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 l F G. (exists dst_positive_code_multiply_exists_unique_input0 dst_positive_scale_multiply_exists_unique_input0 dst_negative_code_multiply_exists_unique_input0 dst_negative_scale_multiply_exists_unique_input0. (((F) = (((((dst_positive_code_multiply_exists_unique_input0) + (dst_positive_scale_multiply_exists_unique_input0)) * S ((dst_positive_code_multiply_exists_unique_input0) + (dst_positive_scale_multiply_exists_unique_input0)) + ((dst_positive_scale_multiply_exists_unique_input0) + (dst_positive_scale_multiply_exists_unique_input0))) + (((dst_negative_code_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)) * S ((dst_negative_code_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)) + ((dst_negative_scale_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)))) * S ((((dst_positive_code_multiply_exists_unique_input0) + (dst_positive_scale_multiply_exists_unique_input0)) * S ((dst_positive_code_multiply_exists_unique_input0) + (dst_positive_scale_multiply_exists_unique_input0)) + ((dst_positive_scale_multiply_exists_unique_input0) + (dst_positive_scale_multiply_exists_unique_input0))) + (((dst_negative_code_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)) * S ((dst_negative_code_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)) + ((dst_negative_scale_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)))) + ((((dst_negative_code_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)) * S ((dst_negative_code_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)) + ((dst_negative_scale_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0))) + (((dst_negative_code_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)) * S ((dst_negative_code_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)) + ((dst_negative_scale_multiply_exists_unique_input0) + (dst_negative_scale_multiply_exists_unique_input0)))))) /\ (forall dst_index_multiply_exists_unique_input0. (exists pvs_le_gap_multiply_exists_unique_input0domain. pvs_le_gap_multiply_exists_unique_input0domain + (dst_index_multiply_exists_unique_input0) = (l)) -> exists dst_positive_multiply_exists_unique_input0 dst_negative_multiply_exists_unique_input0 dst_value_multiply_exists_unique_input0. ((((exists ff_h_pvs_multiply_exists_unique_input0entrypositive. ff_h_pvs_multiply_exists_unique_input0entrypositive + S (dst_positive_multiply_exists_unique_input0) = S ((S (dst_index_multiply_exists_unique_input0)) * dst_positive_scale_multiply_exists_unique_input0)) /\ exists ff_q_pvs_multiply_exists_unique_input0entrypositive. dst_positive_code_multiply_exists_unique_input0 = ff_q_pvs_multiply_exists_unique_input0entrypositive * S ((S (dst_index_multiply_exists_unique_input0)) * dst_positive_scale_multiply_exists_unique_input0) + (dst_positive_multiply_exists_unique_input0))) /\ (((((exists ff_h_pvs_multiply_exists_unique_input0entrynegative. ff_h_pvs_multiply_exists_unique_input0entrynegative + S (dst_negative_multiply_exists_unique_input0) = S ((S (dst_index_multiply_exists_unique_input0)) * dst_negative_scale_multiply_exists_unique_input0)) /\ exists ff_q_pvs_multiply_exists_unique_input0entrynegative. dst_negative_code_multiply_exists_unique_input0 = ff_q_pvs_multiply_exists_unique_input0entrynegative * S ((S (dst_index_multiply_exists_unique_input0)) * dst_negative_scale_multiply_exists_unique_input0) + (dst_negative_multiply_exists_unique_input0))) /\ (exists ge_balance_positive_multiply_exists_unique_input0entryvalue ge_balance_negative_multiply_exists_unique_input0entryvalue. (((((dst_value_multiply_exists_unique_input0) = 2 * (ge_balance_positive_multiply_exists_unique_input0entryvalue) /\ (ge_balance_negative_multiply_exists_unique_input0entryvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_input0entryvaluedecode. (((dst_value_multiply_exists_unique_input0) = 2 * ge_signed_half_multiply_exists_unique_input0entryvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_input0entryvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_input0entryvalue) = S ge_signed_half_multiply_exists_unique_input0entryvaluedecode))) /\ ((dst_positive_multiply_exists_unique_input0) + ge_balance_negative_multiply_exists_unique_input0entryvalue = (dst_negative_multiply_exists_unique_input0) + ge_balance_positive_multiply_exists_unique_input0entryvalue))))))))) -> (exists dst_positive_code_multiply_exists_unique_input1 dst_positive_scale_multiply_exists_unique_input1 dst_negative_code_multiply_exists_unique_input1 dst_negative_scale_multiply_exists_unique_input1. (((G) = (((((dst_positive_code_multiply_exists_unique_input1) + (dst_positive_scale_multiply_exists_unique_input1)) * S ((dst_positive_code_multiply_exists_unique_input1) + (dst_positive_scale_multiply_exists_unique_input1)) + ((dst_positive_scale_multiply_exists_unique_input1) + (dst_positive_scale_multiply_exists_unique_input1))) + (((dst_negative_code_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)) * S ((dst_negative_code_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)) + ((dst_negative_scale_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)))) * S ((((dst_positive_code_multiply_exists_unique_input1) + (dst_positive_scale_multiply_exists_unique_input1)) * S ((dst_positive_code_multiply_exists_unique_input1) + (dst_positive_scale_multiply_exists_unique_input1)) + ((dst_positive_scale_multiply_exists_unique_input1) + (dst_positive_scale_multiply_exists_unique_input1))) + (((dst_negative_code_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)) * S ((dst_negative_code_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)) + ((dst_negative_scale_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)))) + ((((dst_negative_code_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)) * S ((dst_negative_code_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)) + ((dst_negative_scale_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1))) + (((dst_negative_code_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)) * S ((dst_negative_code_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)) + ((dst_negative_scale_multiply_exists_unique_input1) + (dst_negative_scale_multiply_exists_unique_input1)))))) /\ (forall dst_index_multiply_exists_unique_input1. (exists pvs_le_gap_multiply_exists_unique_input1domain. pvs_le_gap_multiply_exists_unique_input1domain + (dst_index_multiply_exists_unique_input1) = (l)) -> exists dst_positive_multiply_exists_unique_input1 dst_negative_multiply_exists_unique_input1 dst_value_multiply_exists_unique_input1. ((((exists ff_h_pvs_multiply_exists_unique_input1entrypositive. ff_h_pvs_multiply_exists_unique_input1entrypositive + S (dst_positive_multiply_exists_unique_input1) = S ((S (dst_index_multiply_exists_unique_input1)) * dst_positive_scale_multiply_exists_unique_input1)) /\ exists ff_q_pvs_multiply_exists_unique_input1entrypositive. dst_positive_code_multiply_exists_unique_input1 = ff_q_pvs_multiply_exists_unique_input1entrypositive * S ((S (dst_index_multiply_exists_unique_input1)) * dst_positive_scale_multiply_exists_unique_input1) + (dst_positive_multiply_exists_unique_input1))) /\ (((((exists ff_h_pvs_multiply_exists_unique_input1entrynegative. ff_h_pvs_multiply_exists_unique_input1entrynegative + S (dst_negative_multiply_exists_unique_input1) = S ((S (dst_index_multiply_exists_unique_input1)) * dst_negative_scale_multiply_exists_unique_input1)) /\ exists ff_q_pvs_multiply_exists_unique_input1entrynegative. dst_negative_code_multiply_exists_unique_input1 = ff_q_pvs_multiply_exists_unique_input1entrynegative * S ((S (dst_index_multiply_exists_unique_input1)) * dst_negative_scale_multiply_exists_unique_input1) + (dst_negative_multiply_exists_unique_input1))) /\ (exists ge_balance_positive_multiply_exists_unique_input1entryvalue ge_balance_negative_multiply_exists_unique_input1entryvalue. (((((dst_value_multiply_exists_unique_input1) = 2 * (ge_balance_positive_multiply_exists_unique_input1entryvalue) /\ (ge_balance_negative_multiply_exists_unique_input1entryvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_input1entryvaluedecode. (((dst_value_multiply_exists_unique_input1) = 2 * ge_signed_half_multiply_exists_unique_input1entryvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_input1entryvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_input1entryvalue) = S ge_signed_half_multiply_exists_unique_input1entryvaluedecode))) /\ ((dst_positive_multiply_exists_unique_input1) + ge_balance_negative_multiply_exists_unique_input1entryvalue = (dst_negative_multiply_exists_unique_input1) + ge_balance_positive_multiply_exists_unique_input1entryvalue))))))))) -> exists H. ((((exists dst_positive_code_multiply_exists_unique_resultleft_table dst_positive_scale_multiply_exists_unique_resultleft_table dst_negative_code_multiply_exists_unique_resultleft_table dst_negative_scale_multiply_exists_unique_resultleft_table. (((F) = (((((dst_positive_code_multiply_exists_unique_resultleft_table) + (dst_positive_scale_multiply_exists_unique_resultleft_table)) * S ((dst_positive_code_multiply_exists_unique_resultleft_table) + (dst_positive_scale_multiply_exists_unique_resultleft_table)) + ((dst_positive_scale_multiply_exists_unique_resultleft_table) + (dst_positive_scale_multiply_exists_unique_resultleft_table))) + (((dst_negative_code_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)) * S ((dst_negative_code_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)) + ((dst_negative_scale_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)))) * S ((((dst_positive_code_multiply_exists_unique_resultleft_table) + (dst_positive_scale_multiply_exists_unique_resultleft_table)) * S ((dst_positive_code_multiply_exists_unique_resultleft_table) + (dst_positive_scale_multiply_exists_unique_resultleft_table)) + ((dst_positive_scale_multiply_exists_unique_resultleft_table) + (dst_positive_scale_multiply_exists_unique_resultleft_table))) + (((dst_negative_code_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)) * S ((dst_negative_code_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)) + ((dst_negative_scale_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)))) + ((((dst_negative_code_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)) * S ((dst_negative_code_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)) + ((dst_negative_scale_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table))) + (((dst_negative_code_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)) * S ((dst_negative_code_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)) + ((dst_negative_scale_multiply_exists_unique_resultleft_table) + (dst_negative_scale_multiply_exists_unique_resultleft_table)))))) /\ (forall dst_index_multiply_exists_unique_resultleft_table. (exists pvs_le_gap_multiply_exists_unique_resultleft_tabledomain. pvs_le_gap_multiply_exists_unique_resultleft_tabledomain + (dst_index_multiply_exists_unique_resultleft_table) = (l)) -> exists dst_positive_multiply_exists_unique_resultleft_table dst_negative_multiply_exists_unique_resultleft_table dst_value_multiply_exists_unique_resultleft_table. ((((exists ff_h_pvs_multiply_exists_unique_resultleft_tableentrypositive. ff_h_pvs_multiply_exists_unique_resultleft_tableentrypositive + S (dst_positive_multiply_exists_unique_resultleft_table) = S ((S (dst_index_multiply_exists_unique_resultleft_table)) * dst_positive_scale_multiply_exists_unique_resultleft_table)) /\ exists ff_q_pvs_multiply_exists_unique_resultleft_tableentrypositive. dst_positive_code_multiply_exists_unique_resultleft_table = ff_q_pvs_multiply_exists_unique_resultleft_tableentrypositive * S ((S (dst_index_multiply_exists_unique_resultleft_table)) * dst_positive_scale_multiply_exists_unique_resultleft_table) + (dst_positive_multiply_exists_unique_resultleft_table))) /\ (((((exists ff_h_pvs_multiply_exists_unique_resultleft_tableentrynegative. ff_h_pvs_multiply_exists_unique_resultleft_tableentrynegative + S (dst_negative_multiply_exists_unique_resultleft_table) = S ((S (dst_index_multiply_exists_unique_resultleft_table)) * dst_negative_scale_multiply_exists_unique_resultleft_table)) /\ exists ff_q_pvs_multiply_exists_unique_resultleft_tableentrynegative. dst_negative_code_multiply_exists_unique_resultleft_table = ff_q_pvs_multiply_exists_unique_resultleft_tableentrynegative * S ((S (dst_index_multiply_exists_unique_resultleft_table)) * dst_negative_scale_multiply_exists_unique_resultleft_table) + (dst_negative_multiply_exists_unique_resultleft_table))) /\ (exists ge_balance_positive_multiply_exists_unique_resultleft_tableentryvalue ge_balance_negative_multiply_exists_unique_resultleft_tableentryvalue. (((((dst_value_multiply_exists_unique_resultleft_table) = 2 * (ge_balance_positive_multiply_exists_unique_resultleft_tableentryvalue) /\ (ge_balance_negative_multiply_exists_unique_resultleft_tableentryvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_resultleft_tableentryvaluedecode. (((dst_value_multiply_exists_unique_resultleft_table) = 2 * ge_signed_half_multiply_exists_unique_resultleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_resultleft_tableentryvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_resultleft_tableentryvalue) = S ge_signed_half_multiply_exists_unique_resultleft_tableentryvaluedecode))) /\ ((dst_positive_multiply_exists_unique_resultleft_table) + ge_balance_negative_multiply_exists_unique_resultleft_tableentryvalue = (dst_negative_multiply_exists_unique_resultleft_table) + ge_balance_positive_multiply_exists_unique_resultleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_multiply_exists_unique_resultright_table dst_positive_scale_multiply_exists_unique_resultright_table dst_negative_code_multiply_exists_unique_resultright_table dst_negative_scale_multiply_exists_unique_resultright_table. (((G) = (((((dst_positive_code_multiply_exists_unique_resultright_table) + (dst_positive_scale_multiply_exists_unique_resultright_table)) * S ((dst_positive_code_multiply_exists_unique_resultright_table) + (dst_positive_scale_multiply_exists_unique_resultright_table)) + ((dst_positive_scale_multiply_exists_unique_resultright_table) + (dst_positive_scale_multiply_exists_unique_resultright_table))) + (((dst_negative_code_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)) * S ((dst_negative_code_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)) + ((dst_negative_scale_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)))) * S ((((dst_positive_code_multiply_exists_unique_resultright_table) + (dst_positive_scale_multiply_exists_unique_resultright_table)) * S ((dst_positive_code_multiply_exists_unique_resultright_table) + (dst_positive_scale_multiply_exists_unique_resultright_table)) + ((dst_positive_scale_multiply_exists_unique_resultright_table) + (dst_positive_scale_multiply_exists_unique_resultright_table))) + (((dst_negative_code_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)) * S ((dst_negative_code_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)) + ((dst_negative_scale_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)))) + ((((dst_negative_code_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)) * S ((dst_negative_code_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)) + ((dst_negative_scale_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table))) + (((dst_negative_code_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)) * S ((dst_negative_code_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)) + ((dst_negative_scale_multiply_exists_unique_resultright_table) + (dst_negative_scale_multiply_exists_unique_resultright_table)))))) /\ (forall dst_index_multiply_exists_unique_resultright_table. (exists pvs_le_gap_multiply_exists_unique_resultright_tabledomain. pvs_le_gap_multiply_exists_unique_resultright_tabledomain + (dst_index_multiply_exists_unique_resultright_table) = (l)) -> exists dst_positive_multiply_exists_unique_resultright_table dst_negative_multiply_exists_unique_resultright_table dst_value_multiply_exists_unique_resultright_table. ((((exists ff_h_pvs_multiply_exists_unique_resultright_tableentrypositive. ff_h_pvs_multiply_exists_unique_resultright_tableentrypositive + S (dst_positive_multiply_exists_unique_resultright_table) = S ((S (dst_index_multiply_exists_unique_resultright_table)) * dst_positive_scale_multiply_exists_unique_resultright_table)) /\ exists ff_q_pvs_multiply_exists_unique_resultright_tableentrypositive. dst_positive_code_multiply_exists_unique_resultright_table = ff_q_pvs_multiply_exists_unique_resultright_tableentrypositive * S ((S (dst_index_multiply_exists_unique_resultright_table)) * dst_positive_scale_multiply_exists_unique_resultright_table) + (dst_positive_multiply_exists_unique_resultright_table))) /\ (((((exists ff_h_pvs_multiply_exists_unique_resultright_tableentrynegative. ff_h_pvs_multiply_exists_unique_resultright_tableentrynegative + S (dst_negative_multiply_exists_unique_resultright_table) = S ((S (dst_index_multiply_exists_unique_resultright_table)) * dst_negative_scale_multiply_exists_unique_resultright_table)) /\ exists ff_q_pvs_multiply_exists_unique_resultright_tableentrynegative. dst_negative_code_multiply_exists_unique_resultright_table = ff_q_pvs_multiply_exists_unique_resultright_tableentrynegative * S ((S (dst_index_multiply_exists_unique_resultright_table)) * dst_negative_scale_multiply_exists_unique_resultright_table) + (dst_negative_multiply_exists_unique_resultright_table))) /\ (exists ge_balance_positive_multiply_exists_unique_resultright_tableentryvalue ge_balance_negative_multiply_exists_unique_resultright_tableentryvalue. (((((dst_value_multiply_exists_unique_resultright_table) = 2 * (ge_balance_positive_multiply_exists_unique_resultright_tableentryvalue) /\ (ge_balance_negative_multiply_exists_unique_resultright_tableentryvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_resultright_tableentryvaluedecode. (((dst_value_multiply_exists_unique_resultright_table) = 2 * ge_signed_half_multiply_exists_unique_resultright_tableentryvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_resultright_tableentryvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_resultright_tableentryvalue) = S ge_signed_half_multiply_exists_unique_resultright_tableentryvaluedecode))) /\ ((dst_positive_multiply_exists_unique_resultright_table) + ge_balance_negative_multiply_exists_unique_resultright_tableentryvalue = (dst_negative_multiply_exists_unique_resultright_table) + ge_balance_positive_multiply_exists_unique_resultright_tableentryvalue))))))))) /\ (((exists dst_positive_code_multiply_exists_unique_resultoutput_table dst_positive_scale_multiply_exists_unique_resultoutput_table dst_negative_code_multiply_exists_unique_resultoutput_table dst_negative_scale_multiply_exists_unique_resultoutput_table. (((H) = (((((dst_positive_code_multiply_exists_unique_resultoutput_table) + (dst_positive_scale_multiply_exists_unique_resultoutput_table)) * S ((dst_positive_code_multiply_exists_unique_resultoutput_table) + (dst_positive_scale_multiply_exists_unique_resultoutput_table)) + ((dst_positive_scale_multiply_exists_unique_resultoutput_table) + (dst_positive_scale_multiply_exists_unique_resultoutput_table))) + (((dst_negative_code_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)) * S ((dst_negative_code_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)) + ((dst_negative_scale_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)))) * S ((((dst_positive_code_multiply_exists_unique_resultoutput_table) + (dst_positive_scale_multiply_exists_unique_resultoutput_table)) * S ((dst_positive_code_multiply_exists_unique_resultoutput_table) + (dst_positive_scale_multiply_exists_unique_resultoutput_table)) + ((dst_positive_scale_multiply_exists_unique_resultoutput_table) + (dst_positive_scale_multiply_exists_unique_resultoutput_table))) + (((dst_negative_code_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)) * S ((dst_negative_code_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)) + ((dst_negative_scale_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)))) + ((((dst_negative_code_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)) * S ((dst_negative_code_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)) + ((dst_negative_scale_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table))) + (((dst_negative_code_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)) * S ((dst_negative_code_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)) + ((dst_negative_scale_multiply_exists_unique_resultoutput_table) + (dst_negative_scale_multiply_exists_unique_resultoutput_table)))))) /\ (forall dst_index_multiply_exists_unique_resultoutput_table. (exists pvs_le_gap_multiply_exists_unique_resultoutput_tabledomain. pvs_le_gap_multiply_exists_unique_resultoutput_tabledomain + (dst_index_multiply_exists_unique_resultoutput_table) = (l)) -> exists dst_positive_multiply_exists_unique_resultoutput_table dst_negative_multiply_exists_unique_resultoutput_table dst_value_multiply_exists_unique_resultoutput_table. ((((exists ff_h_pvs_multiply_exists_unique_resultoutput_tableentrypositive. ff_h_pvs_multiply_exists_unique_resultoutput_tableentrypositive + S (dst_positive_multiply_exists_unique_resultoutput_table) = S ((S (dst_index_multiply_exists_unique_resultoutput_table)) * dst_positive_scale_multiply_exists_unique_resultoutput_table)) /\ exists ff_q_pvs_multiply_exists_unique_resultoutput_tableentrypositive. dst_positive_code_multiply_exists_unique_resultoutput_table = ff_q_pvs_multiply_exists_unique_resultoutput_tableentrypositive * S ((S (dst_index_multiply_exists_unique_resultoutput_table)) * dst_positive_scale_multiply_exists_unique_resultoutput_table) + (dst_positive_multiply_exists_unique_resultoutput_table))) /\ (((((exists ff_h_pvs_multiply_exists_unique_resultoutput_tableentrynegative. ff_h_pvs_multiply_exists_unique_resultoutput_tableentrynegative + S (dst_negative_multiply_exists_unique_resultoutput_table) = S ((S (dst_index_multiply_exists_unique_resultoutput_table)) * dst_negative_scale_multiply_exists_unique_resultoutput_table)) /\ exists ff_q_pvs_multiply_exists_unique_resultoutput_tableentrynegative. dst_negative_code_multiply_exists_unique_resultoutput_table = ff_q_pvs_multiply_exists_unique_resultoutput_tableentrynegative * S ((S (dst_index_multiply_exists_unique_resultoutput_table)) * dst_negative_scale_multiply_exists_unique_resultoutput_table) + (dst_negative_multiply_exists_unique_resultoutput_table))) /\ (exists ge_balance_positive_multiply_exists_unique_resultoutput_tableentryvalue ge_balance_negative_multiply_exists_unique_resultoutput_tableentryvalue. (((((dst_value_multiply_exists_unique_resultoutput_table) = 2 * (ge_balance_positive_multiply_exists_unique_resultoutput_tableentryvalue) /\ (ge_balance_negative_multiply_exists_unique_resultoutput_tableentryvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_resultoutput_tableentryvaluedecode. (((dst_value_multiply_exists_unique_resultoutput_table) = 2 * ge_signed_half_multiply_exists_unique_resultoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_resultoutput_tableentryvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_resultoutput_tableentryvalue) = S ge_signed_half_multiply_exists_unique_resultoutput_tableentryvaluedecode))) /\ ((dst_positive_multiply_exists_unique_resultoutput_table) + ge_balance_negative_multiply_exists_unique_resultoutput_tableentryvalue = (dst_negative_multiply_exists_unique_resultoutput_table) + ge_balance_positive_multiply_exists_unique_resultoutput_tableentryvalue))))))))) /\ (forall sto_index_multiply_exists_unique_resultentries. (exists pvs_gap_multiply_exists_unique_resultentriesbound. pvs_gap_multiply_exists_unique_resultentriesbound + S (sto_index_multiply_exists_unique_resultentries) = (l)) -> exists sto_left_multiply_exists_unique_resultentries sto_right_multiply_exists_unique_resultentries sto_output_multiply_exists_unique_resultentries. ((exists dst_positive_code_multiply_exists_unique_resultentriesentryleft dst_positive_scale_multiply_exists_unique_resultentriesentryleft dst_negative_code_multiply_exists_unique_resultentriesentryleft dst_negative_scale_multiply_exists_unique_resultentriesentryleft dst_positive_multiply_exists_unique_resultentriesentryleft dst_negative_multiply_exists_unique_resultentriesentryleft. (((F) = (((((dst_positive_code_multiply_exists_unique_resultentriesentryleft) + (dst_positive_scale_multiply_exists_unique_resultentriesentryleft)) * S ((dst_positive_code_multiply_exists_unique_resultentriesentryleft) + (dst_positive_scale_multiply_exists_unique_resultentriesentryleft)) + ((dst_positive_scale_multiply_exists_unique_resultentriesentryleft) + (dst_positive_scale_multiply_exists_unique_resultentriesentryleft))) + (((dst_negative_code_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)))) * S ((((dst_positive_code_multiply_exists_unique_resultentriesentryleft) + (dst_positive_scale_multiply_exists_unique_resultentriesentryleft)) * S ((dst_positive_code_multiply_exists_unique_resultentriesentryleft) + (dst_positive_scale_multiply_exists_unique_resultentriesentryleft)) + ((dst_positive_scale_multiply_exists_unique_resultentriesentryleft) + (dst_positive_scale_multiply_exists_unique_resultentriesentryleft))) + (((dst_negative_code_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)))) + ((((dst_negative_code_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft))) + (((dst_negative_code_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryleft) + (dst_negative_scale_multiply_exists_unique_resultentriesentryleft)))))) /\ (((((exists ff_h_pvs_multiply_exists_unique_resultentriesentryleftpositive. ff_h_pvs_multiply_exists_unique_resultentriesentryleftpositive + S (dst_positive_multiply_exists_unique_resultentriesentryleft) = S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_positive_scale_multiply_exists_unique_resultentriesentryleft)) /\ exists ff_q_pvs_multiply_exists_unique_resultentriesentryleftpositive. dst_positive_code_multiply_exists_unique_resultentriesentryleft = ff_q_pvs_multiply_exists_unique_resultentriesentryleftpositive * S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_positive_scale_multiply_exists_unique_resultentriesentryleft) + (dst_positive_multiply_exists_unique_resultentriesentryleft))) /\ (((((exists ff_h_pvs_multiply_exists_unique_resultentriesentryleftnegative. ff_h_pvs_multiply_exists_unique_resultentriesentryleftnegative + S (dst_negative_multiply_exists_unique_resultentriesentryleft) = S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_negative_scale_multiply_exists_unique_resultentriesentryleft)) /\ exists ff_q_pvs_multiply_exists_unique_resultentriesentryleftnegative. dst_negative_code_multiply_exists_unique_resultentriesentryleft = ff_q_pvs_multiply_exists_unique_resultentriesentryleftnegative * S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_negative_scale_multiply_exists_unique_resultentriesentryleft) + (dst_negative_multiply_exists_unique_resultentriesentryleft))) /\ (exists ge_balance_positive_multiply_exists_unique_resultentriesentryleftvalue ge_balance_negative_multiply_exists_unique_resultentriesentryleftvalue. (((((sto_left_multiply_exists_unique_resultentries) = 2 * (ge_balance_positive_multiply_exists_unique_resultentriesentryleftvalue) /\ (ge_balance_negative_multiply_exists_unique_resultentriesentryleftvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_resultentriesentryleftvaluedecode. (((sto_left_multiply_exists_unique_resultentries) = 2 * ge_signed_half_multiply_exists_unique_resultentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_resultentriesentryleftvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_resultentriesentryleftvalue) = S ge_signed_half_multiply_exists_unique_resultentriesentryleftvaluedecode))) /\ ((dst_positive_multiply_exists_unique_resultentriesentryleft) + ge_balance_negative_multiply_exists_unique_resultentriesentryleftvalue = (dst_negative_multiply_exists_unique_resultentriesentryleft) + ge_balance_positive_multiply_exists_unique_resultentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_multiply_exists_unique_resultentriesentryright dst_positive_scale_multiply_exists_unique_resultentriesentryright dst_negative_code_multiply_exists_unique_resultentriesentryright dst_negative_scale_multiply_exists_unique_resultentriesentryright dst_positive_multiply_exists_unique_resultentriesentryright dst_negative_multiply_exists_unique_resultentriesentryright. (((G) = (((((dst_positive_code_multiply_exists_unique_resultentriesentryright) + (dst_positive_scale_multiply_exists_unique_resultentriesentryright)) * S ((dst_positive_code_multiply_exists_unique_resultentriesentryright) + (dst_positive_scale_multiply_exists_unique_resultentriesentryright)) + ((dst_positive_scale_multiply_exists_unique_resultentriesentryright) + (dst_positive_scale_multiply_exists_unique_resultentriesentryright))) + (((dst_negative_code_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)))) * S ((((dst_positive_code_multiply_exists_unique_resultentriesentryright) + (dst_positive_scale_multiply_exists_unique_resultentriesentryright)) * S ((dst_positive_code_multiply_exists_unique_resultentriesentryright) + (dst_positive_scale_multiply_exists_unique_resultentriesentryright)) + ((dst_positive_scale_multiply_exists_unique_resultentriesentryright) + (dst_positive_scale_multiply_exists_unique_resultentriesentryright))) + (((dst_negative_code_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)))) + ((((dst_negative_code_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright))) + (((dst_negative_code_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryright) + (dst_negative_scale_multiply_exists_unique_resultentriesentryright)))))) /\ (((((exists ff_h_pvs_multiply_exists_unique_resultentriesentryrightpositive. ff_h_pvs_multiply_exists_unique_resultentriesentryrightpositive + S (dst_positive_multiply_exists_unique_resultentriesentryright) = S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_positive_scale_multiply_exists_unique_resultentriesentryright)) /\ exists ff_q_pvs_multiply_exists_unique_resultentriesentryrightpositive. dst_positive_code_multiply_exists_unique_resultentriesentryright = ff_q_pvs_multiply_exists_unique_resultentriesentryrightpositive * S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_positive_scale_multiply_exists_unique_resultentriesentryright) + (dst_positive_multiply_exists_unique_resultentriesentryright))) /\ (((((exists ff_h_pvs_multiply_exists_unique_resultentriesentryrightnegative. ff_h_pvs_multiply_exists_unique_resultentriesentryrightnegative + S (dst_negative_multiply_exists_unique_resultentriesentryright) = S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_negative_scale_multiply_exists_unique_resultentriesentryright)) /\ exists ff_q_pvs_multiply_exists_unique_resultentriesentryrightnegative. dst_negative_code_multiply_exists_unique_resultentriesentryright = ff_q_pvs_multiply_exists_unique_resultentriesentryrightnegative * S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_negative_scale_multiply_exists_unique_resultentriesentryright) + (dst_negative_multiply_exists_unique_resultentriesentryright))) /\ (exists ge_balance_positive_multiply_exists_unique_resultentriesentryrightvalue ge_balance_negative_multiply_exists_unique_resultentriesentryrightvalue. (((((sto_right_multiply_exists_unique_resultentries) = 2 * (ge_balance_positive_multiply_exists_unique_resultentriesentryrightvalue) /\ (ge_balance_negative_multiply_exists_unique_resultentriesentryrightvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_resultentriesentryrightvaluedecode. (((sto_right_multiply_exists_unique_resultentries) = 2 * ge_signed_half_multiply_exists_unique_resultentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_resultentriesentryrightvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_resultentriesentryrightvalue) = S ge_signed_half_multiply_exists_unique_resultentriesentryrightvaluedecode))) /\ ((dst_positive_multiply_exists_unique_resultentriesentryright) + ge_balance_negative_multiply_exists_unique_resultentriesentryrightvalue = (dst_negative_multiply_exists_unique_resultentriesentryright) + ge_balance_positive_multiply_exists_unique_resultentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_multiply_exists_unique_resultentriesentryoutput dst_positive_scale_multiply_exists_unique_resultentriesentryoutput dst_negative_code_multiply_exists_unique_resultentriesentryoutput dst_negative_scale_multiply_exists_unique_resultentriesentryoutput dst_positive_multiply_exists_unique_resultentriesentryoutput dst_negative_multiply_exists_unique_resultentriesentryoutput. (((H) = (((((dst_positive_code_multiply_exists_unique_resultentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_resultentriesentryoutput)) * S ((dst_positive_code_multiply_exists_unique_resultentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_resultentriesentryoutput)) + ((dst_positive_scale_multiply_exists_unique_resultentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_resultentriesentryoutput))) + (((dst_negative_code_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)))) * S ((((dst_positive_code_multiply_exists_unique_resultentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_resultentriesentryoutput)) * S ((dst_positive_code_multiply_exists_unique_resultentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_resultentriesentryoutput)) + ((dst_positive_scale_multiply_exists_unique_resultentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_resultentriesentryoutput))) + (((dst_negative_code_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)))) + ((((dst_negative_code_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput))) + (((dst_negative_code_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)) * S ((dst_negative_code_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)) + ((dst_negative_scale_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)))))) /\ (((((exists ff_h_pvs_multiply_exists_unique_resultentriesentryoutputpositive. ff_h_pvs_multiply_exists_unique_resultentriesentryoutputpositive + S (dst_positive_multiply_exists_unique_resultentriesentryoutput) = S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_positive_scale_multiply_exists_unique_resultentriesentryoutput)) /\ exists ff_q_pvs_multiply_exists_unique_resultentriesentryoutputpositive. dst_positive_code_multiply_exists_unique_resultentriesentryoutput = ff_q_pvs_multiply_exists_unique_resultentriesentryoutputpositive * S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_positive_scale_multiply_exists_unique_resultentriesentryoutput) + (dst_positive_multiply_exists_unique_resultentriesentryoutput))) /\ (((((exists ff_h_pvs_multiply_exists_unique_resultentriesentryoutputnegative. ff_h_pvs_multiply_exists_unique_resultentriesentryoutputnegative + S (dst_negative_multiply_exists_unique_resultentriesentryoutput) = S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_negative_scale_multiply_exists_unique_resultentriesentryoutput)) /\ exists ff_q_pvs_multiply_exists_unique_resultentriesentryoutputnegative. dst_negative_code_multiply_exists_unique_resultentriesentryoutput = ff_q_pvs_multiply_exists_unique_resultentriesentryoutputnegative * S ((S (sto_index_multiply_exists_unique_resultentries)) * dst_negative_scale_multiply_exists_unique_resultentriesentryoutput) + (dst_negative_multiply_exists_unique_resultentriesentryoutput))) /\ (exists ge_balance_positive_multiply_exists_unique_resultentriesentryoutputvalue ge_balance_negative_multiply_exists_unique_resultentriesentryoutputvalue. (((((sto_output_multiply_exists_unique_resultentries) = 2 * (ge_balance_positive_multiply_exists_unique_resultentriesentryoutputvalue) /\ (ge_balance_negative_multiply_exists_unique_resultentriesentryoutputvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_resultentriesentryoutputvaluedecode. (((sto_output_multiply_exists_unique_resultentries) = 2 * ge_signed_half_multiply_exists_unique_resultentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_resultentriesentryoutputvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_resultentriesentryoutputvalue) = S ge_signed_half_multiply_exists_unique_resultentriesentryoutputvaluedecode))) /\ ((dst_positive_multiply_exists_unique_resultentriesentryoutput) + ge_balance_negative_multiply_exists_unique_resultentriesentryoutputvalue = (dst_negative_multiply_exists_unique_resultentriesentryoutput) + ge_balance_positive_multiply_exists_unique_resultentriesentryoutputvalue))))))))) /\ (exists sto_ap_multiply_exists_unique_resultentriesentryoperation sto_an_multiply_exists_unique_resultentriesentryoperation sto_bp_multiply_exists_unique_resultentriesentryoperation sto_bn_multiply_exists_unique_resultentriesentryoperation sto_cp_multiply_exists_unique_resultentriesentryoperation sto_cn_multiply_exists_unique_resultentriesentryoperation. (((((sto_left_multiply_exists_unique_resultentries) = 2 * (sto_ap_multiply_exists_unique_resultentriesentryoperation) /\ (sto_an_multiply_exists_unique_resultentriesentryoperation) = 0) \/ exists ge_signed_half_multiply_exists_unique_resultentriesentryoperationleft. (((sto_left_multiply_exists_unique_resultentries) = 2 * ge_signed_half_multiply_exists_unique_resultentriesentryoperationleft + 1 /\ (sto_ap_multiply_exists_unique_resultentriesentryoperation) = 0) /\ (sto_an_multiply_exists_unique_resultentriesentryoperation) = S ge_signed_half_multiply_exists_unique_resultentriesentryoperationleft))) /\ ((((((sto_right_multiply_exists_unique_resultentries) = 2 * (sto_bp_multiply_exists_unique_resultentriesentryoperation) /\ (sto_bn_multiply_exists_unique_resultentriesentryoperation) = 0) \/ exists ge_signed_half_multiply_exists_unique_resultentriesentryoperationright. (((sto_right_multiply_exists_unique_resultentries) = 2 * ge_signed_half_multiply_exists_unique_resultentriesentryoperationright + 1 /\ (sto_bp_multiply_exists_unique_resultentriesentryoperation) = 0) /\ (sto_bn_multiply_exists_unique_resultentriesentryoperation) = S ge_signed_half_multiply_exists_unique_resultentriesentryoperationright))) /\ ((((((sto_output_multiply_exists_unique_resultentries) = 2 * (sto_cp_multiply_exists_unique_resultentriesentryoperation) /\ (sto_cn_multiply_exists_unique_resultentriesentryoperation) = 0) \/ exists ge_signed_half_multiply_exists_unique_resultentriesentryoperationoutput. (((sto_output_multiply_exists_unique_resultentries) = 2 * ge_signed_half_multiply_exists_unique_resultentriesentryoperationoutput + 1 /\ (sto_cp_multiply_exists_unique_resultentriesentryoperation) = 0) /\ (sto_cn_multiply_exists_unique_resultentriesentryoperation) = S ge_signed_half_multiply_exists_unique_resultentriesentryoperationoutput))) /\ ((sto_ap_multiply_exists_unique_resultentriesentryoperation * sto_bp_multiply_exists_unique_resultentriesentryoperation + sto_an_multiply_exists_unique_resultentriesentryoperation * sto_bn_multiply_exists_unique_resultentriesentryoperation) + sto_cn_multiply_exists_unique_resultentriesentryoperation = (sto_ap_multiply_exists_unique_resultentriesentryoperation * sto_bn_multiply_exists_unique_resultentriesentryoperation + sto_an_multiply_exists_unique_resultentriesentryoperation * sto_bp_multiply_exists_unique_resultentriesentryoperation) + sto_cp_multiply_exists_unique_resultentriesentryoperation))))))))))))))))))) /\ (forall K. (((exists dst_positive_code_multiply_exists_unique_otherleft_table dst_positive_scale_multiply_exists_unique_otherleft_table dst_negative_code_multiply_exists_unique_otherleft_table dst_negative_scale_multiply_exists_unique_otherleft_table. (((F) = (((((dst_positive_code_multiply_exists_unique_otherleft_table) + (dst_positive_scale_multiply_exists_unique_otherleft_table)) * S ((dst_positive_code_multiply_exists_unique_otherleft_table) + (dst_positive_scale_multiply_exists_unique_otherleft_table)) + ((dst_positive_scale_multiply_exists_unique_otherleft_table) + (dst_positive_scale_multiply_exists_unique_otherleft_table))) + (((dst_negative_code_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)) * S ((dst_negative_code_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)) + ((dst_negative_scale_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)))) * S ((((dst_positive_code_multiply_exists_unique_otherleft_table) + (dst_positive_scale_multiply_exists_unique_otherleft_table)) * S ((dst_positive_code_multiply_exists_unique_otherleft_table) + (dst_positive_scale_multiply_exists_unique_otherleft_table)) + ((dst_positive_scale_multiply_exists_unique_otherleft_table) + (dst_positive_scale_multiply_exists_unique_otherleft_table))) + (((dst_negative_code_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)) * S ((dst_negative_code_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)) + ((dst_negative_scale_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)))) + ((((dst_negative_code_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)) * S ((dst_negative_code_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)) + ((dst_negative_scale_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table))) + (((dst_negative_code_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)) * S ((dst_negative_code_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)) + ((dst_negative_scale_multiply_exists_unique_otherleft_table) + (dst_negative_scale_multiply_exists_unique_otherleft_table)))))) /\ (forall dst_index_multiply_exists_unique_otherleft_table. (exists pvs_le_gap_multiply_exists_unique_otherleft_tabledomain. pvs_le_gap_multiply_exists_unique_otherleft_tabledomain + (dst_index_multiply_exists_unique_otherleft_table) = (l)) -> exists dst_positive_multiply_exists_unique_otherleft_table dst_negative_multiply_exists_unique_otherleft_table dst_value_multiply_exists_unique_otherleft_table. ((((exists ff_h_pvs_multiply_exists_unique_otherleft_tableentrypositive. ff_h_pvs_multiply_exists_unique_otherleft_tableentrypositive + S (dst_positive_multiply_exists_unique_otherleft_table) = S ((S (dst_index_multiply_exists_unique_otherleft_table)) * dst_positive_scale_multiply_exists_unique_otherleft_table)) /\ exists ff_q_pvs_multiply_exists_unique_otherleft_tableentrypositive. dst_positive_code_multiply_exists_unique_otherleft_table = ff_q_pvs_multiply_exists_unique_otherleft_tableentrypositive * S ((S (dst_index_multiply_exists_unique_otherleft_table)) * dst_positive_scale_multiply_exists_unique_otherleft_table) + (dst_positive_multiply_exists_unique_otherleft_table))) /\ (((((exists ff_h_pvs_multiply_exists_unique_otherleft_tableentrynegative. ff_h_pvs_multiply_exists_unique_otherleft_tableentrynegative + S (dst_negative_multiply_exists_unique_otherleft_table) = S ((S (dst_index_multiply_exists_unique_otherleft_table)) * dst_negative_scale_multiply_exists_unique_otherleft_table)) /\ exists ff_q_pvs_multiply_exists_unique_otherleft_tableentrynegative. dst_negative_code_multiply_exists_unique_otherleft_table = ff_q_pvs_multiply_exists_unique_otherleft_tableentrynegative * S ((S (dst_index_multiply_exists_unique_otherleft_table)) * dst_negative_scale_multiply_exists_unique_otherleft_table) + (dst_negative_multiply_exists_unique_otherleft_table))) /\ (exists ge_balance_positive_multiply_exists_unique_otherleft_tableentryvalue ge_balance_negative_multiply_exists_unique_otherleft_tableentryvalue. (((((dst_value_multiply_exists_unique_otherleft_table) = 2 * (ge_balance_positive_multiply_exists_unique_otherleft_tableentryvalue) /\ (ge_balance_negative_multiply_exists_unique_otherleft_tableentryvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_otherleft_tableentryvaluedecode. (((dst_value_multiply_exists_unique_otherleft_table) = 2 * ge_signed_half_multiply_exists_unique_otherleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_otherleft_tableentryvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_otherleft_tableentryvalue) = S ge_signed_half_multiply_exists_unique_otherleft_tableentryvaluedecode))) /\ ((dst_positive_multiply_exists_unique_otherleft_table) + ge_balance_negative_multiply_exists_unique_otherleft_tableentryvalue = (dst_negative_multiply_exists_unique_otherleft_table) + ge_balance_positive_multiply_exists_unique_otherleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_multiply_exists_unique_otherright_table dst_positive_scale_multiply_exists_unique_otherright_table dst_negative_code_multiply_exists_unique_otherright_table dst_negative_scale_multiply_exists_unique_otherright_table. (((G) = (((((dst_positive_code_multiply_exists_unique_otherright_table) + (dst_positive_scale_multiply_exists_unique_otherright_table)) * S ((dst_positive_code_multiply_exists_unique_otherright_table) + (dst_positive_scale_multiply_exists_unique_otherright_table)) + ((dst_positive_scale_multiply_exists_unique_otherright_table) + (dst_positive_scale_multiply_exists_unique_otherright_table))) + (((dst_negative_code_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)) * S ((dst_negative_code_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)) + ((dst_negative_scale_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)))) * S ((((dst_positive_code_multiply_exists_unique_otherright_table) + (dst_positive_scale_multiply_exists_unique_otherright_table)) * S ((dst_positive_code_multiply_exists_unique_otherright_table) + (dst_positive_scale_multiply_exists_unique_otherright_table)) + ((dst_positive_scale_multiply_exists_unique_otherright_table) + (dst_positive_scale_multiply_exists_unique_otherright_table))) + (((dst_negative_code_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)) * S ((dst_negative_code_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)) + ((dst_negative_scale_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)))) + ((((dst_negative_code_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)) * S ((dst_negative_code_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)) + ((dst_negative_scale_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table))) + (((dst_negative_code_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)) * S ((dst_negative_code_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)) + ((dst_negative_scale_multiply_exists_unique_otherright_table) + (dst_negative_scale_multiply_exists_unique_otherright_table)))))) /\ (forall dst_index_multiply_exists_unique_otherright_table. (exists pvs_le_gap_multiply_exists_unique_otherright_tabledomain. pvs_le_gap_multiply_exists_unique_otherright_tabledomain + (dst_index_multiply_exists_unique_otherright_table) = (l)) -> exists dst_positive_multiply_exists_unique_otherright_table dst_negative_multiply_exists_unique_otherright_table dst_value_multiply_exists_unique_otherright_table. ((((exists ff_h_pvs_multiply_exists_unique_otherright_tableentrypositive. ff_h_pvs_multiply_exists_unique_otherright_tableentrypositive + S (dst_positive_multiply_exists_unique_otherright_table) = S ((S (dst_index_multiply_exists_unique_otherright_table)) * dst_positive_scale_multiply_exists_unique_otherright_table)) /\ exists ff_q_pvs_multiply_exists_unique_otherright_tableentrypositive. dst_positive_code_multiply_exists_unique_otherright_table = ff_q_pvs_multiply_exists_unique_otherright_tableentrypositive * S ((S (dst_index_multiply_exists_unique_otherright_table)) * dst_positive_scale_multiply_exists_unique_otherright_table) + (dst_positive_multiply_exists_unique_otherright_table))) /\ (((((exists ff_h_pvs_multiply_exists_unique_otherright_tableentrynegative. ff_h_pvs_multiply_exists_unique_otherright_tableentrynegative + S (dst_negative_multiply_exists_unique_otherright_table) = S ((S (dst_index_multiply_exists_unique_otherright_table)) * dst_negative_scale_multiply_exists_unique_otherright_table)) /\ exists ff_q_pvs_multiply_exists_unique_otherright_tableentrynegative. dst_negative_code_multiply_exists_unique_otherright_table = ff_q_pvs_multiply_exists_unique_otherright_tableentrynegative * S ((S (dst_index_multiply_exists_unique_otherright_table)) * dst_negative_scale_multiply_exists_unique_otherright_table) + (dst_negative_multiply_exists_unique_otherright_table))) /\ (exists ge_balance_positive_multiply_exists_unique_otherright_tableentryvalue ge_balance_negative_multiply_exists_unique_otherright_tableentryvalue. (((((dst_value_multiply_exists_unique_otherright_table) = 2 * (ge_balance_positive_multiply_exists_unique_otherright_tableentryvalue) /\ (ge_balance_negative_multiply_exists_unique_otherright_tableentryvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_otherright_tableentryvaluedecode. (((dst_value_multiply_exists_unique_otherright_table) = 2 * ge_signed_half_multiply_exists_unique_otherright_tableentryvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_otherright_tableentryvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_otherright_tableentryvalue) = S ge_signed_half_multiply_exists_unique_otherright_tableentryvaluedecode))) /\ ((dst_positive_multiply_exists_unique_otherright_table) + ge_balance_negative_multiply_exists_unique_otherright_tableentryvalue = (dst_negative_multiply_exists_unique_otherright_table) + ge_balance_positive_multiply_exists_unique_otherright_tableentryvalue))))))))) /\ (((exists dst_positive_code_multiply_exists_unique_otheroutput_table dst_positive_scale_multiply_exists_unique_otheroutput_table dst_negative_code_multiply_exists_unique_otheroutput_table dst_negative_scale_multiply_exists_unique_otheroutput_table. (((K) = (((((dst_positive_code_multiply_exists_unique_otheroutput_table) + (dst_positive_scale_multiply_exists_unique_otheroutput_table)) * S ((dst_positive_code_multiply_exists_unique_otheroutput_table) + (dst_positive_scale_multiply_exists_unique_otheroutput_table)) + ((dst_positive_scale_multiply_exists_unique_otheroutput_table) + (dst_positive_scale_multiply_exists_unique_otheroutput_table))) + (((dst_negative_code_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)) * S ((dst_negative_code_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)) + ((dst_negative_scale_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)))) * S ((((dst_positive_code_multiply_exists_unique_otheroutput_table) + (dst_positive_scale_multiply_exists_unique_otheroutput_table)) * S ((dst_positive_code_multiply_exists_unique_otheroutput_table) + (dst_positive_scale_multiply_exists_unique_otheroutput_table)) + ((dst_positive_scale_multiply_exists_unique_otheroutput_table) + (dst_positive_scale_multiply_exists_unique_otheroutput_table))) + (((dst_negative_code_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)) * S ((dst_negative_code_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)) + ((dst_negative_scale_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)))) + ((((dst_negative_code_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)) * S ((dst_negative_code_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)) + ((dst_negative_scale_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table))) + (((dst_negative_code_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)) * S ((dst_negative_code_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)) + ((dst_negative_scale_multiply_exists_unique_otheroutput_table) + (dst_negative_scale_multiply_exists_unique_otheroutput_table)))))) /\ (forall dst_index_multiply_exists_unique_otheroutput_table. (exists pvs_le_gap_multiply_exists_unique_otheroutput_tabledomain. pvs_le_gap_multiply_exists_unique_otheroutput_tabledomain + (dst_index_multiply_exists_unique_otheroutput_table) = (l)) -> exists dst_positive_multiply_exists_unique_otheroutput_table dst_negative_multiply_exists_unique_otheroutput_table dst_value_multiply_exists_unique_otheroutput_table. ((((exists ff_h_pvs_multiply_exists_unique_otheroutput_tableentrypositive. ff_h_pvs_multiply_exists_unique_otheroutput_tableentrypositive + S (dst_positive_multiply_exists_unique_otheroutput_table) = S ((S (dst_index_multiply_exists_unique_otheroutput_table)) * dst_positive_scale_multiply_exists_unique_otheroutput_table)) /\ exists ff_q_pvs_multiply_exists_unique_otheroutput_tableentrypositive. dst_positive_code_multiply_exists_unique_otheroutput_table = ff_q_pvs_multiply_exists_unique_otheroutput_tableentrypositive * S ((S (dst_index_multiply_exists_unique_otheroutput_table)) * dst_positive_scale_multiply_exists_unique_otheroutput_table) + (dst_positive_multiply_exists_unique_otheroutput_table))) /\ (((((exists ff_h_pvs_multiply_exists_unique_otheroutput_tableentrynegative. ff_h_pvs_multiply_exists_unique_otheroutput_tableentrynegative + S (dst_negative_multiply_exists_unique_otheroutput_table) = S ((S (dst_index_multiply_exists_unique_otheroutput_table)) * dst_negative_scale_multiply_exists_unique_otheroutput_table)) /\ exists ff_q_pvs_multiply_exists_unique_otheroutput_tableentrynegative. dst_negative_code_multiply_exists_unique_otheroutput_table = ff_q_pvs_multiply_exists_unique_otheroutput_tableentrynegative * S ((S (dst_index_multiply_exists_unique_otheroutput_table)) * dst_negative_scale_multiply_exists_unique_otheroutput_table) + (dst_negative_multiply_exists_unique_otheroutput_table))) /\ (exists ge_balance_positive_multiply_exists_unique_otheroutput_tableentryvalue ge_balance_negative_multiply_exists_unique_otheroutput_tableentryvalue. (((((dst_value_multiply_exists_unique_otheroutput_table) = 2 * (ge_balance_positive_multiply_exists_unique_otheroutput_tableentryvalue) /\ (ge_balance_negative_multiply_exists_unique_otheroutput_tableentryvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_otheroutput_tableentryvaluedecode. (((dst_value_multiply_exists_unique_otheroutput_table) = 2 * ge_signed_half_multiply_exists_unique_otheroutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_otheroutput_tableentryvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_otheroutput_tableentryvalue) = S ge_signed_half_multiply_exists_unique_otheroutput_tableentryvaluedecode))) /\ ((dst_positive_multiply_exists_unique_otheroutput_table) + ge_balance_negative_multiply_exists_unique_otheroutput_tableentryvalue = (dst_negative_multiply_exists_unique_otheroutput_table) + ge_balance_positive_multiply_exists_unique_otheroutput_tableentryvalue))))))))) /\ (forall sto_index_multiply_exists_unique_otherentries. (exists pvs_gap_multiply_exists_unique_otherentriesbound. pvs_gap_multiply_exists_unique_otherentriesbound + S (sto_index_multiply_exists_unique_otherentries) = (l)) -> exists sto_left_multiply_exists_unique_otherentries sto_right_multiply_exists_unique_otherentries sto_output_multiply_exists_unique_otherentries. ((exists dst_positive_code_multiply_exists_unique_otherentriesentryleft dst_positive_scale_multiply_exists_unique_otherentriesentryleft dst_negative_code_multiply_exists_unique_otherentriesentryleft dst_negative_scale_multiply_exists_unique_otherentriesentryleft dst_positive_multiply_exists_unique_otherentriesentryleft dst_negative_multiply_exists_unique_otherentriesentryleft. (((F) = (((((dst_positive_code_multiply_exists_unique_otherentriesentryleft) + (dst_positive_scale_multiply_exists_unique_otherentriesentryleft)) * S ((dst_positive_code_multiply_exists_unique_otherentriesentryleft) + (dst_positive_scale_multiply_exists_unique_otherentriesentryleft)) + ((dst_positive_scale_multiply_exists_unique_otherentriesentryleft) + (dst_positive_scale_multiply_exists_unique_otherentriesentryleft))) + (((dst_negative_code_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)))) * S ((((dst_positive_code_multiply_exists_unique_otherentriesentryleft) + (dst_positive_scale_multiply_exists_unique_otherentriesentryleft)) * S ((dst_positive_code_multiply_exists_unique_otherentriesentryleft) + (dst_positive_scale_multiply_exists_unique_otherentriesentryleft)) + ((dst_positive_scale_multiply_exists_unique_otherentriesentryleft) + (dst_positive_scale_multiply_exists_unique_otherentriesentryleft))) + (((dst_negative_code_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)))) + ((((dst_negative_code_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft))) + (((dst_negative_code_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryleft) + (dst_negative_scale_multiply_exists_unique_otherentriesentryleft)))))) /\ (((((exists ff_h_pvs_multiply_exists_unique_otherentriesentryleftpositive. ff_h_pvs_multiply_exists_unique_otherentriesentryleftpositive + S (dst_positive_multiply_exists_unique_otherentriesentryleft) = S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_positive_scale_multiply_exists_unique_otherentriesentryleft)) /\ exists ff_q_pvs_multiply_exists_unique_otherentriesentryleftpositive. dst_positive_code_multiply_exists_unique_otherentriesentryleft = ff_q_pvs_multiply_exists_unique_otherentriesentryleftpositive * S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_positive_scale_multiply_exists_unique_otherentriesentryleft) + (dst_positive_multiply_exists_unique_otherentriesentryleft))) /\ (((((exists ff_h_pvs_multiply_exists_unique_otherentriesentryleftnegative. ff_h_pvs_multiply_exists_unique_otherentriesentryleftnegative + S (dst_negative_multiply_exists_unique_otherentriesentryleft) = S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_negative_scale_multiply_exists_unique_otherentriesentryleft)) /\ exists ff_q_pvs_multiply_exists_unique_otherentriesentryleftnegative. dst_negative_code_multiply_exists_unique_otherentriesentryleft = ff_q_pvs_multiply_exists_unique_otherentriesentryleftnegative * S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_negative_scale_multiply_exists_unique_otherentriesentryleft) + (dst_negative_multiply_exists_unique_otherentriesentryleft))) /\ (exists ge_balance_positive_multiply_exists_unique_otherentriesentryleftvalue ge_balance_negative_multiply_exists_unique_otherentriesentryleftvalue. (((((sto_left_multiply_exists_unique_otherentries) = 2 * (ge_balance_positive_multiply_exists_unique_otherentriesentryleftvalue) /\ (ge_balance_negative_multiply_exists_unique_otherentriesentryleftvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_otherentriesentryleftvaluedecode. (((sto_left_multiply_exists_unique_otherentries) = 2 * ge_signed_half_multiply_exists_unique_otherentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_otherentriesentryleftvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_otherentriesentryleftvalue) = S ge_signed_half_multiply_exists_unique_otherentriesentryleftvaluedecode))) /\ ((dst_positive_multiply_exists_unique_otherentriesentryleft) + ge_balance_negative_multiply_exists_unique_otherentriesentryleftvalue = (dst_negative_multiply_exists_unique_otherentriesentryleft) + ge_balance_positive_multiply_exists_unique_otherentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_multiply_exists_unique_otherentriesentryright dst_positive_scale_multiply_exists_unique_otherentriesentryright dst_negative_code_multiply_exists_unique_otherentriesentryright dst_negative_scale_multiply_exists_unique_otherentriesentryright dst_positive_multiply_exists_unique_otherentriesentryright dst_negative_multiply_exists_unique_otherentriesentryright. (((G) = (((((dst_positive_code_multiply_exists_unique_otherentriesentryright) + (dst_positive_scale_multiply_exists_unique_otherentriesentryright)) * S ((dst_positive_code_multiply_exists_unique_otherentriesentryright) + (dst_positive_scale_multiply_exists_unique_otherentriesentryright)) + ((dst_positive_scale_multiply_exists_unique_otherentriesentryright) + (dst_positive_scale_multiply_exists_unique_otherentriesentryright))) + (((dst_negative_code_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)))) * S ((((dst_positive_code_multiply_exists_unique_otherentriesentryright) + (dst_positive_scale_multiply_exists_unique_otherentriesentryright)) * S ((dst_positive_code_multiply_exists_unique_otherentriesentryright) + (dst_positive_scale_multiply_exists_unique_otherentriesentryright)) + ((dst_positive_scale_multiply_exists_unique_otherentriesentryright) + (dst_positive_scale_multiply_exists_unique_otherentriesentryright))) + (((dst_negative_code_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)))) + ((((dst_negative_code_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright))) + (((dst_negative_code_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryright) + (dst_negative_scale_multiply_exists_unique_otherentriesentryright)))))) /\ (((((exists ff_h_pvs_multiply_exists_unique_otherentriesentryrightpositive. ff_h_pvs_multiply_exists_unique_otherentriesentryrightpositive + S (dst_positive_multiply_exists_unique_otherentriesentryright) = S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_positive_scale_multiply_exists_unique_otherentriesentryright)) /\ exists ff_q_pvs_multiply_exists_unique_otherentriesentryrightpositive. dst_positive_code_multiply_exists_unique_otherentriesentryright = ff_q_pvs_multiply_exists_unique_otherentriesentryrightpositive * S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_positive_scale_multiply_exists_unique_otherentriesentryright) + (dst_positive_multiply_exists_unique_otherentriesentryright))) /\ (((((exists ff_h_pvs_multiply_exists_unique_otherentriesentryrightnegative. ff_h_pvs_multiply_exists_unique_otherentriesentryrightnegative + S (dst_negative_multiply_exists_unique_otherentriesentryright) = S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_negative_scale_multiply_exists_unique_otherentriesentryright)) /\ exists ff_q_pvs_multiply_exists_unique_otherentriesentryrightnegative. dst_negative_code_multiply_exists_unique_otherentriesentryright = ff_q_pvs_multiply_exists_unique_otherentriesentryrightnegative * S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_negative_scale_multiply_exists_unique_otherentriesentryright) + (dst_negative_multiply_exists_unique_otherentriesentryright))) /\ (exists ge_balance_positive_multiply_exists_unique_otherentriesentryrightvalue ge_balance_negative_multiply_exists_unique_otherentriesentryrightvalue. (((((sto_right_multiply_exists_unique_otherentries) = 2 * (ge_balance_positive_multiply_exists_unique_otherentriesentryrightvalue) /\ (ge_balance_negative_multiply_exists_unique_otherentriesentryrightvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_otherentriesentryrightvaluedecode. (((sto_right_multiply_exists_unique_otherentries) = 2 * ge_signed_half_multiply_exists_unique_otherentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_otherentriesentryrightvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_otherentriesentryrightvalue) = S ge_signed_half_multiply_exists_unique_otherentriesentryrightvaluedecode))) /\ ((dst_positive_multiply_exists_unique_otherentriesentryright) + ge_balance_negative_multiply_exists_unique_otherentriesentryrightvalue = (dst_negative_multiply_exists_unique_otherentriesentryright) + ge_balance_positive_multiply_exists_unique_otherentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_multiply_exists_unique_otherentriesentryoutput dst_positive_scale_multiply_exists_unique_otherentriesentryoutput dst_negative_code_multiply_exists_unique_otherentriesentryoutput dst_negative_scale_multiply_exists_unique_otherentriesentryoutput dst_positive_multiply_exists_unique_otherentriesentryoutput dst_negative_multiply_exists_unique_otherentriesentryoutput. (((K) = (((((dst_positive_code_multiply_exists_unique_otherentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_otherentriesentryoutput)) * S ((dst_positive_code_multiply_exists_unique_otherentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_otherentriesentryoutput)) + ((dst_positive_scale_multiply_exists_unique_otherentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_otherentriesentryoutput))) + (((dst_negative_code_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)))) * S ((((dst_positive_code_multiply_exists_unique_otherentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_otherentriesentryoutput)) * S ((dst_positive_code_multiply_exists_unique_otherentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_otherentriesentryoutput)) + ((dst_positive_scale_multiply_exists_unique_otherentriesentryoutput) + (dst_positive_scale_multiply_exists_unique_otherentriesentryoutput))) + (((dst_negative_code_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)))) + ((((dst_negative_code_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput))) + (((dst_negative_code_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)) * S ((dst_negative_code_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)) + ((dst_negative_scale_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)))))) /\ (((((exists ff_h_pvs_multiply_exists_unique_otherentriesentryoutputpositive. ff_h_pvs_multiply_exists_unique_otherentriesentryoutputpositive + S (dst_positive_multiply_exists_unique_otherentriesentryoutput) = S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_positive_scale_multiply_exists_unique_otherentriesentryoutput)) /\ exists ff_q_pvs_multiply_exists_unique_otherentriesentryoutputpositive. dst_positive_code_multiply_exists_unique_otherentriesentryoutput = ff_q_pvs_multiply_exists_unique_otherentriesentryoutputpositive * S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_positive_scale_multiply_exists_unique_otherentriesentryoutput) + (dst_positive_multiply_exists_unique_otherentriesentryoutput))) /\ (((((exists ff_h_pvs_multiply_exists_unique_otherentriesentryoutputnegative. ff_h_pvs_multiply_exists_unique_otherentriesentryoutputnegative + S (dst_negative_multiply_exists_unique_otherentriesentryoutput) = S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_negative_scale_multiply_exists_unique_otherentriesentryoutput)) /\ exists ff_q_pvs_multiply_exists_unique_otherentriesentryoutputnegative. dst_negative_code_multiply_exists_unique_otherentriesentryoutput = ff_q_pvs_multiply_exists_unique_otherentriesentryoutputnegative * S ((S (sto_index_multiply_exists_unique_otherentries)) * dst_negative_scale_multiply_exists_unique_otherentriesentryoutput) + (dst_negative_multiply_exists_unique_otherentriesentryoutput))) /\ (exists ge_balance_positive_multiply_exists_unique_otherentriesentryoutputvalue ge_balance_negative_multiply_exists_unique_otherentriesentryoutputvalue. (((((sto_output_multiply_exists_unique_otherentries) = 2 * (ge_balance_positive_multiply_exists_unique_otherentriesentryoutputvalue) /\ (ge_balance_negative_multiply_exists_unique_otherentriesentryoutputvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_otherentriesentryoutputvaluedecode. (((sto_output_multiply_exists_unique_otherentries) = 2 * ge_signed_half_multiply_exists_unique_otherentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_otherentriesentryoutputvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_otherentriesentryoutputvalue) = S ge_signed_half_multiply_exists_unique_otherentriesentryoutputvaluedecode))) /\ ((dst_positive_multiply_exists_unique_otherentriesentryoutput) + ge_balance_negative_multiply_exists_unique_otherentriesentryoutputvalue = (dst_negative_multiply_exists_unique_otherentriesentryoutput) + ge_balance_positive_multiply_exists_unique_otherentriesentryoutputvalue))))))))) /\ (exists sto_ap_multiply_exists_unique_otherentriesentryoperation sto_an_multiply_exists_unique_otherentriesentryoperation sto_bp_multiply_exists_unique_otherentriesentryoperation sto_bn_multiply_exists_unique_otherentriesentryoperation sto_cp_multiply_exists_unique_otherentriesentryoperation sto_cn_multiply_exists_unique_otherentriesentryoperation. (((((sto_left_multiply_exists_unique_otherentries) = 2 * (sto_ap_multiply_exists_unique_otherentriesentryoperation) /\ (sto_an_multiply_exists_unique_otherentriesentryoperation) = 0) \/ exists ge_signed_half_multiply_exists_unique_otherentriesentryoperationleft. (((sto_left_multiply_exists_unique_otherentries) = 2 * ge_signed_half_multiply_exists_unique_otherentriesentryoperationleft + 1 /\ (sto_ap_multiply_exists_unique_otherentriesentryoperation) = 0) /\ (sto_an_multiply_exists_unique_otherentriesentryoperation) = S ge_signed_half_multiply_exists_unique_otherentriesentryoperationleft))) /\ ((((((sto_right_multiply_exists_unique_otherentries) = 2 * (sto_bp_multiply_exists_unique_otherentriesentryoperation) /\ (sto_bn_multiply_exists_unique_otherentriesentryoperation) = 0) \/ exists ge_signed_half_multiply_exists_unique_otherentriesentryoperationright. (((sto_right_multiply_exists_unique_otherentries) = 2 * ge_signed_half_multiply_exists_unique_otherentriesentryoperationright + 1 /\ (sto_bp_multiply_exists_unique_otherentriesentryoperation) = 0) /\ (sto_bn_multiply_exists_unique_otherentriesentryoperation) = S ge_signed_half_multiply_exists_unique_otherentriesentryoperationright))) /\ ((((((sto_output_multiply_exists_unique_otherentries) = 2 * (sto_cp_multiply_exists_unique_otherentriesentryoperation) /\ (sto_cn_multiply_exists_unique_otherentriesentryoperation) = 0) \/ exists ge_signed_half_multiply_exists_unique_otherentriesentryoperationoutput. (((sto_output_multiply_exists_unique_otherentries) = 2 * ge_signed_half_multiply_exists_unique_otherentriesentryoperationoutput + 1 /\ (sto_cp_multiply_exists_unique_otherentriesentryoperation) = 0) /\ (sto_cn_multiply_exists_unique_otherentriesentryoperation) = S ge_signed_half_multiply_exists_unique_otherentriesentryoperationoutput))) /\ ((sto_ap_multiply_exists_unique_otherentriesentryoperation * sto_bp_multiply_exists_unique_otherentriesentryoperation + sto_an_multiply_exists_unique_otherentriesentryoperation * sto_bn_multiply_exists_unique_otherentriesentryoperation) + sto_cn_multiply_exists_unique_otherentriesentryoperation = (sto_ap_multiply_exists_unique_otherentriesentryoperation * sto_bn_multiply_exists_unique_otherentriesentryoperation + sto_an_multiply_exists_unique_otherentriesentryoperation * sto_bp_multiply_exists_unique_otherentriesentryoperation) + sto_cp_multiply_exists_unique_otherentriesentryoperation))))))))))))))))))) -> (forall dst_index_multiply_exists_unique_equal dst_first_multiply_exists_unique_equal dst_second_multiply_exists_unique_equal. (exists pvs_gap_multiply_exists_unique_equalbound. pvs_gap_multiply_exists_unique_equalbound + S (dst_index_multiply_exists_unique_equal) = (l)) -> (exists dst_positive_code_multiply_exists_unique_equalfirst dst_positive_scale_multiply_exists_unique_equalfirst dst_negative_code_multiply_exists_unique_equalfirst dst_negative_scale_multiply_exists_unique_equalfirst dst_positive_multiply_exists_unique_equalfirst dst_negative_multiply_exists_unique_equalfirst. (((H) = (((((dst_positive_code_multiply_exists_unique_equalfirst) + (dst_positive_scale_multiply_exists_unique_equalfirst)) * S ((dst_positive_code_multiply_exists_unique_equalfirst) + (dst_positive_scale_multiply_exists_unique_equalfirst)) + ((dst_positive_scale_multiply_exists_unique_equalfirst) + (dst_positive_scale_multiply_exists_unique_equalfirst))) + (((dst_negative_code_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)) * S ((dst_negative_code_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)) + ((dst_negative_scale_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)))) * S ((((dst_positive_code_multiply_exists_unique_equalfirst) + (dst_positive_scale_multiply_exists_unique_equalfirst)) * S ((dst_positive_code_multiply_exists_unique_equalfirst) + (dst_positive_scale_multiply_exists_unique_equalfirst)) + ((dst_positive_scale_multiply_exists_unique_equalfirst) + (dst_positive_scale_multiply_exists_unique_equalfirst))) + (((dst_negative_code_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)) * S ((dst_negative_code_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)) + ((dst_negative_scale_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)))) + ((((dst_negative_code_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)) * S ((dst_negative_code_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)) + ((dst_negative_scale_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst))) + (((dst_negative_code_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)) * S ((dst_negative_code_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)) + ((dst_negative_scale_multiply_exists_unique_equalfirst) + (dst_negative_scale_multiply_exists_unique_equalfirst)))))) /\ (((((exists ff_h_pvs_multiply_exists_unique_equalfirstpositive. ff_h_pvs_multiply_exists_unique_equalfirstpositive + S (dst_positive_multiply_exists_unique_equalfirst) = S ((S (dst_index_multiply_exists_unique_equal)) * dst_positive_scale_multiply_exists_unique_equalfirst)) /\ exists ff_q_pvs_multiply_exists_unique_equalfirstpositive. dst_positive_code_multiply_exists_unique_equalfirst = ff_q_pvs_multiply_exists_unique_equalfirstpositive * S ((S (dst_index_multiply_exists_unique_equal)) * dst_positive_scale_multiply_exists_unique_equalfirst) + (dst_positive_multiply_exists_unique_equalfirst))) /\ (((((exists ff_h_pvs_multiply_exists_unique_equalfirstnegative. ff_h_pvs_multiply_exists_unique_equalfirstnegative + S (dst_negative_multiply_exists_unique_equalfirst) = S ((S (dst_index_multiply_exists_unique_equal)) * dst_negative_scale_multiply_exists_unique_equalfirst)) /\ exists ff_q_pvs_multiply_exists_unique_equalfirstnegative. dst_negative_code_multiply_exists_unique_equalfirst = ff_q_pvs_multiply_exists_unique_equalfirstnegative * S ((S (dst_index_multiply_exists_unique_equal)) * dst_negative_scale_multiply_exists_unique_equalfirst) + (dst_negative_multiply_exists_unique_equalfirst))) /\ (exists ge_balance_positive_multiply_exists_unique_equalfirstvalue ge_balance_negative_multiply_exists_unique_equalfirstvalue. (((((dst_first_multiply_exists_unique_equal) = 2 * (ge_balance_positive_multiply_exists_unique_equalfirstvalue) /\ (ge_balance_negative_multiply_exists_unique_equalfirstvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_equalfirstvaluedecode. (((dst_first_multiply_exists_unique_equal) = 2 * ge_signed_half_multiply_exists_unique_equalfirstvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_equalfirstvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_equalfirstvalue) = S ge_signed_half_multiply_exists_unique_equalfirstvaluedecode))) /\ ((dst_positive_multiply_exists_unique_equalfirst) + ge_balance_negative_multiply_exists_unique_equalfirstvalue = (dst_negative_multiply_exists_unique_equalfirst) + ge_balance_positive_multiply_exists_unique_equalfirstvalue))))))))) -> (exists dst_positive_code_multiply_exists_unique_equalsecond dst_positive_scale_multiply_exists_unique_equalsecond dst_negative_code_multiply_exists_unique_equalsecond dst_negative_scale_multiply_exists_unique_equalsecond dst_positive_multiply_exists_unique_equalsecond dst_negative_multiply_exists_unique_equalsecond. (((K) = (((((dst_positive_code_multiply_exists_unique_equalsecond) + (dst_positive_scale_multiply_exists_unique_equalsecond)) * S ((dst_positive_code_multiply_exists_unique_equalsecond) + (dst_positive_scale_multiply_exists_unique_equalsecond)) + ((dst_positive_scale_multiply_exists_unique_equalsecond) + (dst_positive_scale_multiply_exists_unique_equalsecond))) + (((dst_negative_code_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)) * S ((dst_negative_code_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)) + ((dst_negative_scale_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)))) * S ((((dst_positive_code_multiply_exists_unique_equalsecond) + (dst_positive_scale_multiply_exists_unique_equalsecond)) * S ((dst_positive_code_multiply_exists_unique_equalsecond) + (dst_positive_scale_multiply_exists_unique_equalsecond)) + ((dst_positive_scale_multiply_exists_unique_equalsecond) + (dst_positive_scale_multiply_exists_unique_equalsecond))) + (((dst_negative_code_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)) * S ((dst_negative_code_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)) + ((dst_negative_scale_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)))) + ((((dst_negative_code_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)) * S ((dst_negative_code_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)) + ((dst_negative_scale_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond))) + (((dst_negative_code_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)) * S ((dst_negative_code_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)) + ((dst_negative_scale_multiply_exists_unique_equalsecond) + (dst_negative_scale_multiply_exists_unique_equalsecond)))))) /\ (((((exists ff_h_pvs_multiply_exists_unique_equalsecondpositive. ff_h_pvs_multiply_exists_unique_equalsecondpositive + S (dst_positive_multiply_exists_unique_equalsecond) = S ((S (dst_index_multiply_exists_unique_equal)) * dst_positive_scale_multiply_exists_unique_equalsecond)) /\ exists ff_q_pvs_multiply_exists_unique_equalsecondpositive. dst_positive_code_multiply_exists_unique_equalsecond = ff_q_pvs_multiply_exists_unique_equalsecondpositive * S ((S (dst_index_multiply_exists_unique_equal)) * dst_positive_scale_multiply_exists_unique_equalsecond) + (dst_positive_multiply_exists_unique_equalsecond))) /\ (((((exists ff_h_pvs_multiply_exists_unique_equalsecondnegative. ff_h_pvs_multiply_exists_unique_equalsecondnegative + S (dst_negative_multiply_exists_unique_equalsecond) = S ((S (dst_index_multiply_exists_unique_equal)) * dst_negative_scale_multiply_exists_unique_equalsecond)) /\ exists ff_q_pvs_multiply_exists_unique_equalsecondnegative. dst_negative_code_multiply_exists_unique_equalsecond = ff_q_pvs_multiply_exists_unique_equalsecondnegative * S ((S (dst_index_multiply_exists_unique_equal)) * dst_negative_scale_multiply_exists_unique_equalsecond) + (dst_negative_multiply_exists_unique_equalsecond))) /\ (exists ge_balance_positive_multiply_exists_unique_equalsecondvalue ge_balance_negative_multiply_exists_unique_equalsecondvalue. (((((dst_second_multiply_exists_unique_equal) = 2 * (ge_balance_positive_multiply_exists_unique_equalsecondvalue) /\ (ge_balance_negative_multiply_exists_unique_equalsecondvalue) = 0) \/ exists ge_signed_half_multiply_exists_unique_equalsecondvaluedecode. (((dst_second_multiply_exists_unique_equal) = 2 * ge_signed_half_multiply_exists_unique_equalsecondvaluedecode + 1 /\ (ge_balance_positive_multiply_exists_unique_equalsecondvalue) = 0) /\ (ge_balance_negative_multiply_exists_unique_equalsecondvalue) = S ge_signed_half_multiply_exists_unique_equalsecondvaluedecode))) /\ ((dst_positive_multiply_exists_unique_equalsecond) + ge_balance_negative_multiply_exists_unique_equalsecondvalue = (dst_negative_multiply_exists_unique_equalsecond) + ge_balance_positive_multiply_exists_unique_equalsecondvalue))))))))) -> dst_first_multiply_exists_unique_equal = dst_second_multiply_exists_unique_equal)))Constructive proof overview
Generated structural guide
Construct an actual pointwise multiply output and prove uniqueness of every represented entry; the raw table code is deliberately not claimed unique.
The unchanged tactic script uses 2 declared prerequisites and contains 26 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct dependents
none
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 hwL6–12
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed table multiply exists.
03Separate the logical casesL13–13
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L13
cases hw
04Construct an explicit witnessL14–14
Supply the displayed value, then prove that it has the required property.
- L14
exists x
05Separate the logical casesL15–15
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L15
split
06Use earlier factsL16–16
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L16
exact hw_witness
07Fix variables and assumptionsL17–18
08Use earlier factsL19–26
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L19
specialize signed_table_multiply_extensional_unique (F) - L20
specialize signed_table_multiply_extensional_unique (G) - L21
specialize signed_table_multiply_extensional_unique (x) - L22
specialize signed_table_multiply_extensional_unique (K) - L23
specialize signed_table_multiply_extensional_unique (l) - L24
apply signed_table_multiply_extensional_unique - L25
exact hw_witness - L26
exact hother
Original exact command ledger · 26 lines
- 0001
intro l - 0002
intro F - 0003
intro G - 0004
intro ht0 - 0005
intro ht1 - 0006
have hw : exists H. (((exists dst_positive_code_multiply_unique_constructleft_table dst_positive_scale_multiply_unique_constructleft_table dst_negative_code_multiply_unique_constructleft_table dst_negative_scale_multiply_unique_constructleft_table. (((F) = (((((dst_positive_code_multiply_unique_constructleft_table) + (dst_positive_scale_multiply_unique_constructleft_table)) * S ((dst_positive_code_multiply_unique_constructleft_table) + (dst_positive_scale_multiply_unique_constructleft_table)) + ((dst_positive_scale_multiply_unique_constructleft_table) + (dst_positive_scale_multiply_unique_constructleft_table))) + (((dst_negative_code_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)) * S ((dst_negative_code_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)) + ((dst_negative_scale_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)))) * S ((((dst_positive_code_multiply_unique_constructleft_table) + (dst_positive_scale_multiply_unique_constructleft_table)) * S ((dst_positive_code_multiply_unique_constructleft_table) + (dst_positive_scale_multiply_unique_constructleft_table)) + ((dst_positive_scale_multiply_unique_constructleft_table) + (dst_positive_scale_multiply_unique_constructleft_table))) + (((dst_negative_code_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)) * S ((dst_negative_code_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)) + ((dst_negative_scale_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)))) + ((((dst_negative_code_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)) * S ((dst_negative_code_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)) + ((dst_negative_scale_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table))) + (((dst_negative_code_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)) * S ((dst_negative_code_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)) + ((dst_negative_scale_multiply_unique_constructleft_table) + (dst_negative_scale_multiply_unique_constructleft_table)))))) /\ (forall dst_index_multiply_unique_constructleft_table. (exists pvs_le_gap_multiply_unique_constructleft_tabledomain. pvs_le_gap_multiply_unique_constructleft_tabledomain + (dst_index_multiply_unique_constructleft_table) = (l)) -> exists dst_positive_multiply_unique_constructleft_table dst_negative_multiply_unique_constructleft_table dst_value_multiply_unique_constructleft_table. ((((exists ff_h_pvs_multiply_unique_constructleft_tableentrypositive. ff_h_pvs_multiply_unique_constructleft_tableentrypositive + S (dst_positive_multiply_unique_constructleft_table) = S ((S (dst_index_multiply_unique_constructleft_table)) * dst_positive_scale_multiply_unique_constructleft_table)) /\ exists ff_q_pvs_multiply_unique_constructleft_tableentrypositive. dst_positive_code_multiply_unique_constructleft_table = ff_q_pvs_multiply_unique_constructleft_tableentrypositive * S ((S (dst_index_multiply_unique_constructleft_table)) * dst_positive_scale_multiply_unique_constructleft_table) + (dst_positive_multiply_unique_constructleft_table))) /\ (((((exists ff_h_pvs_multiply_unique_constructleft_tableentrynegative. ff_h_pvs_multiply_unique_constructleft_tableentrynegative + S (dst_negative_multiply_unique_constructleft_table) = S ((S (dst_index_multiply_unique_constructleft_table)) * dst_negative_scale_multiply_unique_constructleft_table)) /\ exists ff_q_pvs_multiply_unique_constructleft_tableentrynegative. dst_negative_code_multiply_unique_constructleft_table = ff_q_pvs_multiply_unique_constructleft_tableentrynegative * S ((S (dst_index_multiply_unique_constructleft_table)) * dst_negative_scale_multiply_unique_constructleft_table) + (dst_negative_multiply_unique_constructleft_table))) /\ (exists ge_balance_positive_multiply_unique_constructleft_tableentryvalue ge_balance_negative_multiply_unique_constructleft_tableentryvalue. (((((dst_value_multiply_unique_constructleft_table) = 2 * (ge_balance_positive_multiply_unique_constructleft_tableentryvalue) /\ (ge_balance_negative_multiply_unique_constructleft_tableentryvalue) = 0) \/ exists ge_signed_half_multiply_unique_constructleft_tableentryvaluedecode. (((dst_value_multiply_unique_constructleft_table) = 2 * ge_signed_half_multiply_unique_constructleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_multiply_unique_constructleft_tableentryvalue) = 0) /\ (ge_balance_negative_multiply_unique_constructleft_tableentryvalue) = S ge_signed_half_multiply_unique_constructleft_tableentryvaluedecode))) /\ ((dst_positive_multiply_unique_constructleft_table) + ge_balance_negative_multiply_unique_constructleft_tableentryvalue = (dst_negative_multiply_unique_constructleft_table) + ge_balance_positive_multiply_unique_constructleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_multiply_unique_constructright_table dst_positive_scale_multiply_unique_constructright_table dst_negative_code_multiply_unique_constructright_table dst_negative_scale_multiply_unique_constructright_table. (((G) = (((((dst_positive_code_multiply_unique_constructright_table) + (dst_positive_scale_multiply_unique_constructright_table)) * S ((dst_positive_code_multiply_unique_constructright_table) + (dst_positive_scale_multiply_unique_constructright_table)) + ((dst_positive_scale_multiply_unique_constructright_table) + (dst_positive_scale_multiply_unique_constructright_table))) + (((dst_negative_code_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)) * S ((dst_negative_code_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)) + ((dst_negative_scale_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)))) * S ((((dst_positive_code_multiply_unique_constructright_table) + (dst_positive_scale_multiply_unique_constructright_table)) * S ((dst_positive_code_multiply_unique_constructright_table) + (dst_positive_scale_multiply_unique_constructright_table)) + ((dst_positive_scale_multiply_unique_constructright_table) + (dst_positive_scale_multiply_unique_constructright_table))) + (((dst_negative_code_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)) * S ((dst_negative_code_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)) + ((dst_negative_scale_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)))) + ((((dst_negative_code_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)) * S ((dst_negative_code_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)) + ((dst_negative_scale_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table))) + (((dst_negative_code_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)) * S ((dst_negative_code_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)) + ((dst_negative_scale_multiply_unique_constructright_table) + (dst_negative_scale_multiply_unique_constructright_table)))))) /\ (forall dst_index_multiply_unique_constructright_table. (exists pvs_le_gap_multiply_unique_constructright_tabledomain. pvs_le_gap_multiply_unique_constructright_tabledomain + (dst_index_multiply_unique_constructright_table) = (l)) -> exists dst_positive_multiply_unique_constructright_table dst_negative_multiply_unique_constructright_table dst_value_multiply_unique_constructright_table. ((((exists ff_h_pvs_multiply_unique_constructright_tableentrypositive. ff_h_pvs_multiply_unique_constructright_tableentrypositive + S (dst_positive_multiply_unique_constructright_table) = S ((S (dst_index_multiply_unique_constructright_table)) * dst_positive_scale_multiply_unique_constructright_table)) /\ exists ff_q_pvs_multiply_unique_constructright_tableentrypositive. dst_positive_code_multiply_unique_constructright_table = ff_q_pvs_multiply_unique_constructright_tableentrypositive * S ((S (dst_index_multiply_unique_constructright_table)) * dst_positive_scale_multiply_unique_constructright_table) + (dst_positive_multiply_unique_constructright_table))) /\ (((((exists ff_h_pvs_multiply_unique_constructright_tableentrynegative. ff_h_pvs_multiply_unique_constructright_tableentrynegative + S (dst_negative_multiply_unique_constructright_table) = S ((S (dst_index_multiply_unique_constructright_table)) * dst_negative_scale_multiply_unique_constructright_table)) /\ exists ff_q_pvs_multiply_unique_constructright_tableentrynegative. dst_negative_code_multiply_unique_constructright_table = ff_q_pvs_multiply_unique_constructright_tableentrynegative * S ((S (dst_index_multiply_unique_constructright_table)) * dst_negative_scale_multiply_unique_constructright_table) + (dst_negative_multiply_unique_constructright_table))) /\ (exists ge_balance_positive_multiply_unique_constructright_tableentryvalue ge_balance_negative_multiply_unique_constructright_tableentryvalue. (((((dst_value_multiply_unique_constructright_table) = 2 * (ge_balance_positive_multiply_unique_constructright_tableentryvalue) /\ (ge_balance_negative_multiply_unique_constructright_tableentryvalue) = 0) \/ exists ge_signed_half_multiply_unique_constructright_tableentryvaluedecode. (((dst_value_multiply_unique_constructright_table) = 2 * ge_signed_half_multiply_unique_constructright_tableentryvaluedecode + 1 /\ (ge_balance_positive_multiply_unique_constructright_tableentryvalue) = 0) /\ (ge_balance_negative_multiply_unique_constructright_tableentryvalue) = S ge_signed_half_multiply_unique_constructright_tableentryvaluedecode))) /\ ((dst_positive_multiply_unique_constructright_table) + ge_balance_negative_multiply_unique_constructright_tableentryvalue = (dst_negative_multiply_unique_constructright_table) + ge_balance_positive_multiply_unique_constructright_tableentryvalue))))))))) /\ (((exists dst_positive_code_multiply_unique_constructoutput_table dst_positive_scale_multiply_unique_constructoutput_table dst_negative_code_multiply_unique_constructoutput_table dst_negative_scale_multiply_unique_constructoutput_table. (((H) = (((((dst_positive_code_multiply_unique_constructoutput_table) + (dst_positive_scale_multiply_unique_constructoutput_table)) * S ((dst_positive_code_multiply_unique_constructoutput_table) + (dst_positive_scale_multiply_unique_constructoutput_table)) + ((dst_positive_scale_multiply_unique_constructoutput_table) + (dst_positive_scale_multiply_unique_constructoutput_table))) + (((dst_negative_code_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)) * S ((dst_negative_code_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)) + ((dst_negative_scale_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)))) * S ((((dst_positive_code_multiply_unique_constructoutput_table) + (dst_positive_scale_multiply_unique_constructoutput_table)) * S ((dst_positive_code_multiply_unique_constructoutput_table) + (dst_positive_scale_multiply_unique_constructoutput_table)) + ((dst_positive_scale_multiply_unique_constructoutput_table) + (dst_positive_scale_multiply_unique_constructoutput_table))) + (((dst_negative_code_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)) * S ((dst_negative_code_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)) + ((dst_negative_scale_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)))) + ((((dst_negative_code_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)) * S ((dst_negative_code_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)) + ((dst_negative_scale_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table))) + (((dst_negative_code_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)) * S ((dst_negative_code_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)) + ((dst_negative_scale_multiply_unique_constructoutput_table) + (dst_negative_scale_multiply_unique_constructoutput_table)))))) /\ (forall dst_index_multiply_unique_constructoutput_table. (exists pvs_le_gap_multiply_unique_constructoutput_tabledomain. pvs_le_gap_multiply_unique_constructoutput_tabledomain + (dst_index_multiply_unique_constructoutput_table) = (l)) -> exists dst_positive_multiply_unique_constructoutput_table dst_negative_multiply_unique_constructoutput_table dst_value_multiply_unique_constructoutput_table. ((((exists ff_h_pvs_multiply_unique_constructoutput_tableentrypositive. ff_h_pvs_multiply_unique_constructoutput_tableentrypositive + S (dst_positive_multiply_unique_constructoutput_table) = S ((S (dst_index_multiply_unique_constructoutput_table)) * dst_positive_scale_multiply_unique_constructoutput_table)) /\ exists ff_q_pvs_multiply_unique_constructoutput_tableentrypositive. dst_positive_code_multiply_unique_constructoutput_table = ff_q_pvs_multiply_unique_constructoutput_tableentrypositive * S ((S (dst_index_multiply_unique_constructoutput_table)) * dst_positive_scale_multiply_unique_constructoutput_table) + (dst_positive_multiply_unique_constructoutput_table))) /\ (((((exists ff_h_pvs_multiply_unique_constructoutput_tableentrynegative. ff_h_pvs_multiply_unique_constructoutput_tableentrynegative + S (dst_negative_multiply_unique_constructoutput_table) = S ((S (dst_index_multiply_unique_constructoutput_table)) * dst_negative_scale_multiply_unique_constructoutput_table)) /\ exists ff_q_pvs_multiply_unique_constructoutput_tableentrynegative. dst_negative_code_multiply_unique_constructoutput_table = ff_q_pvs_multiply_unique_constructoutput_tableentrynegative * S ((S (dst_index_multiply_unique_constructoutput_table)) * dst_negative_scale_multiply_unique_constructoutput_table) + (dst_negative_multiply_unique_constructoutput_table))) /\ (exists ge_balance_positive_multiply_unique_constructoutput_tableentryvalue ge_balance_negative_multiply_unique_constructoutput_tableentryvalue. (((((dst_value_multiply_unique_constructoutput_table) = 2 * (ge_balance_positive_multiply_unique_constructoutput_tableentryvalue) /\ (ge_balance_negative_multiply_unique_constructoutput_tableentryvalue) = 0) \/ exists ge_signed_half_multiply_unique_constructoutput_tableentryvaluedecode. (((dst_value_multiply_unique_constructoutput_table) = 2 * ge_signed_half_multiply_unique_constructoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_multiply_unique_constructoutput_tableentryvalue) = 0) /\ (ge_balance_negative_multiply_unique_constructoutput_tableentryvalue) = S ge_signed_half_multiply_unique_constructoutput_tableentryvaluedecode))) /\ ((dst_positive_multiply_unique_constructoutput_table) + ge_balance_negative_multiply_unique_constructoutput_tableentryvalue = (dst_negative_multiply_unique_constructoutput_table) + ge_balance_positive_multiply_unique_constructoutput_tableentryvalue))))))))) /\ (forall sto_index_multiply_unique_constructentries. (exists pvs_gap_multiply_unique_constructentriesbound. pvs_gap_multiply_unique_constructentriesbound + S (sto_index_multiply_unique_constructentries) = (l)) -> exists sto_left_multiply_unique_constructentries sto_right_multiply_unique_constructentries sto_output_multiply_unique_constructentries. ((exists dst_positive_code_multiply_unique_constructentriesentryleft dst_positive_scale_multiply_unique_constructentriesentryleft dst_negative_code_multiply_unique_constructentriesentryleft dst_negative_scale_multiply_unique_constructentriesentryleft dst_positive_multiply_unique_constructentriesentryleft dst_negative_multiply_unique_constructentriesentryleft. (((F) = (((((dst_positive_code_multiply_unique_constructentriesentryleft) + (dst_positive_scale_multiply_unique_constructentriesentryleft)) * S ((dst_positive_code_multiply_unique_constructentriesentryleft) + (dst_positive_scale_multiply_unique_constructentriesentryleft)) + ((dst_positive_scale_multiply_unique_constructentriesentryleft) + (dst_positive_scale_multiply_unique_constructentriesentryleft))) + (((dst_negative_code_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)) * S ((dst_negative_code_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)) + ((dst_negative_scale_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)))) * S ((((dst_positive_code_multiply_unique_constructentriesentryleft) + (dst_positive_scale_multiply_unique_constructentriesentryleft)) * S ((dst_positive_code_multiply_unique_constructentriesentryleft) + (dst_positive_scale_multiply_unique_constructentriesentryleft)) + ((dst_positive_scale_multiply_unique_constructentriesentryleft) + (dst_positive_scale_multiply_unique_constructentriesentryleft))) + (((dst_negative_code_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)) * S ((dst_negative_code_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)) + ((dst_negative_scale_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)))) + ((((dst_negative_code_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)) * S ((dst_negative_code_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)) + ((dst_negative_scale_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft))) + (((dst_negative_code_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)) * S ((dst_negative_code_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)) + ((dst_negative_scale_multiply_unique_constructentriesentryleft) + (dst_negative_scale_multiply_unique_constructentriesentryleft)))))) /\ (((((exists ff_h_pvs_multiply_unique_constructentriesentryleftpositive. ff_h_pvs_multiply_unique_constructentriesentryleftpositive + S (dst_positive_multiply_unique_constructentriesentryleft) = S ((S (sto_index_multiply_unique_constructentries)) * dst_positive_scale_multiply_unique_constructentriesentryleft)) /\ exists ff_q_pvs_multiply_unique_constructentriesentryleftpositive. dst_positive_code_multiply_unique_constructentriesentryleft = ff_q_pvs_multiply_unique_constructentriesentryleftpositive * S ((S (sto_index_multiply_unique_constructentries)) * dst_positive_scale_multiply_unique_constructentriesentryleft) + (dst_positive_multiply_unique_constructentriesentryleft))) /\ (((((exists ff_h_pvs_multiply_unique_constructentriesentryleftnegative. ff_h_pvs_multiply_unique_constructentriesentryleftnegative + S (dst_negative_multiply_unique_constructentriesentryleft) = S ((S (sto_index_multiply_unique_constructentries)) * dst_negative_scale_multiply_unique_constructentriesentryleft)) /\ exists ff_q_pvs_multiply_unique_constructentriesentryleftnegative. dst_negative_code_multiply_unique_constructentriesentryleft = ff_q_pvs_multiply_unique_constructentriesentryleftnegative * S ((S (sto_index_multiply_unique_constructentries)) * dst_negative_scale_multiply_unique_constructentriesentryleft) + (dst_negative_multiply_unique_constructentriesentryleft))) /\ (exists ge_balance_positive_multiply_unique_constructentriesentryleftvalue ge_balance_negative_multiply_unique_constructentriesentryleftvalue. (((((sto_left_multiply_unique_constructentries) = 2 * (ge_balance_positive_multiply_unique_constructentriesentryleftvalue) /\ (ge_balance_negative_multiply_unique_constructentriesentryleftvalue) = 0) \/ exists ge_signed_half_multiply_unique_constructentriesentryleftvaluedecode. (((sto_left_multiply_unique_constructentries) = 2 * ge_signed_half_multiply_unique_constructentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_multiply_unique_constructentriesentryleftvalue) = 0) /\ (ge_balance_negative_multiply_unique_constructentriesentryleftvalue) = S ge_signed_half_multiply_unique_constructentriesentryleftvaluedecode))) /\ ((dst_positive_multiply_unique_constructentriesentryleft) + ge_balance_negative_multiply_unique_constructentriesentryleftvalue = (dst_negative_multiply_unique_constructentriesentryleft) + ge_balance_positive_multiply_unique_constructentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_multiply_unique_constructentriesentryright dst_positive_scale_multiply_unique_constructentriesentryright dst_negative_code_multiply_unique_constructentriesentryright dst_negative_scale_multiply_unique_constructentriesentryright dst_positive_multiply_unique_constructentriesentryright dst_negative_multiply_unique_constructentriesentryright. (((G) = (((((dst_positive_code_multiply_unique_constructentriesentryright) + (dst_positive_scale_multiply_unique_constructentriesentryright)) * S ((dst_positive_code_multiply_unique_constructentriesentryright) + (dst_positive_scale_multiply_unique_constructentriesentryright)) + ((dst_positive_scale_multiply_unique_constructentriesentryright) + (dst_positive_scale_multiply_unique_constructentriesentryright))) + (((dst_negative_code_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)) * S ((dst_negative_code_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)) + ((dst_negative_scale_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)))) * S ((((dst_positive_code_multiply_unique_constructentriesentryright) + (dst_positive_scale_multiply_unique_constructentriesentryright)) * S ((dst_positive_code_multiply_unique_constructentriesentryright) + (dst_positive_scale_multiply_unique_constructentriesentryright)) + ((dst_positive_scale_multiply_unique_constructentriesentryright) + (dst_positive_scale_multiply_unique_constructentriesentryright))) + (((dst_negative_code_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)) * S ((dst_negative_code_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)) + ((dst_negative_scale_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)))) + ((((dst_negative_code_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)) * S ((dst_negative_code_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)) + ((dst_negative_scale_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright))) + (((dst_negative_code_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)) * S ((dst_negative_code_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)) + ((dst_negative_scale_multiply_unique_constructentriesentryright) + (dst_negative_scale_multiply_unique_constructentriesentryright)))))) /\ (((((exists ff_h_pvs_multiply_unique_constructentriesentryrightpositive. ff_h_pvs_multiply_unique_constructentriesentryrightpositive + S (dst_positive_multiply_unique_constructentriesentryright) = S ((S (sto_index_multiply_unique_constructentries)) * dst_positive_scale_multiply_unique_constructentriesentryright)) /\ exists ff_q_pvs_multiply_unique_constructentriesentryrightpositive. dst_positive_code_multiply_unique_constructentriesentryright = ff_q_pvs_multiply_unique_constructentriesentryrightpositive * S ((S (sto_index_multiply_unique_constructentries)) * dst_positive_scale_multiply_unique_constructentriesentryright) + (dst_positive_multiply_unique_constructentriesentryright))) /\ (((((exists ff_h_pvs_multiply_unique_constructentriesentryrightnegative. ff_h_pvs_multiply_unique_constructentriesentryrightnegative + S (dst_negative_multiply_unique_constructentriesentryright) = S ((S (sto_index_multiply_unique_constructentries)) * dst_negative_scale_multiply_unique_constructentriesentryright)) /\ exists ff_q_pvs_multiply_unique_constructentriesentryrightnegative. dst_negative_code_multiply_unique_constructentriesentryright = ff_q_pvs_multiply_unique_constructentriesentryrightnegative * S ((S (sto_index_multiply_unique_constructentries)) * dst_negative_scale_multiply_unique_constructentriesentryright) + (dst_negative_multiply_unique_constructentriesentryright))) /\ (exists ge_balance_positive_multiply_unique_constructentriesentryrightvalue ge_balance_negative_multiply_unique_constructentriesentryrightvalue. (((((sto_right_multiply_unique_constructentries) = 2 * (ge_balance_positive_multiply_unique_constructentriesentryrightvalue) /\ (ge_balance_negative_multiply_unique_constructentriesentryrightvalue) = 0) \/ exists ge_signed_half_multiply_unique_constructentriesentryrightvaluedecode. (((sto_right_multiply_unique_constructentries) = 2 * ge_signed_half_multiply_unique_constructentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_multiply_unique_constructentriesentryrightvalue) = 0) /\ (ge_balance_negative_multiply_unique_constructentriesentryrightvalue) = S ge_signed_half_multiply_unique_constructentriesentryrightvaluedecode))) /\ ((dst_positive_multiply_unique_constructentriesentryright) + ge_balance_negative_multiply_unique_constructentriesentryrightvalue = (dst_negative_multiply_unique_constructentriesentryright) + ge_balance_positive_multiply_unique_constructentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_multiply_unique_constructentriesentryoutput dst_positive_scale_multiply_unique_constructentriesentryoutput dst_negative_code_multiply_unique_constructentriesentryoutput dst_negative_scale_multiply_unique_constructentriesentryoutput dst_positive_multiply_unique_constructentriesentryoutput dst_negative_multiply_unique_constructentriesentryoutput. (((H) = (((((dst_positive_code_multiply_unique_constructentriesentryoutput) + (dst_positive_scale_multiply_unique_constructentriesentryoutput)) * S ((dst_positive_code_multiply_unique_constructentriesentryoutput) + (dst_positive_scale_multiply_unique_constructentriesentryoutput)) + ((dst_positive_scale_multiply_unique_constructentriesentryoutput) + (dst_positive_scale_multiply_unique_constructentriesentryoutput))) + (((dst_negative_code_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)) * S ((dst_negative_code_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)) + ((dst_negative_scale_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)))) * S ((((dst_positive_code_multiply_unique_constructentriesentryoutput) + (dst_positive_scale_multiply_unique_constructentriesentryoutput)) * S ((dst_positive_code_multiply_unique_constructentriesentryoutput) + (dst_positive_scale_multiply_unique_constructentriesentryoutput)) + ((dst_positive_scale_multiply_unique_constructentriesentryoutput) + (dst_positive_scale_multiply_unique_constructentriesentryoutput))) + (((dst_negative_code_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)) * S ((dst_negative_code_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)) + ((dst_negative_scale_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)))) + ((((dst_negative_code_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)) * S ((dst_negative_code_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)) + ((dst_negative_scale_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput))) + (((dst_negative_code_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)) * S ((dst_negative_code_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)) + ((dst_negative_scale_multiply_unique_constructentriesentryoutput) + (dst_negative_scale_multiply_unique_constructentriesentryoutput)))))) /\ (((((exists ff_h_pvs_multiply_unique_constructentriesentryoutputpositive. ff_h_pvs_multiply_unique_constructentriesentryoutputpositive + S (dst_positive_multiply_unique_constructentriesentryoutput) = S ((S (sto_index_multiply_unique_constructentries)) * dst_positive_scale_multiply_unique_constructentriesentryoutput)) /\ exists ff_q_pvs_multiply_unique_constructentriesentryoutputpositive. dst_positive_code_multiply_unique_constructentriesentryoutput = ff_q_pvs_multiply_unique_constructentriesentryoutputpositive * S ((S (sto_index_multiply_unique_constructentries)) * dst_positive_scale_multiply_unique_constructentriesentryoutput) + (dst_positive_multiply_unique_constructentriesentryoutput))) /\ (((((exists ff_h_pvs_multiply_unique_constructentriesentryoutputnegative. ff_h_pvs_multiply_unique_constructentriesentryoutputnegative + S (dst_negative_multiply_unique_constructentriesentryoutput) = S ((S (sto_index_multiply_unique_constructentries)) * dst_negative_scale_multiply_unique_constructentriesentryoutput)) /\ exists ff_q_pvs_multiply_unique_constructentriesentryoutputnegative. dst_negative_code_multiply_unique_constructentriesentryoutput = ff_q_pvs_multiply_unique_constructentriesentryoutputnegative * S ((S (sto_index_multiply_unique_constructentries)) * dst_negative_scale_multiply_unique_constructentriesentryoutput) + (dst_negative_multiply_unique_constructentriesentryoutput))) /\ (exists ge_balance_positive_multiply_unique_constructentriesentryoutputvalue ge_balance_negative_multiply_unique_constructentriesentryoutputvalue. (((((sto_output_multiply_unique_constructentries) = 2 * (ge_balance_positive_multiply_unique_constructentriesentryoutputvalue) /\ (ge_balance_negative_multiply_unique_constructentriesentryoutputvalue) = 0) \/ exists ge_signed_half_multiply_unique_constructentriesentryoutputvaluedecode. (((sto_output_multiply_unique_constructentries) = 2 * ge_signed_half_multiply_unique_constructentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_multiply_unique_constructentriesentryoutputvalue) = 0) /\ (ge_balance_negative_multiply_unique_constructentriesentryoutputvalue) = S ge_signed_half_multiply_unique_constructentriesentryoutputvaluedecode))) /\ ((dst_positive_multiply_unique_constructentriesentryoutput) + ge_balance_negative_multiply_unique_constructentriesentryoutputvalue = (dst_negative_multiply_unique_constructentriesentryoutput) + ge_balance_positive_multiply_unique_constructentriesentryoutputvalue))))))))) /\ (exists sto_ap_multiply_unique_constructentriesentryoperation sto_an_multiply_unique_constructentriesentryoperation sto_bp_multiply_unique_constructentriesentryoperation sto_bn_multiply_unique_constructentriesentryoperation sto_cp_multiply_unique_constructentriesentryoperation sto_cn_multiply_unique_constructentriesentryoperation. (((((sto_left_multiply_unique_constructentries) = 2 * (sto_ap_multiply_unique_constructentriesentryoperation) /\ (sto_an_multiply_unique_constructentriesentryoperation) = 0) \/ exists ge_signed_half_multiply_unique_constructentriesentryoperationleft. (((sto_left_multiply_unique_constructentries) = 2 * ge_signed_half_multiply_unique_constructentriesentryoperationleft + 1 /\ (sto_ap_multiply_unique_constructentriesentryoperation) = 0) /\ (sto_an_multiply_unique_constructentriesentryoperation) = S ge_signed_half_multiply_unique_constructentriesentryoperationleft))) /\ ((((((sto_right_multiply_unique_constructentries) = 2 * (sto_bp_multiply_unique_constructentriesentryoperation) /\ (sto_bn_multiply_unique_constructentriesentryoperation) = 0) \/ exists ge_signed_half_multiply_unique_constructentriesentryoperationright. (((sto_right_multiply_unique_constructentries) = 2 * ge_signed_half_multiply_unique_constructentriesentryoperationright + 1 /\ (sto_bp_multiply_unique_constructentriesentryoperation) = 0) /\ (sto_bn_multiply_unique_constructentriesentryoperation) = S ge_signed_half_multiply_unique_constructentriesentryoperationright))) /\ ((((((sto_output_multiply_unique_constructentries) = 2 * (sto_cp_multiply_unique_constructentriesentryoperation) /\ (sto_cn_multiply_unique_constructentriesentryoperation) = 0) \/ exists ge_signed_half_multiply_unique_constructentriesentryoperationoutput. (((sto_output_multiply_unique_constructentries) = 2 * ge_signed_half_multiply_unique_constructentriesentryoperationoutput + 1 /\ (sto_cp_multiply_unique_constructentriesentryoperation) = 0) /\ (sto_cn_multiply_unique_constructentriesentryoperation) = S ge_signed_half_multiply_unique_constructentriesentryoperationoutput))) /\ ((sto_ap_multiply_unique_constructentriesentryoperation * sto_bp_multiply_unique_constructentriesentryoperation + sto_an_multiply_unique_constructentriesentryoperation * sto_bn_multiply_unique_constructentriesentryoperation) + sto_cn_multiply_unique_constructentriesentryoperation = (sto_ap_multiply_unique_constructentriesentryoperation * sto_bn_multiply_unique_constructentriesentryoperation + sto_an_multiply_unique_constructentriesentryoperation * sto_bp_multiply_unique_constructentriesentryoperation) + sto_cp_multiply_unique_constructentriesentryoperation))))))))))))))))))) - 0007
specialize signed_table_multiply_exists (l) - 0008
specialize signed_table_multiply_exists (F) - 0009
specialize signed_table_multiply_exists (G) - 0010
apply signed_table_multiply_exists - 0011
exact ht0 - 0012
exact ht1 - 0013
cases hw - 0014
exists x - 0015
split - 0016
exact hw_witness - 0017
intro K - 0018
intro hother - 0019
specialize signed_table_multiply_extensional_unique (F) - 0020
specialize signed_table_multiply_extensional_unique (G) - 0021
specialize signed_table_multiply_extensional_unique (x) - 0022
specialize signed_table_multiply_extensional_unique (K) - 0023
specialize signed_table_multiply_extensional_unique (l) - 0024
apply signed_table_multiply_extensional_unique - 0025
exact hw_witness - 0026
exact hother