliceslicesource_table. (((F) = (((((dst_positive_code_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table)) * S ((dst_positive_code_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table)) + ((dst_positive_scale_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table))) + (((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) * S ((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) + ((dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)))) * S ((((dst_positive_code_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table)) * S ((dst_positive_code_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table)) + ((dst_positive_scale_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table))) + (((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) * S ((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) + ((dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)))) + ((((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) * S ((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) + ((dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table))) + (((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) * S ((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) + ((dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)))))) /\ (forall dst_index_flat_unit_sliceslicesource_table. (exists pvs_le_gap_flat_unit_sliceslicesource_tabledomain. pvs_le_gap_flat_unit_sliceslicesource_tabledomain + (dst_index_flat_unit_sliceslicesource_table) = (0)) -> exists dst_positive_flat_unit_sliceslicesource_table dst_negative_flat_unit_sliceslicesource_table dst_value_flat_unit_sliceslicesource_table. ((((exists ff_h_pvs_flat_unit_sliceslicesource_tableentrypositive. ff_h_pvs_flat_unit_sliceslicesource_tableentrypositive + S (dst_positive_flat_unit_sliceslicesource_table) = S ((S (dst_index_flat_unit_sliceslicesource_table)) * dst_positive_scale_flat_unit_sliceslicesource_table)) /\ exists ff_q_pvs_flat_unit_sliceslicesource_tableentrypositive. dst_positive_code_flat_unit_sliceslicesource_table = ff_q_pvs_flat_unit_sliceslicesource_tableentrypositive * S ((S (dst_index_flat_unit_sliceslicesource_table)) * dst_positive_scale_flat_unit_sliceslicesource_table) + (dst_positive_flat_unit_sliceslicesource_table))) /\ (((((exists ff_h_pvs_flat_unit_sliceslicesource_tableentrynegative. ff_h_pvs_flat_unit_sliceslicesource_tableentrynegative + S (dst_negative_flat_unit_sliceslicesource_table) = S ((S (dst_index_flat_unit_sliceslicesource_table)) * dst_negative_scale_flat_unit_sliceslicesource_table)) /\ exists ff_q_pvs_flat_unit_sliceslicesource_tableentrynegative. dst_negative_code_flat_unit_sliceslicesource_table = ff_q_pvs_flat_unit_sliceslicesource_tableentrynegative * S ((S (dst_index_flat_unit_sliceslicesource_table)) * dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_flat_unit_sliceslicesource_table))) /\ (exists ge_balance_positive_flat_unit_sliceslicesource_tableentryvalue ge_balance_negative_flat_unit_sliceslicesource_tableentryvalue. (((((dst_value_flat_unit_sliceslicesource_table) = 2 * (ge_balance_positive_flat_unit_sliceslicesource_tableentryvalue) /\ (ge_balance_negative_flat_unit_sliceslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_flat_unit_sliceslicesource_tableentryvaluedecode. (((dst_value_flat_unit_sliceslicesource_table) = 2 * ge_signed_half_flat_unit_sliceslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_unit_sliceslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_flat_unit_sliceslicesource_tableentryvalue) = S ge_signed_half_flat_unit_sliceslicesource_tableentryvaluedecode))) /\ ((dst_positive_flat_unit_sliceslicesource_table) + ge_balance_negative_flat_unit_sliceslicesource_tableentryvalue = (dst_negative_flat_unit_sliceslicesource_table) + ge_balance_positive_flat_unit_sliceslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_flat_unit_slicesliceoutput_table dst_positive_scale_flat_unit_slicesliceoutput_table dst_negative_code_flat_unit_slicesliceoutput_table dst_negative_scale_flat_unit_slicesliceoutput_table. (((srs_slice_flat_unit_slice) = (((((dst_positive_code_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table)) * S ((dst_positive_code_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table)) + ((dst_positive_scale_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table))) + (((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) * S ((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) + ((dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)))) * S ((((dst_positive_code_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table)) * S ((dst_positive_code_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table)) + ((dst_positive_scale_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table))) + (((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) * S ((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) + ((dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)))) + ((((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) * S ((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) + ((dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table))) + (((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) * S ((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) + ((dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)))))) /\ (forall dst_index_flat_unit_slicesliceoutput_table. (exists pvs_le_gap_flat_unit_slicesliceoutput_tabledomain. pvs_le_gap_flat_unit_slicesliceoutput_tabledomain + (dst_index_flat_unit_slicesliceoutput_table) = (m*n)) -> exists dst_positive_flat_unit_slicesliceoutput_table dst_negative_flat_unit_slicesliceoutput_table dst_value_flat_unit_slicesliceoutput_table. ((((exists ff_h_pvs_flat_unit_slicesliceoutput_tableentrypositive. ff_h_pvs_flat_unit_slicesliceoutput_tableentrypositive + S (dst_positive_flat_unit_slicesliceoutput_table) = S ((S (dst_index_flat_unit_slicesliceoutput_table)) * dst_positive_scale_flat_unit_slicesliceoutput_table)) /\ exists ff_q_pvs_flat_unit_slicesliceoutput_tableentrypositive. dst_positive_code_flat_unit_slicesliceoutput_table = ff_q_pvs_flat_unit_slicesliceoutput_tableentrypositive * S ((S (dst_index_flat_unit_slicesliceoutput_table)) * dst_positive_scale_flat_unit_slicesliceoutput_table) + (dst_positive_flat_unit_slicesliceoutput_table))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceoutput_tableentrynegative. ff_h_pvs_flat_unit_slicesliceoutput_tableentrynegative + S (dst_negative_flat_unit_slicesliceoutput_table) = S ((S (dst_index_flat_unit_slicesliceoutput_table)) * dst_negative_scale_flat_unit_slicesliceoutput_table)) /\ exists ff_q_pvs_flat_unit_slicesliceoutput_tableentrynegative. dst_negative_code_flat_unit_slicesliceoutput_table = ff_q_pvs_flat_unit_slicesliceoutput_tableentrynegative * S ((S (dst_index_flat_unit_slicesliceoutput_table)) * dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_flat_unit_slicesliceoutput_table))) /\ (exists ge_balance_positive_flat_unit_slicesliceoutput_tableentryvalue ge_balance_negative_flat_unit_slicesliceoutput_tableentryvalue. (((((dst_value_flat_unit_slicesliceoutput_table) = 2 * (ge_balance_positive_flat_unit_slicesliceoutput_tableentryvalue) /\ (ge_balance_negative_flat_unit_slicesliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_flat_unit_slicesliceoutput_tableentryvaluedecode. (((dst_value_flat_unit_slicesliceoutput_table) = 2 * ge_signed_half_flat_unit_slicesliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_unit_slicesliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_flat_unit_slicesliceoutput_tableentryvalue) = S ge_signed_half_flat_unit_slicesliceoutput_tableentryvaluedecode))) /\ ((dst_positive_flat_unit_slicesliceoutput_table) + ge_balance_negative_flat_unit_slicesliceoutput_tableentryvalue = (dst_negative_flat_unit_slicesliceoutput_table) + ge_balance_positive_flat_unit_slicesliceoutput_tableentryvalue))))))))) /\ (forall srs_index_flat_unit_sliceslice. (exists pvs_gap_flat_unit_sliceslicebound. pvs_gap_flat_unit_sliceslicebound + S (srs_index_flat_unit_sliceslice) = (m*n)) -> exists srs_value_flat_unit_sliceslice. (((exists dst_positive_code_flat_unit_slicesliceentrysource dst_positive_scale_flat_unit_slicesliceentrysource dst_negative_code_flat_unit_slicesliceentrysource dst_negative_scale_flat_unit_slicesliceentrysource dst_positive_flat_unit_slicesliceentrysource dst_negative_flat_unit_slicesliceentrysource. (((F) = (((((dst_positive_code_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource)) * S ((dst_positive_code_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource)) + ((dst_positive_scale_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource))) + (((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) * S ((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) + ((dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)))) * S ((((dst_positive_code_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource)) * S ((dst_positive_code_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource)) + ((dst_positive_scale_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource))) + (((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) * S ((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) + ((dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)))) + ((((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) * S ((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) + ((dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource))) + (((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) * S ((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) + ((dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)))))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceentrysourcepositive. ff_h_pvs_flat_unit_slicesliceentrysourcepositive + S (dst_positive_flat_unit_slicesliceentrysource) = S ((S (((0) + ((1) * (srs_index_flat_unit_sliceslice))))) * dst_positive_scale_flat_unit_slicesliceentrysource)) /\ exists ff_q_pvs_flat_unit_slicesliceentrysourcepositive. dst_positive_code_flat_unit_slicesliceentrysource = ff_q_pvs_flat_unit_slicesliceentrysourcepositive * S ((S (((0) + ((1) * (srs_index_flat_unit_sliceslice))))) * dst_positive_scale_flat_unit_slicesliceentrysource) + (dst_positive_flat_unit_slicesliceentrysource))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceentrysourcenegative. ff_h_pvs_flat_unit_slicesliceentrysourcenegative + S (dst_negative_flat_unit_slicesliceentrysource) = S ((S (((0) + ((1) * (srs_index_flat_unit_sliceslice))))) * dst_negative_scale_flat_unit_slicesliceentrysource)) /\ exists ff_q_pvs_flat_unit_slicesliceentrysourcenegative. dst_negative_code_flat_unit_slicesliceentrysource = ff_q_pvs_flat_unit_slicesliceentrysourcenegative * S ((S (((0) + ((1) * (srs_index_flat_unit_sliceslice))))) * dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_flat_unit_slicesliceentrysource))) /\ (exists ge_balance_positive_flat_unit_slicesliceentrysourcevalue ge_balance_negative_flat_unit_slicesliceentrysourcevalue. (((((srs_value_flat_unit_sliceslice) = 2 * (ge_balance_positive_flat_unit_slicesliceentrysourcevalue) /\ (ge_balance_negative_flat_unit_slicesliceentrysourcevalue) = 0) \/ exists ge_signed_half_flat_unit_slicesliceentrysourcevaluedecode. (((srs_value_flat_unit_sliceslice) = 2 * ge_signed_half_flat_unit_slicesliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_flat_unit_slicesliceentrysourcevalue) = 0) /\ (ge_balance_negative_flat_unit_slicesliceentrysourcevalue) = S ge_signed_half_flat_unit_slicesliceentrysourcevaluedecode))) /\ ((dst_positive_flat_unit_slicesliceentrysource) + ge_balance_negative_flat_unit_slicesliceentrysourcevalue = (dst_negative_flat_unit_slicesliceentrysource) + ge_balance_positive_flat_unit_slicesliceentrysourcevalue))))))))) /\ (exists dst_positive_code_flat_unit_slicesliceentryoutput dst_positive_scale_flat_unit_slicesliceentryoutput dst_negative_code_flat_unit_slicesliceentryoutput dst_negative_scale_flat_unit_slicesliceentryoutput dst_positive_flat_unit_slicesliceentryoutput dst_negative_flat_unit_slicesliceentryoutput. (((srs_slice_flat_unit_slice) = (((((dst_positive_code_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput)) * S ((dst_positive_code_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput)) + ((dst_positive_scale_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput))) + (((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) * S ((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) + ((dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)))) * S ((((dst_positive_code_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput)) * S ((dst_positive_code_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput)) + ((dst_positive_scale_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput))) + (((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) * S ((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) + ((dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)))) + ((((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) * S ((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) + ((dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput))) + (((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) * S ((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) + ((dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)))))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceentryoutputpositive. ff_h_pvs_flat_unit_slicesliceentryoutputpositive + S (dst_positive_flat_unit_slicesliceentryoutput) = S ((S (srs_index_flat_unit_sliceslice)) * dst_positive_scale_flat_unit_slicesliceentryoutput)) /\ exists ff_q_pvs_flat_unit_slicesliceentryoutputpositive. dst_positive_code_flat_unit_slicesliceentryoutput = ff_q_pvs_flat_unit_slicesliceentryoutputpositive * S ((S (srs_index_flat_unit_sliceslice)) * dst_positive_scale_flat_unit_slicesliceentryoutput) + (dst_positive_flat_unit_slicesliceentryoutput))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceentryoutputnegative. ff_h_pvs_flat_unit_slicesliceentryoutputnegative + S (dst_negative_flat_unit_slicesliceentryoutput) = S ((S (srs_index_flat_unit_sliceslice)) * dst_negative_scale_flat_unit_slicesliceentryoutput)) /\ exists ff_q_pvs_flat_unit_slicesliceentryoutputnegative. dst_negative_code_flat_unit_slicesliceentryoutput = ff_q_pvs_flat_unit_slicesliceentryoutputnegative * S ((S (srs_index_flat_unit_sliceslice)) * dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_flat_unit_slicesliceentryoutput))) /\ (exists ge_balance_positive_flat_unit_slicesliceentryoutputvalue ge_balance_negative_flat_unit_slicesliceentryoutputvalue. (((((srs_value_flat_unit_sliceslice) = 2 * (ge_balance_positive_flat_unit_slicesliceentryoutputvalue) /\ (ge_balance_negative_flat_unit_slicesliceentryoutputvalue) = 0) \/ exists ge_signed_half_flat_unit_slicesliceentryoutputvaluedecode. (((srs_value_flat_unit_sliceslice) = 2 * ge_signed_half_flat_unit_slicesliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_flat_unit_slicesliceentryoutputvalue) = 0) /\ (ge_balance_negative_flat_unit_slicesliceentryoutputvalue) = S ge_signed_half_flat_unit_slicesliceentryoutputvaluedecode))) /\ ((dst_positive_flat_unit_slicesliceentryoutput) + ge_balance_negative_flat_unit_slicesliceentryoutputvalue = (dst_negative_flat_unit_slicesliceentryoutput) + ge_balance_positive_flat_unit_slicesliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_flat_unit_slicesum dst_positive_scale_flat_unit_slicesum dst_negative_code_flat_unit_slicesum dst_negative_scale_flat_unit_slicesum dst_positive_sum_flat_unit_slicesum dst_negative_sum_flat_unit_slicesum. (((srs_slice_flat_unit_slice) = (((((dst_positive_code_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum)) * S ((dst_positive_code_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum)) + ((dst_positive_scale_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum))) + (((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) * S ((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) + ((dst_negative_scale_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)))) * S ((((dst_positive_code_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum)) * S ((dst_positive_code_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum)) + ((dst_positive_scale_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum))) + (((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) * S ((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) + ((dst_negative_scale_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)))) + ((((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) * S ((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) + ((dst_negative_scale_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum))) + (((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) * S ((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) + ((dst_negative_scale_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)))))) /\ (((exists fs_u_dst_flat_unit_slicesumpositive fs_v_dst_flat_unit_slicesumpositive. ((((exists fs_h_dst_flat_unit_slicesumpositive_body_start. fs_h_dst_flat_unit_slicesumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_unit_slicesumpositive)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_start. fs_u_dst_flat_unit_slicesumpositive = fs_q_dst_flat_unit_slicesumpositive_body_start * S ((S (0)) * fs_v_dst_flat_unit_slicesumpositive) + (0))) /\ ((((exists fs_h_dst_flat_unit_slicesumpositive_body_terminal. fs_h_dst_flat_unit_slicesumpositive_body_terminal + S (dst_positive_sum_flat_unit_slicesum) = S ((S (m*n)) * fs_v_dst_flat_unit_slicesumpositive)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_terminal. fs_u_dst_flat_unit_slicesumpositive = fs_q_dst_flat_unit_slicesumpositive_body_terminal * S ((S (m*n)) * fs_v_dst_flat_unit_slicesumpositive) + (dst_positive_sum_flat_unit_slicesum))) /\ forall fs_i_dst_flat_unit_slicesumpositive_body_steps. (exists fs_lt_dst_flat_unit_slicesumpositive_body_steps_bound. fs_lt_dst_flat_unit_slicesumpositive_body_steps_bound + S fs_i_dst_flat_unit_slicesumpositive_body_steps = m*n) -> exists fs_a_dst_flat_unit_slicesumpositive_body_steps fs_r_dst_flat_unit_slicesumpositive_body_steps fs_s_dst_flat_unit_slicesumpositive_body_steps. ((((exists fs_h_dst_flat_unit_slicesumpositive_body_steps_summand. fs_h_dst_flat_unit_slicesumpositive_body_steps_summand + S (fs_a_dst_flat_unit_slicesumpositive_body_steps) = S ((S (fs_i_dst_flat_unit_slicesumpositive_body_steps)) * dst_positive_scale_flat_unit_slicesum)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_steps_summand. dst_positive_code_flat_unit_slicesum = fs_q_dst_flat_unit_slicesumpositive_body_steps_summand * S ((S (fs_i_dst_flat_unit_slicesumpositive_body_steps)) * dst_positive_scale_flat_unit_slicesum) + (fs_a_dst_flat_unit_slicesumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_unit_slicesumpositive_body_steps_partial. fs_h_dst_flat_unit_slicesumpositive_body_steps_partial + S (fs_r_dst_flat_unit_slicesumpositive_body_steps) = S ((S (fs_i_dst_flat_unit_slicesumpositive_body_steps)) * fs_v_dst_flat_unit_slicesumpositive)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_steps_partial. fs_u_dst_flat_unit_slicesumpositive = fs_q_dst_flat_unit_slicesumpositive_body_steps_partial * S ((S (fs_i_dst_flat_unit_slicesumpositive_body_steps)) * fs_v_dst_flat_unit_slicesumpositive) + (fs_r_dst_flat_unit_slicesumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_unit_slicesumpositive_body_steps_successor. fs_h_dst_flat_unit_slicesumpositive_body_steps_successor + S (fs_s_dst_flat_unit_slicesumpositive_body_steps) = S ((S (S fs_i_dst_flat_unit_slicesumpositive_body_steps)) * fs_v_dst_flat_unit_slicesumpositive)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_steps_successor. fs_u_dst_flat_unit_slicesumpositive = fs_q_dst_flat_unit_slicesumpositive_body_steps_successor * S ((S (S fs_i_dst_flat_unit_slicesumpositive_body_steps)) * fs_v_dst_flat_unit_slicesumpositive) + (fs_s_dst_flat_unit_slicesumpositive_body_steps))) /\ fs_s_dst_flat_unit_slicesumpositive_body_steps = fs_r_dst_flat_unit_slicesumpositive_body_steps + fs_a_dst_flat_unit_slicesumpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_unit_slicesumnegative fs_v_dst_flat_unit_slicesumnegative. ((((exists fs_h_dst_flat_unit_slicesumnegative_body_start. fs_h_dst_flat_unit_slicesumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_unit_slicesumnegative)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_start. fs_u_dst_flat_unit_slicesumnegative = fs_q_dst_flat_unit_slicesumnegative_body_start * S ((S (0)) * fs_v_dst_flat_unit_slicesumnegative) + (0))) /\ ((((exists fs_h_dst_flat_unit_slicesumnegative_body_terminal. fs_h_dst_flat_unit_slicesumnegative_body_terminal + S (dst_negative_sum_flat_unit_slicesum) = S ((S (m*n)) * fs_v_dst_flat_unit_slicesumnegative)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_terminal. fs_u_dst_flat_unit_slicesumnegative = fs_q_dst_flat_unit_slicesumnegative_body_terminal * S ((S (m*n)) * fs_v_dst_flat_unit_slicesumnegative) + (dst_negative_sum_flat_unit_slicesum))) /\ forall fs_i_dst_flat_unit_slicesumnegative_body_steps. (exists fs_lt_dst_flat_unit_slicesumnegative_body_steps_bound. fs_lt_dst_flat_unit_slicesumnegative_body_steps_bound + S fs_i_dst_flat_unit_slicesumnegative_body_steps = m*n) -> exists fs_a_dst_flat_unit_slicesumnegative_body_steps fs_r_dst_flat_unit_slicesumnegative_body_steps fs_s_dst_flat_unit_slicesumnegative_body_steps. ((((exists fs_h_dst_flat_unit_slicesumnegative_body_steps_summand. fs_h_dst_flat_unit_slicesumnegative_body_steps_summand + S (fs_a_dst_flat_unit_slicesumnegative_body_steps) = S ((S (fs_i_dst_flat_unit_slicesumnegative_body_steps)) * dst_negative_scale_flat_unit_slicesum)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_steps_summand. dst_negative_code_flat_unit_slicesum = fs_q_dst_flat_unit_slicesumnegative_body_steps_summand * S ((S (fs_i_dst_flat_unit_slicesumnegative_body_steps)) * dst_negative_scale_flat_unit_slicesum) + (fs_a_dst_flat_unit_slicesumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_unit_slicesumnegative_body_steps_partial. fs_h_dst_flat_unit_slicesumnegative_body_steps_partial + S (fs_r_dst_flat_unit_slicesumnegative_body_steps) = S ((S (fs_i_dst_flat_unit_slicesumnegative_body_steps)) * fs_v_dst_flat_unit_slicesumnegative)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_steps_partial. fs_u_dst_flat_unit_slicesumnegative = fs_q_dst_flat_unit_slicesumnegative_body_steps_partial * S ((S (fs_i_dst_flat_unit_slicesumnegative_body_steps)) * fs_v_dst_flat_unit_slicesumnegative) + (fs_r_dst_flat_unit_slicesumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_unit_slicesumnegative_body_steps_successor. fs_h_dst_flat_unit_slicesumnegative_body_steps_successor + S (fs_s_dst_flat_unit_slicesumnegative_body_steps) = S ((S (S fs_i_dst_flat_unit_slicesumnegative_body_steps)) * fs_v_dst_flat_unit_slicesumnegative)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_steps_successor. fs_u_dst_flat_unit_slicesumnegative = fs_q_dst_flat_unit_slicesumnegative_body_steps_successor * S ((S (S fs_i_dst_flat_unit_slicesumnegative_body_steps)) * fs_v_dst_flat_unit_slicesumnegative) + (fs_s_dst_flat_unit_slicesumnegative_body_steps))) /\ fs_s_dst_flat_unit_slicesumnegative_body_steps = fs_r_dst_flat_unit_slicesumnegative_body_steps + fs_a_dst_flat_unit_slicesumnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_unit_slicesumresult ge_balance_negative_flat_unit_slicesumresult. (((((z) = 2 * (ge_balance_positive_flat_unit_slicesumresult) /\ (ge_balance_negative_flat_unit_slicesumresult) = 0) \/ exists ge_signed_half_flat_unit_slicesumresultdecode. (((z) = 2 * ge_signed_half_flat_unit_slicesumresultdecode + 1 /\ (ge_balance_positive_flat_unit_slicesumresult) = 0) /\ (ge_balance_negative_flat_unit_slicesumresult) = S ge_signed_half_flat_unit_slicesumresultdecode))) /\ ((dst_positive_sum_flat_unit_slicesum) + ge_balance_negative_flat_unit_slicesumresult = (dst_negative_sum_flat_unit_slicesum) + ge_balance_positive_flat_unit_slicesumresult))))))))))) -> (exists dst_positive_code_flat_unit_prefix dst_positive_scale_flat_unit_prefix dst_negative_code_flat_unit_prefix dst_negative_scale_flat_unit_prefix dst_positive_sum_flat_unit_prefix dst_negative_sum_flat_unit_prefix. (((F) = (((((dst_positive_code_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix)) * S ((dst_positive_code_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix)) + ((dst_positive_scale_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix))) + (((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) * S ((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) + ((dst_negative_scale_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)))) * S ((((dst_positive_code_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix)) * S ((dst_positive_code_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix)) + ((dst_positive_scale_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix))) + (((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) * S ((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) + ((dst_negative_scale_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)))) + ((((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) * S ((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) + ((dst_negative_scale_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix))) + (((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) * S ((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) + ((dst_negative_scale_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)))))) /\ (((exists fs_u_dst_flat_unit_prefixpositive fs_v_dst_flat_unit_prefixpositive. ((((exists fs_h_dst_flat_unit_prefixpositive_body_start. fs_h_dst_flat_unit_prefixpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_unit_prefixpositive)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_start. fs_u_dst_flat_unit_prefixpositive = fs_q_dst_flat_unit_prefixpositive_body_start * S ((S (0)) * fs_v_dst_flat_unit_prefixpositive) + (0))) /\ ((((exists fs_h_dst_flat_unit_prefixpositive_body_terminal. fs_h_dst_flat_unit_prefixpositive_body_terminal + S (dst_positive_sum_flat_unit_prefix) = S ((S (m*n)) * fs_v_dst_flat_unit_prefixpositive)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_terminal. fs_u_dst_flat_unit_prefixpositive = fs_q_dst_flat_unit_prefixpositive_body_terminal * S ((S (m*n)) * fs_v_dst_flat_unit_prefixpositive) + (dst_positive_sum_flat_unit_prefix))) /\ forall fs_i_dst_flat_unit_prefixpositive_body_steps. (exists fs_lt_dst_flat_unit_prefixpositive_body_steps_bound. fs_lt_dst_flat_unit_prefixpositive_body_steps_bound + S fs_i_dst_flat_unit_prefixpositive_body_steps = m*n) -> exists fs_a_dst_flat_unit_prefixpositive_body_steps fs_r_dst_flat_unit_prefixpositive_body_steps fs_s_dst_flat_unit_prefixpositive_body_steps. ((((exists fs_h_dst_flat_unit_prefixpositive_body_steps_summand. fs_h_dst_flat_unit_prefixpositive_body_steps_summand + S (fs_a_dst_flat_unit_prefixpositive_body_steps) = S ((S (fs_i_dst_flat_unit_prefixpositive_body_steps)) * dst_positive_scale_flat_unit_prefix)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_steps_summand. dst_positive_code_flat_unit_prefix = fs_q_dst_flat_unit_prefixpositive_body_steps_summand * S ((S (fs_i_dst_flat_unit_prefixpositive_body_steps)) * dst_positive_scale_flat_unit_prefix) + (fs_a_dst_flat_unit_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_flat_unit_prefixpositive_body_steps_partial. fs_h_dst_flat_unit_prefixpositive_body_steps_partial + S (fs_r_dst_flat_unit_prefixpositive_body_steps) = S ((S (fs_i_dst_flat_unit_prefixpositive_body_steps)) * fs_v_dst_flat_unit_prefixpositive)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_steps_partial. fs_u_dst_flat_unit_prefixpositive = fs_q_dst_flat_unit_prefixpositive_body_steps_partial * S ((S (fs_i_dst_flat_unit_prefixpositive_body_steps)) * fs_v_dst_flat_unit_prefixpositive) + (fs_r_dst_flat_unit_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_flat_unit_prefixpositive_body_steps_successor. fs_h_dst_flat_unit_prefixpositive_body_steps_successor + S (fs_s_dst_flat_unit_prefixpositive_body_steps) = S ((S (S fs_i_dst_flat_unit_prefixpositive_body_steps)) * fs_v_dst_flat_unit_prefixpositive)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_steps_successor. fs_u_dst_flat_unit_prefixpositive = fs_q_dst_flat_unit_prefixpositive_body_steps_successor * S ((S (S fs_i_dst_flat_unit_prefixpositive_body_steps)) * fs_v_dst_flat_unit_prefixpositive) + (fs_s_dst_flat_unit_prefixpositive_body_steps))) /\ fs_s_dst_flat_unit_prefixpositive_body_steps = fs_r_dst_flat_unit_prefixpositive_body_steps + fs_a_dst_flat_unit_prefixpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_unit_prefixnegative fs_v_dst_flat_unit_prefixnegative. ((((exists fs_h_dst_flat_unit_prefixnegative_body_start. fs_h_dst_flat_unit_prefixnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_unit_prefixnegative)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_start. fs_u_dst_flat_unit_prefixnegative = fs_q_dst_flat_unit_prefixnegative_body_start * S ((S (0)) * fs_v_dst_flat_unit_prefixnegative) + (0))) /\ ((((exists fs_h_dst_flat_unit_prefixnegative_body_terminal. fs_h_dst_flat_unit_prefixnegative_body_terminal + S (dst_negative_sum_flat_unit_prefix) = S ((S (m*n)) * fs_v_dst_flat_unit_prefixnegative)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_terminal. fs_u_dst_flat_unit_prefixnegative = fs_q_dst_flat_unit_prefixnegative_body_terminal * S ((S (m*n)) * fs_v_dst_flat_unit_prefixnegative) + (dst_negative_sum_flat_unit_prefix))) /\ forall fs_i_dst_flat_unit_prefixnegative_body_steps. (exists fs_lt_dst_flat_unit_prefixnegative_body_steps_bound. fs_lt_dst_flat_unit_prefixnegative_body_steps_bound + S fs_i_dst_flat_unit_prefixnegative_body_steps = m*n) -> exists fs_a_dst_flat_unit_prefixnegative_body_steps fs_r_dst_flat_unit_prefixnegative_body_steps fs_s_dst_flat_unit_prefixnegative_body_steps. ((((exists fs_h_dst_flat_unit_prefixnegative_body_steps_summand. fs_h_dst_flat_unit_prefixnegative_body_steps_summand + S (fs_a_dst_flat_unit_prefixnegative_body_steps) = S ((S (fs_i_dst_flat_unit_prefixnegative_body_steps)) * dst_negative_scale_flat_unit_prefix)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_steps_summand. dst_negative_code_flat_unit_prefix = fs_q_dst_flat_unit_prefixnegative_body_steps_summand * S ((S (fs_i_dst_flat_unit_prefixnegative_body_steps)) * dst_negative_scale_flat_unit_prefix) + (fs_a_dst_flat_unit_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_flat_unit_prefixnegative_body_steps_partial. fs_h_dst_flat_unit_prefixnegative_body_steps_partial + S (fs_r_dst_flat_unit_prefixnegative_body_steps) = S ((S (fs_i_dst_flat_unit_prefixnegative_body_steps)) * fs_v_dst_flat_unit_prefixnegative)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_steps_partial. fs_u_dst_flat_unit_prefixnegative = fs_q_dst_flat_unit_prefixnegative_body_steps_partial * S ((S (fs_i_dst_flat_unit_prefixnegative_body_steps)) * fs_v_dst_flat_unit_prefixnegative) + (fs_r_dst_flat_unit_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_flat_unit_prefixnegative_body_steps_successor. fs_h_dst_flat_unit_prefixnegative_body_steps_successor + S (fs_s_dst_flat_unit_prefixnegative_body_steps) = S ((S (S fs_i_dst_flat_unit_prefixnegative_body_steps)) * fs_v_dst_flat_unit_prefixnegative)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_steps_successor. fs_u_dst_flat_unit_prefixnegative = fs_q_dst_flat_unit_prefixnegative_body_steps_successor * S ((S (S fs_i_dst_flat_unit_prefixnegative_body_steps)) * fs_v_dst_flat_unit_prefixnegative) + (fs_s_dst_flat_unit_prefixnegative_body_steps))) /\ fs_s_dst_flat_unit_prefixnegative_body_steps = fs_r_dst_flat_unit_prefixnegative_body_steps + fs_a_dst_flat_unit_prefixnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_unit_prefixresult ge_balance_negative_flat_unit_prefixresult. (((((z) = 2 * (ge_balance_positive_flat_unit_prefixresult) /\ (ge_balance_negative_flat_unit_prefixresult) = 0) \/ exists ge_signed_half_flat_unit_prefixresultdecode. (((z) = 2 * ge_signed_half_flat_unit_prefixresultdecode + 1 /\ (ge_balance_positive_flat_unit_prefixresult) = 0) /\ (ge_balance_negative_flat_unit_prefixresult) = S ge_signed_half_flat_unit_prefixresultdecode))) /\ ((dst_positive_sum_flat_unit_prefix) + ge_balance_negative_flat_unit_prefixresult = (dst_negative_sum_flat_unit_prefix) + ge_balance_positive_flat_unit_prefixresult)))))))))) /\ ((exists dst_positive_code_flat_unit_prefix dst_positive_scale_flat_unit_prefix dst_negative_code_flat_unit_prefix dst_negative_scale_flat_unit_prefix dst_positive_sum_flat_unit_prefix dst_negative_sum_flat_unit_prefix. (((F) = (((((dst_positive_code_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix)) * S ((dst_positive_code_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix)) + ((dst_positive_scale_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix))) + (((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) * S ((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) + ((dst_negative_scale_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)))) * S ((((dst_positive_code_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix)) * S ((dst_positive_code_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix)) + ((dst_positive_scale_flat_unit_prefix) + (dst_positive_scale_flat_unit_prefix))) + (((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) * S ((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) + ((dst_negative_scale_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)))) + ((((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) * S ((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) + ((dst_negative_scale_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix))) + (((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) * S ((dst_negative_code_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)) + ((dst_negative_scale_flat_unit_prefix) + (dst_negative_scale_flat_unit_prefix)))))) /\ (((exists fs_u_dst_flat_unit_prefixpositive fs_v_dst_flat_unit_prefixpositive. ((((exists fs_h_dst_flat_unit_prefixpositive_body_start. fs_h_dst_flat_unit_prefixpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_unit_prefixpositive)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_start. fs_u_dst_flat_unit_prefixpositive = fs_q_dst_flat_unit_prefixpositive_body_start * S ((S (0)) * fs_v_dst_flat_unit_prefixpositive) + (0))) /\ ((((exists fs_h_dst_flat_unit_prefixpositive_body_terminal. fs_h_dst_flat_unit_prefixpositive_body_terminal + S (dst_positive_sum_flat_unit_prefix) = S ((S (m*n)) * fs_v_dst_flat_unit_prefixpositive)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_terminal. fs_u_dst_flat_unit_prefixpositive = fs_q_dst_flat_unit_prefixpositive_body_terminal * S ((S (m*n)) * fs_v_dst_flat_unit_prefixpositive) + (dst_positive_sum_flat_unit_prefix))) /\ forall fs_i_dst_flat_unit_prefixpositive_body_steps. (exists fs_lt_dst_flat_unit_prefixpositive_body_steps_bound. fs_lt_dst_flat_unit_prefixpositive_body_steps_bound + S fs_i_dst_flat_unit_prefixpositive_body_steps = m*n) -> exists fs_a_dst_flat_unit_prefixpositive_body_steps fs_r_dst_flat_unit_prefixpositive_body_steps fs_s_dst_flat_unit_prefixpositive_body_steps. ((((exists fs_h_dst_flat_unit_prefixpositive_body_steps_summand. fs_h_dst_flat_unit_prefixpositive_body_steps_summand + S (fs_a_dst_flat_unit_prefixpositive_body_steps) = S ((S (fs_i_dst_flat_unit_prefixpositive_body_steps)) * dst_positive_scale_flat_unit_prefix)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_steps_summand. dst_positive_code_flat_unit_prefix = fs_q_dst_flat_unit_prefixpositive_body_steps_summand * S ((S (fs_i_dst_flat_unit_prefixpositive_body_steps)) * dst_positive_scale_flat_unit_prefix) + (fs_a_dst_flat_unit_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_flat_unit_prefixpositive_body_steps_partial. fs_h_dst_flat_unit_prefixpositive_body_steps_partial + S (fs_r_dst_flat_unit_prefixpositive_body_steps) = S ((S (fs_i_dst_flat_unit_prefixpositive_body_steps)) * fs_v_dst_flat_unit_prefixpositive)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_steps_partial. fs_u_dst_flat_unit_prefixpositive = fs_q_dst_flat_unit_prefixpositive_body_steps_partial * S ((S (fs_i_dst_flat_unit_prefixpositive_body_steps)) * fs_v_dst_flat_unit_prefixpositive) + (fs_r_dst_flat_unit_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_flat_unit_prefixpositive_body_steps_successor. fs_h_dst_flat_unit_prefixpositive_body_steps_successor + S (fs_s_dst_flat_unit_prefixpositive_body_steps) = S ((S (S fs_i_dst_flat_unit_prefixpositive_body_steps)) * fs_v_dst_flat_unit_prefixpositive)) /\ exists fs_q_dst_flat_unit_prefixpositive_body_steps_successor. fs_u_dst_flat_unit_prefixpositive = fs_q_dst_flat_unit_prefixpositive_body_steps_successor * S ((S (S fs_i_dst_flat_unit_prefixpositive_body_steps)) * fs_v_dst_flat_unit_prefixpositive) + (fs_s_dst_flat_unit_prefixpositive_body_steps))) /\ fs_s_dst_flat_unit_prefixpositive_body_steps = fs_r_dst_flat_unit_prefixpositive_body_steps + fs_a_dst_flat_unit_prefixpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_unit_prefixnegative fs_v_dst_flat_unit_prefixnegative. ((((exists fs_h_dst_flat_unit_prefixnegative_body_start. fs_h_dst_flat_unit_prefixnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_unit_prefixnegative)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_start. fs_u_dst_flat_unit_prefixnegative = fs_q_dst_flat_unit_prefixnegative_body_start * S ((S (0)) * fs_v_dst_flat_unit_prefixnegative) + (0))) /\ ((((exists fs_h_dst_flat_unit_prefixnegative_body_terminal. fs_h_dst_flat_unit_prefixnegative_body_terminal + S (dst_negative_sum_flat_unit_prefix) = S ((S (m*n)) * fs_v_dst_flat_unit_prefixnegative)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_terminal. fs_u_dst_flat_unit_prefixnegative = fs_q_dst_flat_unit_prefixnegative_body_terminal * S ((S (m*n)) * fs_v_dst_flat_unit_prefixnegative) + (dst_negative_sum_flat_unit_prefix))) /\ forall fs_i_dst_flat_unit_prefixnegative_body_steps. (exists fs_lt_dst_flat_unit_prefixnegative_body_steps_bound. fs_lt_dst_flat_unit_prefixnegative_body_steps_bound + S fs_i_dst_flat_unit_prefixnegative_body_steps = m*n) -> exists fs_a_dst_flat_unit_prefixnegative_body_steps fs_r_dst_flat_unit_prefixnegative_body_steps fs_s_dst_flat_unit_prefixnegative_body_steps. ((((exists fs_h_dst_flat_unit_prefixnegative_body_steps_summand. fs_h_dst_flat_unit_prefixnegative_body_steps_summand + S (fs_a_dst_flat_unit_prefixnegative_body_steps) = S ((S (fs_i_dst_flat_unit_prefixnegative_body_steps)) * dst_negative_scale_flat_unit_prefix)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_steps_summand. dst_negative_code_flat_unit_prefix = fs_q_dst_flat_unit_prefixnegative_body_steps_summand * S ((S (fs_i_dst_flat_unit_prefixnegative_body_steps)) * dst_negative_scale_flat_unit_prefix) + (fs_a_dst_flat_unit_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_flat_unit_prefixnegative_body_steps_partial. fs_h_dst_flat_unit_prefixnegative_body_steps_partial + S (fs_r_dst_flat_unit_prefixnegative_body_steps) = S ((S (fs_i_dst_flat_unit_prefixnegative_body_steps)) * fs_v_dst_flat_unit_prefixnegative)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_steps_partial. fs_u_dst_flat_unit_prefixnegative = fs_q_dst_flat_unit_prefixnegative_body_steps_partial * S ((S (fs_i_dst_flat_unit_prefixnegative_body_steps)) * fs_v_dst_flat_unit_prefixnegative) + (fs_r_dst_flat_unit_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_flat_unit_prefixnegative_body_steps_successor. fs_h_dst_flat_unit_prefixnegative_body_steps_successor + S (fs_s_dst_flat_unit_prefixnegative_body_steps) = S ((S (S fs_i_dst_flat_unit_prefixnegative_body_steps)) * fs_v_dst_flat_unit_prefixnegative)) /\ exists fs_q_dst_flat_unit_prefixnegative_body_steps_successor. fs_u_dst_flat_unit_prefixnegative = fs_q_dst_flat_unit_prefixnegative_body_steps_successor * S ((S (S fs_i_dst_flat_unit_prefixnegative_body_steps)) * fs_v_dst_flat_unit_prefixnegative) + (fs_s_dst_flat_unit_prefixnegative_body_steps))) /\ fs_s_dst_flat_unit_prefixnegative_body_steps = fs_r_dst_flat_unit_prefixnegative_body_steps + fs_a_dst_flat_unit_prefixnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_unit_prefixresult ge_balance_negative_flat_unit_prefixresult. (((((z) = 2 * (ge_balance_positive_flat_unit_prefixresult) /\ (ge_balance_negative_flat_unit_prefixresult) = 0) \/ exists ge_signed_half_flat_unit_prefixresultdecode. (((z) = 2 * ge_signed_half_flat_unit_prefixresultdecode + 1 /\ (ge_balance_positive_flat_unit_prefixresult) = 0) /\ (ge_balance_negative_flat_unit_prefixresult) = S ge_signed_half_flat_unit_prefixresultdecode))) /\ ((dst_positive_sum_flat_unit_prefix) + ge_balance_negative_flat_unit_prefixresult = (dst_negative_sum_flat_unit_prefix) + ge_balance_positive_flat_unit_prefixresult))))))))) -> (exists srs_slice_flat_unit_slice. ((((exists dst_positive_code_flat_unit_sliceslicesource_table dst_positive_scale_flat_unit_sliceslicesource_table dst_negative_code_flat_unit_sliceslicesource_table dst_negative_scale_flat_unit_sliceslicesource_table. (((F) = (((((dst_positive_code_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table)) * S ((dst_positive_code_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table)) + ((dst_positive_scale_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table))) + (((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) * S ((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) + ((dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)))) * S ((((dst_positive_code_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table)) * S ((dst_positive_code_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table)) + ((dst_positive_scale_flat_unit_sliceslicesource_table) + (dst_positive_scale_flat_unit_sliceslicesource_table))) + (((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) * S ((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) + ((dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)))) + ((((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) * S ((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) + ((dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table))) + (((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) * S ((dst_negative_code_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)) + ((dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_scale_flat_unit_sliceslicesource_table)))))) /\ (forall dst_index_flat_unit_sliceslicesource_table. (exists pvs_le_gap_flat_unit_sliceslicesource_tabledomain. pvs_le_gap_flat_unit_sliceslicesource_tabledomain + (dst_index_flat_unit_sliceslicesource_table) = (0)) -> exists dst_positive_flat_unit_sliceslicesource_table dst_negative_flat_unit_sliceslicesource_table dst_value_flat_unit_sliceslicesource_table. ((((exists ff_h_pvs_flat_unit_sliceslicesource_tableentrypositive. ff_h_pvs_flat_unit_sliceslicesource_tableentrypositive + S (dst_positive_flat_unit_sliceslicesource_table) = S ((S (dst_index_flat_unit_sliceslicesource_table)) * dst_positive_scale_flat_unit_sliceslicesource_table)) /\ exists ff_q_pvs_flat_unit_sliceslicesource_tableentrypositive. dst_positive_code_flat_unit_sliceslicesource_table = ff_q_pvs_flat_unit_sliceslicesource_tableentrypositive * S ((S (dst_index_flat_unit_sliceslicesource_table)) * dst_positive_scale_flat_unit_sliceslicesource_table) + (dst_positive_flat_unit_sliceslicesource_table))) /\ (((((exists ff_h_pvs_flat_unit_sliceslicesource_tableentrynegative. ff_h_pvs_flat_unit_sliceslicesource_tableentrynegative + S (dst_negative_flat_unit_sliceslicesource_table) = S ((S (dst_index_flat_unit_sliceslicesource_table)) * dst_negative_scale_flat_unit_sliceslicesource_table)) /\ exists ff_q_pvs_flat_unit_sliceslicesource_tableentrynegative. dst_negative_code_flat_unit_sliceslicesource_table = ff_q_pvs_flat_unit_sliceslicesource_tableentrynegative * S ((S (dst_index_flat_unit_sliceslicesource_table)) * dst_negative_scale_flat_unit_sliceslicesource_table) + (dst_negative_flat_unit_sliceslicesource_table))) /\ (exists ge_balance_positive_flat_unit_sliceslicesource_tableentryvalue ge_balance_negative_flat_unit_sliceslicesource_tableentryvalue. (((((dst_value_flat_unit_sliceslicesource_table) = 2 * (ge_balance_positive_flat_unit_sliceslicesource_tableentryvalue) /\ (ge_balance_negative_flat_unit_sliceslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_flat_unit_sliceslicesource_tableentryvaluedecode. (((dst_value_flat_unit_sliceslicesource_table) = 2 * ge_signed_half_flat_unit_sliceslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_unit_sliceslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_flat_unit_sliceslicesource_tableentryvalue) = S ge_signed_half_flat_unit_sliceslicesource_tableentryvaluedecode))) /\ ((dst_positive_flat_unit_sliceslicesource_table) + ge_balance_negative_flat_unit_sliceslicesource_tableentryvalue = (dst_negative_flat_unit_sliceslicesource_table) + ge_balance_positive_flat_unit_sliceslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_flat_unit_slicesliceoutput_table dst_positive_scale_flat_unit_slicesliceoutput_table dst_negative_code_flat_unit_slicesliceoutput_table dst_negative_scale_flat_unit_slicesliceoutput_table. (((srs_slice_flat_unit_slice) = (((((dst_positive_code_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table)) * S ((dst_positive_code_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table)) + ((dst_positive_scale_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table))) + (((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) * S ((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) + ((dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)))) * S ((((dst_positive_code_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table)) * S ((dst_positive_code_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table)) + ((dst_positive_scale_flat_unit_slicesliceoutput_table) + (dst_positive_scale_flat_unit_slicesliceoutput_table))) + (((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) * S ((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) + ((dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)))) + ((((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) * S ((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) + ((dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table))) + (((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) * S ((dst_negative_code_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)) + ((dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_scale_flat_unit_slicesliceoutput_table)))))) /\ (forall dst_index_flat_unit_slicesliceoutput_table. (exists pvs_le_gap_flat_unit_slicesliceoutput_tabledomain. pvs_le_gap_flat_unit_slicesliceoutput_tabledomain + (dst_index_flat_unit_slicesliceoutput_table) = (m*n)) -> exists dst_positive_flat_unit_slicesliceoutput_table dst_negative_flat_unit_slicesliceoutput_table dst_value_flat_unit_slicesliceoutput_table. ((((exists ff_h_pvs_flat_unit_slicesliceoutput_tableentrypositive. ff_h_pvs_flat_unit_slicesliceoutput_tableentrypositive + S (dst_positive_flat_unit_slicesliceoutput_table) = S ((S (dst_index_flat_unit_slicesliceoutput_table)) * dst_positive_scale_flat_unit_slicesliceoutput_table)) /\ exists ff_q_pvs_flat_unit_slicesliceoutput_tableentrypositive. dst_positive_code_flat_unit_slicesliceoutput_table = ff_q_pvs_flat_unit_slicesliceoutput_tableentrypositive * S ((S (dst_index_flat_unit_slicesliceoutput_table)) * dst_positive_scale_flat_unit_slicesliceoutput_table) + (dst_positive_flat_unit_slicesliceoutput_table))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceoutput_tableentrynegative. ff_h_pvs_flat_unit_slicesliceoutput_tableentrynegative + S (dst_negative_flat_unit_slicesliceoutput_table) = S ((S (dst_index_flat_unit_slicesliceoutput_table)) * dst_negative_scale_flat_unit_slicesliceoutput_table)) /\ exists ff_q_pvs_flat_unit_slicesliceoutput_tableentrynegative. dst_negative_code_flat_unit_slicesliceoutput_table = ff_q_pvs_flat_unit_slicesliceoutput_tableentrynegative * S ((S (dst_index_flat_unit_slicesliceoutput_table)) * dst_negative_scale_flat_unit_slicesliceoutput_table) + (dst_negative_flat_unit_slicesliceoutput_table))) /\ (exists ge_balance_positive_flat_unit_slicesliceoutput_tableentryvalue ge_balance_negative_flat_unit_slicesliceoutput_tableentryvalue. (((((dst_value_flat_unit_slicesliceoutput_table) = 2 * (ge_balance_positive_flat_unit_slicesliceoutput_tableentryvalue) /\ (ge_balance_negative_flat_unit_slicesliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_flat_unit_slicesliceoutput_tableentryvaluedecode. (((dst_value_flat_unit_slicesliceoutput_table) = 2 * ge_signed_half_flat_unit_slicesliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_unit_slicesliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_flat_unit_slicesliceoutput_tableentryvalue) = S ge_signed_half_flat_unit_slicesliceoutput_tableentryvaluedecode))) /\ ((dst_positive_flat_unit_slicesliceoutput_table) + ge_balance_negative_flat_unit_slicesliceoutput_tableentryvalue = (dst_negative_flat_unit_slicesliceoutput_table) + ge_balance_positive_flat_unit_slicesliceoutput_tableentryvalue))))))))) /\ (forall srs_index_flat_unit_sliceslice. (exists pvs_gap_flat_unit_sliceslicebound. pvs_gap_flat_unit_sliceslicebound + S (srs_index_flat_unit_sliceslice) = (m*n)) -> exists srs_value_flat_unit_sliceslice. (((exists dst_positive_code_flat_unit_slicesliceentrysource dst_positive_scale_flat_unit_slicesliceentrysource dst_negative_code_flat_unit_slicesliceentrysource dst_negative_scale_flat_unit_slicesliceentrysource dst_positive_flat_unit_slicesliceentrysource dst_negative_flat_unit_slicesliceentrysource. (((F) = (((((dst_positive_code_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource)) * S ((dst_positive_code_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource)) + ((dst_positive_scale_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource))) + (((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) * S ((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) + ((dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)))) * S ((((dst_positive_code_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource)) * S ((dst_positive_code_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource)) + ((dst_positive_scale_flat_unit_slicesliceentrysource) + (dst_positive_scale_flat_unit_slicesliceentrysource))) + (((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) * S ((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) + ((dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)))) + ((((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) * S ((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) + ((dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource))) + (((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) * S ((dst_negative_code_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)) + ((dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_scale_flat_unit_slicesliceentrysource)))))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceentrysourcepositive. ff_h_pvs_flat_unit_slicesliceentrysourcepositive + S (dst_positive_flat_unit_slicesliceentrysource) = S ((S (((0) + ((1) * (srs_index_flat_unit_sliceslice))))) * dst_positive_scale_flat_unit_slicesliceentrysource)) /\ exists ff_q_pvs_flat_unit_slicesliceentrysourcepositive. dst_positive_code_flat_unit_slicesliceentrysource = ff_q_pvs_flat_unit_slicesliceentrysourcepositive * S ((S (((0) + ((1) * (srs_index_flat_unit_sliceslice))))) * dst_positive_scale_flat_unit_slicesliceentrysource) + (dst_positive_flat_unit_slicesliceentrysource))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceentrysourcenegative. ff_h_pvs_flat_unit_slicesliceentrysourcenegative + S (dst_negative_flat_unit_slicesliceentrysource) = S ((S (((0) + ((1) * (srs_index_flat_unit_sliceslice))))) * dst_negative_scale_flat_unit_slicesliceentrysource)) /\ exists ff_q_pvs_flat_unit_slicesliceentrysourcenegative. dst_negative_code_flat_unit_slicesliceentrysource = ff_q_pvs_flat_unit_slicesliceentrysourcenegative * S ((S (((0) + ((1) * (srs_index_flat_unit_sliceslice))))) * dst_negative_scale_flat_unit_slicesliceentrysource) + (dst_negative_flat_unit_slicesliceentrysource))) /\ (exists ge_balance_positive_flat_unit_slicesliceentrysourcevalue ge_balance_negative_flat_unit_slicesliceentrysourcevalue. (((((srs_value_flat_unit_sliceslice) = 2 * (ge_balance_positive_flat_unit_slicesliceentrysourcevalue) /\ (ge_balance_negative_flat_unit_slicesliceentrysourcevalue) = 0) \/ exists ge_signed_half_flat_unit_slicesliceentrysourcevaluedecode. (((srs_value_flat_unit_sliceslice) = 2 * ge_signed_half_flat_unit_slicesliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_flat_unit_slicesliceentrysourcevalue) = 0) /\ (ge_balance_negative_flat_unit_slicesliceentrysourcevalue) = S ge_signed_half_flat_unit_slicesliceentrysourcevaluedecode))) /\ ((dst_positive_flat_unit_slicesliceentrysource) + ge_balance_negative_flat_unit_slicesliceentrysourcevalue = (dst_negative_flat_unit_slicesliceentrysource) + ge_balance_positive_flat_unit_slicesliceentrysourcevalue))))))))) /\ (exists dst_positive_code_flat_unit_slicesliceentryoutput dst_positive_scale_flat_unit_slicesliceentryoutput dst_negative_code_flat_unit_slicesliceentryoutput dst_negative_scale_flat_unit_slicesliceentryoutput dst_positive_flat_unit_slicesliceentryoutput dst_negative_flat_unit_slicesliceentryoutput. (((srs_slice_flat_unit_slice) = (((((dst_positive_code_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput)) * S ((dst_positive_code_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput)) + ((dst_positive_scale_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput))) + (((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) * S ((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) + ((dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)))) * S ((((dst_positive_code_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput)) * S ((dst_positive_code_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput)) + ((dst_positive_scale_flat_unit_slicesliceentryoutput) + (dst_positive_scale_flat_unit_slicesliceentryoutput))) + (((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) * S ((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) + ((dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)))) + ((((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) * S ((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) + ((dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput))) + (((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) * S ((dst_negative_code_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)) + ((dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_scale_flat_unit_slicesliceentryoutput)))))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceentryoutputpositive. ff_h_pvs_flat_unit_slicesliceentryoutputpositive + S (dst_positive_flat_unit_slicesliceentryoutput) = S ((S (srs_index_flat_unit_sliceslice)) * dst_positive_scale_flat_unit_slicesliceentryoutput)) /\ exists ff_q_pvs_flat_unit_slicesliceentryoutputpositive. dst_positive_code_flat_unit_slicesliceentryoutput = ff_q_pvs_flat_unit_slicesliceentryoutputpositive * S ((S (srs_index_flat_unit_sliceslice)) * dst_positive_scale_flat_unit_slicesliceentryoutput) + (dst_positive_flat_unit_slicesliceentryoutput))) /\ (((((exists ff_h_pvs_flat_unit_slicesliceentryoutputnegative. ff_h_pvs_flat_unit_slicesliceentryoutputnegative + S (dst_negative_flat_unit_slicesliceentryoutput) = S ((S (srs_index_flat_unit_sliceslice)) * dst_negative_scale_flat_unit_slicesliceentryoutput)) /\ exists ff_q_pvs_flat_unit_slicesliceentryoutputnegative. dst_negative_code_flat_unit_slicesliceentryoutput = ff_q_pvs_flat_unit_slicesliceentryoutputnegative * S ((S (srs_index_flat_unit_sliceslice)) * dst_negative_scale_flat_unit_slicesliceentryoutput) + (dst_negative_flat_unit_slicesliceentryoutput))) /\ (exists ge_balance_positive_flat_unit_slicesliceentryoutputvalue ge_balance_negative_flat_unit_slicesliceentryoutputvalue. (((((srs_value_flat_unit_sliceslice) = 2 * (ge_balance_positive_flat_unit_slicesliceentryoutputvalue) /\ (ge_balance_negative_flat_unit_slicesliceentryoutputvalue) = 0) \/ exists ge_signed_half_flat_unit_slicesliceentryoutputvaluedecode. (((srs_value_flat_unit_sliceslice) = 2 * ge_signed_half_flat_unit_slicesliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_flat_unit_slicesliceentryoutputvalue) = 0) /\ (ge_balance_negative_flat_unit_slicesliceentryoutputvalue) = S ge_signed_half_flat_unit_slicesliceentryoutputvaluedecode))) /\ ((dst_positive_flat_unit_slicesliceentryoutput) + ge_balance_negative_flat_unit_slicesliceentryoutputvalue = (dst_negative_flat_unit_slicesliceentryoutput) + ge_balance_positive_flat_unit_slicesliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_flat_unit_slicesum dst_positive_scale_flat_unit_slicesum dst_negative_code_flat_unit_slicesum dst_negative_scale_flat_unit_slicesum dst_positive_sum_flat_unit_slicesum dst_negative_sum_flat_unit_slicesum. (((srs_slice_flat_unit_slice) = (((((dst_positive_code_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum)) * S ((dst_positive_code_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum)) + ((dst_positive_scale_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum))) + (((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) * S ((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) + ((dst_negative_scale_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)))) * S ((((dst_positive_code_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum)) * S ((dst_positive_code_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum)) + ((dst_positive_scale_flat_unit_slicesum) + (dst_positive_scale_flat_unit_slicesum))) + (((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) * S ((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) + ((dst_negative_scale_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)))) + ((((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) * S ((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) + ((dst_negative_scale_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum))) + (((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) * S ((dst_negative_code_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)) + ((dst_negative_scale_flat_unit_slicesum) + (dst_negative_scale_flat_unit_slicesum)))))) /\ (((exists fs_u_dst_flat_unit_slicesumpositive fs_v_dst_flat_unit_slicesumpositive. ((((exists fs_h_dst_flat_unit_slicesumpositive_body_start. fs_h_dst_flat_unit_slicesumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_unit_slicesumpositive)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_start. fs_u_dst_flat_unit_slicesumpositive = fs_q_dst_flat_unit_slicesumpositive_body_start * S ((S (0)) * fs_v_dst_flat_unit_slicesumpositive) + (0))) /\ ((((exists fs_h_dst_flat_unit_slicesumpositive_body_terminal. fs_h_dst_flat_unit_slicesumpositive_body_terminal + S (dst_positive_sum_flat_unit_slicesum) = S ((S (m*n)) * fs_v_dst_flat_unit_slicesumpositive)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_terminal. fs_u_dst_flat_unit_slicesumpositive = fs_q_dst_flat_unit_slicesumpositive_body_terminal * S ((S (m*n)) * fs_v_dst_flat_unit_slicesumpositive) + (dst_positive_sum_flat_unit_slicesum))) /\ forall fs_i_dst_flat_unit_slicesumpositive_body_steps. (exists fs_lt_dst_flat_unit_slicesumpositive_body_steps_bound. fs_lt_dst_flat_unit_slicesumpositive_body_steps_bound + S fs_i_dst_flat_unit_slicesumpositive_body_steps = m*n) -> exists fs_a_dst_flat_unit_slicesumpositive_body_steps fs_r_dst_flat_unit_slicesumpositive_body_steps fs_s_dst_flat_unit_slicesumpositive_body_steps. ((((exists fs_h_dst_flat_unit_slicesumpositive_body_steps_summand. fs_h_dst_flat_unit_slicesumpositive_body_steps_summand + S (fs_a_dst_flat_unit_slicesumpositive_body_steps) = S ((S (fs_i_dst_flat_unit_slicesumpositive_body_steps)) * dst_positive_scale_flat_unit_slicesum)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_steps_summand. dst_positive_code_flat_unit_slicesum = fs_q_dst_flat_unit_slicesumpositive_body_steps_summand * S ((S (fs_i_dst_flat_unit_slicesumpositive_body_steps)) * dst_positive_scale_flat_unit_slicesum) + (fs_a_dst_flat_unit_slicesumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_unit_slicesumpositive_body_steps_partial. fs_h_dst_flat_unit_slicesumpositive_body_steps_partial + S (fs_r_dst_flat_unit_slicesumpositive_body_steps) = S ((S (fs_i_dst_flat_unit_slicesumpositive_body_steps)) * fs_v_dst_flat_unit_slicesumpositive)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_steps_partial. fs_u_dst_flat_unit_slicesumpositive = fs_q_dst_flat_unit_slicesumpositive_body_steps_partial * S ((S (fs_i_dst_flat_unit_slicesumpositive_body_steps)) * fs_v_dst_flat_unit_slicesumpositive) + (fs_r_dst_flat_unit_slicesumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_unit_slicesumpositive_body_steps_successor. fs_h_dst_flat_unit_slicesumpositive_body_steps_successor + S (fs_s_dst_flat_unit_slicesumpositive_body_steps) = S ((S (S fs_i_dst_flat_unit_slicesumpositive_body_steps)) * fs_v_dst_flat_unit_slicesumpositive)) /\ exists fs_q_dst_flat_unit_slicesumpositive_body_steps_successor. fs_u_dst_flat_unit_slicesumpositive = fs_q_dst_flat_unit_slicesumpositive_body_steps_successor * S ((S (S fs_i_dst_flat_unit_slicesumpositive_body_steps)) * fs_v_dst_flat_unit_slicesumpositive) + (fs_s_dst_flat_unit_slicesumpositive_body_steps))) /\ fs_s_dst_flat_unit_slicesumpositive_body_steps = fs_r_dst_flat_unit_slicesumpositive_body_steps + fs_a_dst_flat_unit_slicesumpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_unit_slicesumnegative fs_v_dst_flat_unit_slicesumnegative. ((((exists fs_h_dst_flat_unit_slicesumnegative_body_start. fs_h_dst_flat_unit_slicesumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_unit_slicesumnegative)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_start. fs_u_dst_flat_unit_slicesumnegative = fs_q_dst_flat_unit_slicesumnegative_body_start * S ((S (0)) * fs_v_dst_flat_unit_slicesumnegative) + (0))) /\ ((((exists fs_h_dst_flat_unit_slicesumnegative_body_terminal. fs_h_dst_flat_unit_slicesumnegative_body_terminal + S (dst_negative_sum_flat_unit_slicesum) = S ((S (m*n)) * fs_v_dst_flat_unit_slicesumnegative)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_terminal. fs_u_dst_flat_unit_slicesumnegative = fs_q_dst_flat_unit_slicesumnegative_body_terminal * S ((S (m*n)) * fs_v_dst_flat_unit_slicesumnegative) + (dst_negative_sum_flat_unit_slicesum))) /\ forall fs_i_dst_flat_unit_slicesumnegative_body_steps. (exists fs_lt_dst_flat_unit_slicesumnegative_body_steps_bound. fs_lt_dst_flat_unit_slicesumnegative_body_steps_bound + S fs_i_dst_flat_unit_slicesumnegative_body_steps = m*n) -> exists fs_a_dst_flat_unit_slicesumnegative_body_steps fs_r_dst_flat_unit_slicesumnegative_body_steps fs_s_dst_flat_unit_slicesumnegative_body_steps. ((((exists fs_h_dst_flat_unit_slicesumnegative_body_steps_summand. fs_h_dst_flat_unit_slicesumnegative_body_steps_summand + S (fs_a_dst_flat_unit_slicesumnegative_body_steps) = S ((S (fs_i_dst_flat_unit_slicesumnegative_body_steps)) * dst_negative_scale_flat_unit_slicesum)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_steps_summand. dst_negative_code_flat_unit_slicesum = fs_q_dst_flat_unit_slicesumnegative_body_steps_summand * S ((S (fs_i_dst_flat_unit_slicesumnegative_body_steps)) * dst_negative_scale_flat_unit_slicesum) + (fs_a_dst_flat_unit_slicesumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_unit_slicesumnegative_body_steps_partial. fs_h_dst_flat_unit_slicesumnegative_body_steps_partial + S (fs_r_dst_flat_unit_slicesumnegative_body_steps) = S ((S (fs_i_dst_flat_unit_slicesumnegative_body_steps)) * fs_v_dst_flat_unit_slicesumnegative)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_steps_partial. fs_u_dst_flat_unit_slicesumnegative = fs_q_dst_flat_unit_slicesumnegative_body_steps_partial * S ((S (fs_i_dst_flat_unit_slicesumnegative_body_steps)) * fs_v_dst_flat_unit_slicesumnegative) + (fs_r_dst_flat_unit_slicesumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_unit_slicesumnegative_body_steps_successor. fs_h_dst_flat_unit_slicesumnegative_body_steps_successor + S (fs_s_dst_flat_unit_slicesumnegative_body_steps) = S ((S (S fs_i_dst_flat_unit_slicesumnegative_body_steps)) * fs_v_dst_flat_unit_slicesumnegative)) /\ exists fs_q_dst_flat_unit_slicesumnegative_body_steps_successor. fs_u_dst_flat_unit_slicesumnegative = fs_q_dst_flat_unit_slicesumnegative_body_steps_successor * S ((S (S fs_i_dst_flat_unit_slicesumnegative_body_steps)) * fs_v_dst_flat_unit_slicesumnegative) + (fs_s_dst_flat_unit_slicesumnegative_body_steps))) /\ fs_s_dst_flat_unit_slicesumnegative_body_steps = fs_r_dst_flat_unit_slicesumnegative_body_steps + fs_a_dst_flat_unit_slicesumnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_unit_slicesumresult ge_balance_negative_flat_unit_slicesumresult. (((((z) = 2 * (ge_balance_positive_flat_unit_slicesumresult) /\ (ge_balance_negative_flat_unit_slicesumresult) = 0) \/ exists ge_signed_half_flat_unit_slicesumresultdecode. (((z) = 2 * ge_signed_half_flat_unit_slicesumresultdecode + 1 /\ (ge_balance_positive_flat_unit_slicesumresult) = 0) /\ (ge_balance_negative_flat_unit_slicesumresult) = S ge_signed_half_flat_unit_slicesumresultdecode))) /\ ((dst_positive_sum_flat_unit_slicesum) + ge_balance_negative_flat_unit_slicesumresult = (dst_negative_sum_flat_unit_slicesum) + ge_balance_positive_flat_unit_slicesumresult))))))))))))) - 0007
specialize signed_slice_sum_unit_prefix_iff (F) - 0008
specialize signed_slice_sum_unit_prefix_iff (m*n) - 0009
specialize signed_slice_sum_unit_prefix_iff (z) - 0010
apply signed_slice_sum_unit_prefix_iff - 0011
exact hF - 0012
cases hi - 0013
split - 0014
intro hs - 0015
have hr : exists R. (((exists dst_positive_code_flat_construct_rowssource_table dst_positive_scale_flat_construct_rowssource_table dst_negative_code_flat_construct_rowssource_table dst_negative_scale_flat_construct_rowssource_table. (((F) = (((((dst_positive_code_flat_construct_rowssource_table) + (dst_positive_scale_flat_construct_rowssource_table)) * S ((dst_positive_code_flat_construct_rowssource_table) + (dst_positive_scale_flat_construct_rowssource_table)) + ((dst_positive_scale_flat_construct_rowssource_table) + (dst_positive_scale_flat_construct_rowssource_table))) + (((dst_negative_code_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)) * S ((dst_negative_code_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)) + ((dst_negative_scale_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)))) * S ((((dst_positive_code_flat_construct_rowssource_table) + (dst_positive_scale_flat_construct_rowssource_table)) * S ((dst_positive_code_flat_construct_rowssource_table) + (dst_positive_scale_flat_construct_rowssource_table)) + ((dst_positive_scale_flat_construct_rowssource_table) + (dst_positive_scale_flat_construct_rowssource_table))) + (((dst_negative_code_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)) * S ((dst_negative_code_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)) + ((dst_negative_scale_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)))) + ((((dst_negative_code_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)) * S ((dst_negative_code_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)) + ((dst_negative_scale_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table))) + (((dst_negative_code_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)) * S ((dst_negative_code_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)) + ((dst_negative_scale_flat_construct_rowssource_table) + (dst_negative_scale_flat_construct_rowssource_table)))))) /\ (forall dst_index_flat_construct_rowssource_table. (exists pvs_le_gap_flat_construct_rowssource_tabledomain. pvs_le_gap_flat_construct_rowssource_tabledomain + (dst_index_flat_construct_rowssource_table) = (0)) -> exists dst_positive_flat_construct_rowssource_table dst_negative_flat_construct_rowssource_table dst_value_flat_construct_rowssource_table. ((((exists ff_h_pvs_flat_construct_rowssource_tableentrypositive. ff_h_pvs_flat_construct_rowssource_tableentrypositive + S (dst_positive_flat_construct_rowssource_table) = S ((S (dst_index_flat_construct_rowssource_table)) * dst_positive_scale_flat_construct_rowssource_table)) /\ exists ff_q_pvs_flat_construct_rowssource_tableentrypositive. dst_positive_code_flat_construct_rowssource_table = ff_q_pvs_flat_construct_rowssource_tableentrypositive * S ((S (dst_index_flat_construct_rowssource_table)) * dst_positive_scale_flat_construct_rowssource_table) + (dst_positive_flat_construct_rowssource_table))) /\ (((((exists ff_h_pvs_flat_construct_rowssource_tableentrynegative. ff_h_pvs_flat_construct_rowssource_tableentrynegative + S (dst_negative_flat_construct_rowssource_table) = S ((S (dst_index_flat_construct_rowssource_table)) * dst_negative_scale_flat_construct_rowssource_table)) /\ exists ff_q_pvs_flat_construct_rowssource_tableentrynegative. dst_negative_code_flat_construct_rowssource_table = ff_q_pvs_flat_construct_rowssource_tableentrynegative * S ((S (dst_index_flat_construct_rowssource_table)) * dst_negative_scale_flat_construct_rowssource_table) + (dst_negative_flat_construct_rowssource_table))) /\ (exists ge_balance_positive_flat_construct_rowssource_tableentryvalue ge_balance_negative_flat_construct_rowssource_tableentryvalue. (((((dst_value_flat_construct_rowssource_table) = 2 * (ge_balance_positive_flat_construct_rowssource_tableentryvalue) /\ (ge_balance_negative_flat_construct_rowssource_tableentryvalue) = 0) \/ exists ge_signed_half_flat_construct_rowssource_tableentryvaluedecode. (((dst_value_flat_construct_rowssource_table) = 2 * ge_signed_half_flat_construct_rowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_construct_rowssource_tableentryvalue) = 0) /\ (ge_balance_negative_flat_construct_rowssource_tableentryvalue) = S ge_signed_half_flat_construct_rowssource_tableentryvaluedecode))) /\ ((dst_positive_flat_construct_rowssource_table) + ge_balance_negative_flat_construct_rowssource_tableentryvalue = (dst_negative_flat_construct_rowssource_table) + ge_balance_positive_flat_construct_rowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_flat_construct_rowsrow_table dst_positive_scale_flat_construct_rowsrow_table dst_negative_code_flat_construct_rowsrow_table dst_negative_scale_flat_construct_rowsrow_table. (((R) = (((((dst_positive_code_flat_construct_rowsrow_table) + (dst_positive_scale_flat_construct_rowsrow_table)) * S ((dst_positive_code_flat_construct_rowsrow_table) + (dst_positive_scale_flat_construct_rowsrow_table)) + ((dst_positive_scale_flat_construct_rowsrow_table) + (dst_positive_scale_flat_construct_rowsrow_table))) + (((dst_negative_code_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)) * S ((dst_negative_code_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)) + ((dst_negative_scale_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)))) * S ((((dst_positive_code_flat_construct_rowsrow_table) + (dst_positive_scale_flat_construct_rowsrow_table)) * S ((dst_positive_code_flat_construct_rowsrow_table) + (dst_positive_scale_flat_construct_rowsrow_table)) + ((dst_positive_scale_flat_construct_rowsrow_table) + (dst_positive_scale_flat_construct_rowsrow_table))) + (((dst_negative_code_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)) * S ((dst_negative_code_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)) + ((dst_negative_scale_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)))) + ((((dst_negative_code_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)) * S ((dst_negative_code_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)) + ((dst_negative_scale_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table))) + (((dst_negative_code_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)) * S ((dst_negative_code_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)) + ((dst_negative_scale_flat_construct_rowsrow_table) + (dst_negative_scale_flat_construct_rowsrow_table)))))) /\ (forall dst_index_flat_construct_rowsrow_table. (exists pvs_le_gap_flat_construct_rowsrow_tabledomain. pvs_le_gap_flat_construct_rowsrow_tabledomain + (dst_index_flat_construct_rowsrow_table) = (m)) -> exists dst_positive_flat_construct_rowsrow_table dst_negative_flat_construct_rowsrow_table dst_value_flat_construct_rowsrow_table. ((((exists ff_h_pvs_flat_construct_rowsrow_tableentrypositive. ff_h_pvs_flat_construct_rowsrow_tableentrypositive + S (dst_positive_flat_construct_rowsrow_table) = S ((S (dst_index_flat_construct_rowsrow_table)) * dst_positive_scale_flat_construct_rowsrow_table)) /\ exists ff_q_pvs_flat_construct_rowsrow_tableentrypositive. dst_positive_code_flat_construct_rowsrow_table = ff_q_pvs_flat_construct_rowsrow_tableentrypositive * S ((S (dst_index_flat_construct_rowsrow_table)) * dst_positive_scale_flat_construct_rowsrow_table) + (dst_positive_flat_construct_rowsrow_table))) /\ (((((exists ff_h_pvs_flat_construct_rowsrow_tableentrynegative. ff_h_pvs_flat_construct_rowsrow_tableentrynegative + S (dst_negative_flat_construct_rowsrow_table) = S ((S (dst_index_flat_construct_rowsrow_table)) * dst_negative_scale_flat_construct_rowsrow_table)) /\ exists ff_q_pvs_flat_construct_rowsrow_tableentrynegative. dst_negative_code_flat_construct_rowsrow_table = ff_q_pvs_flat_construct_rowsrow_tableentrynegative * S ((S (dst_index_flat_construct_rowsrow_table)) * dst_negative_scale_flat_construct_rowsrow_table) + (dst_negative_flat_construct_rowsrow_table))) /\ (exists ge_balance_positive_flat_construct_rowsrow_tableentryvalue ge_balance_negative_flat_construct_rowsrow_tableentryvalue. (((((dst_value_flat_construct_rowsrow_table) = 2 * (ge_balance_positive_flat_construct_rowsrow_tableentryvalue) /\ (ge_balance_negative_flat_construct_rowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_flat_construct_rowsrow_tableentryvaluedecode. (((dst_value_flat_construct_rowsrow_table) = 2 * ge_signed_half_flat_construct_rowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_construct_rowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_flat_construct_rowsrow_tableentryvalue) = S ge_signed_half_flat_construct_rowsrow_tableentryvaluedecode))) /\ ((dst_positive_flat_construct_rowsrow_table) + ge_balance_negative_flat_construct_rowsrow_tableentryvalue = (dst_negative_flat_construct_rowsrow_table) + ge_balance_positive_flat_construct_rowsrow_tableentryvalue))))))))) /\ (forall srt_index_flat_construct_rows. (exists pvs_gap_flat_construct_rowsbound. pvs_gap_flat_construct_rowsbound + S (srt_index_flat_construct_rows) = (m)) -> exists srt_value_flat_construct_rows. (((exists dst_positive_code_flat_construct_rowsrowentry dst_positive_scale_flat_construct_rowsrowentry dst_negative_code_flat_construct_rowsrowentry dst_negative_scale_flat_construct_rowsrowentry dst_positive_flat_construct_rowsrowentry dst_negative_flat_construct_rowsrowentry. (((R) = (((((dst_positive_code_flat_construct_rowsrowentry) + (dst_positive_scale_flat_construct_rowsrowentry)) * S ((dst_positive_code_flat_construct_rowsrowentry) + (dst_positive_scale_flat_construct_rowsrowentry)) + ((dst_positive_scale_flat_construct_rowsrowentry) + (dst_positive_scale_flat_construct_rowsrowentry))) + (((dst_negative_code_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)) * S ((dst_negative_code_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)) + ((dst_negative_scale_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)))) * S ((((dst_positive_code_flat_construct_rowsrowentry) + (dst_positive_scale_flat_construct_rowsrowentry)) * S ((dst_positive_code_flat_construct_rowsrowentry) + (dst_positive_scale_flat_construct_rowsrowentry)) + ((dst_positive_scale_flat_construct_rowsrowentry) + (dst_positive_scale_flat_construct_rowsrowentry))) + (((dst_negative_code_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)) * S ((dst_negative_code_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)) + ((dst_negative_scale_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)))) + ((((dst_negative_code_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)) * S ((dst_negative_code_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)) + ((dst_negative_scale_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry))) + (((dst_negative_code_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)) * S ((dst_negative_code_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)) + ((dst_negative_scale_flat_construct_rowsrowentry) + (dst_negative_scale_flat_construct_rowsrowentry)))))) /\ (((((exists ff_h_pvs_flat_construct_rowsrowentrypositive. ff_h_pvs_flat_construct_rowsrowentrypositive + S (dst_positive_flat_construct_rowsrowentry) = S ((S (srt_index_flat_construct_rows)) * dst_positive_scale_flat_construct_rowsrowentry)) /\ exists ff_q_pvs_flat_construct_rowsrowentrypositive. dst_positive_code_flat_construct_rowsrowentry = ff_q_pvs_flat_construct_rowsrowentrypositive * S ((S (srt_index_flat_construct_rows)) * dst_positive_scale_flat_construct_rowsrowentry) + (dst_positive_flat_construct_rowsrowentry))) /\ (((((exists ff_h_pvs_flat_construct_rowsrowentrynegative. ff_h_pvs_flat_construct_rowsrowentrynegative + S (dst_negative_flat_construct_rowsrowentry) = S ((S (srt_index_flat_construct_rows)) * dst_negative_scale_flat_construct_rowsrowentry)) /\ exists ff_q_pvs_flat_construct_rowsrowentrynegative. dst_negative_code_flat_construct_rowsrowentry = ff_q_pvs_flat_construct_rowsrowentrynegative * S ((S (srt_index_flat_construct_rows)) * dst_negative_scale_flat_construct_rowsrowentry) + (dst_negative_flat_construct_rowsrowentry))) /\ (exists ge_balance_positive_flat_construct_rowsrowentryvalue ge_balance_negative_flat_construct_rowsrowentryvalue. (((((srt_value_flat_construct_rows) = 2 * (ge_balance_positive_flat_construct_rowsrowentryvalue) /\ (ge_balance_negative_flat_construct_rowsrowentryvalue) = 0) \/ exists ge_signed_half_flat_construct_rowsrowentryvaluedecode. (((srt_value_flat_construct_rows) = 2 * ge_signed_half_flat_construct_rowsrowentryvaluedecode + 1 /\ (ge_balance_positive_flat_construct_rowsrowentryvalue) = 0) /\ (ge_balance_negative_flat_construct_rowsrowentryvalue) = S ge_signed_half_flat_construct_rowsrowentryvaluedecode))) /\ ((dst_positive_flat_construct_rowsrowentry) + ge_balance_negative_flat_construct_rowsrowentryvalue = (dst_negative_flat_construct_rowsrowentry) + ge_balance_positive_flat_construct_rowsrowentryvalue))))))))) /\ (exists srs_slice_flat_construct_rowsrowrow_sum. ((((exists dst_positive_code_flat_construct_rowsrowrow_sumslicesource_table dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_flat_construct_rowsrowrow_sumslicesource_table. (exists pvs_le_gap_flat_construct_rowsrowrow_sumslicesource_tabledomain. pvs_le_gap_flat_construct_rowsrowrow_sumslicesource_tabledomain + (dst_index_flat_construct_rowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_flat_construct_rowsrowrow_sumslicesource_table dst_negative_flat_construct_rowsrowrow_sumslicesource_table dst_value_flat_construct_rowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_flat_construct_rowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_flat_construct_rowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_flat_construct_rowsrowrow_sumslicesource_table) = S ((S (dst_index_flat_construct_rowsrowrow_sumslicesource_table)) * dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_flat_construct_rowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_flat_construct_rowsrowrow_sumslicesource_table = ff_q_pvs_flat_construct_rowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_flat_construct_rowsrowrow_sumslicesource_table)) * dst_positive_scale_flat_construct_rowsrowrow_sumslicesource_table) + (dst_positive_flat_construct_rowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_flat_construct_rowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_flat_construct_rowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_flat_construct_rowsrowrow_sumslicesource_table) = S ((S (dst_index_flat_construct_rowsrowrow_sumslicesource_table)) * dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_flat_construct_rowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_flat_construct_rowsrowrow_sumslicesource_table = ff_q_pvs_flat_construct_rowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_flat_construct_rowsrowrow_sumslicesource_table)) * dst_negative_scale_flat_construct_rowsrowrow_sumslicesource_table) + (dst_negative_flat_construct_rowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_flat_construct_rowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_flat_construct_rowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_flat_construct_rowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_flat_construct_rowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_flat_construct_rowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_flat_construct_rowsrowrow_sumslicesource_table) = 2 * ge_signed_half_flat_construct_rowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_construct_rowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_flat_construct_rowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_flat_construct_rowsrowrow_sumslicesource_table) + ge_balance_negative_flat_construct_rowsrowrow_sumslicesource_tableentryvalue = (dst_negative_flat_construct_rowsrowrow_sumslicesource_table) + ge_balance_positive_flat_construct_rowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_flat_construct_rowsrowrow_sumsliceoutput_table dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table. (((srs_slice_flat_construct_rowsrowrow_sum) = (((((dst_positive_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_flat_construct_rowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_flat_construct_rowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_flat_construct_rowsrowrow_sumsliceoutput_tabledomain + (dst_index_flat_construct_rowsrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_flat_construct_rowsrowrow_sumsliceoutput_table dst_negative_flat_construct_rowsrowrow_sumsliceoutput_table dst_value_flat_construct_rowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_flat_construct_rowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_flat_construct_rowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_flat_construct_rowsrowrow_sumsliceoutput_table) = S ((S (dst_index_flat_construct_rowsrowrow_sumsliceoutput_table)) * dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_flat_construct_rowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_flat_construct_rowsrowrow_sumsliceoutput_table = ff_q_pvs_flat_construct_rowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_flat_construct_rowsrowrow_sumsliceoutput_table)) * dst_positive_scale_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_positive_flat_construct_rowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_flat_construct_rowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_flat_construct_rowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_flat_construct_rowsrowrow_sumsliceoutput_table) = S ((S (dst_index_flat_construct_rowsrowrow_sumsliceoutput_table)) * dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_flat_construct_rowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_flat_construct_rowsrowrow_sumsliceoutput_table = ff_q_pvs_flat_construct_rowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_flat_construct_rowsrowrow_sumsliceoutput_table)) * dst_negative_scale_flat_construct_rowsrowrow_sumsliceoutput_table) + (dst_negative_flat_construct_rowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_flat_construct_rowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_flat_construct_rowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_flat_construct_rowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_flat_construct_rowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_flat_construct_rowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_flat_construct_rowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_flat_construct_rowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_construct_rowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_flat_construct_rowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_flat_construct_rowsrowrow_sumsliceoutput_table) + ge_balance_negative_flat_construct_rowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_flat_construct_rowsrowrow_sumsliceoutput_table) + ge_balance_positive_flat_construct_rowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_flat_construct_rowsrowrow_sumslice. (exists pvs_gap_flat_construct_rowsrowrow_sumslicebound. pvs_gap_flat_construct_rowsrowrow_sumslicebound + S (srs_index_flat_construct_rowsrowrow_sumslice) = (n)) -> exists srs_value_flat_construct_rowsrowrow_sumslice. (((exists dst_positive_code_flat_construct_rowsrowrow_sumsliceentrysource dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource dst_positive_flat_construct_rowsrowrow_sumsliceentrysource dst_negative_flat_construct_rowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_flat_construct_rowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_flat_construct_rowsrowrow_sumsliceentrysourcepositive + S (dst_positive_flat_construct_rowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((n) * (srt_index_flat_construct_rows)))) + ((1) * (srs_index_flat_construct_rowsrowrow_sumslice))))) * dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_flat_construct_rowsrowrow_sumsliceentrysourcepositive. dst_positive_code_flat_construct_rowsrowrow_sumsliceentrysource = ff_q_pvs_flat_construct_rowsrowrow_sumsliceentrysourcepositive * S ((S (((((0) + ((n) * (srt_index_flat_construct_rows)))) + ((1) * (srs_index_flat_construct_rowsrowrow_sumslice))))) * dst_positive_scale_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_positive_flat_construct_rowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_flat_construct_rowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_flat_construct_rowsrowrow_sumsliceentrysourcenegative + S (dst_negative_flat_construct_rowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((n) * (srt_index_flat_construct_rows)))) + ((1) * (srs_index_flat_construct_rowsrowrow_sumslice))))) * dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_flat_construct_rowsrowrow_sumsliceentrysourcenegative. dst_negative_code_flat_construct_rowsrowrow_sumsliceentrysource = ff_q_pvs_flat_construct_rowsrowrow_sumsliceentrysourcenegative * S ((S (((((0) + ((n) * (srt_index_flat_construct_rows)))) + ((1) * (srs_index_flat_construct_rowsrowrow_sumslice))))) * dst_negative_scale_flat_construct_rowsrowrow_sumsliceentrysource) + (dst_negative_flat_construct_rowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_flat_construct_rowsrowrow_sumsliceentrysourcevalue ge_balance_negative_flat_construct_rowsrowrow_sumsliceentrysourcevalue. (((((srs_value_flat_construct_rowsrowrow_sumslice) = 2 * (ge_balance_positive_flat_construct_rowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_flat_construct_rowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_flat_construct_rowsrowrow_sumslice) = 2 * ge_signed_half_flat_construct_rowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_flat_construct_rowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_flat_construct_rowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_flat_construct_rowsrowrow_sumsliceentrysource) + ge_balance_negative_flat_construct_rowsrowrow_sumsliceentrysourcevalue = (dst_negative_flat_construct_rowsrowrow_sumsliceentrysource) + ge_balance_positive_flat_construct_rowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_flat_construct_rowsrowrow_sumsliceentryoutput dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput dst_positive_flat_construct_rowsrowrow_sumsliceentryoutput dst_negative_flat_construct_rowsrowrow_sumsliceentryoutput. (((srs_slice_flat_construct_rowsrowrow_sum) = (((((dst_positive_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_flat_construct_rowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_flat_construct_rowsrowrow_sumsliceentryoutputpositive + S (dst_positive_flat_construct_rowsrowrow_sumsliceentryoutput) = S ((S (srs_index_flat_construct_rowsrowrow_sumslice)) * dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_flat_construct_rowsrowrow_sumsliceentryoutputpositive. dst_positive_code_flat_construct_rowsrowrow_sumsliceentryoutput = ff_q_pvs_flat_construct_rowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_flat_construct_rowsrowrow_sumslice)) * dst_positive_scale_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_positive_flat_construct_rowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_flat_construct_rowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_flat_construct_rowsrowrow_sumsliceentryoutputnegative + S (dst_negative_flat_construct_rowsrowrow_sumsliceentryoutput) = S ((S (srs_index_flat_construct_rowsrowrow_sumslice)) * dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_flat_construct_rowsrowrow_sumsliceentryoutputnegative. dst_negative_code_flat_construct_rowsrowrow_sumsliceentryoutput = ff_q_pvs_flat_construct_rowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_flat_construct_rowsrowrow_sumslice)) * dst_negative_scale_flat_construct_rowsrowrow_sumsliceentryoutput) + (dst_negative_flat_construct_rowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_flat_construct_rowsrowrow_sumsliceentryoutputvalue ge_balance_negative_flat_construct_rowsrowrow_sumsliceentryoutputvalue. (((((srs_value_flat_construct_rowsrowrow_sumslice) = 2 * (ge_balance_positive_flat_construct_rowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_flat_construct_rowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_flat_construct_rowsrowrow_sumslice) = 2 * ge_signed_half_flat_construct_rowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_flat_construct_rowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_flat_construct_rowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_flat_construct_rowsrowrow_sumsliceentryoutput) + ge_balance_negative_flat_construct_rowsrowrow_sumsliceentryoutputvalue = (dst_negative_flat_construct_rowsrowrow_sumsliceentryoutput) + ge_balance_positive_flat_construct_rowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_flat_construct_rowsrowrow_sumsum dst_positive_scale_flat_construct_rowsrowrow_sumsum dst_negative_code_flat_construct_rowsrowrow_sumsum dst_negative_scale_flat_construct_rowsrowrow_sumsum dst_positive_sum_flat_construct_rowsrowrow_sumsum dst_negative_sum_flat_construct_rowsrowrow_sumsum. (((srs_slice_flat_construct_rowsrowrow_sum) = (((((dst_positive_code_flat_construct_rowsrowrow_sumsum) + (dst_positive_scale_flat_construct_rowsrowrow_sumsum)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumsum) + (dst_positive_scale_flat_construct_rowsrowrow_sumsum)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumsum) + (dst_positive_scale_flat_construct_rowsrowrow_sumsum))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)))) * S ((((dst_positive_code_flat_construct_rowsrowrow_sumsum) + (dst_positive_scale_flat_construct_rowsrowrow_sumsum)) * S ((dst_positive_code_flat_construct_rowsrowrow_sumsum) + (dst_positive_scale_flat_construct_rowsrowrow_sumsum)) + ((dst_positive_scale_flat_construct_rowsrowrow_sumsum) + (dst_positive_scale_flat_construct_rowsrowrow_sumsum))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)))) + ((((dst_negative_code_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum))) + (((dst_negative_code_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)) * S ((dst_negative_code_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)) + ((dst_negative_scale_flat_construct_rowsrowrow_sumsum) + (dst_negative_scale_flat_construct_rowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_flat_construct_rowsrowrow_sumsumpositive fs_v_dst_flat_construct_rowsrowrow_sumsumpositive. ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_start. fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_construct_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_start. fs_u_dst_flat_construct_rowsrowrow_sumsumpositive = fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_flat_construct_rowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_terminal. fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_flat_construct_rowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_flat_construct_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_terminal. fs_u_dst_flat_construct_rowsrowrow_sumsumpositive = fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_flat_construct_rowsrowrow_sumsumpositive) + (dst_positive_sum_flat_construct_rowsrowrow_sumsum))) /\ forall fs_i_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps fs_r_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps fs_s_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_flat_construct_rowsrowrow_sumsum)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_flat_construct_rowsrowrow_sumsum = fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_flat_construct_rowsrowrow_sumsum) + (fs_a_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_construct_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_flat_construct_rowsrowrow_sumsumpositive = fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_construct_rowsrowrow_sumsumpositive) + (fs_r_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_construct_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_flat_construct_rowsrowrow_sumsumpositive = fs_q_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_flat_construct_rowsrowrow_sumsumpositive) + (fs_s_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps = fs_r_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps + fs_a_dst_flat_construct_rowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_construct_rowsrowrow_sumsumnegative fs_v_dst_flat_construct_rowsrowrow_sumsumnegative. ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_start. fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_construct_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_start. fs_u_dst_flat_construct_rowsrowrow_sumsumnegative = fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_flat_construct_rowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_terminal. fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_flat_construct_rowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_flat_construct_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_terminal. fs_u_dst_flat_construct_rowsrowrow_sumsumnegative = fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_flat_construct_rowsrowrow_sumsumnegative) + (dst_negative_sum_flat_construct_rowsrowrow_sumsum))) /\ forall fs_i_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps fs_r_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps fs_s_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_flat_construct_rowsrowrow_sumsum)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_flat_construct_rowsrowrow_sumsum = fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_flat_construct_rowsrowrow_sumsum) + (fs_a_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_construct_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_flat_construct_rowsrowrow_sumsumnegative = fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_construct_rowsrowrow_sumsumnegative) + (fs_r_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_construct_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_flat_construct_rowsrowrow_sumsumnegative = fs_q_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_flat_construct_rowsrowrow_sumsumnegative) + (fs_s_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps = fs_r_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps + fs_a_dst_flat_construct_rowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_construct_rowsrowrow_sumsumresult ge_balance_negative_flat_construct_rowsrowrow_sumsumresult. (((((srt_value_flat_construct_rows) = 2 * (ge_balance_positive_flat_construct_rowsrowrow_sumsumresult) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_flat_construct_rowsrowrow_sumsumresultdecode. (((srt_value_flat_construct_rows) = 2 * ge_signed_half_flat_construct_rowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_flat_construct_rowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_flat_construct_rowsrowrow_sumsumresult) = S ge_signed_half_flat_construct_rowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_flat_construct_rowsrowrow_sumsum) + ge_balance_negative_flat_construct_rowsrowrow_sumsumresult = (dst_negative_sum_flat_construct_rowsrowrow_sumsum) + ge_balance_positive_flat_construct_rowsrowrow_sumsumresult)))))))))))))))))) - 0016
specialize signed_rectangular_row_sums_exists (m) - 0017
specialize signed_rectangular_row_sums_exists (F) - 0018
specialize signed_rectangular_row_sums_exists (0) - 0019
specialize signed_rectangular_row_sums_exists (n) - 0020
specialize signed_rectangular_row_sums_exists (1) - 0021
specialize signed_rectangular_row_sums_exists (n) - 0022
apply signed_rectangular_row_sums_exists - 0023
exact hF - 0024
cases hr - 0025
have hv : exists v. (exists dst_positive_code_flat_construct_sum dst_positive_scale_flat_construct_sum dst_negative_code_flat_construct_sum dst_negative_scale_flat_construct_sum dst_positive_sum_flat_construct_sum dst_negative_sum_flat_construct_sum. (((x) = (((((dst_positive_code_flat_construct_sum) + (dst_positive_scale_flat_construct_sum)) * S ((dst_positive_code_flat_construct_sum) + (dst_positive_scale_flat_construct_sum)) + ((dst_positive_scale_flat_construct_sum) + (dst_positive_scale_flat_construct_sum))) + (((dst_negative_code_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)) * S ((dst_negative_code_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)) + ((dst_negative_scale_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)))) * S ((((dst_positive_code_flat_construct_sum) + (dst_positive_scale_flat_construct_sum)) * S ((dst_positive_code_flat_construct_sum) + (dst_positive_scale_flat_construct_sum)) + ((dst_positive_scale_flat_construct_sum) + (dst_positive_scale_flat_construct_sum))) + (((dst_negative_code_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)) * S ((dst_negative_code_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)) + ((dst_negative_scale_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)))) + ((((dst_negative_code_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)) * S ((dst_negative_code_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)) + ((dst_negative_scale_flat_construct_sum) + (dst_negative_scale_flat_construct_sum))) + (((dst_negative_code_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)) * S ((dst_negative_code_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)) + ((dst_negative_scale_flat_construct_sum) + (dst_negative_scale_flat_construct_sum)))))) /\ (((exists fs_u_dst_flat_construct_sumpositive fs_v_dst_flat_construct_sumpositive. ((((exists fs_h_dst_flat_construct_sumpositive_body_start. fs_h_dst_flat_construct_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_construct_sumpositive)) /\ exists fs_q_dst_flat_construct_sumpositive_body_start. fs_u_dst_flat_construct_sumpositive = fs_q_dst_flat_construct_sumpositive_body_start * S ((S (0)) * fs_v_dst_flat_construct_sumpositive) + (0))) /\ ((((exists fs_h_dst_flat_construct_sumpositive_body_terminal. fs_h_dst_flat_construct_sumpositive_body_terminal + S (dst_positive_sum_flat_construct_sum) = S ((S (m)) * fs_v_dst_flat_construct_sumpositive)) /\ exists fs_q_dst_flat_construct_sumpositive_body_terminal. fs_u_dst_flat_construct_sumpositive = fs_q_dst_flat_construct_sumpositive_body_terminal * S ((S (m)) * fs_v_dst_flat_construct_sumpositive) + (dst_positive_sum_flat_construct_sum))) /\ forall fs_i_dst_flat_construct_sumpositive_body_steps. (exists fs_lt_dst_flat_construct_sumpositive_body_steps_bound. fs_lt_dst_flat_construct_sumpositive_body_steps_bound + S fs_i_dst_flat_construct_sumpositive_body_steps = m) -> exists fs_a_dst_flat_construct_sumpositive_body_steps fs_r_dst_flat_construct_sumpositive_body_steps fs_s_dst_flat_construct_sumpositive_body_steps. ((((exists fs_h_dst_flat_construct_sumpositive_body_steps_summand. fs_h_dst_flat_construct_sumpositive_body_steps_summand + S (fs_a_dst_flat_construct_sumpositive_body_steps) = S ((S (fs_i_dst_flat_construct_sumpositive_body_steps)) * dst_positive_scale_flat_construct_sum)) /\ exists fs_q_dst_flat_construct_sumpositive_body_steps_summand. dst_positive_code_flat_construct_sum = fs_q_dst_flat_construct_sumpositive_body_steps_summand * S ((S (fs_i_dst_flat_construct_sumpositive_body_steps)) * dst_positive_scale_flat_construct_sum) + (fs_a_dst_flat_construct_sumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_construct_sumpositive_body_steps_partial. fs_h_dst_flat_construct_sumpositive_body_steps_partial + S (fs_r_dst_flat_construct_sumpositive_body_steps) = S ((S (fs_i_dst_flat_construct_sumpositive_body_steps)) * fs_v_dst_flat_construct_sumpositive)) /\ exists fs_q_dst_flat_construct_sumpositive_body_steps_partial. fs_u_dst_flat_construct_sumpositive = fs_q_dst_flat_construct_sumpositive_body_steps_partial * S ((S (fs_i_dst_flat_construct_sumpositive_body_steps)) * fs_v_dst_flat_construct_sumpositive) + (fs_r_dst_flat_construct_sumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_construct_sumpositive_body_steps_successor. fs_h_dst_flat_construct_sumpositive_body_steps_successor + S (fs_s_dst_flat_construct_sumpositive_body_steps) = S ((S (S fs_i_dst_flat_construct_sumpositive_body_steps)) * fs_v_dst_flat_construct_sumpositive)) /\ exists fs_q_dst_flat_construct_sumpositive_body_steps_successor. fs_u_dst_flat_construct_sumpositive = fs_q_dst_flat_construct_sumpositive_body_steps_successor * S ((S (S fs_i_dst_flat_construct_sumpositive_body_steps)) * fs_v_dst_flat_construct_sumpositive) + (fs_s_dst_flat_construct_sumpositive_body_steps))) /\ fs_s_dst_flat_construct_sumpositive_body_steps = fs_r_dst_flat_construct_sumpositive_body_steps + fs_a_dst_flat_construct_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_construct_sumnegative fs_v_dst_flat_construct_sumnegative. ((((exists fs_h_dst_flat_construct_sumnegative_body_start. fs_h_dst_flat_construct_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_construct_sumnegative)) /\ exists fs_q_dst_flat_construct_sumnegative_body_start. fs_u_dst_flat_construct_sumnegative = fs_q_dst_flat_construct_sumnegative_body_start * S ((S (0)) * fs_v_dst_flat_construct_sumnegative) + (0))) /\ ((((exists fs_h_dst_flat_construct_sumnegative_body_terminal. fs_h_dst_flat_construct_sumnegative_body_terminal + S (dst_negative_sum_flat_construct_sum) = S ((S (m)) * fs_v_dst_flat_construct_sumnegative)) /\ exists fs_q_dst_flat_construct_sumnegative_body_terminal. fs_u_dst_flat_construct_sumnegative = fs_q_dst_flat_construct_sumnegative_body_terminal * S ((S (m)) * fs_v_dst_flat_construct_sumnegative) + (dst_negative_sum_flat_construct_sum))) /\ forall fs_i_dst_flat_construct_sumnegative_body_steps. (exists fs_lt_dst_flat_construct_sumnegative_body_steps_bound. fs_lt_dst_flat_construct_sumnegative_body_steps_bound + S fs_i_dst_flat_construct_sumnegative_body_steps = m) -> exists fs_a_dst_flat_construct_sumnegative_body_steps fs_r_dst_flat_construct_sumnegative_body_steps fs_s_dst_flat_construct_sumnegative_body_steps. ((((exists fs_h_dst_flat_construct_sumnegative_body_steps_summand. fs_h_dst_flat_construct_sumnegative_body_steps_summand + S (fs_a_dst_flat_construct_sumnegative_body_steps) = S ((S (fs_i_dst_flat_construct_sumnegative_body_steps)) * dst_negative_scale_flat_construct_sum)) /\ exists fs_q_dst_flat_construct_sumnegative_body_steps_summand. dst_negative_code_flat_construct_sum = fs_q_dst_flat_construct_sumnegative_body_steps_summand * S ((S (fs_i_dst_flat_construct_sumnegative_body_steps)) * dst_negative_scale_flat_construct_sum) + (fs_a_dst_flat_construct_sumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_construct_sumnegative_body_steps_partial. fs_h_dst_flat_construct_sumnegative_body_steps_partial + S (fs_r_dst_flat_construct_sumnegative_body_steps) = S ((S (fs_i_dst_flat_construct_sumnegative_body_steps)) * fs_v_dst_flat_construct_sumnegative)) /\ exists fs_q_dst_flat_construct_sumnegative_body_steps_partial. fs_u_dst_flat_construct_sumnegative = fs_q_dst_flat_construct_sumnegative_body_steps_partial * S ((S (fs_i_dst_flat_construct_sumnegative_body_steps)) * fs_v_dst_flat_construct_sumnegative) + (fs_r_dst_flat_construct_sumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_construct_sumnegative_body_steps_successor. fs_h_dst_flat_construct_sumnegative_body_steps_successor + S (fs_s_dst_flat_construct_sumnegative_body_steps) = S ((S (S fs_i_dst_flat_construct_sumnegative_body_steps)) * fs_v_dst_flat_construct_sumnegative)) /\ exists fs_q_dst_flat_construct_sumnegative_body_steps_successor. fs_u_dst_flat_construct_sumnegative = fs_q_dst_flat_construct_sumnegative_body_steps_successor * S ((S (S fs_i_dst_flat_construct_sumnegative_body_steps)) * fs_v_dst_flat_construct_sumnegative) + (fs_s_dst_flat_construct_sumnegative_body_steps))) /\ fs_s_dst_flat_construct_sumnegative_body_steps = fs_r_dst_flat_construct_sumnegative_body_steps + fs_a_dst_flat_construct_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_construct_sumresult ge_balance_negative_flat_construct_sumresult. (((((v) = 2 * (ge_balance_positive_flat_construct_sumresult) /\ (ge_balance_negative_flat_construct_sumresult) = 0) \/ exists ge_signed_half_flat_construct_sumresultdecode. (((v) = 2 * ge_signed_half_flat_construct_sumresultdecode + 1 /\ (ge_balance_positive_flat_construct_sumresult) = 0) /\ (ge_balance_negative_flat_construct_sumresult) = S ge_signed_half_flat_construct_sumresultdecode))) /\ ((dst_positive_sum_flat_construct_sum) + ge_balance_negative_flat_construct_sumresult = (dst_negative_sum_flat_construct_sum) + ge_balance_positive_flat_construct_sumresult))))))))) - 0026
specialize arithmetic_signed_sum_exists (m) - 0027
specialize arithmetic_signed_sum_exists (x) - 0028
specialize arithmetic_signed_sum_exists (m) - 0029
apply arithmetic_signed_sum_exists - 0030
cases hr_witness - 0031
cases hr_witness_right - 0032
exact hr_witness_right_left - 0033
cases hv - 0034
have hflat : exists srs_slice_flat_construct_flat. ((((exists dst_positive_code_flat_construct_flatslicesource_table dst_positive_scale_flat_construct_flatslicesource_table dst_negative_code_flat_construct_flatslicesource_table dst_negative_scale_flat_construct_flatslicesource_table. (((F) = (((((dst_positive_code_flat_construct_flatslicesource_table) + (dst_positive_scale_flat_construct_flatslicesource_table)) * S ((dst_positive_code_flat_construct_flatslicesource_table) + (dst_positive_scale_flat_construct_flatslicesource_table)) + ((dst_positive_scale_flat_construct_flatslicesource_table) + (dst_positive_scale_flat_construct_flatslicesource_table))) + (((dst_negative_code_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)) * S ((dst_negative_code_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)) + ((dst_negative_scale_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)))) * S ((((dst_positive_code_flat_construct_flatslicesource_table) + (dst_positive_scale_flat_construct_flatslicesource_table)) * S ((dst_positive_code_flat_construct_flatslicesource_table) + (dst_positive_scale_flat_construct_flatslicesource_table)) + ((dst_positive_scale_flat_construct_flatslicesource_table) + (dst_positive_scale_flat_construct_flatslicesource_table))) + (((dst_negative_code_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)) * S ((dst_negative_code_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)) + ((dst_negative_scale_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)))) + ((((dst_negative_code_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)) * S ((dst_negative_code_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)) + ((dst_negative_scale_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table))) + (((dst_negative_code_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)) * S ((dst_negative_code_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)) + ((dst_negative_scale_flat_construct_flatslicesource_table) + (dst_negative_scale_flat_construct_flatslicesource_table)))))) /\ (forall dst_index_flat_construct_flatslicesource_table. (exists pvs_le_gap_flat_construct_flatslicesource_tabledomain. pvs_le_gap_flat_construct_flatslicesource_tabledomain + (dst_index_flat_construct_flatslicesource_table) = (0)) -> exists dst_positive_flat_construct_flatslicesource_table dst_negative_flat_construct_flatslicesource_table dst_value_flat_construct_flatslicesource_table. ((((exists ff_h_pvs_flat_construct_flatslicesource_tableentrypositive. ff_h_pvs_flat_construct_flatslicesource_tableentrypositive + S (dst_positive_flat_construct_flatslicesource_table) = S ((S (dst_index_flat_construct_flatslicesource_table)) * dst_positive_scale_flat_construct_flatslicesource_table)) /\ exists ff_q_pvs_flat_construct_flatslicesource_tableentrypositive. dst_positive_code_flat_construct_flatslicesource_table = ff_q_pvs_flat_construct_flatslicesource_tableentrypositive * S ((S (dst_index_flat_construct_flatslicesource_table)) * dst_positive_scale_flat_construct_flatslicesource_table) + (dst_positive_flat_construct_flatslicesource_table))) /\ (((((exists ff_h_pvs_flat_construct_flatslicesource_tableentrynegative. ff_h_pvs_flat_construct_flatslicesource_tableentrynegative + S (dst_negative_flat_construct_flatslicesource_table) = S ((S (dst_index_flat_construct_flatslicesource_table)) * dst_negative_scale_flat_construct_flatslicesource_table)) /\ exists ff_q_pvs_flat_construct_flatslicesource_tableentrynegative. dst_negative_code_flat_construct_flatslicesource_table = ff_q_pvs_flat_construct_flatslicesource_tableentrynegative * S ((S (dst_index_flat_construct_flatslicesource_table)) * dst_negative_scale_flat_construct_flatslicesource_table) + (dst_negative_flat_construct_flatslicesource_table))) /\ (exists ge_balance_positive_flat_construct_flatslicesource_tableentryvalue ge_balance_negative_flat_construct_flatslicesource_tableentryvalue. (((((dst_value_flat_construct_flatslicesource_table) = 2 * (ge_balance_positive_flat_construct_flatslicesource_tableentryvalue) /\ (ge_balance_negative_flat_construct_flatslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_flat_construct_flatslicesource_tableentryvaluedecode. (((dst_value_flat_construct_flatslicesource_table) = 2 * ge_signed_half_flat_construct_flatslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_construct_flatslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_flat_construct_flatslicesource_tableentryvalue) = S ge_signed_half_flat_construct_flatslicesource_tableentryvaluedecode))) /\ ((dst_positive_flat_construct_flatslicesource_table) + ge_balance_negative_flat_construct_flatslicesource_tableentryvalue = (dst_negative_flat_construct_flatslicesource_table) + ge_balance_positive_flat_construct_flatslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_flat_construct_flatsliceoutput_table dst_positive_scale_flat_construct_flatsliceoutput_table dst_negative_code_flat_construct_flatsliceoutput_table dst_negative_scale_flat_construct_flatsliceoutput_table. (((srs_slice_flat_construct_flat) = (((((dst_positive_code_flat_construct_flatsliceoutput_table) + (dst_positive_scale_flat_construct_flatsliceoutput_table)) * S ((dst_positive_code_flat_construct_flatsliceoutput_table) + (dst_positive_scale_flat_construct_flatsliceoutput_table)) + ((dst_positive_scale_flat_construct_flatsliceoutput_table) + (dst_positive_scale_flat_construct_flatsliceoutput_table))) + (((dst_negative_code_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)) * S ((dst_negative_code_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)) + ((dst_negative_scale_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)))) * S ((((dst_positive_code_flat_construct_flatsliceoutput_table) + (dst_positive_scale_flat_construct_flatsliceoutput_table)) * S ((dst_positive_code_flat_construct_flatsliceoutput_table) + (dst_positive_scale_flat_construct_flatsliceoutput_table)) + ((dst_positive_scale_flat_construct_flatsliceoutput_table) + (dst_positive_scale_flat_construct_flatsliceoutput_table))) + (((dst_negative_code_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)) * S ((dst_negative_code_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)) + ((dst_negative_scale_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)))) + ((((dst_negative_code_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)) * S ((dst_negative_code_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)) + ((dst_negative_scale_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table))) + (((dst_negative_code_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)) * S ((dst_negative_code_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)) + ((dst_negative_scale_flat_construct_flatsliceoutput_table) + (dst_negative_scale_flat_construct_flatsliceoutput_table)))))) /\ (forall dst_index_flat_construct_flatsliceoutput_table. (exists pvs_le_gap_flat_construct_flatsliceoutput_tabledomain. pvs_le_gap_flat_construct_flatsliceoutput_tabledomain + (dst_index_flat_construct_flatsliceoutput_table) = (m*n)) -> exists dst_positive_flat_construct_flatsliceoutput_table dst_negative_flat_construct_flatsliceoutput_table dst_value_flat_construct_flatsliceoutput_table. ((((exists ff_h_pvs_flat_construct_flatsliceoutput_tableentrypositive. ff_h_pvs_flat_construct_flatsliceoutput_tableentrypositive + S (dst_positive_flat_construct_flatsliceoutput_table) = S ((S (dst_index_flat_construct_flatsliceoutput_table)) * dst_positive_scale_flat_construct_flatsliceoutput_table)) /\ exists ff_q_pvs_flat_construct_flatsliceoutput_tableentrypositive. dst_positive_code_flat_construct_flatsliceoutput_table = ff_q_pvs_flat_construct_flatsliceoutput_tableentrypositive * S ((S (dst_index_flat_construct_flatsliceoutput_table)) * dst_positive_scale_flat_construct_flatsliceoutput_table) + (dst_positive_flat_construct_flatsliceoutput_table))) /\ (((((exists ff_h_pvs_flat_construct_flatsliceoutput_tableentrynegative. ff_h_pvs_flat_construct_flatsliceoutput_tableentrynegative + S (dst_negative_flat_construct_flatsliceoutput_table) = S ((S (dst_index_flat_construct_flatsliceoutput_table)) * dst_negative_scale_flat_construct_flatsliceoutput_table)) /\ exists ff_q_pvs_flat_construct_flatsliceoutput_tableentrynegative. dst_negative_code_flat_construct_flatsliceoutput_table = ff_q_pvs_flat_construct_flatsliceoutput_tableentrynegative * S ((S (dst_index_flat_construct_flatsliceoutput_table)) * dst_negative_scale_flat_construct_flatsliceoutput_table) + (dst_negative_flat_construct_flatsliceoutput_table))) /\ (exists ge_balance_positive_flat_construct_flatsliceoutput_tableentryvalue ge_balance_negative_flat_construct_flatsliceoutput_tableentryvalue. (((((dst_value_flat_construct_flatsliceoutput_table) = 2 * (ge_balance_positive_flat_construct_flatsliceoutput_tableentryvalue) /\ (ge_balance_negative_flat_construct_flatsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_flat_construct_flatsliceoutput_tableentryvaluedecode. (((dst_value_flat_construct_flatsliceoutput_table) = 2 * ge_signed_half_flat_construct_flatsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_flat_construct_flatsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_flat_construct_flatsliceoutput_tableentryvalue) = S ge_signed_half_flat_construct_flatsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_flat_construct_flatsliceoutput_table) + ge_balance_negative_flat_construct_flatsliceoutput_tableentryvalue = (dst_negative_flat_construct_flatsliceoutput_table) + ge_balance_positive_flat_construct_flatsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_flat_construct_flatslice. (exists pvs_gap_flat_construct_flatslicebound. pvs_gap_flat_construct_flatslicebound + S (srs_index_flat_construct_flatslice) = (m*n)) -> exists srs_value_flat_construct_flatslice. (((exists dst_positive_code_flat_construct_flatsliceentrysource dst_positive_scale_flat_construct_flatsliceentrysource dst_negative_code_flat_construct_flatsliceentrysource dst_negative_scale_flat_construct_flatsliceentrysource dst_positive_flat_construct_flatsliceentrysource dst_negative_flat_construct_flatsliceentrysource. (((F) = (((((dst_positive_code_flat_construct_flatsliceentrysource) + (dst_positive_scale_flat_construct_flatsliceentrysource)) * S ((dst_positive_code_flat_construct_flatsliceentrysource) + (dst_positive_scale_flat_construct_flatsliceentrysource)) + ((dst_positive_scale_flat_construct_flatsliceentrysource) + (dst_positive_scale_flat_construct_flatsliceentrysource))) + (((dst_negative_code_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)) * S ((dst_negative_code_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)) + ((dst_negative_scale_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)))) * S ((((dst_positive_code_flat_construct_flatsliceentrysource) + (dst_positive_scale_flat_construct_flatsliceentrysource)) * S ((dst_positive_code_flat_construct_flatsliceentrysource) + (dst_positive_scale_flat_construct_flatsliceentrysource)) + ((dst_positive_scale_flat_construct_flatsliceentrysource) + (dst_positive_scale_flat_construct_flatsliceentrysource))) + (((dst_negative_code_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)) * S ((dst_negative_code_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)) + ((dst_negative_scale_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)))) + ((((dst_negative_code_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)) * S ((dst_negative_code_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)) + ((dst_negative_scale_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource))) + (((dst_negative_code_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)) * S ((dst_negative_code_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)) + ((dst_negative_scale_flat_construct_flatsliceentrysource) + (dst_negative_scale_flat_construct_flatsliceentrysource)))))) /\ (((((exists ff_h_pvs_flat_construct_flatsliceentrysourcepositive. ff_h_pvs_flat_construct_flatsliceentrysourcepositive + S (dst_positive_flat_construct_flatsliceentrysource) = S ((S (((0) + ((1) * (srs_index_flat_construct_flatslice))))) * dst_positive_scale_flat_construct_flatsliceentrysource)) /\ exists ff_q_pvs_flat_construct_flatsliceentrysourcepositive. dst_positive_code_flat_construct_flatsliceentrysource = ff_q_pvs_flat_construct_flatsliceentrysourcepositive * S ((S (((0) + ((1) * (srs_index_flat_construct_flatslice))))) * dst_positive_scale_flat_construct_flatsliceentrysource) + (dst_positive_flat_construct_flatsliceentrysource))) /\ (((((exists ff_h_pvs_flat_construct_flatsliceentrysourcenegative. ff_h_pvs_flat_construct_flatsliceentrysourcenegative + S (dst_negative_flat_construct_flatsliceentrysource) = S ((S (((0) + ((1) * (srs_index_flat_construct_flatslice))))) * dst_negative_scale_flat_construct_flatsliceentrysource)) /\ exists ff_q_pvs_flat_construct_flatsliceentrysourcenegative. dst_negative_code_flat_construct_flatsliceentrysource = ff_q_pvs_flat_construct_flatsliceentrysourcenegative * S ((S (((0) + ((1) * (srs_index_flat_construct_flatslice))))) * dst_negative_scale_flat_construct_flatsliceentrysource) + (dst_negative_flat_construct_flatsliceentrysource))) /\ (exists ge_balance_positive_flat_construct_flatsliceentrysourcevalue ge_balance_negative_flat_construct_flatsliceentrysourcevalue. (((((srs_value_flat_construct_flatslice) = 2 * (ge_balance_positive_flat_construct_flatsliceentrysourcevalue) /\ (ge_balance_negative_flat_construct_flatsliceentrysourcevalue) = 0) \/ exists ge_signed_half_flat_construct_flatsliceentrysourcevaluedecode. (((srs_value_flat_construct_flatslice) = 2 * ge_signed_half_flat_construct_flatsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_flat_construct_flatsliceentrysourcevalue) = 0) /\ (ge_balance_negative_flat_construct_flatsliceentrysourcevalue) = S ge_signed_half_flat_construct_flatsliceentrysourcevaluedecode))) /\ ((dst_positive_flat_construct_flatsliceentrysource) + ge_balance_negative_flat_construct_flatsliceentrysourcevalue = (dst_negative_flat_construct_flatsliceentrysource) + ge_balance_positive_flat_construct_flatsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_flat_construct_flatsliceentryoutput dst_positive_scale_flat_construct_flatsliceentryoutput dst_negative_code_flat_construct_flatsliceentryoutput dst_negative_scale_flat_construct_flatsliceentryoutput dst_positive_flat_construct_flatsliceentryoutput dst_negative_flat_construct_flatsliceentryoutput. (((srs_slice_flat_construct_flat) = (((((dst_positive_code_flat_construct_flatsliceentryoutput) + (dst_positive_scale_flat_construct_flatsliceentryoutput)) * S ((dst_positive_code_flat_construct_flatsliceentryoutput) + (dst_positive_scale_flat_construct_flatsliceentryoutput)) + ((dst_positive_scale_flat_construct_flatsliceentryoutput) + (dst_positive_scale_flat_construct_flatsliceentryoutput))) + (((dst_negative_code_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)) * S ((dst_negative_code_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)) + ((dst_negative_scale_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)))) * S ((((dst_positive_code_flat_construct_flatsliceentryoutput) + (dst_positive_scale_flat_construct_flatsliceentryoutput)) * S ((dst_positive_code_flat_construct_flatsliceentryoutput) + (dst_positive_scale_flat_construct_flatsliceentryoutput)) + ((dst_positive_scale_flat_construct_flatsliceentryoutput) + (dst_positive_scale_flat_construct_flatsliceentryoutput))) + (((dst_negative_code_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)) * S ((dst_negative_code_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)) + ((dst_negative_scale_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)))) + ((((dst_negative_code_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)) * S ((dst_negative_code_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)) + ((dst_negative_scale_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput))) + (((dst_negative_code_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)) * S ((dst_negative_code_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)) + ((dst_negative_scale_flat_construct_flatsliceentryoutput) + (dst_negative_scale_flat_construct_flatsliceentryoutput)))))) /\ (((((exists ff_h_pvs_flat_construct_flatsliceentryoutputpositive. ff_h_pvs_flat_construct_flatsliceentryoutputpositive + S (dst_positive_flat_construct_flatsliceentryoutput) = S ((S (srs_index_flat_construct_flatslice)) * dst_positive_scale_flat_construct_flatsliceentryoutput)) /\ exists ff_q_pvs_flat_construct_flatsliceentryoutputpositive. dst_positive_code_flat_construct_flatsliceentryoutput = ff_q_pvs_flat_construct_flatsliceentryoutputpositive * S ((S (srs_index_flat_construct_flatslice)) * dst_positive_scale_flat_construct_flatsliceentryoutput) + (dst_positive_flat_construct_flatsliceentryoutput))) /\ (((((exists ff_h_pvs_flat_construct_flatsliceentryoutputnegative. ff_h_pvs_flat_construct_flatsliceentryoutputnegative + S (dst_negative_flat_construct_flatsliceentryoutput) = S ((S (srs_index_flat_construct_flatslice)) * dst_negative_scale_flat_construct_flatsliceentryoutput)) /\ exists ff_q_pvs_flat_construct_flatsliceentryoutputnegative. dst_negative_code_flat_construct_flatsliceentryoutput = ff_q_pvs_flat_construct_flatsliceentryoutputnegative * S ((S (srs_index_flat_construct_flatslice)) * dst_negative_scale_flat_construct_flatsliceentryoutput) + (dst_negative_flat_construct_flatsliceentryoutput))) /\ (exists ge_balance_positive_flat_construct_flatsliceentryoutputvalue ge_balance_negative_flat_construct_flatsliceentryoutputvalue. (((((srs_value_flat_construct_flatslice) = 2 * (ge_balance_positive_flat_construct_flatsliceentryoutputvalue) /\ (ge_balance_negative_flat_construct_flatsliceentryoutputvalue) = 0) \/ exists ge_signed_half_flat_construct_flatsliceentryoutputvaluedecode. (((srs_value_flat_construct_flatslice) = 2 * ge_signed_half_flat_construct_flatsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_flat_construct_flatsliceentryoutputvalue) = 0) /\ (ge_balance_negative_flat_construct_flatsliceentryoutputvalue) = S ge_signed_half_flat_construct_flatsliceentryoutputvaluedecode))) /\ ((dst_positive_flat_construct_flatsliceentryoutput) + ge_balance_negative_flat_construct_flatsliceentryoutputvalue = (dst_negative_flat_construct_flatsliceentryoutput) + ge_balance_positive_flat_construct_flatsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_flat_construct_flatsum dst_positive_scale_flat_construct_flatsum dst_negative_code_flat_construct_flatsum dst_negative_scale_flat_construct_flatsum dst_positive_sum_flat_construct_flatsum dst_negative_sum_flat_construct_flatsum. (((srs_slice_flat_construct_flat) = (((((dst_positive_code_flat_construct_flatsum) + (dst_positive_scale_flat_construct_flatsum)) * S ((dst_positive_code_flat_construct_flatsum) + (dst_positive_scale_flat_construct_flatsum)) + ((dst_positive_scale_flat_construct_flatsum) + (dst_positive_scale_flat_construct_flatsum))) + (((dst_negative_code_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)) * S ((dst_negative_code_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)) + ((dst_negative_scale_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)))) * S ((((dst_positive_code_flat_construct_flatsum) + (dst_positive_scale_flat_construct_flatsum)) * S ((dst_positive_code_flat_construct_flatsum) + (dst_positive_scale_flat_construct_flatsum)) + ((dst_positive_scale_flat_construct_flatsum) + (dst_positive_scale_flat_construct_flatsum))) + (((dst_negative_code_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)) * S ((dst_negative_code_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)) + ((dst_negative_scale_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)))) + ((((dst_negative_code_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)) * S ((dst_negative_code_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)) + ((dst_negative_scale_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum))) + (((dst_negative_code_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)) * S ((dst_negative_code_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)) + ((dst_negative_scale_flat_construct_flatsum) + (dst_negative_scale_flat_construct_flatsum)))))) /\ (((exists fs_u_dst_flat_construct_flatsumpositive fs_v_dst_flat_construct_flatsumpositive. ((((exists fs_h_dst_flat_construct_flatsumpositive_body_start. fs_h_dst_flat_construct_flatsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_construct_flatsumpositive)) /\ exists fs_q_dst_flat_construct_flatsumpositive_body_start. fs_u_dst_flat_construct_flatsumpositive = fs_q_dst_flat_construct_flatsumpositive_body_start * S ((S (0)) * fs_v_dst_flat_construct_flatsumpositive) + (0))) /\ ((((exists fs_h_dst_flat_construct_flatsumpositive_body_terminal. fs_h_dst_flat_construct_flatsumpositive_body_terminal + S (dst_positive_sum_flat_construct_flatsum) = S ((S (m*n)) * fs_v_dst_flat_construct_flatsumpositive)) /\ exists fs_q_dst_flat_construct_flatsumpositive_body_terminal. fs_u_dst_flat_construct_flatsumpositive = fs_q_dst_flat_construct_flatsumpositive_body_terminal * S ((S (m*n)) * fs_v_dst_flat_construct_flatsumpositive) + (dst_positive_sum_flat_construct_flatsum))) /\ forall fs_i_dst_flat_construct_flatsumpositive_body_steps. (exists fs_lt_dst_flat_construct_flatsumpositive_body_steps_bound. fs_lt_dst_flat_construct_flatsumpositive_body_steps_bound + S fs_i_dst_flat_construct_flatsumpositive_body_steps = m*n) -> exists fs_a_dst_flat_construct_flatsumpositive_body_steps fs_r_dst_flat_construct_flatsumpositive_body_steps fs_s_dst_flat_construct_flatsumpositive_body_steps. ((((exists fs_h_dst_flat_construct_flatsumpositive_body_steps_summand. fs_h_dst_flat_construct_flatsumpositive_body_steps_summand + S (fs_a_dst_flat_construct_flatsumpositive_body_steps) = S ((S (fs_i_dst_flat_construct_flatsumpositive_body_steps)) * dst_positive_scale_flat_construct_flatsum)) /\ exists fs_q_dst_flat_construct_flatsumpositive_body_steps_summand. dst_positive_code_flat_construct_flatsum = fs_q_dst_flat_construct_flatsumpositive_body_steps_summand * S ((S (fs_i_dst_flat_construct_flatsumpositive_body_steps)) * dst_positive_scale_flat_construct_flatsum) + (fs_a_dst_flat_construct_flatsumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_construct_flatsumpositive_body_steps_partial. fs_h_dst_flat_construct_flatsumpositive_body_steps_partial + S (fs_r_dst_flat_construct_flatsumpositive_body_steps) = S ((S (fs_i_dst_flat_construct_flatsumpositive_body_steps)) * fs_v_dst_flat_construct_flatsumpositive)) /\ exists fs_q_dst_flat_construct_flatsumpositive_body_steps_partial. fs_u_dst_flat_construct_flatsumpositive = fs_q_dst_flat_construct_flatsumpositive_body_steps_partial * S ((S (fs_i_dst_flat_construct_flatsumpositive_body_steps)) * fs_v_dst_flat_construct_flatsumpositive) + (fs_r_dst_flat_construct_flatsumpositive_body_steps))) /\ ((((exists fs_h_dst_flat_construct_flatsumpositive_body_steps_successor. fs_h_dst_flat_construct_flatsumpositive_body_steps_successor + S (fs_s_dst_flat_construct_flatsumpositive_body_steps) = S ((S (S fs_i_dst_flat_construct_flatsumpositive_body_steps)) * fs_v_dst_flat_construct_flatsumpositive)) /\ exists fs_q_dst_flat_construct_flatsumpositive_body_steps_successor. fs_u_dst_flat_construct_flatsumpositive = fs_q_dst_flat_construct_flatsumpositive_body_steps_successor * S ((S (S fs_i_dst_flat_construct_flatsumpositive_body_steps)) * fs_v_dst_flat_construct_flatsumpositive) + (fs_s_dst_flat_construct_flatsumpositive_body_steps))) /\ fs_s_dst_flat_construct_flatsumpositive_body_steps = fs_r_dst_flat_construct_flatsumpositive_body_steps + fs_a_dst_flat_construct_flatsumpositive_body_steps)))))) /\ (((exists fs_u_dst_flat_construct_flatsumnegative fs_v_dst_flat_construct_flatsumnegative. ((((exists fs_h_dst_flat_construct_flatsumnegative_body_start. fs_h_dst_flat_construct_flatsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_flat_construct_flatsumnegative)) /\ exists fs_q_dst_flat_construct_flatsumnegative_body_start. fs_u_dst_flat_construct_flatsumnegative = fs_q_dst_flat_construct_flatsumnegative_body_start * S ((S (0)) * fs_v_dst_flat_construct_flatsumnegative) + (0))) /\ ((((exists fs_h_dst_flat_construct_flatsumnegative_body_terminal. fs_h_dst_flat_construct_flatsumnegative_body_terminal + S (dst_negative_sum_flat_construct_flatsum) = S ((S (m*n)) * fs_v_dst_flat_construct_flatsumnegative)) /\ exists fs_q_dst_flat_construct_flatsumnegative_body_terminal. fs_u_dst_flat_construct_flatsumnegative = fs_q_dst_flat_construct_flatsumnegative_body_terminal * S ((S (m*n)) * fs_v_dst_flat_construct_flatsumnegative) + (dst_negative_sum_flat_construct_flatsum))) /\ forall fs_i_dst_flat_construct_flatsumnegative_body_steps. (exists fs_lt_dst_flat_construct_flatsumnegative_body_steps_bound. fs_lt_dst_flat_construct_flatsumnegative_body_steps_bound + S fs_i_dst_flat_construct_flatsumnegative_body_steps = m*n) -> exists fs_a_dst_flat_construct_flatsumnegative_body_steps fs_r_dst_flat_construct_flatsumnegative_body_steps fs_s_dst_flat_construct_flatsumnegative_body_steps. ((((exists fs_h_dst_flat_construct_flatsumnegative_body_steps_summand. fs_h_dst_flat_construct_flatsumnegative_body_steps_summand + S (fs_a_dst_flat_construct_flatsumnegative_body_steps) = S ((S (fs_i_dst_flat_construct_flatsumnegative_body_steps)) * dst_negative_scale_flat_construct_flatsum)) /\ exists fs_q_dst_flat_construct_flatsumnegative_body_steps_summand. dst_negative_code_flat_construct_flatsum = fs_q_dst_flat_construct_flatsumnegative_body_steps_summand * S ((S (fs_i_dst_flat_construct_flatsumnegative_body_steps)) * dst_negative_scale_flat_construct_flatsum) + (fs_a_dst_flat_construct_flatsumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_construct_flatsumnegative_body_steps_partial. fs_h_dst_flat_construct_flatsumnegative_body_steps_partial + S (fs_r_dst_flat_construct_flatsumnegative_body_steps) = S ((S (fs_i_dst_flat_construct_flatsumnegative_body_steps)) * fs_v_dst_flat_construct_flatsumnegative)) /\ exists fs_q_dst_flat_construct_flatsumnegative_body_steps_partial. fs_u_dst_flat_construct_flatsumnegative = fs_q_dst_flat_construct_flatsumnegative_body_steps_partial * S ((S (fs_i_dst_flat_construct_flatsumnegative_body_steps)) * fs_v_dst_flat_construct_flatsumnegative) + (fs_r_dst_flat_construct_flatsumnegative_body_steps))) /\ ((((exists fs_h_dst_flat_construct_flatsumnegative_body_steps_successor. fs_h_dst_flat_construct_flatsumnegative_body_steps_successor + S (fs_s_dst_flat_construct_flatsumnegative_body_steps) = S ((S (S fs_i_dst_flat_construct_flatsumnegative_body_steps)) * fs_v_dst_flat_construct_flatsumnegative)) /\ exists fs_q_dst_flat_construct_flatsumnegative_body_steps_successor. fs_u_dst_flat_construct_flatsumnegative = fs_q_dst_flat_construct_flatsumnegative_body_steps_successor * S ((S (S fs_i_dst_flat_construct_flatsumnegative_body_steps)) * fs_v_dst_flat_construct_flatsumnegative) + (fs_s_dst_flat_construct_flatsumnegative_body_steps))) /\ fs_s_dst_flat_construct_flatsumnegative_body_steps = fs_r_dst_flat_construct_flatsumnegative_body_steps + fs_a_dst_flat_construct_flatsumnegative_body_steps)))))) /\ (exists ge_balance_positive_flat_construct_flatsumresult ge_balance_negative_flat_construct_flatsumresult. (((((x1) = 2 * (ge_balance_positive_flat_construct_flatsumresult) /\ (ge_balance_negative_flat_construct_flatsumresult) = 0) \/ exists ge_signed_half_flat_construct_flatsumresultdecode. (((x1) = 2 * ge_signed_half_flat_construct_flatsumresultdecode + 1 /\ (ge_balance_positive_flat_construct_flatsumresult) = 0) /\ (ge_balance_negative_flat_construct_flatsumresult) = S ge_signed_half_flat_construct_flatsumresultdecode))) /\ ((dst_positive_sum_flat_construct_flatsum) + ge_balance_negative_flat_construct_flatsumresult = (dst_negative_sum_flat_construct_flatsum) + ge_balance_positive_flat_construct_flatsumresult)))))))))) - 0035
specialize signed_row_sums_flatten (m) - 0036
specialize signed_row_sums_flatten (F) - 0037
specialize signed_row_sums_flatten (x) - 0038
specialize signed_row_sums_flatten (n) - 0039
specialize signed_row_sums_flatten (x1) - 0040
apply signed_row_sums_flatten - 0041
exact hr_witness - 0042
exact hv_witness - 0043
have heq : x1=z - 0044
specialize signed_rectangular_slice_sum_functional (F) - 0045
specialize signed_rectangular_slice_sum_functional (0) - 0046
specialize signed_rectangular_slice_sum_functional (1) - 0047
specialize signed_rectangular_slice_sum_functional (m*n) - 0048
specialize signed_rectangular_slice_sum_functional (x1) - 0049
specialize signed_rectangular_slice_sum_functional (z) - 0050
apply signed_rectangular_slice_sum_functional - 0051
exact hflat - 0052
apply hi_right - 0053
exact hs - 0054
rewrite heq at hv_witness - 0055
rewrite heq at hv_witness - 0056
exists x - 0057
split - 0058
exact hr_witness - 0059
exact hv_witness - 0060
intro hr - 0061
cases hr - 0062
cases hr_witness - 0063
apply hi_left - 0064
specialize signed_row_sums_flatten (m) - 0065
specialize signed_row_sums_flatten (F) - 0066
specialize signed_row_sums_flatten (x) - 0067
specialize signed_row_sums_flatten (n) - 0068
specialize signed_row_sums_flatten (z) - 0069
apply signed_row_sums_flatten - 0070
exact hr_witness_left - 0071
exact hr_witness_right