Exact research checkpoint receipt

forall F pb pc nb nc i p n z. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (((exists ff_h_pvs_entry_positive. ff_h_pvs_entry_positive + S (p) = S ((S (i)) * pc)) /\ exists ff_q_pvs_entry_positive. pb = ff_q_pvs_entry_positive * S ((S (i)) * pc) + (p))) -> (((exists ff_h_pvs_entry_negative. ff_h_pvs_entry_negative + S (n) = S ((S (i)) * nc)) /\ exists ff_q_pvs_entry_negative. nb = ff_q_pvs_entry_negative * S ((S (i)) * nc) + (n))) -> (exists ge_balance_positive_entry_balance ge_balance_negative_entry_balance. (((((z) = 2 * (ge_balance_positive_entry_balance) /\ (ge_balance_negative_entry_balance) = 0) \/ exists ge_signed_half_entry_balancedecode. (((z) = 2 * ge_signed_half_entry_balancedecode + 1 /\ (ge_balance_positive_entry_balance) = 0) /\ (ge_balance_negative_entry_balance) = S ge_signed_half_entry_balancedecode))) /\ ((p) + ge_balance_negative_entry_balance = (n) + ge_balance_positive_entry_balance))) -> (exists dst_positive_code_entry_result dst_positive_scale_entry_result dst_negative_code_entry_result dst_negative_scale_entry_result dst_positive_entry_result dst_negative_entry_result. (((F) = (((((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) * S ((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) + ((dst_positive_scale_entry_result) + (dst_positive_scale_entry_result))) + (((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result)))) * S ((((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) * S ((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) + ((dst_positive_scale_entry_result) + (dst_positive_scale_entry_result))) + (((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result)))) + ((((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result))) + (((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result)))))) /\ (((((exists ff_h_pvs_entry_resultpositive. ff_h_pvs_entry_resultpositive + S (dst_positive_entry_result) = S ((S (i)) * dst_positive_scale_entry_result)) /\ exists ff_q_pvs_entry_resultpositive. dst_positive_code_entry_result = ff_q_pvs_entry_resultpositive * S ((S (i)) * dst_positive_scale_entry_result) + (dst_positive_entry_result))) /\ (((((exists ff_h_pvs_entry_resultnegative. ff_h_pvs_entry_resultnegative + S (dst_negative_entry_result) = S ((S (i)) * dst_negative_scale_entry_result)) /\ exists ff_q_pvs_entry_resultnegative. dst_negative_code_entry_result = ff_q_pvs_entry_resultnegative * S ((S (i)) * dst_negative_scale_entry_result) + (dst_negative_entry_result))) /\ (exists ge_balance_positive_entry_resultvalue ge_balance_negative_entry_resultvalue. (((((z) = 2 * (ge_balance_positive_entry_resultvalue) /\ (ge_balance_negative_entry_resultvalue) = 0) \/ exists ge_signed_half_entry_resultvaluedecode. (((z) = 2 * ge_signed_half_entry_resultvaluedecode + 1 /\ (ge_balance_positive_entry_resultvalue) = 0) /\ (ge_balance_negative_entry_resultvalue) = S ge_signed_half_entry_resultvaluedecode))) /\ ((dst_positive_entry_result) + ge_balance_negative_entry_resultvalue = (dst_negative_entry_result) + ge_balance_positive_entry_resultvalue)))))))))

forall F pb pc nb nc i z. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (exists dst_positive_code_unpack_entry dst_positive_scale_unpack_entry dst_negative_code_unpack_entry dst_negative_scale_unpack_entry dst_positive_unpack_entry dst_negative_unpack_entry. (((F) = (((((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) * S ((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) + ((dst_positive_scale_unpack_entry) + (dst_positive_scale_unpack_entry))) + (((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry)))) * S ((((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) * S ((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) + ((dst_positive_scale_unpack_entry) + (dst_positive_scale_unpack_entry))) + (((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry)))) + ((((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry))) + (((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry)))))) /\ (((((exists ff_h_pvs_unpack_entrypositive. ff_h_pvs_unpack_entrypositive + S (dst_positive_unpack_entry) = S ((S (i)) * dst_positive_scale_unpack_entry)) /\ exists ff_q_pvs_unpack_entrypositive. dst_positive_code_unpack_entry = ff_q_pvs_unpack_entrypositive * S ((S (i)) * dst_positive_scale_unpack_entry) + (dst_positive_unpack_entry))) /\ (((((exists ff_h_pvs_unpack_entrynegative. ff_h_pvs_unpack_entrynegative + S (dst_negative_unpack_entry) = S ((S (i)) * dst_negative_scale_unpack_entry)) /\ exists ff_q_pvs_unpack_entrynegative. dst_negative_code_unpack_entry = ff_q_pvs_unpack_entrynegative * S ((S (i)) * dst_negative_scale_unpack_entry) + (dst_negative_unpack_entry))) /\ (exists ge_balance_positive_unpack_entryvalue ge_balance_negative_unpack_entryvalue. (((((z) = 2 * (ge_balance_positive_unpack_entryvalue) /\ (ge_balance_negative_unpack_entryvalue) = 0) \/ exists ge_signed_half_unpack_entryvaluedecode. (((z) = 2 * ge_signed_half_unpack_entryvaluedecode + 1 /\ (ge_balance_positive_unpack_entryvalue) = 0) /\ (ge_balance_negative_unpack_entryvalue) = S ge_signed_half_unpack_entryvaluedecode))) /\ ((dst_positive_unpack_entry) + ge_balance_negative_unpack_entryvalue = (dst_negative_unpack_entry) + ge_balance_positive_unpack_entryvalue))))))))) -> exists p n. (((((exists ff_h_pvs_unpack_resultpositive. ff_h_pvs_unpack_resultpositive + S (p) = S ((S (i)) * pc)) /\ exists ff_q_pvs_unpack_resultpositive. pb = ff_q_pvs_unpack_resultpositive * S ((S (i)) * pc) + (p))) /\ (((((exists ff_h_pvs_unpack_resultnegative. ff_h_pvs_unpack_resultnegative + S (n) = S ((S (i)) * nc)) /\ exists ff_q_pvs_unpack_resultnegative. nb = ff_q_pvs_unpack_resultnegative * S ((S (i)) * nc) + (n))) /\ (exists ge_balance_positive_unpack_resultvalue ge_balance_negative_unpack_resultvalue. (((((z) = 2 * (ge_balance_positive_unpack_resultvalue) /\ (ge_balance_negative_unpack_resultvalue) = 0) \/ exists ge_signed_half_unpack_resultvaluedecode. (((z) = 2 * ge_signed_half_unpack_resultvaluedecode + 1 /\ (ge_balance_positive_unpack_resultvalue) = 0) /\ (ge_balance_negative_unpack_resultvalue) = S ge_signed_half_unpack_resultvaluedecode))) /\ ((p) + ge_balance_negative_unpack_resultvalue = (n) + ge_balance_positive_unpack_resultvalue)))))))

forall N F pb pc nb nc. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (exists dst_positive_code_constructor_table dst_positive_scale_constructor_table dst_negative_code_constructor_table dst_negative_scale_constructor_table. (((F) = (((((dst_positive_code_constructor_table) + (dst_positive_scale_constructor_table)) * S ((dst_positive_code_constructor_table) + (dst_positive_scale_constructor_table)) + ((dst_positive_scale_constructor_table) + (dst_positive_scale_constructor_table))) + (((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) * S ((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) + ((dst_negative_scale_constructor_table) + (dst_negative_scale_constructor_table)))) * S ((((dst_positive_code_constructor_table) + (dst_positive_scale_constructor_table)) * S ((dst_positive_code_constructor_table) + (dst_positive_scale_constructor_table)) + ((dst_positive_scale_constructor_table) + (dst_positive_scale_constructor_table))) + (((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) * S ((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) + ((dst_negative_scale_constructor_table) + (dst_negative_scale_constructor_table)))) + ((((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) * S ((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) + ((dst_negative_scale_constructor_table) + (dst_negative_scale_constructor_table))) + (((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) * S ((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) + ((dst_negative_scale_constructor_table) + (dst_negative_scale_constructor_table)))))) /\ (forall dst_index_constructor_table. (exists pvs_le_gap_constructor_tabledomain. pvs_le_gap_constructor_tabledomain + (dst_index_constructor_table) = (N)) -> exists dst_positive_constructor_table dst_negative_constructor_table dst_value_constructor_table. ((((exists ff_h_pvs_constructor_tableentrypositive. ff_h_pvs_constructor_tableentrypositive + S (dst_positive_constructor_table) = S ((S (dst_index_constructor_table)) * dst_positive_scale_constructor_table)) /\ exists ff_q_pvs_constructor_tableentrypositive. dst_positive_code_constructor_table = ff_q_pvs_constructor_tableentrypositive * S ((S (dst_index_constructor_table)) * dst_positive_scale_constructor_table) + (dst_positive_constructor_table))) /\ (((((exists ff_h_pvs_constructor_tableentrynegative. ff_h_pvs_constructor_tableentrynegative + S (dst_negative_constructor_table) = S ((S (dst_index_constructor_table)) * dst_negative_scale_constructor_table)) /\ exists ff_q_pvs_constructor_tableentrynegative. dst_negative_code_constructor_table = ff_q_pvs_constructor_tableentrynegative * S ((S (dst_index_constructor_table)) * dst_negative_scale_constructor_table) + (dst_negative_constructor_table))) /\ (exists ge_balance_positive_constructor_tableentryvalue ge_balance_negative_constructor_tableentryvalue. (((((dst_value_constructor_table) = 2 * (ge_balance_positive_constructor_tableentryvalue) /\ (ge_balance_negative_constructor_tableentryvalue) = 0) \/ exists ge_signed_half_constructor_tableentryvaluedecode. (((dst_value_constructor_table) = 2 * ge_signed_half_constructor_tableentryvaluedecode + 1 /\ (ge_balance_positive_constructor_tableentryvalue) = 0) /\ (ge_balance_negative_constructor_tableentryvalue) = S ge_signed_half_constructor_tableentryvaluedecode))) /\ ((dst_positive_constructor_table) + ge_balance_negative_constructor_tableentryvalue = (dst_negative_constructor_table) + ge_balance_positive_constructor_tableentryvalue)))))))))

forall N pb pc nb nc. exists F. (exists dst_positive_code_constructed dst_positive_scale_constructed dst_negative_code_constructed dst_negative_scale_constructed. (((F) = (((((dst_positive_code_constructed) + (dst_positive_scale_constructed)) * S ((dst_positive_code_constructed) + (dst_positive_scale_constructed)) + ((dst_positive_scale_constructed) + (dst_positive_scale_constructed))) + (((dst_negative_code_constructed) + (dst_negative_scale_constructed)) * S ((dst_negative_code_constructed) + (dst_negative_scale_constructed)) + ((dst_negative_scale_constructed) + (dst_negative_scale_constructed)))) * S ((((dst_positive_code_constructed) + (dst_positive_scale_constructed)) * S ((dst_positive_code_constructed) + (dst_positive_scale_constructed)) + ((dst_positive_scale_constructed) + (dst_positive_scale_constructed))) + (((dst_negative_code_constructed) + (dst_negative_scale_constructed)) * S ((dst_negative_code_constructed) + (dst_negative_scale_constructed)) + ((dst_negative_scale_constructed) + (dst_negative_scale_constructed)))) + ((((dst_negative_code_constructed) + (dst_negative_scale_constructed)) * S ((dst_negative_code_constructed) + (dst_negative_scale_constructed)) + ((dst_negative_scale_constructed) + (dst_negative_scale_constructed))) + (((dst_negative_code_constructed) + (dst_negative_scale_constructed)) * S ((dst_negative_code_constructed) + (dst_negative_scale_constructed)) + ((dst_negative_scale_constructed) + (dst_negative_scale_constructed)))))) /\ (forall dst_index_constructed. (exists pvs_le_gap_constructeddomain. pvs_le_gap_constructeddomain + (dst_index_constructed) = (N)) -> exists dst_positive_constructed dst_negative_constructed dst_value_constructed. ((((exists ff_h_pvs_constructedentrypositive. ff_h_pvs_constructedentrypositive + S (dst_positive_constructed) = S ((S (dst_index_constructed)) * dst_positive_scale_constructed)) /\ exists ff_q_pvs_constructedentrypositive. dst_positive_code_constructed = ff_q_pvs_constructedentrypositive * S ((S (dst_index_constructed)) * dst_positive_scale_constructed) + (dst_positive_constructed))) /\ (((((exists ff_h_pvs_constructedentrynegative. ff_h_pvs_constructedentrynegative + S (dst_negative_constructed) = S ((S (dst_index_constructed)) * dst_negative_scale_constructed)) /\ exists ff_q_pvs_constructedentrynegative. dst_negative_code_constructed = ff_q_pvs_constructedentrynegative * S ((S (dst_index_constructed)) * dst_negative_scale_constructed) + (dst_negative_constructed))) /\ (exists ge_balance_positive_constructedentryvalue ge_balance_negative_constructedentryvalue. (((((dst_value_constructed) = 2 * (ge_balance_positive_constructedentryvalue) /\ (ge_balance_negative_constructedentryvalue) = 0) \/ exists ge_signed_half_constructedentryvaluedecode. (((dst_value_constructed) = 2 * ge_signed_half_constructedentryvaluedecode + 1 /\ (ge_balance_positive_constructedentryvalue) = 0) /\ (ge_balance_negative_constructedentryvalue) = S ge_signed_half_constructedentryvaluedecode))) /\ ((dst_positive_constructed) + ge_balance_negative_constructedentryvalue = (dst_negative_constructed) + ge_balance_positive_constructedentryvalue))))))))) /\ ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))))))

forall N F. (exists dst_positive_code_extract_table dst_positive_scale_extract_table dst_negative_code_extract_table dst_negative_scale_extract_table. (((F) = (((((dst_positive_code_extract_table) + (dst_positive_scale_extract_table)) * S ((dst_positive_code_extract_table) + (dst_positive_scale_extract_table)) + ((dst_positive_scale_extract_table) + (dst_positive_scale_extract_table))) + (((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) * S ((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) + ((dst_negative_scale_extract_table) + (dst_negative_scale_extract_table)))) * S ((((dst_positive_code_extract_table) + (dst_positive_scale_extract_table)) * S ((dst_positive_code_extract_table) + (dst_positive_scale_extract_table)) + ((dst_positive_scale_extract_table) + (dst_positive_scale_extract_table))) + (((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) * S ((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) + ((dst_negative_scale_extract_table) + (dst_negative_scale_extract_table)))) + ((((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) * S ((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) + ((dst_negative_scale_extract_table) + (dst_negative_scale_extract_table))) + (((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) * S ((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) + ((dst_negative_scale_extract_table) + (dst_negative_scale_extract_table)))))) /\ (forall dst_index_extract_table. (exists pvs_le_gap_extract_tabledomain. pvs_le_gap_extract_tabledomain + (dst_index_extract_table) = (N)) -> exists dst_positive_extract_table dst_negative_extract_table dst_value_extract_table. ((((exists ff_h_pvs_extract_tableentrypositive. ff_h_pvs_extract_tableentrypositive + S (dst_positive_extract_table) = S ((S (dst_index_extract_table)) * dst_positive_scale_extract_table)) /\ exists ff_q_pvs_extract_tableentrypositive. dst_positive_code_extract_table = ff_q_pvs_extract_tableentrypositive * S ((S (dst_index_extract_table)) * dst_positive_scale_extract_table) + (dst_positive_extract_table))) /\ (((((exists ff_h_pvs_extract_tableentrynegative. ff_h_pvs_extract_tableentrynegative + S (dst_negative_extract_table) = S ((S (dst_index_extract_table)) * dst_negative_scale_extract_table)) /\ exists ff_q_pvs_extract_tableentrynegative. dst_negative_code_extract_table = ff_q_pvs_extract_tableentrynegative * S ((S (dst_index_extract_table)) * dst_negative_scale_extract_table) + (dst_negative_extract_table))) /\ (exists ge_balance_positive_extract_tableentryvalue ge_balance_negative_extract_tableentryvalue. (((((dst_value_extract_table) = 2 * (ge_balance_positive_extract_tableentryvalue) /\ (ge_balance_negative_extract_tableentryvalue) = 0) \/ exists ge_signed_half_extract_tableentryvaluedecode. (((dst_value_extract_table) = 2 * ge_signed_half_extract_tableentryvaluedecode + 1 /\ (ge_balance_positive_extract_tableentryvalue) = 0) /\ (ge_balance_negative_extract_tableentryvalue) = S ge_signed_half_extract_tableentryvaluedecode))) /\ ((dst_positive_extract_table) + ge_balance_negative_extract_tableentryvalue = (dst_negative_extract_table) + ge_balance_positive_extract_tableentryvalue))))))))) -> exists pb pc nb nc. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))))))

forall N F i. (exists dst_positive_code_lookup_table dst_positive_scale_lookup_table dst_negative_code_lookup_table dst_negative_scale_lookup_table. (((F) = (((((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) * S ((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) + ((dst_positive_scale_lookup_table) + (dst_positive_scale_lookup_table))) + (((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table)))) * S ((((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) * S ((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) + ((dst_positive_scale_lookup_table) + (dst_positive_scale_lookup_table))) + (((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table)))) + ((((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table))) + (((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table)))))) /\ (forall dst_index_lookup_table. (exists pvs_le_gap_lookup_tabledomain. pvs_le_gap_lookup_tabledomain + (dst_index_lookup_table) = (N)) -> exists dst_positive_lookup_table dst_negative_lookup_table dst_value_lookup_table. ((((exists ff_h_pvs_lookup_tableentrypositive. ff_h_pvs_lookup_tableentrypositive + S (dst_positive_lookup_table) = S ((S (dst_index_lookup_table)) * dst_positive_scale_lookup_table)) /\ exists ff_q_pvs_lookup_tableentrypositive. dst_positive_code_lookup_table = ff_q_pvs_lookup_tableentrypositive * S ((S (dst_index_lookup_table)) * dst_positive_scale_lookup_table) + (dst_positive_lookup_table))) /\ (((((exists ff_h_pvs_lookup_tableentrynegative. ff_h_pvs_lookup_tableentrynegative + S (dst_negative_lookup_table) = S ((S (dst_index_lookup_table)) * dst_negative_scale_lookup_table)) /\ exists ff_q_pvs_lookup_tableentrynegative. dst_negative_code_lookup_table = ff_q_pvs_lookup_tableentrynegative * S ((S (dst_index_lookup_table)) * dst_negative_scale_lookup_table) + (dst_negative_lookup_table))) /\ (exists ge_balance_positive_lookup_tableentryvalue ge_balance_negative_lookup_tableentryvalue. (((((dst_value_lookup_table) = 2 * (ge_balance_positive_lookup_tableentryvalue) /\ (ge_balance_negative_lookup_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_tableentryvaluedecode. (((dst_value_lookup_table) = 2 * ge_signed_half_lookup_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_tableentryvalue) = S ge_signed_half_lookup_tableentryvaluedecode))) /\ ((dst_positive_lookup_table) + ge_balance_negative_lookup_tableentryvalue = (dst_negative_lookup_table) + ge_balance_positive_lookup_tableentryvalue))))))))) -> (exists pvs_le_gap_lookup_domain. pvs_le_gap_lookup_domain + (i) = (N)) -> exists z. (exists dst_positive_code_lookup_result dst_positive_scale_lookup_result dst_negative_code_lookup_result dst_negative_scale_lookup_result dst_positive_lookup_result dst_negative_lookup_result. (((F) = (((((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) * S ((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) + ((dst_positive_scale_lookup_result) + (dst_positive_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))) * S ((((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) * S ((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) + ((dst_positive_scale_lookup_result) + (dst_positive_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))) + ((((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))))) /\ (((((exists ff_h_pvs_lookup_resultpositive. ff_h_pvs_lookup_resultpositive + S (dst_positive_lookup_result) = S ((S (i)) * dst_positive_scale_lookup_result)) /\ exists ff_q_pvs_lookup_resultpositive. dst_positive_code_lookup_result = ff_q_pvs_lookup_resultpositive * S ((S (i)) * dst_positive_scale_lookup_result) + (dst_positive_lookup_result))) /\ (((((exists ff_h_pvs_lookup_resultnegative. ff_h_pvs_lookup_resultnegative + S (dst_negative_lookup_result) = S ((S (i)) * dst_negative_scale_lookup_result)) /\ exists ff_q_pvs_lookup_resultnegative. dst_negative_code_lookup_result = ff_q_pvs_lookup_resultnegative * S ((S (i)) * dst_negative_scale_lookup_result) + (dst_negative_lookup_result))) /\ (exists ge_balance_positive_lookup_resultvalue ge_balance_negative_lookup_resultvalue. (((((z) = 2 * (ge_balance_positive_lookup_resultvalue) /\ (ge_balance_negative_lookup_resultvalue) = 0) \/ exists ge_signed_half_lookup_resultvaluedecode. (((z) = 2 * ge_signed_half_lookup_resultvaluedecode + 1 /\ (ge_balance_positive_lookup_resultvalue) = 0) /\ (ge_balance_negative_lookup_resultvalue) = S ge_signed_half_lookup_resultvaluedecode))) /\ ((dst_positive_lookup_result) + ge_balance_negative_lookup_resultvalue = (dst_negative_lookup_result) + ge_balance_positive_lookup_resultvalue)))))))))

forall F i a b. (exists dst_positive_code_functional_first dst_positive_scale_functional_first dst_negative_code_functional_first dst_negative_scale_functional_first dst_positive_functional_first dst_negative_functional_first. (((F) = (((((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) * S ((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) + ((dst_positive_scale_functional_first) + (dst_positive_scale_functional_first))) + (((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first)))) * S ((((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) * S ((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) + ((dst_positive_scale_functional_first) + (dst_positive_scale_functional_first))) + (((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first)))) + ((((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first))) + (((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first)))))) /\ (((((exists ff_h_pvs_functional_firstpositive. ff_h_pvs_functional_firstpositive + S (dst_positive_functional_first) = S ((S (i)) * dst_positive_scale_functional_first)) /\ exists ff_q_pvs_functional_firstpositive. dst_positive_code_functional_first = ff_q_pvs_functional_firstpositive * S ((S (i)) * dst_positive_scale_functional_first) + (dst_positive_functional_first))) /\ (((((exists ff_h_pvs_functional_firstnegative. ff_h_pvs_functional_firstnegative + S (dst_negative_functional_first) = S ((S (i)) * dst_negative_scale_functional_first)) /\ exists ff_q_pvs_functional_firstnegative. dst_negative_code_functional_first = ff_q_pvs_functional_firstnegative * S ((S (i)) * dst_negative_scale_functional_first) + (dst_negative_functional_first))) /\ (exists ge_balance_positive_functional_firstvalue ge_balance_negative_functional_firstvalue. (((((a) = 2 * (ge_balance_positive_functional_firstvalue) /\ (ge_balance_negative_functional_firstvalue) = 0) \/ exists ge_signed_half_functional_firstvaluedecode. (((a) = 2 * ge_signed_half_functional_firstvaluedecode + 1 /\ (ge_balance_positive_functional_firstvalue) = 0) /\ (ge_balance_negative_functional_firstvalue) = S ge_signed_half_functional_firstvaluedecode))) /\ ((dst_positive_functional_first) + ge_balance_negative_functional_firstvalue = (dst_negative_functional_first) + ge_balance_positive_functional_firstvalue))))))))) -> (exists dst_positive_code_functional_second dst_positive_scale_functional_second dst_negative_code_functional_second dst_negative_scale_functional_second dst_positive_functional_second dst_negative_functional_second. (((F) = (((((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) * S ((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) + ((dst_positive_scale_functional_second) + (dst_positive_scale_functional_second))) + (((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second)))) * S ((((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) * S ((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) + ((dst_positive_scale_functional_second) + (dst_positive_scale_functional_second))) + (((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second)))) + ((((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second))) + (((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second)))))) /\ (((((exists ff_h_pvs_functional_secondpositive. ff_h_pvs_functional_secondpositive + S (dst_positive_functional_second) = S ((S (i)) * dst_positive_scale_functional_second)) /\ exists ff_q_pvs_functional_secondpositive. dst_positive_code_functional_second = ff_q_pvs_functional_secondpositive * S ((S (i)) * dst_positive_scale_functional_second) + (dst_positive_functional_second))) /\ (((((exists ff_h_pvs_functional_secondnegative. ff_h_pvs_functional_secondnegative + S (dst_negative_functional_second) = S ((S (i)) * dst_negative_scale_functional_second)) /\ exists ff_q_pvs_functional_secondnegative. dst_negative_code_functional_second = ff_q_pvs_functional_secondnegative * S ((S (i)) * dst_negative_scale_functional_second) + (dst_negative_functional_second))) /\ (exists ge_balance_positive_functional_secondvalue ge_balance_negative_functional_secondvalue. (((((b) = 2 * (ge_balance_positive_functional_secondvalue) /\ (ge_balance_negative_functional_secondvalue) = 0) \/ exists ge_signed_half_functional_secondvaluedecode. (((b) = 2 * ge_signed_half_functional_secondvaluedecode + 1 /\ (ge_balance_positive_functional_secondvalue) = 0) /\ (ge_balance_negative_functional_secondvalue) = S ge_signed_half_functional_secondvaluedecode))) /\ ((dst_positive_functional_second) + ge_balance_negative_functional_secondvalue = (dst_negative_functional_second) + ge_balance_positive_functional_secondvalue))))))))) -> a = b

forall N K F. (exists dst_positive_code_restriction_source dst_positive_scale_restriction_source dst_negative_code_restriction_source dst_negative_scale_restriction_source. (((F) = (((((dst_positive_code_restriction_source) + (dst_positive_scale_restriction_source)) * S ((dst_positive_code_restriction_source) + (dst_positive_scale_restriction_source)) + ((dst_positive_scale_restriction_source) + (dst_positive_scale_restriction_source))) + (((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) * S ((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) + ((dst_negative_scale_restriction_source) + (dst_negative_scale_restriction_source)))) * S ((((dst_positive_code_restriction_source) + (dst_positive_scale_restriction_source)) * S ((dst_positive_code_restriction_source) + (dst_positive_scale_restriction_source)) + ((dst_positive_scale_restriction_source) + (dst_positive_scale_restriction_source))) + (((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) * S ((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) + ((dst_negative_scale_restriction_source) + (dst_negative_scale_restriction_source)))) + ((((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) * S ((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) + ((dst_negative_scale_restriction_source) + (dst_negative_scale_restriction_source))) + (((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) * S ((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) + ((dst_negative_scale_restriction_source) + (dst_negative_scale_restriction_source)))))) /\ (forall dst_index_restriction_source. (exists pvs_le_gap_restriction_sourcedomain. pvs_le_gap_restriction_sourcedomain + (dst_index_restriction_source) = (N)) -> exists dst_positive_restriction_source dst_negative_restriction_source dst_value_restriction_source. ((((exists ff_h_pvs_restriction_sourceentrypositive. ff_h_pvs_restriction_sourceentrypositive + S (dst_positive_restriction_source) = S ((S (dst_index_restriction_source)) * dst_positive_scale_restriction_source)) /\ exists ff_q_pvs_restriction_sourceentrypositive. dst_positive_code_restriction_source = ff_q_pvs_restriction_sourceentrypositive * S ((S (dst_index_restriction_source)) * dst_positive_scale_restriction_source) + (dst_positive_restriction_source))) /\ (((((exists ff_h_pvs_restriction_sourceentrynegative. ff_h_pvs_restriction_sourceentrynegative + S (dst_negative_restriction_source) = S ((S (dst_index_restriction_source)) * dst_negative_scale_restriction_source)) /\ exists ff_q_pvs_restriction_sourceentrynegative. dst_negative_code_restriction_source = ff_q_pvs_restriction_sourceentrynegative * S ((S (dst_index_restriction_source)) * dst_negative_scale_restriction_source) + (dst_negative_restriction_source))) /\ (exists ge_balance_positive_restriction_sourceentryvalue ge_balance_negative_restriction_sourceentryvalue. (((((dst_value_restriction_source) = 2 * (ge_balance_positive_restriction_sourceentryvalue) /\ (ge_balance_negative_restriction_sourceentryvalue) = 0) \/ exists ge_signed_half_restriction_sourceentryvaluedecode. (((dst_value_restriction_source) = 2 * ge_signed_half_restriction_sourceentryvaluedecode + 1 /\ (ge_balance_positive_restriction_sourceentryvalue) = 0) /\ (ge_balance_negative_restriction_sourceentryvalue) = S ge_signed_half_restriction_sourceentryvaluedecode))) /\ ((dst_positive_restriction_source) + ge_balance_negative_restriction_sourceentryvalue = (dst_negative_restriction_source) + ge_balance_positive_restriction_sourceentryvalue))))))))) -> (exists pvs_le_gap_restriction_bound. pvs_le_gap_restriction_bound + (K) = (N)) -> (exists dst_positive_code_restriction_target dst_positive_scale_restriction_target dst_negative_code_restriction_target dst_negative_scale_restriction_target. (((F) = (((((dst_positive_code_restriction_target) + (dst_positive_scale_restriction_target)) * S ((dst_positive_code_restriction_target) + (dst_positive_scale_restriction_target)) + ((dst_positive_scale_restriction_target) + (dst_positive_scale_restriction_target))) + (((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) * S ((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) + ((dst_negative_scale_restriction_target) + (dst_negative_scale_restriction_target)))) * S ((((dst_positive_code_restriction_target) + (dst_positive_scale_restriction_target)) * S ((dst_positive_code_restriction_target) + (dst_positive_scale_restriction_target)) + ((dst_positive_scale_restriction_target) + (dst_positive_scale_restriction_target))) + (((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) * S ((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) + ((dst_negative_scale_restriction_target) + (dst_negative_scale_restriction_target)))) + ((((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) * S ((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) + ((dst_negative_scale_restriction_target) + (dst_negative_scale_restriction_target))) + (((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) * S ((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) + ((dst_negative_scale_restriction_target) + (dst_negative_scale_restriction_target)))))) /\ (forall dst_index_restriction_target. (exists pvs_le_gap_restriction_targetdomain. pvs_le_gap_restriction_targetdomain + (dst_index_restriction_target) = (K)) -> exists dst_positive_restriction_target dst_negative_restriction_target dst_value_restriction_target. ((((exists ff_h_pvs_restriction_targetentrypositive. ff_h_pvs_restriction_targetentrypositive + S (dst_positive_restriction_target) = S ((S (dst_index_restriction_target)) * dst_positive_scale_restriction_target)) /\ exists ff_q_pvs_restriction_targetentrypositive. dst_positive_code_restriction_target = ff_q_pvs_restriction_targetentrypositive * S ((S (dst_index_restriction_target)) * dst_positive_scale_restriction_target) + (dst_positive_restriction_target))) /\ (((((exists ff_h_pvs_restriction_targetentrynegative. ff_h_pvs_restriction_targetentrynegative + S (dst_negative_restriction_target) = S ((S (dst_index_restriction_target)) * dst_negative_scale_restriction_target)) /\ exists ff_q_pvs_restriction_targetentrynegative. dst_negative_code_restriction_target = ff_q_pvs_restriction_targetentrynegative * S ((S (dst_index_restriction_target)) * dst_negative_scale_restriction_target) + (dst_negative_restriction_target))) /\ (exists ge_balance_positive_restriction_targetentryvalue ge_balance_negative_restriction_targetentryvalue. (((((dst_value_restriction_target) = 2 * (ge_balance_positive_restriction_targetentryvalue) /\ (ge_balance_negative_restriction_targetentryvalue) = 0) \/ exists ge_signed_half_restriction_targetentryvaluedecode. (((dst_value_restriction_target) = 2 * ge_signed_half_restriction_targetentryvaluedecode + 1 /\ (ge_balance_positive_restriction_targetentryvalue) = 0) /\ (ge_balance_negative_restriction_targetentryvalue) = S ge_signed_half_restriction_targetentryvaluedecode))) /\ ((dst_positive_restriction_target) + ge_balance_negative_restriction_targetentryvalue = (dst_negative_restriction_target) + ge_balance_positive_restriction_targetentryvalue)))))))))

forall F pb pc nb nc l p n z. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (exists fs_u_dst_sum_constructor_positive fs_v_dst_sum_constructor_positive. ((((exists fs_h_dst_sum_constructor_positive_body_start. fs_h_dst_sum_constructor_positive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_constructor_positive)) /\ exists fs_q_dst_sum_constructor_positive_body_start. fs_u_dst_sum_constructor_positive = fs_q_dst_sum_constructor_positive_body_start * S ((S (0)) * fs_v_dst_sum_constructor_positive) + (0))) /\ ((((exists fs_h_dst_sum_constructor_positive_body_terminal. fs_h_dst_sum_constructor_positive_body_terminal + S (p) = S ((S (l)) * fs_v_dst_sum_constructor_positive)) /\ exists fs_q_dst_sum_constructor_positive_body_terminal. fs_u_dst_sum_constructor_positive = fs_q_dst_sum_constructor_positive_body_terminal * S ((S (l)) * fs_v_dst_sum_constructor_positive) + (p))) /\ forall fs_i_dst_sum_constructor_positive_body_steps. (exists fs_lt_dst_sum_constructor_positive_body_steps_bound. fs_lt_dst_sum_constructor_positive_body_steps_bound + S fs_i_dst_sum_constructor_positive_body_steps = l) -> exists fs_a_dst_sum_constructor_positive_body_steps fs_r_dst_sum_constructor_positive_body_steps fs_s_dst_sum_constructor_positive_body_steps. ((((exists fs_h_dst_sum_constructor_positive_body_steps_summand. fs_h_dst_sum_constructor_positive_body_steps_summand + S (fs_a_dst_sum_constructor_positive_body_steps) = S ((S (fs_i_dst_sum_constructor_positive_body_steps)) * pc)) /\ exists fs_q_dst_sum_constructor_positive_body_steps_summand. pb = fs_q_dst_sum_constructor_positive_body_steps_summand * S ((S (fs_i_dst_sum_constructor_positive_body_steps)) * pc) + (fs_a_dst_sum_constructor_positive_body_steps))) /\ ((((exists fs_h_dst_sum_constructor_positive_body_steps_partial. fs_h_dst_sum_constructor_positive_body_steps_partial + S (fs_r_dst_sum_constructor_positive_body_steps) = S ((S (fs_i_dst_sum_constructor_positive_body_steps)) * fs_v_dst_sum_constructor_positive)) /\ exists fs_q_dst_sum_constructor_positive_body_steps_partial. fs_u_dst_sum_constructor_positive = fs_q_dst_sum_constructor_positive_body_steps_partial * S ((S (fs_i_dst_sum_constructor_positive_body_steps)) * fs_v_dst_sum_constructor_positive) + (fs_r_dst_sum_constructor_positive_body_steps))) /\ ((((exists fs_h_dst_sum_constructor_positive_body_steps_successor. fs_h_dst_sum_constructor_positive_body_steps_successor + S (fs_s_dst_sum_constructor_positive_body_steps) = S ((S (S fs_i_dst_sum_constructor_positive_body_steps)) * fs_v_dst_sum_constructor_positive)) /\ exists fs_q_dst_sum_constructor_positive_body_steps_successor. fs_u_dst_sum_constructor_positive = fs_q_dst_sum_constructor_positive_body_steps_successor * S ((S (S fs_i_dst_sum_constructor_positive_body_steps)) * fs_v_dst_sum_constructor_positive) + (fs_s_dst_sum_constructor_positive_body_steps))) /\ fs_s_dst_sum_constructor_positive_body_steps = fs_r_dst_sum_constructor_positive_body_steps + fs_a_dst_sum_constructor_positive_body_steps)))))) -> (exists fs_u_dst_sum_constructor_negative fs_v_dst_sum_constructor_negative. ((((exists fs_h_dst_sum_constructor_negative_body_start. fs_h_dst_sum_constructor_negative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_constructor_negative)) /\ exists fs_q_dst_sum_constructor_negative_body_start. fs_u_dst_sum_constructor_negative = fs_q_dst_sum_constructor_negative_body_start * S ((S (0)) * fs_v_dst_sum_constructor_negative) + (0))) /\ ((((exists fs_h_dst_sum_constructor_negative_body_terminal. fs_h_dst_sum_constructor_negative_body_terminal + S (n) = S ((S (l)) * fs_v_dst_sum_constructor_negative)) /\ exists fs_q_dst_sum_constructor_negative_body_terminal. fs_u_dst_sum_constructor_negative = fs_q_dst_sum_constructor_negative_body_terminal * S ((S (l)) * fs_v_dst_sum_constructor_negative) + (n))) /\ forall fs_i_dst_sum_constructor_negative_body_steps. (exists fs_lt_dst_sum_constructor_negative_body_steps_bound. fs_lt_dst_sum_constructor_negative_body_steps_bound + S fs_i_dst_sum_constructor_negative_body_steps = l) -> exists fs_a_dst_sum_constructor_negative_body_steps fs_r_dst_sum_constructor_negative_body_steps fs_s_dst_sum_constructor_negative_body_steps. ((((exists fs_h_dst_sum_constructor_negative_body_steps_summand. fs_h_dst_sum_constructor_negative_body_steps_summand + S (fs_a_dst_sum_constructor_negative_body_steps) = S ((S (fs_i_dst_sum_constructor_negative_body_steps)) * nc)) /\ exists fs_q_dst_sum_constructor_negative_body_steps_summand. nb = fs_q_dst_sum_constructor_negative_body_steps_summand * S ((S (fs_i_dst_sum_constructor_negative_body_steps)) * nc) + (fs_a_dst_sum_constructor_negative_body_steps))) /\ ((((exists fs_h_dst_sum_constructor_negative_body_steps_partial. fs_h_dst_sum_constructor_negative_body_steps_partial + S (fs_r_dst_sum_constructor_negative_body_steps) = S ((S (fs_i_dst_sum_constructor_negative_body_steps)) * fs_v_dst_sum_constructor_negative)) /\ exists fs_q_dst_sum_constructor_negative_body_steps_partial. fs_u_dst_sum_constructor_negative = fs_q_dst_sum_constructor_negative_body_steps_partial * S ((S (fs_i_dst_sum_constructor_negative_body_steps)) * fs_v_dst_sum_constructor_negative) + (fs_r_dst_sum_constructor_negative_body_steps))) /\ ((((exists fs_h_dst_sum_constructor_negative_body_steps_successor. fs_h_dst_sum_constructor_negative_body_steps_successor + S (fs_s_dst_sum_constructor_negative_body_steps) = S ((S (S fs_i_dst_sum_constructor_negative_body_steps)) * fs_v_dst_sum_constructor_negative)) /\ exists fs_q_dst_sum_constructor_negative_body_steps_successor. fs_u_dst_sum_constructor_negative = fs_q_dst_sum_constructor_negative_body_steps_successor * S ((S (S fs_i_dst_sum_constructor_negative_body_steps)) * fs_v_dst_sum_constructor_negative) + (fs_s_dst_sum_constructor_negative_body_steps))) /\ fs_s_dst_sum_constructor_negative_body_steps = fs_r_dst_sum_constructor_negative_body_steps + fs_a_dst_sum_constructor_negative_body_steps)))))) -> (exists ge_balance_positive_sum_constructor_balance ge_balance_negative_sum_constructor_balance. (((((z) = 2 * (ge_balance_positive_sum_constructor_balance) /\ (ge_balance_negative_sum_constructor_balance) = 0) \/ exists ge_signed_half_sum_constructor_balancedecode. (((z) = 2 * ge_signed_half_sum_constructor_balancedecode + 1 /\ (ge_balance_positive_sum_constructor_balance) = 0) /\ (ge_balance_negative_sum_constructor_balance) = S ge_signed_half_sum_constructor_balancedecode))) /\ ((p) + ge_balance_negative_sum_constructor_balance = (n) + ge_balance_positive_sum_constructor_balance))) -> (exists dst_positive_code_sum_constructor_result dst_positive_scale_sum_constructor_result dst_negative_code_sum_constructor_result dst_negative_scale_sum_constructor_result dst_positive_sum_sum_constructor_result dst_negative_sum_sum_constructor_result. (((F) = (((((dst_positive_code_sum_constructor_result) + (dst_positive_scale_sum_constructor_result)) * S ((dst_positive_code_sum_constructor_result) + (dst_positive_scale_sum_constructor_result)) + ((dst_positive_scale_sum_constructor_result) + (dst_positive_scale_sum_constructor_result))) + (((dst_negative_code_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)) * S ((dst_negative_code_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)) + ((dst_negative_scale_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)))) * S ((((dst_positive_code_sum_constructor_result) + (dst_positive_scale_sum_constructor_result)) * S ((dst_positive_code_sum_constructor_result) + (dst_positive_scale_sum_constructor_result)) + ((dst_positive_scale_sum_constructor_result) + (dst_positive_scale_sum_constructor_result))) + (((dst_negative_code_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)) * S ((dst_negative_code_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)) + ((dst_negative_scale_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)))) + ((((dst_negative_code_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)) * S ((dst_negative_code_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)) + ((dst_negative_scale_sum_constructor_result) + (dst_negative_scale_sum_constructor_result))) + (((dst_negative_code_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)) * S ((dst_negative_code_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)) + ((dst_negative_scale_sum_constructor_result) + (dst_negative_scale_sum_constructor_result)))))) /\ (((exists fs_u_dst_sum_constructor_resultpositive fs_v_dst_sum_constructor_resultpositive. ((((exists fs_h_dst_sum_constructor_resultpositive_body_start. fs_h_dst_sum_constructor_resultpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_constructor_resultpositive)) /\ exists fs_q_dst_sum_constructor_resultpositive_body_start. fs_u_dst_sum_constructor_resultpositive = fs_q_dst_sum_constructor_resultpositive_body_start * S ((S (0)) * fs_v_dst_sum_constructor_resultpositive) + (0))) /\ ((((exists fs_h_dst_sum_constructor_resultpositive_body_terminal. fs_h_dst_sum_constructor_resultpositive_body_terminal + S (dst_positive_sum_sum_constructor_result) = S ((S (l)) * fs_v_dst_sum_constructor_resultpositive)) /\ exists fs_q_dst_sum_constructor_resultpositive_body_terminal. fs_u_dst_sum_constructor_resultpositive = fs_q_dst_sum_constructor_resultpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_constructor_resultpositive) + (dst_positive_sum_sum_constructor_result))) /\ forall fs_i_dst_sum_constructor_resultpositive_body_steps. (exists fs_lt_dst_sum_constructor_resultpositive_body_steps_bound. fs_lt_dst_sum_constructor_resultpositive_body_steps_bound + S fs_i_dst_sum_constructor_resultpositive_body_steps = l) -> exists fs_a_dst_sum_constructor_resultpositive_body_steps fs_r_dst_sum_constructor_resultpositive_body_steps fs_s_dst_sum_constructor_resultpositive_body_steps. ((((exists fs_h_dst_sum_constructor_resultpositive_body_steps_summand. fs_h_dst_sum_constructor_resultpositive_body_steps_summand + S (fs_a_dst_sum_constructor_resultpositive_body_steps) = S ((S (fs_i_dst_sum_constructor_resultpositive_body_steps)) * dst_positive_scale_sum_constructor_result)) /\ exists fs_q_dst_sum_constructor_resultpositive_body_steps_summand. dst_positive_code_sum_constructor_result = fs_q_dst_sum_constructor_resultpositive_body_steps_summand * S ((S (fs_i_dst_sum_constructor_resultpositive_body_steps)) * dst_positive_scale_sum_constructor_result) + (fs_a_dst_sum_constructor_resultpositive_body_steps))) /\ ((((exists fs_h_dst_sum_constructor_resultpositive_body_steps_partial. fs_h_dst_sum_constructor_resultpositive_body_steps_partial + S (fs_r_dst_sum_constructor_resultpositive_body_steps) = S ((S (fs_i_dst_sum_constructor_resultpositive_body_steps)) * fs_v_dst_sum_constructor_resultpositive)) /\ exists fs_q_dst_sum_constructor_resultpositive_body_steps_partial. fs_u_dst_sum_constructor_resultpositive = fs_q_dst_sum_constructor_resultpositive_body_steps_partial * S ((S (fs_i_dst_sum_constructor_resultpositive_body_steps)) * fs_v_dst_sum_constructor_resultpositive) + (fs_r_dst_sum_constructor_resultpositive_body_steps))) /\ ((((exists fs_h_dst_sum_constructor_resultpositive_body_steps_successor. fs_h_dst_sum_constructor_resultpositive_body_steps_successor + S (fs_s_dst_sum_constructor_resultpositive_body_steps) = S ((S (S fs_i_dst_sum_constructor_resultpositive_body_steps)) * fs_v_dst_sum_constructor_resultpositive)) /\ exists fs_q_dst_sum_constructor_resultpositive_body_steps_successor. fs_u_dst_sum_constructor_resultpositive = fs_q_dst_sum_constructor_resultpositive_body_steps_successor * S ((S (S fs_i_dst_sum_constructor_resultpositive_body_steps)) * fs_v_dst_sum_constructor_resultpositive) + (fs_s_dst_sum_constructor_resultpositive_body_steps))) /\ fs_s_dst_sum_constructor_resultpositive_body_steps = fs_r_dst_sum_constructor_resultpositive_body_steps + fs_a_dst_sum_constructor_resultpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_constructor_resultnegative fs_v_dst_sum_constructor_resultnegative. ((((exists fs_h_dst_sum_constructor_resultnegative_body_start. fs_h_dst_sum_constructor_resultnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_constructor_resultnegative)) /\ exists fs_q_dst_sum_constructor_resultnegative_body_start. fs_u_dst_sum_constructor_resultnegative = fs_q_dst_sum_constructor_resultnegative_body_start * S ((S (0)) * fs_v_dst_sum_constructor_resultnegative) + (0))) /\ ((((exists fs_h_dst_sum_constructor_resultnegative_body_terminal. fs_h_dst_sum_constructor_resultnegative_body_terminal + S (dst_negative_sum_sum_constructor_result) = S ((S (l)) * fs_v_dst_sum_constructor_resultnegative)) /\ exists fs_q_dst_sum_constructor_resultnegative_body_terminal. fs_u_dst_sum_constructor_resultnegative = fs_q_dst_sum_constructor_resultnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_constructor_resultnegative) + (dst_negative_sum_sum_constructor_result))) /\ forall fs_i_dst_sum_constructor_resultnegative_body_steps. (exists fs_lt_dst_sum_constructor_resultnegative_body_steps_bound. fs_lt_dst_sum_constructor_resultnegative_body_steps_bound + S fs_i_dst_sum_constructor_resultnegative_body_steps = l) -> exists fs_a_dst_sum_constructor_resultnegative_body_steps fs_r_dst_sum_constructor_resultnegative_body_steps fs_s_dst_sum_constructor_resultnegative_body_steps. ((((exists fs_h_dst_sum_constructor_resultnegative_body_steps_summand. fs_h_dst_sum_constructor_resultnegative_body_steps_summand + S (fs_a_dst_sum_constructor_resultnegative_body_steps) = S ((S (fs_i_dst_sum_constructor_resultnegative_body_steps)) * dst_negative_scale_sum_constructor_result)) /\ exists fs_q_dst_sum_constructor_resultnegative_body_steps_summand. dst_negative_code_sum_constructor_result = fs_q_dst_sum_constructor_resultnegative_body_steps_summand * S ((S (fs_i_dst_sum_constructor_resultnegative_body_steps)) * dst_negative_scale_sum_constructor_result) + (fs_a_dst_sum_constructor_resultnegative_body_steps))) /\ ((((exists fs_h_dst_sum_constructor_resultnegative_body_steps_partial. fs_h_dst_sum_constructor_resultnegative_body_steps_partial + S (fs_r_dst_sum_constructor_resultnegative_body_steps) = S ((S (fs_i_dst_sum_constructor_resultnegative_body_steps)) * fs_v_dst_sum_constructor_resultnegative)) /\ exists fs_q_dst_sum_constructor_resultnegative_body_steps_partial. fs_u_dst_sum_constructor_resultnegative = fs_q_dst_sum_constructor_resultnegative_body_steps_partial * S ((S (fs_i_dst_sum_constructor_resultnegative_body_steps)) * fs_v_dst_sum_constructor_resultnegative) + (fs_r_dst_sum_constructor_resultnegative_body_steps))) /\ ((((exists fs_h_dst_sum_constructor_resultnegative_body_steps_successor. fs_h_dst_sum_constructor_resultnegative_body_steps_successor + S (fs_s_dst_sum_constructor_resultnegative_body_steps) = S ((S (S fs_i_dst_sum_constructor_resultnegative_body_steps)) * fs_v_dst_sum_constructor_resultnegative)) /\ exists fs_q_dst_sum_constructor_resultnegative_body_steps_successor. fs_u_dst_sum_constructor_resultnegative = fs_q_dst_sum_constructor_resultnegative_body_steps_successor * S ((S (S fs_i_dst_sum_constructor_resultnegative_body_steps)) * fs_v_dst_sum_constructor_resultnegative) + (fs_s_dst_sum_constructor_resultnegative_body_steps))) /\ fs_s_dst_sum_constructor_resultnegative_body_steps = fs_r_dst_sum_constructor_resultnegative_body_steps + fs_a_dst_sum_constructor_resultnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_constructor_resultresult ge_balance_negative_sum_constructor_resultresult. (((((z) = 2 * (ge_balance_positive_sum_constructor_resultresult) /\ (ge_balance_negative_sum_constructor_resultresult) = 0) \/ exists ge_signed_half_sum_constructor_resultresultdecode. (((z) = 2 * ge_signed_half_sum_constructor_resultresultdecode + 1 /\ (ge_balance_positive_sum_constructor_resultresult) = 0) /\ (ge_balance_negative_sum_constructor_resultresult) = S ge_signed_half_sum_constructor_resultresultdecode))) /\ ((dst_positive_sum_sum_constructor_result) + ge_balance_negative_sum_constructor_resultresult = (dst_negative_sum_sum_constructor_result) + ge_balance_positive_sum_constructor_resultresult)))))))))

forall F pb pc nb nc l z. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (exists dst_positive_code_sum_unpacked_input dst_positive_scale_sum_unpacked_input dst_negative_code_sum_unpacked_input dst_negative_scale_sum_unpacked_input dst_positive_sum_sum_unpacked_input dst_negative_sum_sum_unpacked_input. (((F) = (((((dst_positive_code_sum_unpacked_input) + (dst_positive_scale_sum_unpacked_input)) * S ((dst_positive_code_sum_unpacked_input) + (dst_positive_scale_sum_unpacked_input)) + ((dst_positive_scale_sum_unpacked_input) + (dst_positive_scale_sum_unpacked_input))) + (((dst_negative_code_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)) * S ((dst_negative_code_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)) + ((dst_negative_scale_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)))) * S ((((dst_positive_code_sum_unpacked_input) + (dst_positive_scale_sum_unpacked_input)) * S ((dst_positive_code_sum_unpacked_input) + (dst_positive_scale_sum_unpacked_input)) + ((dst_positive_scale_sum_unpacked_input) + (dst_positive_scale_sum_unpacked_input))) + (((dst_negative_code_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)) * S ((dst_negative_code_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)) + ((dst_negative_scale_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)))) + ((((dst_negative_code_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)) * S ((dst_negative_code_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)) + ((dst_negative_scale_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input))) + (((dst_negative_code_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)) * S ((dst_negative_code_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)) + ((dst_negative_scale_sum_unpacked_input) + (dst_negative_scale_sum_unpacked_input)))))) /\ (((exists fs_u_dst_sum_unpacked_inputpositive fs_v_dst_sum_unpacked_inputpositive. ((((exists fs_h_dst_sum_unpacked_inputpositive_body_start. fs_h_dst_sum_unpacked_inputpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unpacked_inputpositive)) /\ exists fs_q_dst_sum_unpacked_inputpositive_body_start. fs_u_dst_sum_unpacked_inputpositive = fs_q_dst_sum_unpacked_inputpositive_body_start * S ((S (0)) * fs_v_dst_sum_unpacked_inputpositive) + (0))) /\ ((((exists fs_h_dst_sum_unpacked_inputpositive_body_terminal. fs_h_dst_sum_unpacked_inputpositive_body_terminal + S (dst_positive_sum_sum_unpacked_input) = S ((S (l)) * fs_v_dst_sum_unpacked_inputpositive)) /\ exists fs_q_dst_sum_unpacked_inputpositive_body_terminal. fs_u_dst_sum_unpacked_inputpositive = fs_q_dst_sum_unpacked_inputpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_unpacked_inputpositive) + (dst_positive_sum_sum_unpacked_input))) /\ forall fs_i_dst_sum_unpacked_inputpositive_body_steps. (exists fs_lt_dst_sum_unpacked_inputpositive_body_steps_bound. fs_lt_dst_sum_unpacked_inputpositive_body_steps_bound + S fs_i_dst_sum_unpacked_inputpositive_body_steps = l) -> exists fs_a_dst_sum_unpacked_inputpositive_body_steps fs_r_dst_sum_unpacked_inputpositive_body_steps fs_s_dst_sum_unpacked_inputpositive_body_steps. ((((exists fs_h_dst_sum_unpacked_inputpositive_body_steps_summand. fs_h_dst_sum_unpacked_inputpositive_body_steps_summand + S (fs_a_dst_sum_unpacked_inputpositive_body_steps) = S ((S (fs_i_dst_sum_unpacked_inputpositive_body_steps)) * dst_positive_scale_sum_unpacked_input)) /\ exists fs_q_dst_sum_unpacked_inputpositive_body_steps_summand. dst_positive_code_sum_unpacked_input = fs_q_dst_sum_unpacked_inputpositive_body_steps_summand * S ((S (fs_i_dst_sum_unpacked_inputpositive_body_steps)) * dst_positive_scale_sum_unpacked_input) + (fs_a_dst_sum_unpacked_inputpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unpacked_inputpositive_body_steps_partial. fs_h_dst_sum_unpacked_inputpositive_body_steps_partial + S (fs_r_dst_sum_unpacked_inputpositive_body_steps) = S ((S (fs_i_dst_sum_unpacked_inputpositive_body_steps)) * fs_v_dst_sum_unpacked_inputpositive)) /\ exists fs_q_dst_sum_unpacked_inputpositive_body_steps_partial. fs_u_dst_sum_unpacked_inputpositive = fs_q_dst_sum_unpacked_inputpositive_body_steps_partial * S ((S (fs_i_dst_sum_unpacked_inputpositive_body_steps)) * fs_v_dst_sum_unpacked_inputpositive) + (fs_r_dst_sum_unpacked_inputpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unpacked_inputpositive_body_steps_successor. fs_h_dst_sum_unpacked_inputpositive_body_steps_successor + S (fs_s_dst_sum_unpacked_inputpositive_body_steps) = S ((S (S fs_i_dst_sum_unpacked_inputpositive_body_steps)) * fs_v_dst_sum_unpacked_inputpositive)) /\ exists fs_q_dst_sum_unpacked_inputpositive_body_steps_successor. fs_u_dst_sum_unpacked_inputpositive = fs_q_dst_sum_unpacked_inputpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unpacked_inputpositive_body_steps)) * fs_v_dst_sum_unpacked_inputpositive) + (fs_s_dst_sum_unpacked_inputpositive_body_steps))) /\ fs_s_dst_sum_unpacked_inputpositive_body_steps = fs_r_dst_sum_unpacked_inputpositive_body_steps + fs_a_dst_sum_unpacked_inputpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unpacked_inputnegative fs_v_dst_sum_unpacked_inputnegative. ((((exists fs_h_dst_sum_unpacked_inputnegative_body_start. fs_h_dst_sum_unpacked_inputnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unpacked_inputnegative)) /\ exists fs_q_dst_sum_unpacked_inputnegative_body_start. fs_u_dst_sum_unpacked_inputnegative = fs_q_dst_sum_unpacked_inputnegative_body_start * S ((S (0)) * fs_v_dst_sum_unpacked_inputnegative) + (0))) /\ ((((exists fs_h_dst_sum_unpacked_inputnegative_body_terminal. fs_h_dst_sum_unpacked_inputnegative_body_terminal + S (dst_negative_sum_sum_unpacked_input) = S ((S (l)) * fs_v_dst_sum_unpacked_inputnegative)) /\ exists fs_q_dst_sum_unpacked_inputnegative_body_terminal. fs_u_dst_sum_unpacked_inputnegative = fs_q_dst_sum_unpacked_inputnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_unpacked_inputnegative) + (dst_negative_sum_sum_unpacked_input))) /\ forall fs_i_dst_sum_unpacked_inputnegative_body_steps. (exists fs_lt_dst_sum_unpacked_inputnegative_body_steps_bound. fs_lt_dst_sum_unpacked_inputnegative_body_steps_bound + S fs_i_dst_sum_unpacked_inputnegative_body_steps = l) -> exists fs_a_dst_sum_unpacked_inputnegative_body_steps fs_r_dst_sum_unpacked_inputnegative_body_steps fs_s_dst_sum_unpacked_inputnegative_body_steps. ((((exists fs_h_dst_sum_unpacked_inputnegative_body_steps_summand. fs_h_dst_sum_unpacked_inputnegative_body_steps_summand + S (fs_a_dst_sum_unpacked_inputnegative_body_steps) = S ((S (fs_i_dst_sum_unpacked_inputnegative_body_steps)) * dst_negative_scale_sum_unpacked_input)) /\ exists fs_q_dst_sum_unpacked_inputnegative_body_steps_summand. dst_negative_code_sum_unpacked_input = fs_q_dst_sum_unpacked_inputnegative_body_steps_summand * S ((S (fs_i_dst_sum_unpacked_inputnegative_body_steps)) * dst_negative_scale_sum_unpacked_input) + (fs_a_dst_sum_unpacked_inputnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unpacked_inputnegative_body_steps_partial. fs_h_dst_sum_unpacked_inputnegative_body_steps_partial + S (fs_r_dst_sum_unpacked_inputnegative_body_steps) = S ((S (fs_i_dst_sum_unpacked_inputnegative_body_steps)) * fs_v_dst_sum_unpacked_inputnegative)) /\ exists fs_q_dst_sum_unpacked_inputnegative_body_steps_partial. fs_u_dst_sum_unpacked_inputnegative = fs_q_dst_sum_unpacked_inputnegative_body_steps_partial * S ((S (fs_i_dst_sum_unpacked_inputnegative_body_steps)) * fs_v_dst_sum_unpacked_inputnegative) + (fs_r_dst_sum_unpacked_inputnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unpacked_inputnegative_body_steps_successor. fs_h_dst_sum_unpacked_inputnegative_body_steps_successor + S (fs_s_dst_sum_unpacked_inputnegative_body_steps) = S ((S (S fs_i_dst_sum_unpacked_inputnegative_body_steps)) * fs_v_dst_sum_unpacked_inputnegative)) /\ exists fs_q_dst_sum_unpacked_inputnegative_body_steps_successor. fs_u_dst_sum_unpacked_inputnegative = fs_q_dst_sum_unpacked_inputnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unpacked_inputnegative_body_steps)) * fs_v_dst_sum_unpacked_inputnegative) + (fs_s_dst_sum_unpacked_inputnegative_body_steps))) /\ fs_s_dst_sum_unpacked_inputnegative_body_steps = fs_r_dst_sum_unpacked_inputnegative_body_steps + fs_a_dst_sum_unpacked_inputnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unpacked_inputresult ge_balance_negative_sum_unpacked_inputresult. (((((z) = 2 * (ge_balance_positive_sum_unpacked_inputresult) /\ (ge_balance_negative_sum_unpacked_inputresult) = 0) \/ exists ge_signed_half_sum_unpacked_inputresultdecode. (((z) = 2 * ge_signed_half_sum_unpacked_inputresultdecode + 1 /\ (ge_balance_positive_sum_unpacked_inputresult) = 0) /\ (ge_balance_negative_sum_unpacked_inputresult) = S ge_signed_half_sum_unpacked_inputresultdecode))) /\ ((dst_positive_sum_sum_unpacked_input) + ge_balance_negative_sum_unpacked_inputresult = (dst_negative_sum_sum_unpacked_input) + ge_balance_positive_sum_unpacked_inputresult))))))))) -> exists p n. ((exists fs_u_dst_sum_unpacked_positive fs_v_dst_sum_unpacked_positive. ((((exists fs_h_dst_sum_unpacked_positive_body_start. fs_h_dst_sum_unpacked_positive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unpacked_positive)) /\ exists fs_q_dst_sum_unpacked_positive_body_start. fs_u_dst_sum_unpacked_positive = fs_q_dst_sum_unpacked_positive_body_start * S ((S (0)) * fs_v_dst_sum_unpacked_positive) + (0))) /\ ((((exists fs_h_dst_sum_unpacked_positive_body_terminal. fs_h_dst_sum_unpacked_positive_body_terminal + S (p) = S ((S (l)) * fs_v_dst_sum_unpacked_positive)) /\ exists fs_q_dst_sum_unpacked_positive_body_terminal. fs_u_dst_sum_unpacked_positive = fs_q_dst_sum_unpacked_positive_body_terminal * S ((S (l)) * fs_v_dst_sum_unpacked_positive) + (p))) /\ forall fs_i_dst_sum_unpacked_positive_body_steps. (exists fs_lt_dst_sum_unpacked_positive_body_steps_bound. fs_lt_dst_sum_unpacked_positive_body_steps_bound + S fs_i_dst_sum_unpacked_positive_body_steps = l) -> exists fs_a_dst_sum_unpacked_positive_body_steps fs_r_dst_sum_unpacked_positive_body_steps fs_s_dst_sum_unpacked_positive_body_steps. ((((exists fs_h_dst_sum_unpacked_positive_body_steps_summand. fs_h_dst_sum_unpacked_positive_body_steps_summand + S (fs_a_dst_sum_unpacked_positive_body_steps) = S ((S (fs_i_dst_sum_unpacked_positive_body_steps)) * pc)) /\ exists fs_q_dst_sum_unpacked_positive_body_steps_summand. pb = fs_q_dst_sum_unpacked_positive_body_steps_summand * S ((S (fs_i_dst_sum_unpacked_positive_body_steps)) * pc) + (fs_a_dst_sum_unpacked_positive_body_steps))) /\ ((((exists fs_h_dst_sum_unpacked_positive_body_steps_partial. fs_h_dst_sum_unpacked_positive_body_steps_partial + S (fs_r_dst_sum_unpacked_positive_body_steps) = S ((S (fs_i_dst_sum_unpacked_positive_body_steps)) * fs_v_dst_sum_unpacked_positive)) /\ exists fs_q_dst_sum_unpacked_positive_body_steps_partial. fs_u_dst_sum_unpacked_positive = fs_q_dst_sum_unpacked_positive_body_steps_partial * S ((S (fs_i_dst_sum_unpacked_positive_body_steps)) * fs_v_dst_sum_unpacked_positive) + (fs_r_dst_sum_unpacked_positive_body_steps))) /\ ((((exists fs_h_dst_sum_unpacked_positive_body_steps_successor. fs_h_dst_sum_unpacked_positive_body_steps_successor + S (fs_s_dst_sum_unpacked_positive_body_steps) = S ((S (S fs_i_dst_sum_unpacked_positive_body_steps)) * fs_v_dst_sum_unpacked_positive)) /\ exists fs_q_dst_sum_unpacked_positive_body_steps_successor. fs_u_dst_sum_unpacked_positive = fs_q_dst_sum_unpacked_positive_body_steps_successor * S ((S (S fs_i_dst_sum_unpacked_positive_body_steps)) * fs_v_dst_sum_unpacked_positive) + (fs_s_dst_sum_unpacked_positive_body_steps))) /\ fs_s_dst_sum_unpacked_positive_body_steps = fs_r_dst_sum_unpacked_positive_body_steps + fs_a_dst_sum_unpacked_positive_body_steps)))))) /\ (((exists fs_u_dst_sum_unpacked_negative fs_v_dst_sum_unpacked_negative. ((((exists fs_h_dst_sum_unpacked_negative_body_start. fs_h_dst_sum_unpacked_negative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unpacked_negative)) /\ exists fs_q_dst_sum_unpacked_negative_body_start. fs_u_dst_sum_unpacked_negative = fs_q_dst_sum_unpacked_negative_body_start * S ((S (0)) * fs_v_dst_sum_unpacked_negative) + (0))) /\ ((((exists fs_h_dst_sum_unpacked_negative_body_terminal. fs_h_dst_sum_unpacked_negative_body_terminal + S (n) = S ((S (l)) * fs_v_dst_sum_unpacked_negative)) /\ exists fs_q_dst_sum_unpacked_negative_body_terminal. fs_u_dst_sum_unpacked_negative = fs_q_dst_sum_unpacked_negative_body_terminal * S ((S (l)) * fs_v_dst_sum_unpacked_negative) + (n))) /\ forall fs_i_dst_sum_unpacked_negative_body_steps. (exists fs_lt_dst_sum_unpacked_negative_body_steps_bound. fs_lt_dst_sum_unpacked_negative_body_steps_bound + S fs_i_dst_sum_unpacked_negative_body_steps = l) -> exists fs_a_dst_sum_unpacked_negative_body_steps fs_r_dst_sum_unpacked_negative_body_steps fs_s_dst_sum_unpacked_negative_body_steps. ((((exists fs_h_dst_sum_unpacked_negative_body_steps_summand. fs_h_dst_sum_unpacked_negative_body_steps_summand + S (fs_a_dst_sum_unpacked_negative_body_steps) = S ((S (fs_i_dst_sum_unpacked_negative_body_steps)) * nc)) /\ exists fs_q_dst_sum_unpacked_negative_body_steps_summand. nb = fs_q_dst_sum_unpacked_negative_body_steps_summand * S ((S (fs_i_dst_sum_unpacked_negative_body_steps)) * nc) + (fs_a_dst_sum_unpacked_negative_body_steps))) /\ ((((exists fs_h_dst_sum_unpacked_negative_body_steps_partial. fs_h_dst_sum_unpacked_negative_body_steps_partial + S (fs_r_dst_sum_unpacked_negative_body_steps) = S ((S (fs_i_dst_sum_unpacked_negative_body_steps)) * fs_v_dst_sum_unpacked_negative)) /\ exists fs_q_dst_sum_unpacked_negative_body_steps_partial. fs_u_dst_sum_unpacked_negative = fs_q_dst_sum_unpacked_negative_body_steps_partial * S ((S (fs_i_dst_sum_unpacked_negative_body_steps)) * fs_v_dst_sum_unpacked_negative) + (fs_r_dst_sum_unpacked_negative_body_steps))) /\ ((((exists fs_h_dst_sum_unpacked_negative_body_steps_successor. fs_h_dst_sum_unpacked_negative_body_steps_successor + S (fs_s_dst_sum_unpacked_negative_body_steps) = S ((S (S fs_i_dst_sum_unpacked_negative_body_steps)) * fs_v_dst_sum_unpacked_negative)) /\ exists fs_q_dst_sum_unpacked_negative_body_steps_successor. fs_u_dst_sum_unpacked_negative = fs_q_dst_sum_unpacked_negative_body_steps_successor * S ((S (S fs_i_dst_sum_unpacked_negative_body_steps)) * fs_v_dst_sum_unpacked_negative) + (fs_s_dst_sum_unpacked_negative_body_steps))) /\ fs_s_dst_sum_unpacked_negative_body_steps = fs_r_dst_sum_unpacked_negative_body_steps + fs_a_dst_sum_unpacked_negative_body_steps)))))) /\ (exists ge_balance_positive_sum_unpacked_balance ge_balance_negative_sum_unpacked_balance. (((((z) = 2 * (ge_balance_positive_sum_unpacked_balance) /\ (ge_balance_negative_sum_unpacked_balance) = 0) \/ exists ge_signed_half_sum_unpacked_balancedecode. (((z) = 2 * ge_signed_half_sum_unpacked_balancedecode + 1 /\ (ge_balance_positive_sum_unpacked_balance) = 0) /\ (ge_balance_negative_sum_unpacked_balance) = S ge_signed_half_sum_unpacked_balancedecode))) /\ ((p) + ge_balance_negative_sum_unpacked_balance = (n) + ge_balance_positive_sum_unpacked_balance))))))

forall F pb pc nb nc l. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> exists z. (exists dst_positive_code_sum_exists_result dst_positive_scale_sum_exists_result dst_negative_code_sum_exists_result dst_negative_scale_sum_exists_result dst_positive_sum_sum_exists_result dst_negative_sum_sum_exists_result. (((F) = (((((dst_positive_code_sum_exists_result) + (dst_positive_scale_sum_exists_result)) * S ((dst_positive_code_sum_exists_result) + (dst_positive_scale_sum_exists_result)) + ((dst_positive_scale_sum_exists_result) + (dst_positive_scale_sum_exists_result))) + (((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) * S ((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) + ((dst_negative_scale_sum_exists_result) + (dst_negative_scale_sum_exists_result)))) * S ((((dst_positive_code_sum_exists_result) + (dst_positive_scale_sum_exists_result)) * S ((dst_positive_code_sum_exists_result) + (dst_positive_scale_sum_exists_result)) + ((dst_positive_scale_sum_exists_result) + (dst_positive_scale_sum_exists_result))) + (((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) * S ((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) + ((dst_negative_scale_sum_exists_result) + (dst_negative_scale_sum_exists_result)))) + ((((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) * S ((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) + ((dst_negative_scale_sum_exists_result) + (dst_negative_scale_sum_exists_result))) + (((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) * S ((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) + ((dst_negative_scale_sum_exists_result) + (dst_negative_scale_sum_exists_result)))))) /\ (((exists fs_u_dst_sum_exists_resultpositive fs_v_dst_sum_exists_resultpositive. ((((exists fs_h_dst_sum_exists_resultpositive_body_start. fs_h_dst_sum_exists_resultpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_exists_resultpositive)) /\ exists fs_q_dst_sum_exists_resultpositive_body_start. fs_u_dst_sum_exists_resultpositive = fs_q_dst_sum_exists_resultpositive_body_start * S ((S (0)) * fs_v_dst_sum_exists_resultpositive) + (0))) /\ ((((exists fs_h_dst_sum_exists_resultpositive_body_terminal. fs_h_dst_sum_exists_resultpositive_body_terminal + S (dst_positive_sum_sum_exists_result) = S ((S (l)) * fs_v_dst_sum_exists_resultpositive)) /\ exists fs_q_dst_sum_exists_resultpositive_body_terminal. fs_u_dst_sum_exists_resultpositive = fs_q_dst_sum_exists_resultpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_exists_resultpositive) + (dst_positive_sum_sum_exists_result))) /\ forall fs_i_dst_sum_exists_resultpositive_body_steps. (exists fs_lt_dst_sum_exists_resultpositive_body_steps_bound. fs_lt_dst_sum_exists_resultpositive_body_steps_bound + S fs_i_dst_sum_exists_resultpositive_body_steps = l) -> exists fs_a_dst_sum_exists_resultpositive_body_steps fs_r_dst_sum_exists_resultpositive_body_steps fs_s_dst_sum_exists_resultpositive_body_steps. ((((exists fs_h_dst_sum_exists_resultpositive_body_steps_summand. fs_h_dst_sum_exists_resultpositive_body_steps_summand + S (fs_a_dst_sum_exists_resultpositive_body_steps) = S ((S (fs_i_dst_sum_exists_resultpositive_body_steps)) * dst_positive_scale_sum_exists_result)) /\ exists fs_q_dst_sum_exists_resultpositive_body_steps_summand. dst_positive_code_sum_exists_result = fs_q_dst_sum_exists_resultpositive_body_steps_summand * S ((S (fs_i_dst_sum_exists_resultpositive_body_steps)) * dst_positive_scale_sum_exists_result) + (fs_a_dst_sum_exists_resultpositive_body_steps))) /\ ((((exists fs_h_dst_sum_exists_resultpositive_body_steps_partial. fs_h_dst_sum_exists_resultpositive_body_steps_partial + S (fs_r_dst_sum_exists_resultpositive_body_steps) = S ((S (fs_i_dst_sum_exists_resultpositive_body_steps)) * fs_v_dst_sum_exists_resultpositive)) /\ exists fs_q_dst_sum_exists_resultpositive_body_steps_partial. fs_u_dst_sum_exists_resultpositive = fs_q_dst_sum_exists_resultpositive_body_steps_partial * S ((S (fs_i_dst_sum_exists_resultpositive_body_steps)) * fs_v_dst_sum_exists_resultpositive) + (fs_r_dst_sum_exists_resultpositive_body_steps))) /\ ((((exists fs_h_dst_sum_exists_resultpositive_body_steps_successor. fs_h_dst_sum_exists_resultpositive_body_steps_successor + S (fs_s_dst_sum_exists_resultpositive_body_steps) = S ((S (S fs_i_dst_sum_exists_resultpositive_body_steps)) * fs_v_dst_sum_exists_resultpositive)) /\ exists fs_q_dst_sum_exists_resultpositive_body_steps_successor. fs_u_dst_sum_exists_resultpositive = fs_q_dst_sum_exists_resultpositive_body_steps_successor * S ((S (S fs_i_dst_sum_exists_resultpositive_body_steps)) * fs_v_dst_sum_exists_resultpositive) + (fs_s_dst_sum_exists_resultpositive_body_steps))) /\ fs_s_dst_sum_exists_resultpositive_body_steps = fs_r_dst_sum_exists_resultpositive_body_steps + fs_a_dst_sum_exists_resultpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_exists_resultnegative fs_v_dst_sum_exists_resultnegative. ((((exists fs_h_dst_sum_exists_resultnegative_body_start. fs_h_dst_sum_exists_resultnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_exists_resultnegative)) /\ exists fs_q_dst_sum_exists_resultnegative_body_start. fs_u_dst_sum_exists_resultnegative = fs_q_dst_sum_exists_resultnegative_body_start * S ((S (0)) * fs_v_dst_sum_exists_resultnegative) + (0))) /\ ((((exists fs_h_dst_sum_exists_resultnegative_body_terminal. fs_h_dst_sum_exists_resultnegative_body_terminal + S (dst_negative_sum_sum_exists_result) = S ((S (l)) * fs_v_dst_sum_exists_resultnegative)) /\ exists fs_q_dst_sum_exists_resultnegative_body_terminal. fs_u_dst_sum_exists_resultnegative = fs_q_dst_sum_exists_resultnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_exists_resultnegative) + (dst_negative_sum_sum_exists_result))) /\ forall fs_i_dst_sum_exists_resultnegative_body_steps. (exists fs_lt_dst_sum_exists_resultnegative_body_steps_bound. fs_lt_dst_sum_exists_resultnegative_body_steps_bound + S fs_i_dst_sum_exists_resultnegative_body_steps = l) -> exists fs_a_dst_sum_exists_resultnegative_body_steps fs_r_dst_sum_exists_resultnegative_body_steps fs_s_dst_sum_exists_resultnegative_body_steps. ((((exists fs_h_dst_sum_exists_resultnegative_body_steps_summand. fs_h_dst_sum_exists_resultnegative_body_steps_summand + S (fs_a_dst_sum_exists_resultnegative_body_steps) = S ((S (fs_i_dst_sum_exists_resultnegative_body_steps)) * dst_negative_scale_sum_exists_result)) /\ exists fs_q_dst_sum_exists_resultnegative_body_steps_summand. dst_negative_code_sum_exists_result = fs_q_dst_sum_exists_resultnegative_body_steps_summand * S ((S (fs_i_dst_sum_exists_resultnegative_body_steps)) * dst_negative_scale_sum_exists_result) + (fs_a_dst_sum_exists_resultnegative_body_steps))) /\ ((((exists fs_h_dst_sum_exists_resultnegative_body_steps_partial. fs_h_dst_sum_exists_resultnegative_body_steps_partial + S (fs_r_dst_sum_exists_resultnegative_body_steps) = S ((S (fs_i_dst_sum_exists_resultnegative_body_steps)) * fs_v_dst_sum_exists_resultnegative)) /\ exists fs_q_dst_sum_exists_resultnegative_body_steps_partial. fs_u_dst_sum_exists_resultnegative = fs_q_dst_sum_exists_resultnegative_body_steps_partial * S ((S (fs_i_dst_sum_exists_resultnegative_body_steps)) * fs_v_dst_sum_exists_resultnegative) + (fs_r_dst_sum_exists_resultnegative_body_steps))) /\ ((((exists fs_h_dst_sum_exists_resultnegative_body_steps_successor. fs_h_dst_sum_exists_resultnegative_body_steps_successor + S (fs_s_dst_sum_exists_resultnegative_body_steps) = S ((S (S fs_i_dst_sum_exists_resultnegative_body_steps)) * fs_v_dst_sum_exists_resultnegative)) /\ exists fs_q_dst_sum_exists_resultnegative_body_steps_successor. fs_u_dst_sum_exists_resultnegative = fs_q_dst_sum_exists_resultnegative_body_steps_successor * S ((S (S fs_i_dst_sum_exists_resultnegative_body_steps)) * fs_v_dst_sum_exists_resultnegative) + (fs_s_dst_sum_exists_resultnegative_body_steps))) /\ fs_s_dst_sum_exists_resultnegative_body_steps = fs_r_dst_sum_exists_resultnegative_body_steps + fs_a_dst_sum_exists_resultnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_exists_resultresult ge_balance_negative_sum_exists_resultresult. (((((z) = 2 * (ge_balance_positive_sum_exists_resultresult) /\ (ge_balance_negative_sum_exists_resultresult) = 0) \/ exists ge_signed_half_sum_exists_resultresultdecode. (((z) = 2 * ge_signed_half_sum_exists_resultresultdecode + 1 /\ (ge_balance_positive_sum_exists_resultresult) = 0) /\ (ge_balance_negative_sum_exists_resultresult) = S ge_signed_half_sum_exists_resultresultdecode))) /\ ((dst_positive_sum_sum_exists_result) + ge_balance_negative_sum_exists_resultresult = (dst_negative_sum_sum_exists_result) + ge_balance_positive_sum_exists_resultresult)))))))))

forall F l a b. (exists dst_positive_code_sum_unique_first dst_positive_scale_sum_unique_first dst_negative_code_sum_unique_first dst_negative_scale_sum_unique_first dst_positive_sum_sum_unique_first dst_negative_sum_sum_unique_first. (((F) = (((((dst_positive_code_sum_unique_first) + (dst_positive_scale_sum_unique_first)) * S ((dst_positive_code_sum_unique_first) + (dst_positive_scale_sum_unique_first)) + ((dst_positive_scale_sum_unique_first) + (dst_positive_scale_sum_unique_first))) + (((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) * S ((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) + ((dst_negative_scale_sum_unique_first) + (dst_negative_scale_sum_unique_first)))) * S ((((dst_positive_code_sum_unique_first) + (dst_positive_scale_sum_unique_first)) * S ((dst_positive_code_sum_unique_first) + (dst_positive_scale_sum_unique_first)) + ((dst_positive_scale_sum_unique_first) + (dst_positive_scale_sum_unique_first))) + (((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) * S ((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) + ((dst_negative_scale_sum_unique_first) + (dst_negative_scale_sum_unique_first)))) + ((((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) * S ((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) + ((dst_negative_scale_sum_unique_first) + (dst_negative_scale_sum_unique_first))) + (((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) * S ((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) + ((dst_negative_scale_sum_unique_first) + (dst_negative_scale_sum_unique_first)))))) /\ (((exists fs_u_dst_sum_unique_firstpositive fs_v_dst_sum_unique_firstpositive. ((((exists fs_h_dst_sum_unique_firstpositive_body_start. fs_h_dst_sum_unique_firstpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_firstpositive)) /\ exists fs_q_dst_sum_unique_firstpositive_body_start. fs_u_dst_sum_unique_firstpositive = fs_q_dst_sum_unique_firstpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_firstpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_firstpositive_body_terminal. fs_h_dst_sum_unique_firstpositive_body_terminal + S (dst_positive_sum_sum_unique_first) = S ((S (l)) * fs_v_dst_sum_unique_firstpositive)) /\ exists fs_q_dst_sum_unique_firstpositive_body_terminal. fs_u_dst_sum_unique_firstpositive = fs_q_dst_sum_unique_firstpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_unique_firstpositive) + (dst_positive_sum_sum_unique_first))) /\ forall fs_i_dst_sum_unique_firstpositive_body_steps. (exists fs_lt_dst_sum_unique_firstpositive_body_steps_bound. fs_lt_dst_sum_unique_firstpositive_body_steps_bound + S fs_i_dst_sum_unique_firstpositive_body_steps = l) -> exists fs_a_dst_sum_unique_firstpositive_body_steps fs_r_dst_sum_unique_firstpositive_body_steps fs_s_dst_sum_unique_firstpositive_body_steps. ((((exists fs_h_dst_sum_unique_firstpositive_body_steps_summand. fs_h_dst_sum_unique_firstpositive_body_steps_summand + S (fs_a_dst_sum_unique_firstpositive_body_steps) = S ((S (fs_i_dst_sum_unique_firstpositive_body_steps)) * dst_positive_scale_sum_unique_first)) /\ exists fs_q_dst_sum_unique_firstpositive_body_steps_summand. dst_positive_code_sum_unique_first = fs_q_dst_sum_unique_firstpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_firstpositive_body_steps)) * dst_positive_scale_sum_unique_first) + (fs_a_dst_sum_unique_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstpositive_body_steps_partial. fs_h_dst_sum_unique_firstpositive_body_steps_partial + S (fs_r_dst_sum_unique_firstpositive_body_steps) = S ((S (fs_i_dst_sum_unique_firstpositive_body_steps)) * fs_v_dst_sum_unique_firstpositive)) /\ exists fs_q_dst_sum_unique_firstpositive_body_steps_partial. fs_u_dst_sum_unique_firstpositive = fs_q_dst_sum_unique_firstpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_firstpositive_body_steps)) * fs_v_dst_sum_unique_firstpositive) + (fs_r_dst_sum_unique_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstpositive_body_steps_successor. fs_h_dst_sum_unique_firstpositive_body_steps_successor + S (fs_s_dst_sum_unique_firstpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_firstpositive_body_steps)) * fs_v_dst_sum_unique_firstpositive)) /\ exists fs_q_dst_sum_unique_firstpositive_body_steps_successor. fs_u_dst_sum_unique_firstpositive = fs_q_dst_sum_unique_firstpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_firstpositive_body_steps)) * fs_v_dst_sum_unique_firstpositive) + (fs_s_dst_sum_unique_firstpositive_body_steps))) /\ fs_s_dst_sum_unique_firstpositive_body_steps = fs_r_dst_sum_unique_firstpositive_body_steps + fs_a_dst_sum_unique_firstpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_firstnegative fs_v_dst_sum_unique_firstnegative. ((((exists fs_h_dst_sum_unique_firstnegative_body_start. fs_h_dst_sum_unique_firstnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_firstnegative)) /\ exists fs_q_dst_sum_unique_firstnegative_body_start. fs_u_dst_sum_unique_firstnegative = fs_q_dst_sum_unique_firstnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_firstnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_firstnegative_body_terminal. fs_h_dst_sum_unique_firstnegative_body_terminal + S (dst_negative_sum_sum_unique_first) = S ((S (l)) * fs_v_dst_sum_unique_firstnegative)) /\ exists fs_q_dst_sum_unique_firstnegative_body_terminal. fs_u_dst_sum_unique_firstnegative = fs_q_dst_sum_unique_firstnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_unique_firstnegative) + (dst_negative_sum_sum_unique_first))) /\ forall fs_i_dst_sum_unique_firstnegative_body_steps. (exists fs_lt_dst_sum_unique_firstnegative_body_steps_bound. fs_lt_dst_sum_unique_firstnegative_body_steps_bound + S fs_i_dst_sum_unique_firstnegative_body_steps = l) -> exists fs_a_dst_sum_unique_firstnegative_body_steps fs_r_dst_sum_unique_firstnegative_body_steps fs_s_dst_sum_unique_firstnegative_body_steps. ((((exists fs_h_dst_sum_unique_firstnegative_body_steps_summand. fs_h_dst_sum_unique_firstnegative_body_steps_summand + S (fs_a_dst_sum_unique_firstnegative_body_steps) = S ((S (fs_i_dst_sum_unique_firstnegative_body_steps)) * dst_negative_scale_sum_unique_first)) /\ exists fs_q_dst_sum_unique_firstnegative_body_steps_summand. dst_negative_code_sum_unique_first = fs_q_dst_sum_unique_firstnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_firstnegative_body_steps)) * dst_negative_scale_sum_unique_first) + (fs_a_dst_sum_unique_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstnegative_body_steps_partial. fs_h_dst_sum_unique_firstnegative_body_steps_partial + S (fs_r_dst_sum_unique_firstnegative_body_steps) = S ((S (fs_i_dst_sum_unique_firstnegative_body_steps)) * fs_v_dst_sum_unique_firstnegative)) /\ exists fs_q_dst_sum_unique_firstnegative_body_steps_partial. fs_u_dst_sum_unique_firstnegative = fs_q_dst_sum_unique_firstnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_firstnegative_body_steps)) * fs_v_dst_sum_unique_firstnegative) + (fs_r_dst_sum_unique_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstnegative_body_steps_successor. fs_h_dst_sum_unique_firstnegative_body_steps_successor + S (fs_s_dst_sum_unique_firstnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_firstnegative_body_steps)) * fs_v_dst_sum_unique_firstnegative)) /\ exists fs_q_dst_sum_unique_firstnegative_body_steps_successor. fs_u_dst_sum_unique_firstnegative = fs_q_dst_sum_unique_firstnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_firstnegative_body_steps)) * fs_v_dst_sum_unique_firstnegative) + (fs_s_dst_sum_unique_firstnegative_body_steps))) /\ fs_s_dst_sum_unique_firstnegative_body_steps = fs_r_dst_sum_unique_firstnegative_body_steps + fs_a_dst_sum_unique_firstnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_firstresult ge_balance_negative_sum_unique_firstresult. (((((a) = 2 * (ge_balance_positive_sum_unique_firstresult) /\ (ge_balance_negative_sum_unique_firstresult) = 0) \/ exists ge_signed_half_sum_unique_firstresultdecode. (((a) = 2 * ge_signed_half_sum_unique_firstresultdecode + 1 /\ (ge_balance_positive_sum_unique_firstresult) = 0) /\ (ge_balance_negative_sum_unique_firstresult) = S ge_signed_half_sum_unique_firstresultdecode))) /\ ((dst_positive_sum_sum_unique_first) + ge_balance_negative_sum_unique_firstresult = (dst_negative_sum_sum_unique_first) + ge_balance_positive_sum_unique_firstresult))))))))) -> (exists dst_positive_code_sum_unique_second dst_positive_scale_sum_unique_second dst_negative_code_sum_unique_second dst_negative_scale_sum_unique_second dst_positive_sum_sum_unique_second dst_negative_sum_sum_unique_second. (((F) = (((((dst_positive_code_sum_unique_second) + (dst_positive_scale_sum_unique_second)) * S ((dst_positive_code_sum_unique_second) + (dst_positive_scale_sum_unique_second)) + ((dst_positive_scale_sum_unique_second) + (dst_positive_scale_sum_unique_second))) + (((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) * S ((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) + ((dst_negative_scale_sum_unique_second) + (dst_negative_scale_sum_unique_second)))) * S ((((dst_positive_code_sum_unique_second) + (dst_positive_scale_sum_unique_second)) * S ((dst_positive_code_sum_unique_second) + (dst_positive_scale_sum_unique_second)) + ((dst_positive_scale_sum_unique_second) + (dst_positive_scale_sum_unique_second))) + (((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) * S ((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) + ((dst_negative_scale_sum_unique_second) + (dst_negative_scale_sum_unique_second)))) + ((((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) * S ((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) + ((dst_negative_scale_sum_unique_second) + (dst_negative_scale_sum_unique_second))) + (((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) * S ((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) + ((dst_negative_scale_sum_unique_second) + (dst_negative_scale_sum_unique_second)))))) /\ (((exists fs_u_dst_sum_unique_secondpositive fs_v_dst_sum_unique_secondpositive. ((((exists fs_h_dst_sum_unique_secondpositive_body_start. fs_h_dst_sum_unique_secondpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_secondpositive)) /\ exists fs_q_dst_sum_unique_secondpositive_body_start. fs_u_dst_sum_unique_secondpositive = fs_q_dst_sum_unique_secondpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_secondpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_secondpositive_body_terminal. fs_h_dst_sum_unique_secondpositive_body_terminal + S (dst_positive_sum_sum_unique_second) = S ((S (l)) * fs_v_dst_sum_unique_secondpositive)) /\ exists fs_q_dst_sum_unique_secondpositive_body_terminal. fs_u_dst_sum_unique_secondpositive = fs_q_dst_sum_unique_secondpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_unique_secondpositive) + (dst_positive_sum_sum_unique_second))) /\ forall fs_i_dst_sum_unique_secondpositive_body_steps. (exists fs_lt_dst_sum_unique_secondpositive_body_steps_bound. fs_lt_dst_sum_unique_secondpositive_body_steps_bound + S fs_i_dst_sum_unique_secondpositive_body_steps = l) -> exists fs_a_dst_sum_unique_secondpositive_body_steps fs_r_dst_sum_unique_secondpositive_body_steps fs_s_dst_sum_unique_secondpositive_body_steps. ((((exists fs_h_dst_sum_unique_secondpositive_body_steps_summand. fs_h_dst_sum_unique_secondpositive_body_steps_summand + S (fs_a_dst_sum_unique_secondpositive_body_steps) = S ((S (fs_i_dst_sum_unique_secondpositive_body_steps)) * dst_positive_scale_sum_unique_second)) /\ exists fs_q_dst_sum_unique_secondpositive_body_steps_summand. dst_positive_code_sum_unique_second = fs_q_dst_sum_unique_secondpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_secondpositive_body_steps)) * dst_positive_scale_sum_unique_second) + (fs_a_dst_sum_unique_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondpositive_body_steps_partial. fs_h_dst_sum_unique_secondpositive_body_steps_partial + S (fs_r_dst_sum_unique_secondpositive_body_steps) = S ((S (fs_i_dst_sum_unique_secondpositive_body_steps)) * fs_v_dst_sum_unique_secondpositive)) /\ exists fs_q_dst_sum_unique_secondpositive_body_steps_partial. fs_u_dst_sum_unique_secondpositive = fs_q_dst_sum_unique_secondpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_secondpositive_body_steps)) * fs_v_dst_sum_unique_secondpositive) + (fs_r_dst_sum_unique_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondpositive_body_steps_successor. fs_h_dst_sum_unique_secondpositive_body_steps_successor + S (fs_s_dst_sum_unique_secondpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_secondpositive_body_steps)) * fs_v_dst_sum_unique_secondpositive)) /\ exists fs_q_dst_sum_unique_secondpositive_body_steps_successor. fs_u_dst_sum_unique_secondpositive = fs_q_dst_sum_unique_secondpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_secondpositive_body_steps)) * fs_v_dst_sum_unique_secondpositive) + (fs_s_dst_sum_unique_secondpositive_body_steps))) /\ fs_s_dst_sum_unique_secondpositive_body_steps = fs_r_dst_sum_unique_secondpositive_body_steps + fs_a_dst_sum_unique_secondpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_secondnegative fs_v_dst_sum_unique_secondnegative. ((((exists fs_h_dst_sum_unique_secondnegative_body_start. fs_h_dst_sum_unique_secondnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_secondnegative)) /\ exists fs_q_dst_sum_unique_secondnegative_body_start. fs_u_dst_sum_unique_secondnegative = fs_q_dst_sum_unique_secondnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_secondnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_secondnegative_body_terminal. fs_h_dst_sum_unique_secondnegative_body_terminal + S (dst_negative_sum_sum_unique_second) = S ((S (l)) * fs_v_dst_sum_unique_secondnegative)) /\ exists fs_q_dst_sum_unique_secondnegative_body_terminal. fs_u_dst_sum_unique_secondnegative = fs_q_dst_sum_unique_secondnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_unique_secondnegative) + (dst_negative_sum_sum_unique_second))) /\ forall fs_i_dst_sum_unique_secondnegative_body_steps. (exists fs_lt_dst_sum_unique_secondnegative_body_steps_bound. fs_lt_dst_sum_unique_secondnegative_body_steps_bound + S fs_i_dst_sum_unique_secondnegative_body_steps = l) -> exists fs_a_dst_sum_unique_secondnegative_body_steps fs_r_dst_sum_unique_secondnegative_body_steps fs_s_dst_sum_unique_secondnegative_body_steps. ((((exists fs_h_dst_sum_unique_secondnegative_body_steps_summand. fs_h_dst_sum_unique_secondnegative_body_steps_summand + S (fs_a_dst_sum_unique_secondnegative_body_steps) = S ((S (fs_i_dst_sum_unique_secondnegative_body_steps)) * dst_negative_scale_sum_unique_second)) /\ exists fs_q_dst_sum_unique_secondnegative_body_steps_summand. dst_negative_code_sum_unique_second = fs_q_dst_sum_unique_secondnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_secondnegative_body_steps)) * dst_negative_scale_sum_unique_second) + (fs_a_dst_sum_unique_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondnegative_body_steps_partial. fs_h_dst_sum_unique_secondnegative_body_steps_partial + S (fs_r_dst_sum_unique_secondnegative_body_steps) = S ((S (fs_i_dst_sum_unique_secondnegative_body_steps)) * fs_v_dst_sum_unique_secondnegative)) /\ exists fs_q_dst_sum_unique_secondnegative_body_steps_partial. fs_u_dst_sum_unique_secondnegative = fs_q_dst_sum_unique_secondnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_secondnegative_body_steps)) * fs_v_dst_sum_unique_secondnegative) + (fs_r_dst_sum_unique_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondnegative_body_steps_successor. fs_h_dst_sum_unique_secondnegative_body_steps_successor + S (fs_s_dst_sum_unique_secondnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_secondnegative_body_steps)) * fs_v_dst_sum_unique_secondnegative)) /\ exists fs_q_dst_sum_unique_secondnegative_body_steps_successor. fs_u_dst_sum_unique_secondnegative = fs_q_dst_sum_unique_secondnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_secondnegative_body_steps)) * fs_v_dst_sum_unique_secondnegative) + (fs_s_dst_sum_unique_secondnegative_body_steps))) /\ fs_s_dst_sum_unique_secondnegative_body_steps = fs_r_dst_sum_unique_secondnegative_body_steps + fs_a_dst_sum_unique_secondnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_secondresult ge_balance_negative_sum_unique_secondresult. (((((b) = 2 * (ge_balance_positive_sum_unique_secondresult) /\ (ge_balance_negative_sum_unique_secondresult) = 0) \/ exists ge_signed_half_sum_unique_secondresultdecode. (((b) = 2 * ge_signed_half_sum_unique_secondresultdecode + 1 /\ (ge_balance_positive_sum_unique_secondresult) = 0) /\ (ge_balance_negative_sum_unique_secondresult) = S ge_signed_half_sum_unique_secondresultdecode))) /\ ((dst_positive_sum_sum_unique_second) + ge_balance_negative_sum_unique_secondresult = (dst_negative_sum_sum_unique_second) + ge_balance_positive_sum_unique_secondresult))))))))) -> a = b

forall F z. (exists dst_positive_code_empty_sum dst_positive_scale_empty_sum dst_negative_code_empty_sum dst_negative_scale_empty_sum dst_positive_sum_empty_sum dst_negative_sum_empty_sum. (((F) = (((((dst_positive_code_empty_sum) + (dst_positive_scale_empty_sum)) * S ((dst_positive_code_empty_sum) + (dst_positive_scale_empty_sum)) + ((dst_positive_scale_empty_sum) + (dst_positive_scale_empty_sum))) + (((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) * S ((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) + ((dst_negative_scale_empty_sum) + (dst_negative_scale_empty_sum)))) * S ((((dst_positive_code_empty_sum) + (dst_positive_scale_empty_sum)) * S ((dst_positive_code_empty_sum) + (dst_positive_scale_empty_sum)) + ((dst_positive_scale_empty_sum) + (dst_positive_scale_empty_sum))) + (((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) * S ((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) + ((dst_negative_scale_empty_sum) + (dst_negative_scale_empty_sum)))) + ((((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) * S ((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) + ((dst_negative_scale_empty_sum) + (dst_negative_scale_empty_sum))) + (((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) * S ((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) + ((dst_negative_scale_empty_sum) + (dst_negative_scale_empty_sum)))))) /\ (((exists fs_u_dst_empty_sumpositive fs_v_dst_empty_sumpositive. ((((exists fs_h_dst_empty_sumpositive_body_start. fs_h_dst_empty_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_empty_sumpositive)) /\ exists fs_q_dst_empty_sumpositive_body_start. fs_u_dst_empty_sumpositive = fs_q_dst_empty_sumpositive_body_start * S ((S (0)) * fs_v_dst_empty_sumpositive) + (0))) /\ ((((exists fs_h_dst_empty_sumpositive_body_terminal. fs_h_dst_empty_sumpositive_body_terminal + S (dst_positive_sum_empty_sum) = S ((S (0)) * fs_v_dst_empty_sumpositive)) /\ exists fs_q_dst_empty_sumpositive_body_terminal. fs_u_dst_empty_sumpositive = fs_q_dst_empty_sumpositive_body_terminal * S ((S (0)) * fs_v_dst_empty_sumpositive) + (dst_positive_sum_empty_sum))) /\ forall fs_i_dst_empty_sumpositive_body_steps. (exists fs_lt_dst_empty_sumpositive_body_steps_bound. fs_lt_dst_empty_sumpositive_body_steps_bound + S fs_i_dst_empty_sumpositive_body_steps = 0) -> exists fs_a_dst_empty_sumpositive_body_steps fs_r_dst_empty_sumpositive_body_steps fs_s_dst_empty_sumpositive_body_steps. ((((exists fs_h_dst_empty_sumpositive_body_steps_summand. fs_h_dst_empty_sumpositive_body_steps_summand + S (fs_a_dst_empty_sumpositive_body_steps) = S ((S (fs_i_dst_empty_sumpositive_body_steps)) * dst_positive_scale_empty_sum)) /\ exists fs_q_dst_empty_sumpositive_body_steps_summand. dst_positive_code_empty_sum = fs_q_dst_empty_sumpositive_body_steps_summand * S ((S (fs_i_dst_empty_sumpositive_body_steps)) * dst_positive_scale_empty_sum) + (fs_a_dst_empty_sumpositive_body_steps))) /\ ((((exists fs_h_dst_empty_sumpositive_body_steps_partial. fs_h_dst_empty_sumpositive_body_steps_partial + S (fs_r_dst_empty_sumpositive_body_steps) = S ((S (fs_i_dst_empty_sumpositive_body_steps)) * fs_v_dst_empty_sumpositive)) /\ exists fs_q_dst_empty_sumpositive_body_steps_partial. fs_u_dst_empty_sumpositive = fs_q_dst_empty_sumpositive_body_steps_partial * S ((S (fs_i_dst_empty_sumpositive_body_steps)) * fs_v_dst_empty_sumpositive) + (fs_r_dst_empty_sumpositive_body_steps))) /\ ((((exists fs_h_dst_empty_sumpositive_body_steps_successor. fs_h_dst_empty_sumpositive_body_steps_successor + S (fs_s_dst_empty_sumpositive_body_steps) = S ((S (S fs_i_dst_empty_sumpositive_body_steps)) * fs_v_dst_empty_sumpositive)) /\ exists fs_q_dst_empty_sumpositive_body_steps_successor. fs_u_dst_empty_sumpositive = fs_q_dst_empty_sumpositive_body_steps_successor * S ((S (S fs_i_dst_empty_sumpositive_body_steps)) * fs_v_dst_empty_sumpositive) + (fs_s_dst_empty_sumpositive_body_steps))) /\ fs_s_dst_empty_sumpositive_body_steps = fs_r_dst_empty_sumpositive_body_steps + fs_a_dst_empty_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_empty_sumnegative fs_v_dst_empty_sumnegative. ((((exists fs_h_dst_empty_sumnegative_body_start. fs_h_dst_empty_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_empty_sumnegative)) /\ exists fs_q_dst_empty_sumnegative_body_start. fs_u_dst_empty_sumnegative = fs_q_dst_empty_sumnegative_body_start * S ((S (0)) * fs_v_dst_empty_sumnegative) + (0))) /\ ((((exists fs_h_dst_empty_sumnegative_body_terminal. fs_h_dst_empty_sumnegative_body_terminal + S (dst_negative_sum_empty_sum) = S ((S (0)) * fs_v_dst_empty_sumnegative)) /\ exists fs_q_dst_empty_sumnegative_body_terminal. fs_u_dst_empty_sumnegative = fs_q_dst_empty_sumnegative_body_terminal * S ((S (0)) * fs_v_dst_empty_sumnegative) + (dst_negative_sum_empty_sum))) /\ forall fs_i_dst_empty_sumnegative_body_steps. (exists fs_lt_dst_empty_sumnegative_body_steps_bound. fs_lt_dst_empty_sumnegative_body_steps_bound + S fs_i_dst_empty_sumnegative_body_steps = 0) -> exists fs_a_dst_empty_sumnegative_body_steps fs_r_dst_empty_sumnegative_body_steps fs_s_dst_empty_sumnegative_body_steps. ((((exists fs_h_dst_empty_sumnegative_body_steps_summand. fs_h_dst_empty_sumnegative_body_steps_summand + S (fs_a_dst_empty_sumnegative_body_steps) = S ((S (fs_i_dst_empty_sumnegative_body_steps)) * dst_negative_scale_empty_sum)) /\ exists fs_q_dst_empty_sumnegative_body_steps_summand. dst_negative_code_empty_sum = fs_q_dst_empty_sumnegative_body_steps_summand * S ((S (fs_i_dst_empty_sumnegative_body_steps)) * dst_negative_scale_empty_sum) + (fs_a_dst_empty_sumnegative_body_steps))) /\ ((((exists fs_h_dst_empty_sumnegative_body_steps_partial. fs_h_dst_empty_sumnegative_body_steps_partial + S (fs_r_dst_empty_sumnegative_body_steps) = S ((S (fs_i_dst_empty_sumnegative_body_steps)) * fs_v_dst_empty_sumnegative)) /\ exists fs_q_dst_empty_sumnegative_body_steps_partial. fs_u_dst_empty_sumnegative = fs_q_dst_empty_sumnegative_body_steps_partial * S ((S (fs_i_dst_empty_sumnegative_body_steps)) * fs_v_dst_empty_sumnegative) + (fs_r_dst_empty_sumnegative_body_steps))) /\ ((((exists fs_h_dst_empty_sumnegative_body_steps_successor. fs_h_dst_empty_sumnegative_body_steps_successor + S (fs_s_dst_empty_sumnegative_body_steps) = S ((S (S fs_i_dst_empty_sumnegative_body_steps)) * fs_v_dst_empty_sumnegative)) /\ exists fs_q_dst_empty_sumnegative_body_steps_successor. fs_u_dst_empty_sumnegative = fs_q_dst_empty_sumnegative_body_steps_successor * S ((S (S fs_i_dst_empty_sumnegative_body_steps)) * fs_v_dst_empty_sumnegative) + (fs_s_dst_empty_sumnegative_body_steps))) /\ fs_s_dst_empty_sumnegative_body_steps = fs_r_dst_empty_sumnegative_body_steps + fs_a_dst_empty_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_empty_sumresult ge_balance_negative_empty_sumresult. (((((z) = 2 * (ge_balance_positive_empty_sumresult) /\ (ge_balance_negative_empty_sumresult) = 0) \/ exists ge_signed_half_empty_sumresultdecode. (((z) = 2 * ge_signed_half_empty_sumresultdecode + 1 /\ (ge_balance_positive_empty_sumresult) = 0) /\ (ge_balance_negative_empty_sumresult) = S ge_signed_half_empty_sumresultdecode))) /\ ((dst_positive_sum_empty_sum) + ge_balance_negative_empty_sumresult = (dst_negative_sum_empty_sum) + ge_balance_positive_empty_sumresult))))))))) -> z = 0

forall F pb pc nb nc. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (exists dst_positive_code_empty_result dst_positive_scale_empty_result dst_negative_code_empty_result dst_negative_scale_empty_result dst_positive_sum_empty_result dst_negative_sum_empty_result. (((F) = (((((dst_positive_code_empty_result) + (dst_positive_scale_empty_result)) * S ((dst_positive_code_empty_result) + (dst_positive_scale_empty_result)) + ((dst_positive_scale_empty_result) + (dst_positive_scale_empty_result))) + (((dst_negative_code_empty_result) + (dst_negative_scale_empty_result)) * S ((dst_negative_code_empty_result) + (dst_negative_scale_empty_result)) + ((dst_negative_scale_empty_result) + (dst_negative_scale_empty_result)))) * S ((((dst_positive_code_empty_result) + (dst_positive_scale_empty_result)) * S ((dst_positive_code_empty_result) + (dst_positive_scale_empty_result)) + ((dst_positive_scale_empty_result) + (dst_positive_scale_empty_result))) + (((dst_negative_code_empty_result) + (dst_negative_scale_empty_result)) * S ((dst_negative_code_empty_result) + (dst_negative_scale_empty_result)) + ((dst_negative_scale_empty_result) + (dst_negative_scale_empty_result)))) + ((((dst_negative_code_empty_result) + (dst_negative_scale_empty_result)) * S ((dst_negative_code_empty_result) + (dst_negative_scale_empty_result)) + ((dst_negative_scale_empty_result) + (dst_negative_scale_empty_result))) + (((dst_negative_code_empty_result) + (dst_negative_scale_empty_result)) * S ((dst_negative_code_empty_result) + (dst_negative_scale_empty_result)) + ((dst_negative_scale_empty_result) + (dst_negative_scale_empty_result)))))) /\ (((exists fs_u_dst_empty_resultpositive fs_v_dst_empty_resultpositive. ((((exists fs_h_dst_empty_resultpositive_body_start. fs_h_dst_empty_resultpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_empty_resultpositive)) /\ exists fs_q_dst_empty_resultpositive_body_start. fs_u_dst_empty_resultpositive = fs_q_dst_empty_resultpositive_body_start * S ((S (0)) * fs_v_dst_empty_resultpositive) + (0))) /\ ((((exists fs_h_dst_empty_resultpositive_body_terminal. fs_h_dst_empty_resultpositive_body_terminal + S (dst_positive_sum_empty_result) = S ((S (0)) * fs_v_dst_empty_resultpositive)) /\ exists fs_q_dst_empty_resultpositive_body_terminal. fs_u_dst_empty_resultpositive = fs_q_dst_empty_resultpositive_body_terminal * S ((S (0)) * fs_v_dst_empty_resultpositive) + (dst_positive_sum_empty_result))) /\ forall fs_i_dst_empty_resultpositive_body_steps. (exists fs_lt_dst_empty_resultpositive_body_steps_bound. fs_lt_dst_empty_resultpositive_body_steps_bound + S fs_i_dst_empty_resultpositive_body_steps = 0) -> exists fs_a_dst_empty_resultpositive_body_steps fs_r_dst_empty_resultpositive_body_steps fs_s_dst_empty_resultpositive_body_steps. ((((exists fs_h_dst_empty_resultpositive_body_steps_summand. fs_h_dst_empty_resultpositive_body_steps_summand + S (fs_a_dst_empty_resultpositive_body_steps) = S ((S (fs_i_dst_empty_resultpositive_body_steps)) * dst_positive_scale_empty_result)) /\ exists fs_q_dst_empty_resultpositive_body_steps_summand. dst_positive_code_empty_result = fs_q_dst_empty_resultpositive_body_steps_summand * S ((S (fs_i_dst_empty_resultpositive_body_steps)) * dst_positive_scale_empty_result) + (fs_a_dst_empty_resultpositive_body_steps))) /\ ((((exists fs_h_dst_empty_resultpositive_body_steps_partial. fs_h_dst_empty_resultpositive_body_steps_partial + S (fs_r_dst_empty_resultpositive_body_steps) = S ((S (fs_i_dst_empty_resultpositive_body_steps)) * fs_v_dst_empty_resultpositive)) /\ exists fs_q_dst_empty_resultpositive_body_steps_partial. fs_u_dst_empty_resultpositive = fs_q_dst_empty_resultpositive_body_steps_partial * S ((S (fs_i_dst_empty_resultpositive_body_steps)) * fs_v_dst_empty_resultpositive) + (fs_r_dst_empty_resultpositive_body_steps))) /\ ((((exists fs_h_dst_empty_resultpositive_body_steps_successor. fs_h_dst_empty_resultpositive_body_steps_successor + S (fs_s_dst_empty_resultpositive_body_steps) = S ((S (S fs_i_dst_empty_resultpositive_body_steps)) * fs_v_dst_empty_resultpositive)) /\ exists fs_q_dst_empty_resultpositive_body_steps_successor. fs_u_dst_empty_resultpositive = fs_q_dst_empty_resultpositive_body_steps_successor * S ((S (S fs_i_dst_empty_resultpositive_body_steps)) * fs_v_dst_empty_resultpositive) + (fs_s_dst_empty_resultpositive_body_steps))) /\ fs_s_dst_empty_resultpositive_body_steps = fs_r_dst_empty_resultpositive_body_steps + fs_a_dst_empty_resultpositive_body_steps)))))) /\ (((exists fs_u_dst_empty_resultnegative fs_v_dst_empty_resultnegative. ((((exists fs_h_dst_empty_resultnegative_body_start. fs_h_dst_empty_resultnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_empty_resultnegative)) /\ exists fs_q_dst_empty_resultnegative_body_start. fs_u_dst_empty_resultnegative = fs_q_dst_empty_resultnegative_body_start * S ((S (0)) * fs_v_dst_empty_resultnegative) + (0))) /\ ((((exists fs_h_dst_empty_resultnegative_body_terminal. fs_h_dst_empty_resultnegative_body_terminal + S (dst_negative_sum_empty_result) = S ((S (0)) * fs_v_dst_empty_resultnegative)) /\ exists fs_q_dst_empty_resultnegative_body_terminal. fs_u_dst_empty_resultnegative = fs_q_dst_empty_resultnegative_body_terminal * S ((S (0)) * fs_v_dst_empty_resultnegative) + (dst_negative_sum_empty_result))) /\ forall fs_i_dst_empty_resultnegative_body_steps. (exists fs_lt_dst_empty_resultnegative_body_steps_bound. fs_lt_dst_empty_resultnegative_body_steps_bound + S fs_i_dst_empty_resultnegative_body_steps = 0) -> exists fs_a_dst_empty_resultnegative_body_steps fs_r_dst_empty_resultnegative_body_steps fs_s_dst_empty_resultnegative_body_steps. ((((exists fs_h_dst_empty_resultnegative_body_steps_summand. fs_h_dst_empty_resultnegative_body_steps_summand + S (fs_a_dst_empty_resultnegative_body_steps) = S ((S (fs_i_dst_empty_resultnegative_body_steps)) * dst_negative_scale_empty_result)) /\ exists fs_q_dst_empty_resultnegative_body_steps_summand. dst_negative_code_empty_result = fs_q_dst_empty_resultnegative_body_steps_summand * S ((S (fs_i_dst_empty_resultnegative_body_steps)) * dst_negative_scale_empty_result) + (fs_a_dst_empty_resultnegative_body_steps))) /\ ((((exists fs_h_dst_empty_resultnegative_body_steps_partial. fs_h_dst_empty_resultnegative_body_steps_partial + S (fs_r_dst_empty_resultnegative_body_steps) = S ((S (fs_i_dst_empty_resultnegative_body_steps)) * fs_v_dst_empty_resultnegative)) /\ exists fs_q_dst_empty_resultnegative_body_steps_partial. fs_u_dst_empty_resultnegative = fs_q_dst_empty_resultnegative_body_steps_partial * S ((S (fs_i_dst_empty_resultnegative_body_steps)) * fs_v_dst_empty_resultnegative) + (fs_r_dst_empty_resultnegative_body_steps))) /\ ((((exists fs_h_dst_empty_resultnegative_body_steps_successor. fs_h_dst_empty_resultnegative_body_steps_successor + S (fs_s_dst_empty_resultnegative_body_steps) = S ((S (S fs_i_dst_empty_resultnegative_body_steps)) * fs_v_dst_empty_resultnegative)) /\ exists fs_q_dst_empty_resultnegative_body_steps_successor. fs_u_dst_empty_resultnegative = fs_q_dst_empty_resultnegative_body_steps_successor * S ((S (S fs_i_dst_empty_resultnegative_body_steps)) * fs_v_dst_empty_resultnegative) + (fs_s_dst_empty_resultnegative_body_steps))) /\ fs_s_dst_empty_resultnegative_body_steps = fs_r_dst_empty_resultnegative_body_steps + fs_a_dst_empty_resultnegative_body_steps)))))) /\ (exists ge_balance_positive_empty_resultresult ge_balance_negative_empty_resultresult. (((((0) = 2 * (ge_balance_positive_empty_resultresult) /\ (ge_balance_negative_empty_resultresult) = 0) \/ exists ge_signed_half_empty_resultresultdecode. (((0) = 2 * ge_signed_half_empty_resultresultdecode + 1 /\ (ge_balance_positive_empty_resultresult) = 0) /\ (ge_balance_negative_empty_resultresult) = S ge_signed_half_empty_resultresultdecode))) /\ ((dst_positive_sum_empty_result) + ge_balance_negative_empty_resultresult = (dst_negative_sum_empty_result) + ge_balance_positive_empty_resultresult)))))))))

forall a b p n. (exists ge_balance_positive_negate_balance ge_balance_negative_negate_balance. (((((a) = 2 * (ge_balance_positive_negate_balance) /\ (ge_balance_negative_negate_balance) = 0) \/ exists ge_signed_half_negate_balancedecode. (((a) = 2 * ge_signed_half_negate_balancedecode + 1 /\ (ge_balance_positive_negate_balance) = 0) /\ (ge_balance_negative_negate_balance) = S ge_signed_half_negate_balancedecode))) /\ ((p) + ge_balance_negative_negate_balance = (n) + ge_balance_positive_negate_balance))) -> (exists mps_positive_negate_graph mps_negative_negate_graph. (((((a) = 2 * (mps_positive_negate_graph) /\ (mps_negative_negate_graph) = 0) \/ exists ge_signed_half_negate_graphsource. (((a) = 2 * ge_signed_half_negate_graphsource + 1 /\ (mps_positive_negate_graph) = 0) /\ (mps_negative_negate_graph) = S ge_signed_half_negate_graphsource))) /\ ((((b) = 2 * (mps_negative_negate_graph) /\ (mps_positive_negate_graph) = 0) \/ exists ge_signed_half_negate_graphtarget. (((b) = 2 * ge_signed_half_negate_graphtarget + 1 /\ (mps_negative_negate_graph) = 0) /\ (mps_positive_negate_graph) = S ge_signed_half_negate_graphtarget))))) -> (exists ge_balance_positive_negate_result ge_balance_negative_negate_result. (((((b) = 2 * (ge_balance_positive_negate_result) /\ (ge_balance_negative_negate_result) = 0) \/ exists ge_signed_half_negate_resultdecode. (((b) = 2 * ge_signed_half_negate_resultdecode + 1 /\ (ge_balance_positive_negate_result) = 0) /\ (ge_balance_negative_negate_result) = S ge_signed_half_negate_resultdecode))) /\ ((n) + ge_balance_negative_negate_result = (p) + ge_balance_positive_negate_result)))

forall a b p n. (exists ge_balance_positive_negate_intro_first ge_balance_negative_negate_intro_first. (((((a) = 2 * (ge_balance_positive_negate_intro_first) /\ (ge_balance_negative_negate_intro_first) = 0) \/ exists ge_signed_half_negate_intro_firstdecode. (((a) = 2 * ge_signed_half_negate_intro_firstdecode + 1 /\ (ge_balance_positive_negate_intro_first) = 0) /\ (ge_balance_negative_negate_intro_first) = S ge_signed_half_negate_intro_firstdecode))) /\ ((p) + ge_balance_negative_negate_intro_first = (n) + ge_balance_positive_negate_intro_first))) -> (exists ge_balance_positive_negate_intro_second ge_balance_negative_negate_intro_second. (((((b) = 2 * (ge_balance_positive_negate_intro_second) /\ (ge_balance_negative_negate_intro_second) = 0) \/ exists ge_signed_half_negate_intro_seconddecode. (((b) = 2 * ge_signed_half_negate_intro_seconddecode + 1 /\ (ge_balance_positive_negate_intro_second) = 0) /\ (ge_balance_negative_negate_intro_second) = S ge_signed_half_negate_intro_seconddecode))) /\ ((n) + ge_balance_negative_negate_intro_second = (p) + ge_balance_positive_negate_intro_second))) -> (exists mps_positive_negate_intro_result mps_negative_negate_intro_result. (((((a) = 2 * (mps_positive_negate_intro_result) /\ (mps_negative_negate_intro_result) = 0) \/ exists ge_signed_half_negate_intro_resultsource. (((a) = 2 * ge_signed_half_negate_intro_resultsource + 1 /\ (mps_positive_negate_intro_result) = 0) /\ (mps_negative_negate_intro_result) = S ge_signed_half_negate_intro_resultsource))) /\ ((((b) = 2 * (mps_negative_negate_intro_result) /\ (mps_positive_negate_intro_result) = 0) \/ exists ge_signed_half_negate_intro_resulttarget. (((b) = 2 * ge_signed_half_negate_intro_resulttarget + 1 /\ (mps_negative_negate_intro_result) = 0) /\ (mps_positive_negate_intro_result) = S ge_signed_half_negate_intro_resulttarget)))))

forall a. (exists mps_positive_fixed_negation mps_negative_fixed_negation. (((((a) = 2 * (mps_positive_fixed_negation) /\ (mps_negative_fixed_negation) = 0) \/ exists ge_signed_half_fixed_negationsource. (((a) = 2 * ge_signed_half_fixed_negationsource + 1 /\ (mps_positive_fixed_negation) = 0) /\ (mps_negative_fixed_negation) = S ge_signed_half_fixed_negationsource))) /\ ((((a) = 2 * (mps_negative_fixed_negation) /\ (mps_positive_fixed_negation) = 0) \/ exists ge_signed_half_fixed_negationtarget. (((a) = 2 * ge_signed_half_fixed_negationtarget + 1 /\ (mps_negative_fixed_negation) = 0) /\ (mps_positive_fixed_negation) = S ge_signed_half_fixed_negationtarget))))) -> a = 0

forall b c l r a. (exists fs_u_dst_natural_step_prefix fs_v_dst_natural_step_prefix. ((((exists fs_h_dst_natural_step_prefix_body_start. fs_h_dst_natural_step_prefix_body_start + S (0) = S ((S (0)) * fs_v_dst_natural_step_prefix)) /\ exists fs_q_dst_natural_step_prefix_body_start. fs_u_dst_natural_step_prefix = fs_q_dst_natural_step_prefix_body_start * S ((S (0)) * fs_v_dst_natural_step_prefix) + (0))) /\ ((((exists fs_h_dst_natural_step_prefix_body_terminal. fs_h_dst_natural_step_prefix_body_terminal + S (r) = S ((S (l)) * fs_v_dst_natural_step_prefix)) /\ exists fs_q_dst_natural_step_prefix_body_terminal. fs_u_dst_natural_step_prefix = fs_q_dst_natural_step_prefix_body_terminal * S ((S (l)) * fs_v_dst_natural_step_prefix) + (r))) /\ forall fs_i_dst_natural_step_prefix_body_steps. (exists fs_lt_dst_natural_step_prefix_body_steps_bound. fs_lt_dst_natural_step_prefix_body_steps_bound + S fs_i_dst_natural_step_prefix_body_steps = l) -> exists fs_a_dst_natural_step_prefix_body_steps fs_r_dst_natural_step_prefix_body_steps fs_s_dst_natural_step_prefix_body_steps. ((((exists fs_h_dst_natural_step_prefix_body_steps_summand. fs_h_dst_natural_step_prefix_body_steps_summand + S (fs_a_dst_natural_step_prefix_body_steps) = S ((S (fs_i_dst_natural_step_prefix_body_steps)) * c)) /\ exists fs_q_dst_natural_step_prefix_body_steps_summand. b = fs_q_dst_natural_step_prefix_body_steps_summand * S ((S (fs_i_dst_natural_step_prefix_body_steps)) * c) + (fs_a_dst_natural_step_prefix_body_steps))) /\ ((((exists fs_h_dst_natural_step_prefix_body_steps_partial. fs_h_dst_natural_step_prefix_body_steps_partial + S (fs_r_dst_natural_step_prefix_body_steps) = S ((S (fs_i_dst_natural_step_prefix_body_steps)) * fs_v_dst_natural_step_prefix)) /\ exists fs_q_dst_natural_step_prefix_body_steps_partial. fs_u_dst_natural_step_prefix = fs_q_dst_natural_step_prefix_body_steps_partial * S ((S (fs_i_dst_natural_step_prefix_body_steps)) * fs_v_dst_natural_step_prefix) + (fs_r_dst_natural_step_prefix_body_steps))) /\ ((((exists fs_h_dst_natural_step_prefix_body_steps_successor. fs_h_dst_natural_step_prefix_body_steps_successor + S (fs_s_dst_natural_step_prefix_body_steps) = S ((S (S fs_i_dst_natural_step_prefix_body_steps)) * fs_v_dst_natural_step_prefix)) /\ exists fs_q_dst_natural_step_prefix_body_steps_successor. fs_u_dst_natural_step_prefix = fs_q_dst_natural_step_prefix_body_steps_successor * S ((S (S fs_i_dst_natural_step_prefix_body_steps)) * fs_v_dst_natural_step_prefix) + (fs_s_dst_natural_step_prefix_body_steps))) /\ fs_s_dst_natural_step_prefix_body_steps = fs_r_dst_natural_step_prefix_body_steps + fs_a_dst_natural_step_prefix_body_steps)))))) -> (((exists ff_h_pvs_natural_step_last. ff_h_pvs_natural_step_last + S (a) = S ((S (l)) * c)) /\ exists ff_q_pvs_natural_step_last. b = ff_q_pvs_natural_step_last * S ((S (l)) * c) + (a))) -> (exists fs_u_dst_natural_step_result fs_v_dst_natural_step_result. ((((exists fs_h_dst_natural_step_result_body_start. fs_h_dst_natural_step_result_body_start + S (0) = S ((S (0)) * fs_v_dst_natural_step_result)) /\ exists fs_q_dst_natural_step_result_body_start. fs_u_dst_natural_step_result = fs_q_dst_natural_step_result_body_start * S ((S (0)) * fs_v_dst_natural_step_result) + (0))) /\ ((((exists fs_h_dst_natural_step_result_body_terminal. fs_h_dst_natural_step_result_body_terminal + S (r + a) = S ((S (S l)) * fs_v_dst_natural_step_result)) /\ exists fs_q_dst_natural_step_result_body_terminal. fs_u_dst_natural_step_result = fs_q_dst_natural_step_result_body_terminal * S ((S (S l)) * fs_v_dst_natural_step_result) + (r + a))) /\ forall fs_i_dst_natural_step_result_body_steps. (exists fs_lt_dst_natural_step_result_body_steps_bound. fs_lt_dst_natural_step_result_body_steps_bound + S fs_i_dst_natural_step_result_body_steps = S l) -> exists fs_a_dst_natural_step_result_body_steps fs_r_dst_natural_step_result_body_steps fs_s_dst_natural_step_result_body_steps. ((((exists fs_h_dst_natural_step_result_body_steps_summand. fs_h_dst_natural_step_result_body_steps_summand + S (fs_a_dst_natural_step_result_body_steps) = S ((S (fs_i_dst_natural_step_result_body_steps)) * c)) /\ exists fs_q_dst_natural_step_result_body_steps_summand. b = fs_q_dst_natural_step_result_body_steps_summand * S ((S (fs_i_dst_natural_step_result_body_steps)) * c) + (fs_a_dst_natural_step_result_body_steps))) /\ ((((exists fs_h_dst_natural_step_result_body_steps_partial. fs_h_dst_natural_step_result_body_steps_partial + S (fs_r_dst_natural_step_result_body_steps) = S ((S (fs_i_dst_natural_step_result_body_steps)) * fs_v_dst_natural_step_result)) /\ exists fs_q_dst_natural_step_result_body_steps_partial. fs_u_dst_natural_step_result = fs_q_dst_natural_step_result_body_steps_partial * S ((S (fs_i_dst_natural_step_result_body_steps)) * fs_v_dst_natural_step_result) + (fs_r_dst_natural_step_result_body_steps))) /\ ((((exists fs_h_dst_natural_step_result_body_steps_successor. fs_h_dst_natural_step_result_body_steps_successor + S (fs_s_dst_natural_step_result_body_steps) = S ((S (S fs_i_dst_natural_step_result_body_steps)) * fs_v_dst_natural_step_result)) /\ exists fs_q_dst_natural_step_result_body_steps_successor. fs_u_dst_natural_step_result = fs_q_dst_natural_step_result_body_steps_successor * S ((S (S fs_i_dst_natural_step_result_body_steps)) * fs_v_dst_natural_step_result) + (fs_s_dst_natural_step_result_body_steps))) /\ fs_s_dst_natural_step_result_body_steps = fs_r_dst_natural_step_result_body_steps + fs_a_dst_natural_step_result_body_steps))))))

forall F G pb pc nb nc qb qc mb mc l. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> ((G) = (((((qb) + (qc)) * S ((qb) + (qc)) + ((qc) + (qc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))) * S ((((qb) + (qc)) * S ((qb) + (qc)) + ((qc) + (qc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))) + ((((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))))) -> (forall dst_index_equal_codes dst_first_equal_codes dst_second_equal_codes. (exists pvs_gap_equal_codesbound. pvs_gap_equal_codesbound + S (dst_index_equal_codes) = (l)) -> (exists dst_positive_code_equal_codesfirst dst_positive_scale_equal_codesfirst dst_negative_code_equal_codesfirst dst_negative_scale_equal_codesfirst dst_positive_equal_codesfirst dst_negative_equal_codesfirst. (((F) = (((((dst_positive_code_equal_codesfirst) + (dst_positive_scale_equal_codesfirst)) * S ((dst_positive_code_equal_codesfirst) + (dst_positive_scale_equal_codesfirst)) + ((dst_positive_scale_equal_codesfirst) + (dst_positive_scale_equal_codesfirst))) + (((dst_negative_code_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)) * S ((dst_negative_code_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)) + ((dst_negative_scale_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)))) * S ((((dst_positive_code_equal_codesfirst) + (dst_positive_scale_equal_codesfirst)) * S ((dst_positive_code_equal_codesfirst) + (dst_positive_scale_equal_codesfirst)) + ((dst_positive_scale_equal_codesfirst) + (dst_positive_scale_equal_codesfirst))) + (((dst_negative_code_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)) * S ((dst_negative_code_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)) + ((dst_negative_scale_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)))) + ((((dst_negative_code_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)) * S ((dst_negative_code_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)) + ((dst_negative_scale_equal_codesfirst) + (dst_negative_scale_equal_codesfirst))) + (((dst_negative_code_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)) * S ((dst_negative_code_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)) + ((dst_negative_scale_equal_codesfirst) + (dst_negative_scale_equal_codesfirst)))))) /\ (((((exists ff_h_pvs_equal_codesfirstpositive. ff_h_pvs_equal_codesfirstpositive + S (dst_positive_equal_codesfirst) = S ((S (dst_index_equal_codes)) * dst_positive_scale_equal_codesfirst)) /\ exists ff_q_pvs_equal_codesfirstpositive. dst_positive_code_equal_codesfirst = ff_q_pvs_equal_codesfirstpositive * S ((S (dst_index_equal_codes)) * dst_positive_scale_equal_codesfirst) + (dst_positive_equal_codesfirst))) /\ (((((exists ff_h_pvs_equal_codesfirstnegative. ff_h_pvs_equal_codesfirstnegative + S (dst_negative_equal_codesfirst) = S ((S (dst_index_equal_codes)) * dst_negative_scale_equal_codesfirst)) /\ exists ff_q_pvs_equal_codesfirstnegative. dst_negative_code_equal_codesfirst = ff_q_pvs_equal_codesfirstnegative * S ((S (dst_index_equal_codes)) * dst_negative_scale_equal_codesfirst) + (dst_negative_equal_codesfirst))) /\ (exists ge_balance_positive_equal_codesfirstvalue ge_balance_negative_equal_codesfirstvalue. (((((dst_first_equal_codes) = 2 * (ge_balance_positive_equal_codesfirstvalue) /\ (ge_balance_negative_equal_codesfirstvalue) = 0) \/ exists ge_signed_half_equal_codesfirstvaluedecode. (((dst_first_equal_codes) = 2 * ge_signed_half_equal_codesfirstvaluedecode + 1 /\ (ge_balance_positive_equal_codesfirstvalue) = 0) /\ (ge_balance_negative_equal_codesfirstvalue) = S ge_signed_half_equal_codesfirstvaluedecode))) /\ ((dst_positive_equal_codesfirst) + ge_balance_negative_equal_codesfirstvalue = (dst_negative_equal_codesfirst) + ge_balance_positive_equal_codesfirstvalue))))))))) -> (exists dst_positive_code_equal_codessecond dst_positive_scale_equal_codessecond dst_negative_code_equal_codessecond dst_negative_scale_equal_codessecond dst_positive_equal_codessecond dst_negative_equal_codessecond. (((G) = (((((dst_positive_code_equal_codessecond) + (dst_positive_scale_equal_codessecond)) * S ((dst_positive_code_equal_codessecond) + (dst_positive_scale_equal_codessecond)) + ((dst_positive_scale_equal_codessecond) + (dst_positive_scale_equal_codessecond))) + (((dst_negative_code_equal_codessecond) + (dst_negative_scale_equal_codessecond)) * S ((dst_negative_code_equal_codessecond) + (dst_negative_scale_equal_codessecond)) + ((dst_negative_scale_equal_codessecond) + (dst_negative_scale_equal_codessecond)))) * S ((((dst_positive_code_equal_codessecond) + (dst_positive_scale_equal_codessecond)) * S ((dst_positive_code_equal_codessecond) + (dst_positive_scale_equal_codessecond)) + ((dst_positive_scale_equal_codessecond) + (dst_positive_scale_equal_codessecond))) + (((dst_negative_code_equal_codessecond) + (dst_negative_scale_equal_codessecond)) * S ((dst_negative_code_equal_codessecond) + (dst_negative_scale_equal_codessecond)) + ((dst_negative_scale_equal_codessecond) + (dst_negative_scale_equal_codessecond)))) + ((((dst_negative_code_equal_codessecond) + (dst_negative_scale_equal_codessecond)) * S ((dst_negative_code_equal_codessecond) + (dst_negative_scale_equal_codessecond)) + ((dst_negative_scale_equal_codessecond) + (dst_negative_scale_equal_codessecond))) + (((dst_negative_code_equal_codessecond) + (dst_negative_scale_equal_codessecond)) * S ((dst_negative_code_equal_codessecond) + (dst_negative_scale_equal_codessecond)) + ((dst_negative_scale_equal_codessecond) + (dst_negative_scale_equal_codessecond)))))) /\ (((((exists ff_h_pvs_equal_codessecondpositive. ff_h_pvs_equal_codessecondpositive + S (dst_positive_equal_codessecond) = S ((S (dst_index_equal_codes)) * dst_positive_scale_equal_codessecond)) /\ exists ff_q_pvs_equal_codessecondpositive. dst_positive_code_equal_codessecond = ff_q_pvs_equal_codessecondpositive * S ((S (dst_index_equal_codes)) * dst_positive_scale_equal_codessecond) + (dst_positive_equal_codessecond))) /\ (((((exists ff_h_pvs_equal_codessecondnegative. ff_h_pvs_equal_codessecondnegative + S (dst_negative_equal_codessecond) = S ((S (dst_index_equal_codes)) * dst_negative_scale_equal_codessecond)) /\ exists ff_q_pvs_equal_codessecondnegative. dst_negative_code_equal_codessecond = ff_q_pvs_equal_codessecondnegative * S ((S (dst_index_equal_codes)) * dst_negative_scale_equal_codessecond) + (dst_negative_equal_codessecond))) /\ (exists ge_balance_positive_equal_codessecondvalue ge_balance_negative_equal_codessecondvalue. (((((dst_second_equal_codes) = 2 * (ge_balance_positive_equal_codessecondvalue) /\ (ge_balance_negative_equal_codessecondvalue) = 0) \/ exists ge_signed_half_equal_codessecondvaluedecode. (((dst_second_equal_codes) = 2 * ge_signed_half_equal_codessecondvaluedecode + 1 /\ (ge_balance_positive_equal_codessecondvalue) = 0) /\ (ge_balance_negative_equal_codessecondvalue) = S ge_signed_half_equal_codessecondvaluedecode))) /\ ((dst_positive_equal_codessecond) + ge_balance_negative_equal_codessecondvalue = (dst_negative_equal_codessecond) + ge_balance_positive_equal_codessecondvalue))))))))) -> dst_first_equal_codes = dst_second_equal_codes) -> (forall ics_index_equal_components ics_value0_equal_components ics_value1_equal_components ics_value2_equal_components ics_value3_equal_components. (exists ics_gap_equal_components_bound. ics_gap_equal_components_bound + S (ics_index_equal_components) = (l)) -> (((exists fs_h_ics_equal_components_at0. fs_h_ics_equal_components_at0 + S (ics_value0_equal_components) = S ((S (ics_index_equal_components)) * pc)) /\ exists fs_q_ics_equal_components_at0. pb = fs_q_ics_equal_components_at0 * S ((S (ics_index_equal_components)) * pc) + (ics_value0_equal_components))) -> (((exists fs_h_ics_equal_components_at1. fs_h_ics_equal_components_at1 + S (ics_value1_equal_components) = S ((S (ics_index_equal_components)) * nc)) /\ exists fs_q_ics_equal_components_at1. nb = fs_q_ics_equal_components_at1 * S ((S (ics_index_equal_components)) * nc) + (ics_value1_equal_components))) -> (((exists fs_h_ics_equal_components_at2. fs_h_ics_equal_components_at2 + S (ics_value2_equal_components) = S ((S (ics_index_equal_components)) * qc)) /\ exists fs_q_ics_equal_components_at2. qb = fs_q_ics_equal_components_at2 * S ((S (ics_index_equal_components)) * qc) + (ics_value2_equal_components))) -> (((exists fs_h_ics_equal_components_at3. fs_h_ics_equal_components_at3 + S (ics_value3_equal_components) = S ((S (ics_index_equal_components)) * mc)) /\ exists fs_q_ics_equal_components_at3. mb = fs_q_ics_equal_components_at3 * S ((S (ics_index_equal_components)) * mc) + (ics_value3_equal_components))) -> ics_value0_equal_components + ics_value3_equal_components = ics_value2_equal_components + ics_value1_equal_components)

forall F G l a b. (forall dst_index_sum_ext_entries dst_first_sum_ext_entries dst_second_sum_ext_entries. (exists pvs_gap_sum_ext_entriesbound. pvs_gap_sum_ext_entriesbound + S (dst_index_sum_ext_entries) = (l)) -> (exists dst_positive_code_sum_ext_entriesfirst dst_positive_scale_sum_ext_entriesfirst dst_negative_code_sum_ext_entriesfirst dst_negative_scale_sum_ext_entriesfirst dst_positive_sum_ext_entriesfirst dst_negative_sum_ext_entriesfirst. (((F) = (((((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) * S ((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) + ((dst_positive_scale_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst))) + (((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)))) * S ((((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) * S ((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) + ((dst_positive_scale_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst))) + (((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)))) + ((((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst))) + (((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)))))) /\ (((((exists ff_h_pvs_sum_ext_entriesfirstpositive. ff_h_pvs_sum_ext_entriesfirstpositive + S (dst_positive_sum_ext_entriesfirst) = S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriesfirst)) /\ exists ff_q_pvs_sum_ext_entriesfirstpositive. dst_positive_code_sum_ext_entriesfirst = ff_q_pvs_sum_ext_entriesfirstpositive * S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriesfirst) + (dst_positive_sum_ext_entriesfirst))) /\ (((((exists ff_h_pvs_sum_ext_entriesfirstnegative. ff_h_pvs_sum_ext_entriesfirstnegative + S (dst_negative_sum_ext_entriesfirst) = S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriesfirst)) /\ exists ff_q_pvs_sum_ext_entriesfirstnegative. dst_negative_code_sum_ext_entriesfirst = ff_q_pvs_sum_ext_entriesfirstnegative * S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_sum_ext_entriesfirst))) /\ (exists ge_balance_positive_sum_ext_entriesfirstvalue ge_balance_negative_sum_ext_entriesfirstvalue. (((((dst_first_sum_ext_entries) = 2 * (ge_balance_positive_sum_ext_entriesfirstvalue) /\ (ge_balance_negative_sum_ext_entriesfirstvalue) = 0) \/ exists ge_signed_half_sum_ext_entriesfirstvaluedecode. (((dst_first_sum_ext_entries) = 2 * ge_signed_half_sum_ext_entriesfirstvaluedecode + 1 /\ (ge_balance_positive_sum_ext_entriesfirstvalue) = 0) /\ (ge_balance_negative_sum_ext_entriesfirstvalue) = S ge_signed_half_sum_ext_entriesfirstvaluedecode))) /\ ((dst_positive_sum_ext_entriesfirst) + ge_balance_negative_sum_ext_entriesfirstvalue = (dst_negative_sum_ext_entriesfirst) + ge_balance_positive_sum_ext_entriesfirstvalue))))))))) -> (exists dst_positive_code_sum_ext_entriessecond dst_positive_scale_sum_ext_entriessecond dst_negative_code_sum_ext_entriessecond dst_negative_scale_sum_ext_entriessecond dst_positive_sum_ext_entriessecond dst_negative_sum_ext_entriessecond. (((G) = (((((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) * S ((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) + ((dst_positive_scale_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond))) + (((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)))) * S ((((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) * S ((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) + ((dst_positive_scale_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond))) + (((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)))) + ((((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond))) + (((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)))))) /\ (((((exists ff_h_pvs_sum_ext_entriessecondpositive. ff_h_pvs_sum_ext_entriessecondpositive + S (dst_positive_sum_ext_entriessecond) = S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriessecond)) /\ exists ff_q_pvs_sum_ext_entriessecondpositive. dst_positive_code_sum_ext_entriessecond = ff_q_pvs_sum_ext_entriessecondpositive * S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriessecond) + (dst_positive_sum_ext_entriessecond))) /\ (((((exists ff_h_pvs_sum_ext_entriessecondnegative. ff_h_pvs_sum_ext_entriessecondnegative + S (dst_negative_sum_ext_entriessecond) = S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriessecond)) /\ exists ff_q_pvs_sum_ext_entriessecondnegative. dst_negative_code_sum_ext_entriessecond = ff_q_pvs_sum_ext_entriessecondnegative * S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriessecond) + (dst_negative_sum_ext_entriessecond))) /\ (exists ge_balance_positive_sum_ext_entriessecondvalue ge_balance_negative_sum_ext_entriessecondvalue. (((((dst_second_sum_ext_entries) = 2 * (ge_balance_positive_sum_ext_entriessecondvalue) /\ (ge_balance_negative_sum_ext_entriessecondvalue) = 0) \/ exists ge_signed_half_sum_ext_entriessecondvaluedecode. (((dst_second_sum_ext_entries) = 2 * ge_signed_half_sum_ext_entriessecondvaluedecode + 1 /\ (ge_balance_positive_sum_ext_entriessecondvalue) = 0) /\ (ge_balance_negative_sum_ext_entriessecondvalue) = S ge_signed_half_sum_ext_entriessecondvaluedecode))) /\ ((dst_positive_sum_ext_entriessecond) + ge_balance_negative_sum_ext_entriessecondvalue = (dst_negative_sum_ext_entriessecond) + ge_balance_positive_sum_ext_entriessecondvalue))))))))) -> dst_first_sum_ext_entries = dst_second_sum_ext_entries) -> (exists dst_positive_code_sum_ext_first dst_positive_scale_sum_ext_first dst_negative_code_sum_ext_first dst_negative_scale_sum_ext_first dst_positive_sum_sum_ext_first dst_negative_sum_sum_ext_first. (((F) = (((((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) * S ((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) + ((dst_positive_scale_sum_ext_first) + (dst_positive_scale_sum_ext_first))) + (((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first)))) * S ((((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) * S ((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) + ((dst_positive_scale_sum_ext_first) + (dst_positive_scale_sum_ext_first))) + (((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first)))) + ((((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first))) + (((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first)))))) /\ (((exists fs_u_dst_sum_ext_firstpositive fs_v_dst_sum_ext_firstpositive. ((((exists fs_h_dst_sum_ext_firstpositive_body_start. fs_h_dst_sum_ext_firstpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_start. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_start * S ((S (0)) * fs_v_dst_sum_ext_firstpositive) + (0))) /\ ((((exists fs_h_dst_sum_ext_firstpositive_body_terminal. fs_h_dst_sum_ext_firstpositive_body_terminal + S (dst_positive_sum_sum_ext_first) = S ((S (l)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_terminal. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_firstpositive) + (dst_positive_sum_sum_ext_first))) /\ forall fs_i_dst_sum_ext_firstpositive_body_steps. (exists fs_lt_dst_sum_ext_firstpositive_body_steps_bound. fs_lt_dst_sum_ext_firstpositive_body_steps_bound + S fs_i_dst_sum_ext_firstpositive_body_steps = l) -> exists fs_a_dst_sum_ext_firstpositive_body_steps fs_r_dst_sum_ext_firstpositive_body_steps fs_s_dst_sum_ext_firstpositive_body_steps. ((((exists fs_h_dst_sum_ext_firstpositive_body_steps_summand. fs_h_dst_sum_ext_firstpositive_body_steps_summand + S (fs_a_dst_sum_ext_firstpositive_body_steps) = S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * dst_positive_scale_sum_ext_first)) /\ exists fs_q_dst_sum_ext_firstpositive_body_steps_summand. dst_positive_code_sum_ext_first = fs_q_dst_sum_ext_firstpositive_body_steps_summand * S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * dst_positive_scale_sum_ext_first) + (fs_a_dst_sum_ext_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstpositive_body_steps_partial. fs_h_dst_sum_ext_firstpositive_body_steps_partial + S (fs_r_dst_sum_ext_firstpositive_body_steps) = S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_steps_partial. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_steps_partial * S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive) + (fs_r_dst_sum_ext_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstpositive_body_steps_successor. fs_h_dst_sum_ext_firstpositive_body_steps_successor + S (fs_s_dst_sum_ext_firstpositive_body_steps) = S ((S (S fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_steps_successor. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_steps_successor * S ((S (S fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive) + (fs_s_dst_sum_ext_firstpositive_body_steps))) /\ fs_s_dst_sum_ext_firstpositive_body_steps = fs_r_dst_sum_ext_firstpositive_body_steps + fs_a_dst_sum_ext_firstpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_ext_firstnegative fs_v_dst_sum_ext_firstnegative. ((((exists fs_h_dst_sum_ext_firstnegative_body_start. fs_h_dst_sum_ext_firstnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_start. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_start * S ((S (0)) * fs_v_dst_sum_ext_firstnegative) + (0))) /\ ((((exists fs_h_dst_sum_ext_firstnegative_body_terminal. fs_h_dst_sum_ext_firstnegative_body_terminal + S (dst_negative_sum_sum_ext_first) = S ((S (l)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_terminal. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_firstnegative) + (dst_negative_sum_sum_ext_first))) /\ forall fs_i_dst_sum_ext_firstnegative_body_steps. (exists fs_lt_dst_sum_ext_firstnegative_body_steps_bound. fs_lt_dst_sum_ext_firstnegative_body_steps_bound + S fs_i_dst_sum_ext_firstnegative_body_steps = l) -> exists fs_a_dst_sum_ext_firstnegative_body_steps fs_r_dst_sum_ext_firstnegative_body_steps fs_s_dst_sum_ext_firstnegative_body_steps. ((((exists fs_h_dst_sum_ext_firstnegative_body_steps_summand. fs_h_dst_sum_ext_firstnegative_body_steps_summand + S (fs_a_dst_sum_ext_firstnegative_body_steps) = S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * dst_negative_scale_sum_ext_first)) /\ exists fs_q_dst_sum_ext_firstnegative_body_steps_summand. dst_negative_code_sum_ext_first = fs_q_dst_sum_ext_firstnegative_body_steps_summand * S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * dst_negative_scale_sum_ext_first) + (fs_a_dst_sum_ext_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstnegative_body_steps_partial. fs_h_dst_sum_ext_firstnegative_body_steps_partial + S (fs_r_dst_sum_ext_firstnegative_body_steps) = S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_steps_partial. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_steps_partial * S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative) + (fs_r_dst_sum_ext_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstnegative_body_steps_successor. fs_h_dst_sum_ext_firstnegative_body_steps_successor + S (fs_s_dst_sum_ext_firstnegative_body_steps) = S ((S (S fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_steps_successor. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_steps_successor * S ((S (S fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative) + (fs_s_dst_sum_ext_firstnegative_body_steps))) /\ fs_s_dst_sum_ext_firstnegative_body_steps = fs_r_dst_sum_ext_firstnegative_body_steps + fs_a_dst_sum_ext_firstnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_ext_firstresult ge_balance_negative_sum_ext_firstresult. (((((a) = 2 * (ge_balance_positive_sum_ext_firstresult) /\ (ge_balance_negative_sum_ext_firstresult) = 0) \/ exists ge_signed_half_sum_ext_firstresultdecode. (((a) = 2 * ge_signed_half_sum_ext_firstresultdecode + 1 /\ (ge_balance_positive_sum_ext_firstresult) = 0) /\ (ge_balance_negative_sum_ext_firstresult) = S ge_signed_half_sum_ext_firstresultdecode))) /\ ((dst_positive_sum_sum_ext_first) + ge_balance_negative_sum_ext_firstresult = (dst_negative_sum_sum_ext_first) + ge_balance_positive_sum_ext_firstresult))))))))) -> (exists dst_positive_code_sum_ext_second dst_positive_scale_sum_ext_second dst_negative_code_sum_ext_second dst_negative_scale_sum_ext_second dst_positive_sum_sum_ext_second dst_negative_sum_sum_ext_second. (((G) = (((((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) * S ((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) + ((dst_positive_scale_sum_ext_second) + (dst_positive_scale_sum_ext_second))) + (((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second)))) * S ((((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) * S ((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) + ((dst_positive_scale_sum_ext_second) + (dst_positive_scale_sum_ext_second))) + (((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second)))) + ((((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second))) + (((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second)))))) /\ (((exists fs_u_dst_sum_ext_secondpositive fs_v_dst_sum_ext_secondpositive. ((((exists fs_h_dst_sum_ext_secondpositive_body_start. fs_h_dst_sum_ext_secondpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_start. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_start * S ((S (0)) * fs_v_dst_sum_ext_secondpositive) + (0))) /\ ((((exists fs_h_dst_sum_ext_secondpositive_body_terminal. fs_h_dst_sum_ext_secondpositive_body_terminal + S (dst_positive_sum_sum_ext_second) = S ((S (l)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_terminal. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_secondpositive) + (dst_positive_sum_sum_ext_second))) /\ forall fs_i_dst_sum_ext_secondpositive_body_steps. (exists fs_lt_dst_sum_ext_secondpositive_body_steps_bound. fs_lt_dst_sum_ext_secondpositive_body_steps_bound + S fs_i_dst_sum_ext_secondpositive_body_steps = l) -> exists fs_a_dst_sum_ext_secondpositive_body_steps fs_r_dst_sum_ext_secondpositive_body_steps fs_s_dst_sum_ext_secondpositive_body_steps. ((((exists fs_h_dst_sum_ext_secondpositive_body_steps_summand. fs_h_dst_sum_ext_secondpositive_body_steps_summand + S (fs_a_dst_sum_ext_secondpositive_body_steps) = S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * dst_positive_scale_sum_ext_second)) /\ exists fs_q_dst_sum_ext_secondpositive_body_steps_summand. dst_positive_code_sum_ext_second = fs_q_dst_sum_ext_secondpositive_body_steps_summand * S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * dst_positive_scale_sum_ext_second) + (fs_a_dst_sum_ext_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondpositive_body_steps_partial. fs_h_dst_sum_ext_secondpositive_body_steps_partial + S (fs_r_dst_sum_ext_secondpositive_body_steps) = S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_steps_partial. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_steps_partial * S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive) + (fs_r_dst_sum_ext_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondpositive_body_steps_successor. fs_h_dst_sum_ext_secondpositive_body_steps_successor + S (fs_s_dst_sum_ext_secondpositive_body_steps) = S ((S (S fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_steps_successor. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_steps_successor * S ((S (S fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive) + (fs_s_dst_sum_ext_secondpositive_body_steps))) /\ fs_s_dst_sum_ext_secondpositive_body_steps = fs_r_dst_sum_ext_secondpositive_body_steps + fs_a_dst_sum_ext_secondpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_ext_secondnegative fs_v_dst_sum_ext_secondnegative. ((((exists fs_h_dst_sum_ext_secondnegative_body_start. fs_h_dst_sum_ext_secondnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_start. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_start * S ((S (0)) * fs_v_dst_sum_ext_secondnegative) + (0))) /\ ((((exists fs_h_dst_sum_ext_secondnegative_body_terminal. fs_h_dst_sum_ext_secondnegative_body_terminal + S (dst_negative_sum_sum_ext_second) = S ((S (l)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_terminal. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_secondnegative) + (dst_negative_sum_sum_ext_second))) /\ forall fs_i_dst_sum_ext_secondnegative_body_steps. (exists fs_lt_dst_sum_ext_secondnegative_body_steps_bound. fs_lt_dst_sum_ext_secondnegative_body_steps_bound + S fs_i_dst_sum_ext_secondnegative_body_steps = l) -> exists fs_a_dst_sum_ext_secondnegative_body_steps fs_r_dst_sum_ext_secondnegative_body_steps fs_s_dst_sum_ext_secondnegative_body_steps. ((((exists fs_h_dst_sum_ext_secondnegative_body_steps_summand. fs_h_dst_sum_ext_secondnegative_body_steps_summand + S (fs_a_dst_sum_ext_secondnegative_body_steps) = S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * dst_negative_scale_sum_ext_second)) /\ exists fs_q_dst_sum_ext_secondnegative_body_steps_summand. dst_negative_code_sum_ext_second = fs_q_dst_sum_ext_secondnegative_body_steps_summand * S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * dst_negative_scale_sum_ext_second) + (fs_a_dst_sum_ext_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondnegative_body_steps_partial. fs_h_dst_sum_ext_secondnegative_body_steps_partial + S (fs_r_dst_sum_ext_secondnegative_body_steps) = S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_steps_partial. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_steps_partial * S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative) + (fs_r_dst_sum_ext_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondnegative_body_steps_successor. fs_h_dst_sum_ext_secondnegative_body_steps_successor + S (fs_s_dst_sum_ext_secondnegative_body_steps) = S ((S (S fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_steps_successor. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_steps_successor * S ((S (S fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative) + (fs_s_dst_sum_ext_secondnegative_body_steps))) /\ fs_s_dst_sum_ext_secondnegative_body_steps = fs_r_dst_sum_ext_secondnegative_body_steps + fs_a_dst_sum_ext_secondnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_ext_secondresult ge_balance_negative_sum_ext_secondresult. (((((b) = 2 * (ge_balance_positive_sum_ext_secondresult) /\ (ge_balance_negative_sum_ext_secondresult) = 0) \/ exists ge_signed_half_sum_ext_secondresultdecode. (((b) = 2 * ge_signed_half_sum_ext_secondresultdecode + 1 /\ (ge_balance_positive_sum_ext_secondresult) = 0) /\ (ge_balance_negative_sum_ext_secondresult) = S ge_signed_half_sum_ext_secondresultdecode))) /\ ((dst_positive_sum_sum_ext_second) + ge_balance_negative_sum_ext_secondresult = (dst_negative_sum_sum_ext_second) + ge_balance_positive_sum_ext_secondresult))))))))) -> a = b

forall F G pb pc nb nc l a b. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> ((G) = (((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc)))) * S ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc)))) + ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc)))))) -> (exists dst_positive_code_negation_source_sum dst_positive_scale_negation_source_sum dst_negative_code_negation_source_sum dst_negative_scale_negation_source_sum dst_positive_sum_negation_source_sum dst_negative_sum_negation_source_sum. (((F) = (((((dst_positive_code_negation_source_sum) + (dst_positive_scale_negation_source_sum)) * S ((dst_positive_code_negation_source_sum) + (dst_positive_scale_negation_source_sum)) + ((dst_positive_scale_negation_source_sum) + (dst_positive_scale_negation_source_sum))) + (((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) * S ((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) + ((dst_negative_scale_negation_source_sum) + (dst_negative_scale_negation_source_sum)))) * S ((((dst_positive_code_negation_source_sum) + (dst_positive_scale_negation_source_sum)) * S ((dst_positive_code_negation_source_sum) + (dst_positive_scale_negation_source_sum)) + ((dst_positive_scale_negation_source_sum) + (dst_positive_scale_negation_source_sum))) + (((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) * S ((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) + ((dst_negative_scale_negation_source_sum) + (dst_negative_scale_negation_source_sum)))) + ((((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) * S ((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) + ((dst_negative_scale_negation_source_sum) + (dst_negative_scale_negation_source_sum))) + (((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) * S ((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) + ((dst_negative_scale_negation_source_sum) + (dst_negative_scale_negation_source_sum)))))) /\ (((exists fs_u_dst_negation_source_sumpositive fs_v_dst_negation_source_sumpositive. ((((exists fs_h_dst_negation_source_sumpositive_body_start. fs_h_dst_negation_source_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_negation_source_sumpositive)) /\ exists fs_q_dst_negation_source_sumpositive_body_start. fs_u_dst_negation_source_sumpositive = fs_q_dst_negation_source_sumpositive_body_start * S ((S (0)) * fs_v_dst_negation_source_sumpositive) + (0))) /\ ((((exists fs_h_dst_negation_source_sumpositive_body_terminal. fs_h_dst_negation_source_sumpositive_body_terminal + S (dst_positive_sum_negation_source_sum) = S ((S (l)) * fs_v_dst_negation_source_sumpositive)) /\ exists fs_q_dst_negation_source_sumpositive_body_terminal. fs_u_dst_negation_source_sumpositive = fs_q_dst_negation_source_sumpositive_body_terminal * S ((S (l)) * fs_v_dst_negation_source_sumpositive) + (dst_positive_sum_negation_source_sum))) /\ forall fs_i_dst_negation_source_sumpositive_body_steps. (exists fs_lt_dst_negation_source_sumpositive_body_steps_bound. fs_lt_dst_negation_source_sumpositive_body_steps_bound + S fs_i_dst_negation_source_sumpositive_body_steps = l) -> exists fs_a_dst_negation_source_sumpositive_body_steps fs_r_dst_negation_source_sumpositive_body_steps fs_s_dst_negation_source_sumpositive_body_steps. ((((exists fs_h_dst_negation_source_sumpositive_body_steps_summand. fs_h_dst_negation_source_sumpositive_body_steps_summand + S (fs_a_dst_negation_source_sumpositive_body_steps) = S ((S (fs_i_dst_negation_source_sumpositive_body_steps)) * dst_positive_scale_negation_source_sum)) /\ exists fs_q_dst_negation_source_sumpositive_body_steps_summand. dst_positive_code_negation_source_sum = fs_q_dst_negation_source_sumpositive_body_steps_summand * S ((S (fs_i_dst_negation_source_sumpositive_body_steps)) * dst_positive_scale_negation_source_sum) + (fs_a_dst_negation_source_sumpositive_body_steps))) /\ ((((exists fs_h_dst_negation_source_sumpositive_body_steps_partial. fs_h_dst_negation_source_sumpositive_body_steps_partial + S (fs_r_dst_negation_source_sumpositive_body_steps) = S ((S (fs_i_dst_negation_source_sumpositive_body_steps)) * fs_v_dst_negation_source_sumpositive)) /\ exists fs_q_dst_negation_source_sumpositive_body_steps_partial. fs_u_dst_negation_source_sumpositive = fs_q_dst_negation_source_sumpositive_body_steps_partial * S ((S (fs_i_dst_negation_source_sumpositive_body_steps)) * fs_v_dst_negation_source_sumpositive) + (fs_r_dst_negation_source_sumpositive_body_steps))) /\ ((((exists fs_h_dst_negation_source_sumpositive_body_steps_successor. fs_h_dst_negation_source_sumpositive_body_steps_successor + S (fs_s_dst_negation_source_sumpositive_body_steps) = S ((S (S fs_i_dst_negation_source_sumpositive_body_steps)) * fs_v_dst_negation_source_sumpositive)) /\ exists fs_q_dst_negation_source_sumpositive_body_steps_successor. fs_u_dst_negation_source_sumpositive = fs_q_dst_negation_source_sumpositive_body_steps_successor * S ((S (S fs_i_dst_negation_source_sumpositive_body_steps)) * fs_v_dst_negation_source_sumpositive) + (fs_s_dst_negation_source_sumpositive_body_steps))) /\ fs_s_dst_negation_source_sumpositive_body_steps = fs_r_dst_negation_source_sumpositive_body_steps + fs_a_dst_negation_source_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_negation_source_sumnegative fs_v_dst_negation_source_sumnegative. ((((exists fs_h_dst_negation_source_sumnegative_body_start. fs_h_dst_negation_source_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_negation_source_sumnegative)) /\ exists fs_q_dst_negation_source_sumnegative_body_start. fs_u_dst_negation_source_sumnegative = fs_q_dst_negation_source_sumnegative_body_start * S ((S (0)) * fs_v_dst_negation_source_sumnegative) + (0))) /\ ((((exists fs_h_dst_negation_source_sumnegative_body_terminal. fs_h_dst_negation_source_sumnegative_body_terminal + S (dst_negative_sum_negation_source_sum) = S ((S (l)) * fs_v_dst_negation_source_sumnegative)) /\ exists fs_q_dst_negation_source_sumnegative_body_terminal. fs_u_dst_negation_source_sumnegative = fs_q_dst_negation_source_sumnegative_body_terminal * S ((S (l)) * fs_v_dst_negation_source_sumnegative) + (dst_negative_sum_negation_source_sum))) /\ forall fs_i_dst_negation_source_sumnegative_body_steps. (exists fs_lt_dst_negation_source_sumnegative_body_steps_bound. fs_lt_dst_negation_source_sumnegative_body_steps_bound + S fs_i_dst_negation_source_sumnegative_body_steps = l) -> exists fs_a_dst_negation_source_sumnegative_body_steps fs_r_dst_negation_source_sumnegative_body_steps fs_s_dst_negation_source_sumnegative_body_steps. ((((exists fs_h_dst_negation_source_sumnegative_body_steps_summand. fs_h_dst_negation_source_sumnegative_body_steps_summand + S (fs_a_dst_negation_source_sumnegative_body_steps) = S ((S (fs_i_dst_negation_source_sumnegative_body_steps)) * dst_negative_scale_negation_source_sum)) /\ exists fs_q_dst_negation_source_sumnegative_body_steps_summand. dst_negative_code_negation_source_sum = fs_q_dst_negation_source_sumnegative_body_steps_summand * S ((S (fs_i_dst_negation_source_sumnegative_body_steps)) * dst_negative_scale_negation_source_sum) + (fs_a_dst_negation_source_sumnegative_body_steps))) /\ ((((exists fs_h_dst_negation_source_sumnegative_body_steps_partial. fs_h_dst_negation_source_sumnegative_body_steps_partial + S (fs_r_dst_negation_source_sumnegative_body_steps) = S ((S (fs_i_dst_negation_source_sumnegative_body_steps)) * fs_v_dst_negation_source_sumnegative)) /\ exists fs_q_dst_negation_source_sumnegative_body_steps_partial. fs_u_dst_negation_source_sumnegative = fs_q_dst_negation_source_sumnegative_body_steps_partial * S ((S (fs_i_dst_negation_source_sumnegative_body_steps)) * fs_v_dst_negation_source_sumnegative) + (fs_r_dst_negation_source_sumnegative_body_steps))) /\ ((((exists fs_h_dst_negation_source_sumnegative_body_steps_successor. fs_h_dst_negation_source_sumnegative_body_steps_successor + S (fs_s_dst_negation_source_sumnegative_body_steps) = S ((S (S fs_i_dst_negation_source_sumnegative_body_steps)) * fs_v_dst_negation_source_sumnegative)) /\ exists fs_q_dst_negation_source_sumnegative_body_steps_successor. fs_u_dst_negation_source_sumnegative = fs_q_dst_negation_source_sumnegative_body_steps_successor * S ((S (S fs_i_dst_negation_source_sumnegative_body_steps)) * fs_v_dst_negation_source_sumnegative) + (fs_s_dst_negation_source_sumnegative_body_steps))) /\ fs_s_dst_negation_source_sumnegative_body_steps = fs_r_dst_negation_source_sumnegative_body_steps + fs_a_dst_negation_source_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_negation_source_sumresult ge_balance_negative_negation_source_sumresult. (((((a) = 2 * (ge_balance_positive_negation_source_sumresult) /\ (ge_balance_negative_negation_source_sumresult) = 0) \/ exists ge_signed_half_negation_source_sumresultdecode. (((a) = 2 * ge_signed_half_negation_source_sumresultdecode + 1 /\ (ge_balance_positive_negation_source_sumresult) = 0) /\ (ge_balance_negative_negation_source_sumresult) = S ge_signed_half_negation_source_sumresultdecode))) /\ ((dst_positive_sum_negation_source_sum) + ge_balance_negative_negation_source_sumresult = (dst_negative_sum_negation_source_sum) + ge_balance_positive_negation_source_sumresult))))))))) -> (exists mps_positive_negation_relation mps_negative_negation_relation. (((((a) = 2 * (mps_positive_negation_relation) /\ (mps_negative_negation_relation) = 0) \/ exists ge_signed_half_negation_relationsource. (((a) = 2 * ge_signed_half_negation_relationsource + 1 /\ (mps_positive_negation_relation) = 0) /\ (mps_negative_negation_relation) = S ge_signed_half_negation_relationsource))) /\ ((((b) = 2 * (mps_negative_negation_relation) /\ (mps_positive_negation_relation) = 0) \/ exists ge_signed_half_negation_relationtarget. (((b) = 2 * ge_signed_half_negation_relationtarget + 1 /\ (mps_negative_negation_relation) = 0) /\ (mps_positive_negation_relation) = S ge_signed_half_negation_relationtarget))))) -> (exists dst_positive_code_negation_target_sum dst_positive_scale_negation_target_sum dst_negative_code_negation_target_sum dst_negative_scale_negation_target_sum dst_positive_sum_negation_target_sum dst_negative_sum_negation_target_sum. (((G) = (((((dst_positive_code_negation_target_sum) + (dst_positive_scale_negation_target_sum)) * S ((dst_positive_code_negation_target_sum) + (dst_positive_scale_negation_target_sum)) + ((dst_positive_scale_negation_target_sum) + (dst_positive_scale_negation_target_sum))) + (((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) * S ((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) + ((dst_negative_scale_negation_target_sum) + (dst_negative_scale_negation_target_sum)))) * S ((((dst_positive_code_negation_target_sum) + (dst_positive_scale_negation_target_sum)) * S ((dst_positive_code_negation_target_sum) + (dst_positive_scale_negation_target_sum)) + ((dst_positive_scale_negation_target_sum) + (dst_positive_scale_negation_target_sum))) + (((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) * S ((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) + ((dst_negative_scale_negation_target_sum) + (dst_negative_scale_negation_target_sum)))) + ((((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) * S ((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) + ((dst_negative_scale_negation_target_sum) + (dst_negative_scale_negation_target_sum))) + (((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) * S ((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) + ((dst_negative_scale_negation_target_sum) + (dst_negative_scale_negation_target_sum)))))) /\ (((exists fs_u_dst_negation_target_sumpositive fs_v_dst_negation_target_sumpositive. ((((exists fs_h_dst_negation_target_sumpositive_body_start. fs_h_dst_negation_target_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_negation_target_sumpositive)) /\ exists fs_q_dst_negation_target_sumpositive_body_start. fs_u_dst_negation_target_sumpositive = fs_q_dst_negation_target_sumpositive_body_start * S ((S (0)) * fs_v_dst_negation_target_sumpositive) + (0))) /\ ((((exists fs_h_dst_negation_target_sumpositive_body_terminal. fs_h_dst_negation_target_sumpositive_body_terminal + S (dst_positive_sum_negation_target_sum) = S ((S (l)) * fs_v_dst_negation_target_sumpositive)) /\ exists fs_q_dst_negation_target_sumpositive_body_terminal. fs_u_dst_negation_target_sumpositive = fs_q_dst_negation_target_sumpositive_body_terminal * S ((S (l)) * fs_v_dst_negation_target_sumpositive) + (dst_positive_sum_negation_target_sum))) /\ forall fs_i_dst_negation_target_sumpositive_body_steps. (exists fs_lt_dst_negation_target_sumpositive_body_steps_bound. fs_lt_dst_negation_target_sumpositive_body_steps_bound + S fs_i_dst_negation_target_sumpositive_body_steps = l) -> exists fs_a_dst_negation_target_sumpositive_body_steps fs_r_dst_negation_target_sumpositive_body_steps fs_s_dst_negation_target_sumpositive_body_steps. ((((exists fs_h_dst_negation_target_sumpositive_body_steps_summand. fs_h_dst_negation_target_sumpositive_body_steps_summand + S (fs_a_dst_negation_target_sumpositive_body_steps) = S ((S (fs_i_dst_negation_target_sumpositive_body_steps)) * dst_positive_scale_negation_target_sum)) /\ exists fs_q_dst_negation_target_sumpositive_body_steps_summand. dst_positive_code_negation_target_sum = fs_q_dst_negation_target_sumpositive_body_steps_summand * S ((S (fs_i_dst_negation_target_sumpositive_body_steps)) * dst_positive_scale_negation_target_sum) + (fs_a_dst_negation_target_sumpositive_body_steps))) /\ ((((exists fs_h_dst_negation_target_sumpositive_body_steps_partial. fs_h_dst_negation_target_sumpositive_body_steps_partial + S (fs_r_dst_negation_target_sumpositive_body_steps) = S ((S (fs_i_dst_negation_target_sumpositive_body_steps)) * fs_v_dst_negation_target_sumpositive)) /\ exists fs_q_dst_negation_target_sumpositive_body_steps_partial. fs_u_dst_negation_target_sumpositive = fs_q_dst_negation_target_sumpositive_body_steps_partial * S ((S (fs_i_dst_negation_target_sumpositive_body_steps)) * fs_v_dst_negation_target_sumpositive) + (fs_r_dst_negation_target_sumpositive_body_steps))) /\ ((((exists fs_h_dst_negation_target_sumpositive_body_steps_successor. fs_h_dst_negation_target_sumpositive_body_steps_successor + S (fs_s_dst_negation_target_sumpositive_body_steps) = S ((S (S fs_i_dst_negation_target_sumpositive_body_steps)) * fs_v_dst_negation_target_sumpositive)) /\ exists fs_q_dst_negation_target_sumpositive_body_steps_successor. fs_u_dst_negation_target_sumpositive = fs_q_dst_negation_target_sumpositive_body_steps_successor * S ((S (S fs_i_dst_negation_target_sumpositive_body_steps)) * fs_v_dst_negation_target_sumpositive) + (fs_s_dst_negation_target_sumpositive_body_steps))) /\ fs_s_dst_negation_target_sumpositive_body_steps = fs_r_dst_negation_target_sumpositive_body_steps + fs_a_dst_negation_target_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_negation_target_sumnegative fs_v_dst_negation_target_sumnegative. ((((exists fs_h_dst_negation_target_sumnegative_body_start. fs_h_dst_negation_target_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_negation_target_sumnegative)) /\ exists fs_q_dst_negation_target_sumnegative_body_start. fs_u_dst_negation_target_sumnegative = fs_q_dst_negation_target_sumnegative_body_start * S ((S (0)) * fs_v_dst_negation_target_sumnegative) + (0))) /\ ((((exists fs_h_dst_negation_target_sumnegative_body_terminal. fs_h_dst_negation_target_sumnegative_body_terminal + S (dst_negative_sum_negation_target_sum) = S ((S (l)) * fs_v_dst_negation_target_sumnegative)) /\ exists fs_q_dst_negation_target_sumnegative_body_terminal. fs_u_dst_negation_target_sumnegative = fs_q_dst_negation_target_sumnegative_body_terminal * S ((S (l)) * fs_v_dst_negation_target_sumnegative) + (dst_negative_sum_negation_target_sum))) /\ forall fs_i_dst_negation_target_sumnegative_body_steps. (exists fs_lt_dst_negation_target_sumnegative_body_steps_bound. fs_lt_dst_negation_target_sumnegative_body_steps_bound + S fs_i_dst_negation_target_sumnegative_body_steps = l) -> exists fs_a_dst_negation_target_sumnegative_body_steps fs_r_dst_negation_target_sumnegative_body_steps fs_s_dst_negation_target_sumnegative_body_steps. ((((exists fs_h_dst_negation_target_sumnegative_body_steps_summand. fs_h_dst_negation_target_sumnegative_body_steps_summand + S (fs_a_dst_negation_target_sumnegative_body_steps) = S ((S (fs_i_dst_negation_target_sumnegative_body_steps)) * dst_negative_scale_negation_target_sum)) /\ exists fs_q_dst_negation_target_sumnegative_body_steps_summand. dst_negative_code_negation_target_sum = fs_q_dst_negation_target_sumnegative_body_steps_summand * S ((S (fs_i_dst_negation_target_sumnegative_body_steps)) * dst_negative_scale_negation_target_sum) + (fs_a_dst_negation_target_sumnegative_body_steps))) /\ ((((exists fs_h_dst_negation_target_sumnegative_body_steps_partial. fs_h_dst_negation_target_sumnegative_body_steps_partial + S (fs_r_dst_negation_target_sumnegative_body_steps) = S ((S (fs_i_dst_negation_target_sumnegative_body_steps)) * fs_v_dst_negation_target_sumnegative)) /\ exists fs_q_dst_negation_target_sumnegative_body_steps_partial. fs_u_dst_negation_target_sumnegative = fs_q_dst_negation_target_sumnegative_body_steps_partial * S ((S (fs_i_dst_negation_target_sumnegative_body_steps)) * fs_v_dst_negation_target_sumnegative) + (fs_r_dst_negation_target_sumnegative_body_steps))) /\ ((((exists fs_h_dst_negation_target_sumnegative_body_steps_successor. fs_h_dst_negation_target_sumnegative_body_steps_successor + S (fs_s_dst_negation_target_sumnegative_body_steps) = S ((S (S fs_i_dst_negation_target_sumnegative_body_steps)) * fs_v_dst_negation_target_sumnegative)) /\ exists fs_q_dst_negation_target_sumnegative_body_steps_successor. fs_u_dst_negation_target_sumnegative = fs_q_dst_negation_target_sumnegative_body_steps_successor * S ((S (S fs_i_dst_negation_target_sumnegative_body_steps)) * fs_v_dst_negation_target_sumnegative) + (fs_s_dst_negation_target_sumnegative_body_steps))) /\ fs_s_dst_negation_target_sumnegative_body_steps = fs_r_dst_negation_target_sumnegative_body_steps + fs_a_dst_negation_target_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_negation_target_sumresult ge_balance_negative_negation_target_sumresult. (((((b) = 2 * (ge_balance_positive_negation_target_sumresult) /\ (ge_balance_negative_negation_target_sumresult) = 0) \/ exists ge_signed_half_negation_target_sumresultdecode. (((b) = 2 * ge_signed_half_negation_target_sumresultdecode + 1 /\ (ge_balance_positive_negation_target_sumresult) = 0) /\ (ge_balance_negative_negation_target_sumresult) = S ge_signed_half_negation_target_sumresultdecode))) /\ ((dst_positive_sum_negation_target_sum) + ge_balance_negative_negation_target_sumresult = (dst_negative_sum_negation_target_sum) + ge_balance_positive_negation_target_sumresult)))))))))

forall F l a b c. (exists dst_positive_code_step_sum dst_positive_scale_step_sum dst_negative_code_step_sum dst_negative_scale_step_sum dst_positive_sum_step_sum dst_negative_sum_step_sum. (((F) = (((((dst_positive_code_step_sum) + (dst_positive_scale_step_sum)) * S ((dst_positive_code_step_sum) + (dst_positive_scale_step_sum)) + ((dst_positive_scale_step_sum) + (dst_positive_scale_step_sum))) + (((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) * S ((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) + ((dst_negative_scale_step_sum) + (dst_negative_scale_step_sum)))) * S ((((dst_positive_code_step_sum) + (dst_positive_scale_step_sum)) * S ((dst_positive_code_step_sum) + (dst_positive_scale_step_sum)) + ((dst_positive_scale_step_sum) + (dst_positive_scale_step_sum))) + (((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) * S ((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) + ((dst_negative_scale_step_sum) + (dst_negative_scale_step_sum)))) + ((((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) * S ((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) + ((dst_negative_scale_step_sum) + (dst_negative_scale_step_sum))) + (((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) * S ((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) + ((dst_negative_scale_step_sum) + (dst_negative_scale_step_sum)))))) /\ (((exists fs_u_dst_step_sumpositive fs_v_dst_step_sumpositive. ((((exists fs_h_dst_step_sumpositive_body_start. fs_h_dst_step_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_step_sumpositive)) /\ exists fs_q_dst_step_sumpositive_body_start. fs_u_dst_step_sumpositive = fs_q_dst_step_sumpositive_body_start * S ((S (0)) * fs_v_dst_step_sumpositive) + (0))) /\ ((((exists fs_h_dst_step_sumpositive_body_terminal. fs_h_dst_step_sumpositive_body_terminal + S (dst_positive_sum_step_sum) = S ((S (l)) * fs_v_dst_step_sumpositive)) /\ exists fs_q_dst_step_sumpositive_body_terminal. fs_u_dst_step_sumpositive = fs_q_dst_step_sumpositive_body_terminal * S ((S (l)) * fs_v_dst_step_sumpositive) + (dst_positive_sum_step_sum))) /\ forall fs_i_dst_step_sumpositive_body_steps. (exists fs_lt_dst_step_sumpositive_body_steps_bound. fs_lt_dst_step_sumpositive_body_steps_bound + S fs_i_dst_step_sumpositive_body_steps = l) -> exists fs_a_dst_step_sumpositive_body_steps fs_r_dst_step_sumpositive_body_steps fs_s_dst_step_sumpositive_body_steps. ((((exists fs_h_dst_step_sumpositive_body_steps_summand. fs_h_dst_step_sumpositive_body_steps_summand + S (fs_a_dst_step_sumpositive_body_steps) = S ((S (fs_i_dst_step_sumpositive_body_steps)) * dst_positive_scale_step_sum)) /\ exists fs_q_dst_step_sumpositive_body_steps_summand. dst_positive_code_step_sum = fs_q_dst_step_sumpositive_body_steps_summand * S ((S (fs_i_dst_step_sumpositive_body_steps)) * dst_positive_scale_step_sum) + (fs_a_dst_step_sumpositive_body_steps))) /\ ((((exists fs_h_dst_step_sumpositive_body_steps_partial. fs_h_dst_step_sumpositive_body_steps_partial + S (fs_r_dst_step_sumpositive_body_steps) = S ((S (fs_i_dst_step_sumpositive_body_steps)) * fs_v_dst_step_sumpositive)) /\ exists fs_q_dst_step_sumpositive_body_steps_partial. fs_u_dst_step_sumpositive = fs_q_dst_step_sumpositive_body_steps_partial * S ((S (fs_i_dst_step_sumpositive_body_steps)) * fs_v_dst_step_sumpositive) + (fs_r_dst_step_sumpositive_body_steps))) /\ ((((exists fs_h_dst_step_sumpositive_body_steps_successor. fs_h_dst_step_sumpositive_body_steps_successor + S (fs_s_dst_step_sumpositive_body_steps) = S ((S (S fs_i_dst_step_sumpositive_body_steps)) * fs_v_dst_step_sumpositive)) /\ exists fs_q_dst_step_sumpositive_body_steps_successor. fs_u_dst_step_sumpositive = fs_q_dst_step_sumpositive_body_steps_successor * S ((S (S fs_i_dst_step_sumpositive_body_steps)) * fs_v_dst_step_sumpositive) + (fs_s_dst_step_sumpositive_body_steps))) /\ fs_s_dst_step_sumpositive_body_steps = fs_r_dst_step_sumpositive_body_steps + fs_a_dst_step_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_step_sumnegative fs_v_dst_step_sumnegative. ((((exists fs_h_dst_step_sumnegative_body_start. fs_h_dst_step_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_step_sumnegative)) /\ exists fs_q_dst_step_sumnegative_body_start. fs_u_dst_step_sumnegative = fs_q_dst_step_sumnegative_body_start * S ((S (0)) * fs_v_dst_step_sumnegative) + (0))) /\ ((((exists fs_h_dst_step_sumnegative_body_terminal. fs_h_dst_step_sumnegative_body_terminal + S (dst_negative_sum_step_sum) = S ((S (l)) * fs_v_dst_step_sumnegative)) /\ exists fs_q_dst_step_sumnegative_body_terminal. fs_u_dst_step_sumnegative = fs_q_dst_step_sumnegative_body_terminal * S ((S (l)) * fs_v_dst_step_sumnegative) + (dst_negative_sum_step_sum))) /\ forall fs_i_dst_step_sumnegative_body_steps. (exists fs_lt_dst_step_sumnegative_body_steps_bound. fs_lt_dst_step_sumnegative_body_steps_bound + S fs_i_dst_step_sumnegative_body_steps = l) -> exists fs_a_dst_step_sumnegative_body_steps fs_r_dst_step_sumnegative_body_steps fs_s_dst_step_sumnegative_body_steps. ((((exists fs_h_dst_step_sumnegative_body_steps_summand. fs_h_dst_step_sumnegative_body_steps_summand + S (fs_a_dst_step_sumnegative_body_steps) = S ((S (fs_i_dst_step_sumnegative_body_steps)) * dst_negative_scale_step_sum)) /\ exists fs_q_dst_step_sumnegative_body_steps_summand. dst_negative_code_step_sum = fs_q_dst_step_sumnegative_body_steps_summand * S ((S (fs_i_dst_step_sumnegative_body_steps)) * dst_negative_scale_step_sum) + (fs_a_dst_step_sumnegative_body_steps))) /\ ((((exists fs_h_dst_step_sumnegative_body_steps_partial. fs_h_dst_step_sumnegative_body_steps_partial + S (fs_r_dst_step_sumnegative_body_steps) = S ((S (fs_i_dst_step_sumnegative_body_steps)) * fs_v_dst_step_sumnegative)) /\ exists fs_q_dst_step_sumnegative_body_steps_partial. fs_u_dst_step_sumnegative = fs_q_dst_step_sumnegative_body_steps_partial * S ((S (fs_i_dst_step_sumnegative_body_steps)) * fs_v_dst_step_sumnegative) + (fs_r_dst_step_sumnegative_body_steps))) /\ ((((exists fs_h_dst_step_sumnegative_body_steps_successor. fs_h_dst_step_sumnegative_body_steps_successor + S (fs_s_dst_step_sumnegative_body_steps) = S ((S (S fs_i_dst_step_sumnegative_body_steps)) * fs_v_dst_step_sumnegative)) /\ exists fs_q_dst_step_sumnegative_body_steps_successor. fs_u_dst_step_sumnegative = fs_q_dst_step_sumnegative_body_steps_successor * S ((S (S fs_i_dst_step_sumnegative_body_steps)) * fs_v_dst_step_sumnegative) + (fs_s_dst_step_sumnegative_body_steps))) /\ fs_s_dst_step_sumnegative_body_steps = fs_r_dst_step_sumnegative_body_steps + fs_a_dst_step_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_step_sumresult ge_balance_negative_step_sumresult. (((((a) = 2 * (ge_balance_positive_step_sumresult) /\ (ge_balance_negative_step_sumresult) = 0) \/ exists ge_signed_half_step_sumresultdecode. (((a) = 2 * ge_signed_half_step_sumresultdecode + 1 /\ (ge_balance_positive_step_sumresult) = 0) /\ (ge_balance_negative_step_sumresult) = S ge_signed_half_step_sumresultdecode))) /\ ((dst_positive_sum_step_sum) + ge_balance_negative_step_sumresult = (dst_negative_sum_step_sum) + ge_balance_positive_step_sumresult))))))))) -> (exists dst_positive_code_step_entry dst_positive_scale_step_entry dst_negative_code_step_entry dst_negative_scale_step_entry dst_positive_step_entry dst_negative_step_entry. (((F) = (((((dst_positive_code_step_entry) + (dst_positive_scale_step_entry)) * S ((dst_positive_code_step_entry) + (dst_positive_scale_step_entry)) + ((dst_positive_scale_step_entry) + (dst_positive_scale_step_entry))) + (((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) * S ((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) + ((dst_negative_scale_step_entry) + (dst_negative_scale_step_entry)))) * S ((((dst_positive_code_step_entry) + (dst_positive_scale_step_entry)) * S ((dst_positive_code_step_entry) + (dst_positive_scale_step_entry)) + ((dst_positive_scale_step_entry) + (dst_positive_scale_step_entry))) + (((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) * S ((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) + ((dst_negative_scale_step_entry) + (dst_negative_scale_step_entry)))) + ((((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) * S ((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) + ((dst_negative_scale_step_entry) + (dst_negative_scale_step_entry))) + (((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) * S ((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) + ((dst_negative_scale_step_entry) + (dst_negative_scale_step_entry)))))) /\ (((((exists ff_h_pvs_step_entrypositive. ff_h_pvs_step_entrypositive + S (dst_positive_step_entry) = S ((S (l)) * dst_positive_scale_step_entry)) /\ exists ff_q_pvs_step_entrypositive. dst_positive_code_step_entry = ff_q_pvs_step_entrypositive * S ((S (l)) * dst_positive_scale_step_entry) + (dst_positive_step_entry))) /\ (((((exists ff_h_pvs_step_entrynegative. ff_h_pvs_step_entrynegative + S (dst_negative_step_entry) = S ((S (l)) * dst_negative_scale_step_entry)) /\ exists ff_q_pvs_step_entrynegative. dst_negative_code_step_entry = ff_q_pvs_step_entrynegative * S ((S (l)) * dst_negative_scale_step_entry) + (dst_negative_step_entry))) /\ (exists ge_balance_positive_step_entryvalue ge_balance_negative_step_entryvalue. (((((b) = 2 * (ge_balance_positive_step_entryvalue) /\ (ge_balance_negative_step_entryvalue) = 0) \/ exists ge_signed_half_step_entryvaluedecode. (((b) = 2 * ge_signed_half_step_entryvaluedecode + 1 /\ (ge_balance_positive_step_entryvalue) = 0) /\ (ge_balance_negative_step_entryvalue) = S ge_signed_half_step_entryvaluedecode))) /\ ((dst_positive_step_entry) + ge_balance_negative_step_entryvalue = (dst_negative_step_entry) + ge_balance_positive_step_entryvalue))))))))) -> (exists dsa_ap_step_add dsa_an_step_add dsa_bp_step_add dsa_bn_step_add dsa_cp_step_add dsa_cn_step_add. (((((a) = 2 * (dsa_ap_step_add) /\ (dsa_an_step_add) = 0) \/ exists ge_signed_half_step_addleft. (((a) = 2 * ge_signed_half_step_addleft + 1 /\ (dsa_ap_step_add) = 0) /\ (dsa_an_step_add) = S ge_signed_half_step_addleft))) /\ ((((((b) = 2 * (dsa_bp_step_add) /\ (dsa_bn_step_add) = 0) \/ exists ge_signed_half_step_addright. (((b) = 2 * ge_signed_half_step_addright + 1 /\ (dsa_bp_step_add) = 0) /\ (dsa_bn_step_add) = S ge_signed_half_step_addright))) /\ ((((((c) = 2 * (dsa_cp_step_add) /\ (dsa_cn_step_add) = 0) \/ exists ge_signed_half_step_addoutput. (((c) = 2 * ge_signed_half_step_addoutput + 1 /\ (dsa_cp_step_add) = 0) /\ (dsa_cn_step_add) = S ge_signed_half_step_addoutput))) /\ ((dsa_ap_step_add + dsa_bp_step_add) + dsa_cn_step_add = (dsa_an_step_add + dsa_bn_step_add) + dsa_cp_step_add))))))) -> (exists dst_positive_code_step_result dst_positive_scale_step_result dst_negative_code_step_result dst_negative_scale_step_result dst_positive_sum_step_result dst_negative_sum_step_result. (((F) = (((((dst_positive_code_step_result) + (dst_positive_scale_step_result)) * S ((dst_positive_code_step_result) + (dst_positive_scale_step_result)) + ((dst_positive_scale_step_result) + (dst_positive_scale_step_result))) + (((dst_negative_code_step_result) + (dst_negative_scale_step_result)) * S ((dst_negative_code_step_result) + (dst_negative_scale_step_result)) + ((dst_negative_scale_step_result) + (dst_negative_scale_step_result)))) * S ((((dst_positive_code_step_result) + (dst_positive_scale_step_result)) * S ((dst_positive_code_step_result) + (dst_positive_scale_step_result)) + ((dst_positive_scale_step_result) + (dst_positive_scale_step_result))) + (((dst_negative_code_step_result) + (dst_negative_scale_step_result)) * S ((dst_negative_code_step_result) + (dst_negative_scale_step_result)) + ((dst_negative_scale_step_result) + (dst_negative_scale_step_result)))) + ((((dst_negative_code_step_result) + (dst_negative_scale_step_result)) * S ((dst_negative_code_step_result) + (dst_negative_scale_step_result)) + ((dst_negative_scale_step_result) + (dst_negative_scale_step_result))) + (((dst_negative_code_step_result) + (dst_negative_scale_step_result)) * S ((dst_negative_code_step_result) + (dst_negative_scale_step_result)) + ((dst_negative_scale_step_result) + (dst_negative_scale_step_result)))))) /\ (((exists fs_u_dst_step_resultpositive fs_v_dst_step_resultpositive. ((((exists fs_h_dst_step_resultpositive_body_start. fs_h_dst_step_resultpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_step_resultpositive)) /\ exists fs_q_dst_step_resultpositive_body_start. fs_u_dst_step_resultpositive = fs_q_dst_step_resultpositive_body_start * S ((S (0)) * fs_v_dst_step_resultpositive) + (0))) /\ ((((exists fs_h_dst_step_resultpositive_body_terminal. fs_h_dst_step_resultpositive_body_terminal + S (dst_positive_sum_step_result) = S ((S (S l)) * fs_v_dst_step_resultpositive)) /\ exists fs_q_dst_step_resultpositive_body_terminal. fs_u_dst_step_resultpositive = fs_q_dst_step_resultpositive_body_terminal * S ((S (S l)) * fs_v_dst_step_resultpositive) + (dst_positive_sum_step_result))) /\ forall fs_i_dst_step_resultpositive_body_steps. (exists fs_lt_dst_step_resultpositive_body_steps_bound. fs_lt_dst_step_resultpositive_body_steps_bound + S fs_i_dst_step_resultpositive_body_steps = S l) -> exists fs_a_dst_step_resultpositive_body_steps fs_r_dst_step_resultpositive_body_steps fs_s_dst_step_resultpositive_body_steps. ((((exists fs_h_dst_step_resultpositive_body_steps_summand. fs_h_dst_step_resultpositive_body_steps_summand + S (fs_a_dst_step_resultpositive_body_steps) = S ((S (fs_i_dst_step_resultpositive_body_steps)) * dst_positive_scale_step_result)) /\ exists fs_q_dst_step_resultpositive_body_steps_summand. dst_positive_code_step_result = fs_q_dst_step_resultpositive_body_steps_summand * S ((S (fs_i_dst_step_resultpositive_body_steps)) * dst_positive_scale_step_result) + (fs_a_dst_step_resultpositive_body_steps))) /\ ((((exists fs_h_dst_step_resultpositive_body_steps_partial. fs_h_dst_step_resultpositive_body_steps_partial + S (fs_r_dst_step_resultpositive_body_steps) = S ((S (fs_i_dst_step_resultpositive_body_steps)) * fs_v_dst_step_resultpositive)) /\ exists fs_q_dst_step_resultpositive_body_steps_partial. fs_u_dst_step_resultpositive = fs_q_dst_step_resultpositive_body_steps_partial * S ((S (fs_i_dst_step_resultpositive_body_steps)) * fs_v_dst_step_resultpositive) + (fs_r_dst_step_resultpositive_body_steps))) /\ ((((exists fs_h_dst_step_resultpositive_body_steps_successor. fs_h_dst_step_resultpositive_body_steps_successor + S (fs_s_dst_step_resultpositive_body_steps) = S ((S (S fs_i_dst_step_resultpositive_body_steps)) * fs_v_dst_step_resultpositive)) /\ exists fs_q_dst_step_resultpositive_body_steps_successor. fs_u_dst_step_resultpositive = fs_q_dst_step_resultpositive_body_steps_successor * S ((S (S fs_i_dst_step_resultpositive_body_steps)) * fs_v_dst_step_resultpositive) + (fs_s_dst_step_resultpositive_body_steps))) /\ fs_s_dst_step_resultpositive_body_steps = fs_r_dst_step_resultpositive_body_steps + fs_a_dst_step_resultpositive_body_steps)))))) /\ (((exists fs_u_dst_step_resultnegative fs_v_dst_step_resultnegative. ((((exists fs_h_dst_step_resultnegative_body_start. fs_h_dst_step_resultnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_step_resultnegative)) /\ exists fs_q_dst_step_resultnegative_body_start. fs_u_dst_step_resultnegative = fs_q_dst_step_resultnegative_body_start * S ((S (0)) * fs_v_dst_step_resultnegative) + (0))) /\ ((((exists fs_h_dst_step_resultnegative_body_terminal. fs_h_dst_step_resultnegative_body_terminal + S (dst_negative_sum_step_result) = S ((S (S l)) * fs_v_dst_step_resultnegative)) /\ exists fs_q_dst_step_resultnegative_body_terminal. fs_u_dst_step_resultnegative = fs_q_dst_step_resultnegative_body_terminal * S ((S (S l)) * fs_v_dst_step_resultnegative) + (dst_negative_sum_step_result))) /\ forall fs_i_dst_step_resultnegative_body_steps. (exists fs_lt_dst_step_resultnegative_body_steps_bound. fs_lt_dst_step_resultnegative_body_steps_bound + S fs_i_dst_step_resultnegative_body_steps = S l) -> exists fs_a_dst_step_resultnegative_body_steps fs_r_dst_step_resultnegative_body_steps fs_s_dst_step_resultnegative_body_steps. ((((exists fs_h_dst_step_resultnegative_body_steps_summand. fs_h_dst_step_resultnegative_body_steps_summand + S (fs_a_dst_step_resultnegative_body_steps) = S ((S (fs_i_dst_step_resultnegative_body_steps)) * dst_negative_scale_step_result)) /\ exists fs_q_dst_step_resultnegative_body_steps_summand. dst_negative_code_step_result = fs_q_dst_step_resultnegative_body_steps_summand * S ((S (fs_i_dst_step_resultnegative_body_steps)) * dst_negative_scale_step_result) + (fs_a_dst_step_resultnegative_body_steps))) /\ ((((exists fs_h_dst_step_resultnegative_body_steps_partial. fs_h_dst_step_resultnegative_body_steps_partial + S (fs_r_dst_step_resultnegative_body_steps) = S ((S (fs_i_dst_step_resultnegative_body_steps)) * fs_v_dst_step_resultnegative)) /\ exists fs_q_dst_step_resultnegative_body_steps_partial. fs_u_dst_step_resultnegative = fs_q_dst_step_resultnegative_body_steps_partial * S ((S (fs_i_dst_step_resultnegative_body_steps)) * fs_v_dst_step_resultnegative) + (fs_r_dst_step_resultnegative_body_steps))) /\ ((((exists fs_h_dst_step_resultnegative_body_steps_successor. fs_h_dst_step_resultnegative_body_steps_successor + S (fs_s_dst_step_resultnegative_body_steps) = S ((S (S fs_i_dst_step_resultnegative_body_steps)) * fs_v_dst_step_resultnegative)) /\ exists fs_q_dst_step_resultnegative_body_steps_successor. fs_u_dst_step_resultnegative = fs_q_dst_step_resultnegative_body_steps_successor * S ((S (S fs_i_dst_step_resultnegative_body_steps)) * fs_v_dst_step_resultnegative) + (fs_s_dst_step_resultnegative_body_steps))) /\ fs_s_dst_step_resultnegative_body_steps = fs_r_dst_step_resultnegative_body_steps + fs_a_dst_step_resultnegative_body_steps)))))) /\ (exists ge_balance_positive_step_resultresult ge_balance_negative_step_resultresult. (((((c) = 2 * (ge_balance_positive_step_resultresult) /\ (ge_balance_negative_step_resultresult) = 0) \/ exists ge_signed_half_step_resultresultdecode. (((c) = 2 * ge_signed_half_step_resultresultdecode + 1 /\ (ge_balance_positive_step_resultresult) = 0) /\ (ge_balance_negative_step_resultresult) = S ge_signed_half_step_resultresultdecode))) /\ ((dst_positive_sum_step_result) + ge_balance_negative_step_resultresult = (dst_negative_sum_step_result) + ge_balance_positive_step_resultresult)))))))))

forall F l z. (exists dst_positive_code_decomp_sum dst_positive_scale_decomp_sum dst_negative_code_decomp_sum dst_negative_scale_decomp_sum dst_positive_sum_decomp_sum dst_negative_sum_decomp_sum. (((F) = (((((dst_positive_code_decomp_sum) + (dst_positive_scale_decomp_sum)) * S ((dst_positive_code_decomp_sum) + (dst_positive_scale_decomp_sum)) + ((dst_positive_scale_decomp_sum) + (dst_positive_scale_decomp_sum))) + (((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) * S ((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) + ((dst_negative_scale_decomp_sum) + (dst_negative_scale_decomp_sum)))) * S ((((dst_positive_code_decomp_sum) + (dst_positive_scale_decomp_sum)) * S ((dst_positive_code_decomp_sum) + (dst_positive_scale_decomp_sum)) + ((dst_positive_scale_decomp_sum) + (dst_positive_scale_decomp_sum))) + (((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) * S ((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) + ((dst_negative_scale_decomp_sum) + (dst_negative_scale_decomp_sum)))) + ((((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) * S ((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) + ((dst_negative_scale_decomp_sum) + (dst_negative_scale_decomp_sum))) + (((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) * S ((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) + ((dst_negative_scale_decomp_sum) + (dst_negative_scale_decomp_sum)))))) /\ (((exists fs_u_dst_decomp_sumpositive fs_v_dst_decomp_sumpositive. ((((exists fs_h_dst_decomp_sumpositive_body_start. fs_h_dst_decomp_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_decomp_sumpositive)) /\ exists fs_q_dst_decomp_sumpositive_body_start. fs_u_dst_decomp_sumpositive = fs_q_dst_decomp_sumpositive_body_start * S ((S (0)) * fs_v_dst_decomp_sumpositive) + (0))) /\ ((((exists fs_h_dst_decomp_sumpositive_body_terminal. fs_h_dst_decomp_sumpositive_body_terminal + S (dst_positive_sum_decomp_sum) = S ((S (S l)) * fs_v_dst_decomp_sumpositive)) /\ exists fs_q_dst_decomp_sumpositive_body_terminal. fs_u_dst_decomp_sumpositive = fs_q_dst_decomp_sumpositive_body_terminal * S ((S (S l)) * fs_v_dst_decomp_sumpositive) + (dst_positive_sum_decomp_sum))) /\ forall fs_i_dst_decomp_sumpositive_body_steps. (exists fs_lt_dst_decomp_sumpositive_body_steps_bound. fs_lt_dst_decomp_sumpositive_body_steps_bound + S fs_i_dst_decomp_sumpositive_body_steps = S l) -> exists fs_a_dst_decomp_sumpositive_body_steps fs_r_dst_decomp_sumpositive_body_steps fs_s_dst_decomp_sumpositive_body_steps. ((((exists fs_h_dst_decomp_sumpositive_body_steps_summand. fs_h_dst_decomp_sumpositive_body_steps_summand + S (fs_a_dst_decomp_sumpositive_body_steps) = S ((S (fs_i_dst_decomp_sumpositive_body_steps)) * dst_positive_scale_decomp_sum)) /\ exists fs_q_dst_decomp_sumpositive_body_steps_summand. dst_positive_code_decomp_sum = fs_q_dst_decomp_sumpositive_body_steps_summand * S ((S (fs_i_dst_decomp_sumpositive_body_steps)) * dst_positive_scale_decomp_sum) + (fs_a_dst_decomp_sumpositive_body_steps))) /\ ((((exists fs_h_dst_decomp_sumpositive_body_steps_partial. fs_h_dst_decomp_sumpositive_body_steps_partial + S (fs_r_dst_decomp_sumpositive_body_steps) = S ((S (fs_i_dst_decomp_sumpositive_body_steps)) * fs_v_dst_decomp_sumpositive)) /\ exists fs_q_dst_decomp_sumpositive_body_steps_partial. fs_u_dst_decomp_sumpositive = fs_q_dst_decomp_sumpositive_body_steps_partial * S ((S (fs_i_dst_decomp_sumpositive_body_steps)) * fs_v_dst_decomp_sumpositive) + (fs_r_dst_decomp_sumpositive_body_steps))) /\ ((((exists fs_h_dst_decomp_sumpositive_body_steps_successor. fs_h_dst_decomp_sumpositive_body_steps_successor + S (fs_s_dst_decomp_sumpositive_body_steps) = S ((S (S fs_i_dst_decomp_sumpositive_body_steps)) * fs_v_dst_decomp_sumpositive)) /\ exists fs_q_dst_decomp_sumpositive_body_steps_successor. fs_u_dst_decomp_sumpositive = fs_q_dst_decomp_sumpositive_body_steps_successor * S ((S (S fs_i_dst_decomp_sumpositive_body_steps)) * fs_v_dst_decomp_sumpositive) + (fs_s_dst_decomp_sumpositive_body_steps))) /\ fs_s_dst_decomp_sumpositive_body_steps = fs_r_dst_decomp_sumpositive_body_steps + fs_a_dst_decomp_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_decomp_sumnegative fs_v_dst_decomp_sumnegative. ((((exists fs_h_dst_decomp_sumnegative_body_start. fs_h_dst_decomp_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_decomp_sumnegative)) /\ exists fs_q_dst_decomp_sumnegative_body_start. fs_u_dst_decomp_sumnegative = fs_q_dst_decomp_sumnegative_body_start * S ((S (0)) * fs_v_dst_decomp_sumnegative) + (0))) /\ ((((exists fs_h_dst_decomp_sumnegative_body_terminal. fs_h_dst_decomp_sumnegative_body_terminal + S (dst_negative_sum_decomp_sum) = S ((S (S l)) * fs_v_dst_decomp_sumnegative)) /\ exists fs_q_dst_decomp_sumnegative_body_terminal. fs_u_dst_decomp_sumnegative = fs_q_dst_decomp_sumnegative_body_terminal * S ((S (S l)) * fs_v_dst_decomp_sumnegative) + (dst_negative_sum_decomp_sum))) /\ forall fs_i_dst_decomp_sumnegative_body_steps. (exists fs_lt_dst_decomp_sumnegative_body_steps_bound. fs_lt_dst_decomp_sumnegative_body_steps_bound + S fs_i_dst_decomp_sumnegative_body_steps = S l) -> exists fs_a_dst_decomp_sumnegative_body_steps fs_r_dst_decomp_sumnegative_body_steps fs_s_dst_decomp_sumnegative_body_steps. ((((exists fs_h_dst_decomp_sumnegative_body_steps_summand. fs_h_dst_decomp_sumnegative_body_steps_summand + S (fs_a_dst_decomp_sumnegative_body_steps) = S ((S (fs_i_dst_decomp_sumnegative_body_steps)) * dst_negative_scale_decomp_sum)) /\ exists fs_q_dst_decomp_sumnegative_body_steps_summand. dst_negative_code_decomp_sum = fs_q_dst_decomp_sumnegative_body_steps_summand * S ((S (fs_i_dst_decomp_sumnegative_body_steps)) * dst_negative_scale_decomp_sum) + (fs_a_dst_decomp_sumnegative_body_steps))) /\ ((((exists fs_h_dst_decomp_sumnegative_body_steps_partial. fs_h_dst_decomp_sumnegative_body_steps_partial + S (fs_r_dst_decomp_sumnegative_body_steps) = S ((S (fs_i_dst_decomp_sumnegative_body_steps)) * fs_v_dst_decomp_sumnegative)) /\ exists fs_q_dst_decomp_sumnegative_body_steps_partial. fs_u_dst_decomp_sumnegative = fs_q_dst_decomp_sumnegative_body_steps_partial * S ((S (fs_i_dst_decomp_sumnegative_body_steps)) * fs_v_dst_decomp_sumnegative) + (fs_r_dst_decomp_sumnegative_body_steps))) /\ ((((exists fs_h_dst_decomp_sumnegative_body_steps_successor. fs_h_dst_decomp_sumnegative_body_steps_successor + S (fs_s_dst_decomp_sumnegative_body_steps) = S ((S (S fs_i_dst_decomp_sumnegative_body_steps)) * fs_v_dst_decomp_sumnegative)) /\ exists fs_q_dst_decomp_sumnegative_body_steps_successor. fs_u_dst_decomp_sumnegative = fs_q_dst_decomp_sumnegative_body_steps_successor * S ((S (S fs_i_dst_decomp_sumnegative_body_steps)) * fs_v_dst_decomp_sumnegative) + (fs_s_dst_decomp_sumnegative_body_steps))) /\ fs_s_dst_decomp_sumnegative_body_steps = fs_r_dst_decomp_sumnegative_body_steps + fs_a_dst_decomp_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_decomp_sumresult ge_balance_negative_decomp_sumresult. (((((z) = 2 * (ge_balance_positive_decomp_sumresult) /\ (ge_balance_negative_decomp_sumresult) = 0) \/ exists ge_signed_half_decomp_sumresultdecode. (((z) = 2 * ge_signed_half_decomp_sumresultdecode + 1 /\ (ge_balance_positive_decomp_sumresult) = 0) /\ (ge_balance_negative_decomp_sumresult) = S ge_signed_half_decomp_sumresultdecode))) /\ ((dst_positive_sum_decomp_sum) + ge_balance_negative_decomp_sumresult = (dst_negative_sum_decomp_sum) + ge_balance_positive_decomp_sumresult))))))))) -> exists a b. ((exists dst_positive_code_decomp_prefix dst_positive_scale_decomp_prefix dst_negative_code_decomp_prefix dst_negative_scale_decomp_prefix dst_positive_sum_decomp_prefix dst_negative_sum_decomp_prefix. (((F) = (((((dst_positive_code_decomp_prefix) + (dst_positive_scale_decomp_prefix)) * S ((dst_positive_code_decomp_prefix) + (dst_positive_scale_decomp_prefix)) + ((dst_positive_scale_decomp_prefix) + (dst_positive_scale_decomp_prefix))) + (((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) * S ((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) + ((dst_negative_scale_decomp_prefix) + (dst_negative_scale_decomp_prefix)))) * S ((((dst_positive_code_decomp_prefix) + (dst_positive_scale_decomp_prefix)) * S ((dst_positive_code_decomp_prefix) + (dst_positive_scale_decomp_prefix)) + ((dst_positive_scale_decomp_prefix) + (dst_positive_scale_decomp_prefix))) + (((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) * S ((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) + ((dst_negative_scale_decomp_prefix) + (dst_negative_scale_decomp_prefix)))) + ((((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) * S ((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) + ((dst_negative_scale_decomp_prefix) + (dst_negative_scale_decomp_prefix))) + (((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) * S ((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) + ((dst_negative_scale_decomp_prefix) + (dst_negative_scale_decomp_prefix)))))) /\ (((exists fs_u_dst_decomp_prefixpositive fs_v_dst_decomp_prefixpositive. ((((exists fs_h_dst_decomp_prefixpositive_body_start. fs_h_dst_decomp_prefixpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_decomp_prefixpositive)) /\ exists fs_q_dst_decomp_prefixpositive_body_start. fs_u_dst_decomp_prefixpositive = fs_q_dst_decomp_prefixpositive_body_start * S ((S (0)) * fs_v_dst_decomp_prefixpositive) + (0))) /\ ((((exists fs_h_dst_decomp_prefixpositive_body_terminal. fs_h_dst_decomp_prefixpositive_body_terminal + S (dst_positive_sum_decomp_prefix) = S ((S (l)) * fs_v_dst_decomp_prefixpositive)) /\ exists fs_q_dst_decomp_prefixpositive_body_terminal. fs_u_dst_decomp_prefixpositive = fs_q_dst_decomp_prefixpositive_body_terminal * S ((S (l)) * fs_v_dst_decomp_prefixpositive) + (dst_positive_sum_decomp_prefix))) /\ forall fs_i_dst_decomp_prefixpositive_body_steps. (exists fs_lt_dst_decomp_prefixpositive_body_steps_bound. fs_lt_dst_decomp_prefixpositive_body_steps_bound + S fs_i_dst_decomp_prefixpositive_body_steps = l) -> exists fs_a_dst_decomp_prefixpositive_body_steps fs_r_dst_decomp_prefixpositive_body_steps fs_s_dst_decomp_prefixpositive_body_steps. ((((exists fs_h_dst_decomp_prefixpositive_body_steps_summand. fs_h_dst_decomp_prefixpositive_body_steps_summand + S (fs_a_dst_decomp_prefixpositive_body_steps) = S ((S (fs_i_dst_decomp_prefixpositive_body_steps)) * dst_positive_scale_decomp_prefix)) /\ exists fs_q_dst_decomp_prefixpositive_body_steps_summand. dst_positive_code_decomp_prefix = fs_q_dst_decomp_prefixpositive_body_steps_summand * S ((S (fs_i_dst_decomp_prefixpositive_body_steps)) * dst_positive_scale_decomp_prefix) + (fs_a_dst_decomp_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_decomp_prefixpositive_body_steps_partial. fs_h_dst_decomp_prefixpositive_body_steps_partial + S (fs_r_dst_decomp_prefixpositive_body_steps) = S ((S (fs_i_dst_decomp_prefixpositive_body_steps)) * fs_v_dst_decomp_prefixpositive)) /\ exists fs_q_dst_decomp_prefixpositive_body_steps_partial. fs_u_dst_decomp_prefixpositive = fs_q_dst_decomp_prefixpositive_body_steps_partial * S ((S (fs_i_dst_decomp_prefixpositive_body_steps)) * fs_v_dst_decomp_prefixpositive) + (fs_r_dst_decomp_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_decomp_prefixpositive_body_steps_successor. fs_h_dst_decomp_prefixpositive_body_steps_successor + S (fs_s_dst_decomp_prefixpositive_body_steps) = S ((S (S fs_i_dst_decomp_prefixpositive_body_steps)) * fs_v_dst_decomp_prefixpositive)) /\ exists fs_q_dst_decomp_prefixpositive_body_steps_successor. fs_u_dst_decomp_prefixpositive = fs_q_dst_decomp_prefixpositive_body_steps_successor * S ((S (S fs_i_dst_decomp_prefixpositive_body_steps)) * fs_v_dst_decomp_prefixpositive) + (fs_s_dst_decomp_prefixpositive_body_steps))) /\ fs_s_dst_decomp_prefixpositive_body_steps = fs_r_dst_decomp_prefixpositive_body_steps + fs_a_dst_decomp_prefixpositive_body_steps)))))) /\ (((exists fs_u_dst_decomp_prefixnegative fs_v_dst_decomp_prefixnegative. ((((exists fs_h_dst_decomp_prefixnegative_body_start. fs_h_dst_decomp_prefixnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_decomp_prefixnegative)) /\ exists fs_q_dst_decomp_prefixnegative_body_start. fs_u_dst_decomp_prefixnegative = fs_q_dst_decomp_prefixnegative_body_start * S ((S (0)) * fs_v_dst_decomp_prefixnegative) + (0))) /\ ((((exists fs_h_dst_decomp_prefixnegative_body_terminal. fs_h_dst_decomp_prefixnegative_body_terminal + S (dst_negative_sum_decomp_prefix) = S ((S (l)) * fs_v_dst_decomp_prefixnegative)) /\ exists fs_q_dst_decomp_prefixnegative_body_terminal. fs_u_dst_decomp_prefixnegative = fs_q_dst_decomp_prefixnegative_body_terminal * S ((S (l)) * fs_v_dst_decomp_prefixnegative) + (dst_negative_sum_decomp_prefix))) /\ forall fs_i_dst_decomp_prefixnegative_body_steps. (exists fs_lt_dst_decomp_prefixnegative_body_steps_bound. fs_lt_dst_decomp_prefixnegative_body_steps_bound + S fs_i_dst_decomp_prefixnegative_body_steps = l) -> exists fs_a_dst_decomp_prefixnegative_body_steps fs_r_dst_decomp_prefixnegative_body_steps fs_s_dst_decomp_prefixnegative_body_steps. ((((exists fs_h_dst_decomp_prefixnegative_body_steps_summand. fs_h_dst_decomp_prefixnegative_body_steps_summand + S (fs_a_dst_decomp_prefixnegative_body_steps) = S ((S (fs_i_dst_decomp_prefixnegative_body_steps)) * dst_negative_scale_decomp_prefix)) /\ exists fs_q_dst_decomp_prefixnegative_body_steps_summand. dst_negative_code_decomp_prefix = fs_q_dst_decomp_prefixnegative_body_steps_summand * S ((S (fs_i_dst_decomp_prefixnegative_body_steps)) * dst_negative_scale_decomp_prefix) + (fs_a_dst_decomp_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_decomp_prefixnegative_body_steps_partial. fs_h_dst_decomp_prefixnegative_body_steps_partial + S (fs_r_dst_decomp_prefixnegative_body_steps) = S ((S (fs_i_dst_decomp_prefixnegative_body_steps)) * fs_v_dst_decomp_prefixnegative)) /\ exists fs_q_dst_decomp_prefixnegative_body_steps_partial. fs_u_dst_decomp_prefixnegative = fs_q_dst_decomp_prefixnegative_body_steps_partial * S ((S (fs_i_dst_decomp_prefixnegative_body_steps)) * fs_v_dst_decomp_prefixnegative) + (fs_r_dst_decomp_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_decomp_prefixnegative_body_steps_successor. fs_h_dst_decomp_prefixnegative_body_steps_successor + S (fs_s_dst_decomp_prefixnegative_body_steps) = S ((S (S fs_i_dst_decomp_prefixnegative_body_steps)) * fs_v_dst_decomp_prefixnegative)) /\ exists fs_q_dst_decomp_prefixnegative_body_steps_successor. fs_u_dst_decomp_prefixnegative = fs_q_dst_decomp_prefixnegative_body_steps_successor * S ((S (S fs_i_dst_decomp_prefixnegative_body_steps)) * fs_v_dst_decomp_prefixnegative) + (fs_s_dst_decomp_prefixnegative_body_steps))) /\ fs_s_dst_decomp_prefixnegative_body_steps = fs_r_dst_decomp_prefixnegative_body_steps + fs_a_dst_decomp_prefixnegative_body_steps)))))) /\ (exists ge_balance_positive_decomp_prefixresult ge_balance_negative_decomp_prefixresult. (((((a) = 2 * (ge_balance_positive_decomp_prefixresult) /\ (ge_balance_negative_decomp_prefixresult) = 0) \/ exists ge_signed_half_decomp_prefixresultdecode. (((a) = 2 * ge_signed_half_decomp_prefixresultdecode + 1 /\ (ge_balance_positive_decomp_prefixresult) = 0) /\ (ge_balance_negative_decomp_prefixresult) = S ge_signed_half_decomp_prefixresultdecode))) /\ ((dst_positive_sum_decomp_prefix) + ge_balance_negative_decomp_prefixresult = (dst_negative_sum_decomp_prefix) + ge_balance_positive_decomp_prefixresult))))))))) /\ (((exists dst_positive_code_decomp_entry dst_positive_scale_decomp_entry dst_negative_code_decomp_entry dst_negative_scale_decomp_entry dst_positive_decomp_entry dst_negative_decomp_entry. (((F) = (((((dst_positive_code_decomp_entry) + (dst_positive_scale_decomp_entry)) * S ((dst_positive_code_decomp_entry) + (dst_positive_scale_decomp_entry)) + ((dst_positive_scale_decomp_entry) + (dst_positive_scale_decomp_entry))) + (((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) * S ((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) + ((dst_negative_scale_decomp_entry) + (dst_negative_scale_decomp_entry)))) * S ((((dst_positive_code_decomp_entry) + (dst_positive_scale_decomp_entry)) * S ((dst_positive_code_decomp_entry) + (dst_positive_scale_decomp_entry)) + ((dst_positive_scale_decomp_entry) + (dst_positive_scale_decomp_entry))) + (((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) * S ((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) + ((dst_negative_scale_decomp_entry) + (dst_negative_scale_decomp_entry)))) + ((((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) * S ((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) + ((dst_negative_scale_decomp_entry) + (dst_negative_scale_decomp_entry))) + (((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) * S ((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) + ((dst_negative_scale_decomp_entry) + (dst_negative_scale_decomp_entry)))))) /\ (((((exists ff_h_pvs_decomp_entrypositive. ff_h_pvs_decomp_entrypositive + S (dst_positive_decomp_entry) = S ((S (l)) * dst_positive_scale_decomp_entry)) /\ exists ff_q_pvs_decomp_entrypositive. dst_positive_code_decomp_entry = ff_q_pvs_decomp_entrypositive * S ((S (l)) * dst_positive_scale_decomp_entry) + (dst_positive_decomp_entry))) /\ (((((exists ff_h_pvs_decomp_entrynegative. ff_h_pvs_decomp_entrynegative + S (dst_negative_decomp_entry) = S ((S (l)) * dst_negative_scale_decomp_entry)) /\ exists ff_q_pvs_decomp_entrynegative. dst_negative_code_decomp_entry = ff_q_pvs_decomp_entrynegative * S ((S (l)) * dst_negative_scale_decomp_entry) + (dst_negative_decomp_entry))) /\ (exists ge_balance_positive_decomp_entryvalue ge_balance_negative_decomp_entryvalue. (((((b) = 2 * (ge_balance_positive_decomp_entryvalue) /\ (ge_balance_negative_decomp_entryvalue) = 0) \/ exists ge_signed_half_decomp_entryvaluedecode. (((b) = 2 * ge_signed_half_decomp_entryvaluedecode + 1 /\ (ge_balance_positive_decomp_entryvalue) = 0) /\ (ge_balance_negative_decomp_entryvalue) = S ge_signed_half_decomp_entryvaluedecode))) /\ ((dst_positive_decomp_entry) + ge_balance_negative_decomp_entryvalue = (dst_negative_decomp_entry) + ge_balance_positive_decomp_entryvalue))))))))) /\ (exists dsa_ap_decomp_add dsa_an_decomp_add dsa_bp_decomp_add dsa_bn_decomp_add dsa_cp_decomp_add dsa_cn_decomp_add. (((((a) = 2 * (dsa_ap_decomp_add) /\ (dsa_an_decomp_add) = 0) \/ exists ge_signed_half_decomp_addleft. (((a) = 2 * ge_signed_half_decomp_addleft + 1 /\ (dsa_ap_decomp_add) = 0) /\ (dsa_an_decomp_add) = S ge_signed_half_decomp_addleft))) /\ ((((((b) = 2 * (dsa_bp_decomp_add) /\ (dsa_bn_decomp_add) = 0) \/ exists ge_signed_half_decomp_addright. (((b) = 2 * ge_signed_half_decomp_addright + 1 /\ (dsa_bp_decomp_add) = 0) /\ (dsa_bn_decomp_add) = S ge_signed_half_decomp_addright))) /\ ((((((z) = 2 * (dsa_cp_decomp_add) /\ (dsa_cn_decomp_add) = 0) \/ exists ge_signed_half_decomp_addoutput. (((z) = 2 * ge_signed_half_decomp_addoutput + 1 /\ (dsa_cp_decomp_add) = 0) /\ (dsa_cn_decomp_add) = S ge_signed_half_decomp_addoutput))) /\ ((dsa_ap_decomp_add + dsa_bp_decomp_add) + dsa_cn_decomp_add = (dsa_an_decomp_add + dsa_bn_decomp_add) + dsa_cp_decomp_add))))))))))

forall F pb pc nb nc i. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> exists z. (exists dst_positive_code_lookup_result dst_positive_scale_lookup_result dst_negative_code_lookup_result dst_negative_scale_lookup_result dst_positive_lookup_result dst_negative_lookup_result. (((F) = (((((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) * S ((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) + ((dst_positive_scale_lookup_result) + (dst_positive_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))) * S ((((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) * S ((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) + ((dst_positive_scale_lookup_result) + (dst_positive_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))) + ((((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))))) /\ (((((exists ff_h_pvs_lookup_resultpositive. ff_h_pvs_lookup_resultpositive + S (dst_positive_lookup_result) = S ((S (i)) * dst_positive_scale_lookup_result)) /\ exists ff_q_pvs_lookup_resultpositive. dst_positive_code_lookup_result = ff_q_pvs_lookup_resultpositive * S ((S (i)) * dst_positive_scale_lookup_result) + (dst_positive_lookup_result))) /\ (((((exists ff_h_pvs_lookup_resultnegative. ff_h_pvs_lookup_resultnegative + S (dst_negative_lookup_result) = S ((S (i)) * dst_negative_scale_lookup_result)) /\ exists ff_q_pvs_lookup_resultnegative. dst_negative_code_lookup_result = ff_q_pvs_lookup_resultnegative * S ((S (i)) * dst_negative_scale_lookup_result) + (dst_negative_lookup_result))) /\ (exists ge_balance_positive_lookup_resultvalue ge_balance_negative_lookup_resultvalue. (((((z) = 2 * (ge_balance_positive_lookup_resultvalue) /\ (ge_balance_negative_lookup_resultvalue) = 0) \/ exists ge_signed_half_lookup_resultvaluedecode. (((z) = 2 * ge_signed_half_lookup_resultvaluedecode + 1 /\ (ge_balance_positive_lookup_resultvalue) = 0) /\ (ge_balance_negative_lookup_resultvalue) = S ge_signed_half_lookup_resultvaluedecode))) /\ ((dst_positive_lookup_result) + ge_balance_negative_lookup_resultvalue = (dst_negative_lookup_result) + ge_balance_positive_lookup_resultvalue)))))))))

forall pb pc nb nc r s l. exists qb qc mb mc. (((forall fms_i_datapositive fms_j_datapositive fms_v_datapositive. (exists fms_gap_datapositive. fms_gap_datapositive + S (fms_i_datapositive) = (l)) -> (((exists fs_h_fms_datapositive_index. fs_h_fms_datapositive_index + S (fms_j_datapositive) = S ((S (fms_i_datapositive)) * s)) /\ exists fs_q_fms_datapositive_index. r = fs_q_fms_datapositive_index * S ((S (fms_i_datapositive)) * s) + (fms_j_datapositive))) -> (((exists fs_h_fms_datapositive_source. fs_h_fms_datapositive_source + S (fms_v_datapositive) = S ((S (fms_j_datapositive)) * pc)) /\ exists fs_q_fms_datapositive_source. pb = fs_q_fms_datapositive_source * S ((S (fms_j_datapositive)) * pc) + (fms_v_datapositive))) -> (((exists fs_h_fms_datapositive_target. fs_h_fms_datapositive_target + S (fms_v_datapositive) = S ((S (fms_i_datapositive)) * qc)) /\ exists fs_q_fms_datapositive_target. qb = fs_q_fms_datapositive_target * S ((S (fms_i_datapositive)) * qc) + (fms_v_datapositive)))) /\ (forall fms_i_datanegative fms_j_datanegative fms_v_datanegative. (exists fms_gap_datanegative. fms_gap_datanegative + S (fms_i_datanegative) = (l)) -> (((exists fs_h_fms_datanegative_index. fs_h_fms_datanegative_index + S (fms_j_datanegative) = S ((S (fms_i_datanegative)) * s)) /\ exists fs_q_fms_datanegative_index. r = fs_q_fms_datanegative_index * S ((S (fms_i_datanegative)) * s) + (fms_j_datanegative))) -> (((exists fs_h_fms_datanegative_source. fs_h_fms_datanegative_source + S (fms_v_datanegative) = S ((S (fms_j_datanegative)) * nc)) /\ exists fs_q_fms_datanegative_source. nb = fs_q_fms_datanegative_source * S ((S (fms_j_datanegative)) * nc) + (fms_v_datanegative))) -> (((exists fs_h_fms_datanegative_target. fs_h_fms_datanegative_target + S (fms_v_datanegative) = S ((S (fms_i_datanegative)) * mc)) /\ exists fs_q_fms_datanegative_target. mb = fs_q_fms_datanegative_target * S ((S (fms_i_datanegative)) * mc) + (fms_v_datanegative))))))

forall F G pb pc nb nc qb qc mb mc r s l. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> ((G) = (((((qb) + (qc)) * S ((qb) + (qc)) + ((qc) + (qc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))) * S ((((qb) + (qc)) * S ((qb) + (qc)) + ((qc) + (qc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))) + ((((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))))) -> (((forall fms_i_component_datapositive fms_j_component_datapositive fms_v_component_datapositive. (exists fms_gap_component_datapositive. fms_gap_component_datapositive + S (fms_i_component_datapositive) = (l)) -> (((exists fs_h_fms_component_datapositive_index. fs_h_fms_component_datapositive_index + S (fms_j_component_datapositive) = S ((S (fms_i_component_datapositive)) * s)) /\ exists fs_q_fms_component_datapositive_index. r = fs_q_fms_component_datapositive_index * S ((S (fms_i_component_datapositive)) * s) + (fms_j_component_datapositive))) -> (((exists fs_h_fms_component_datapositive_source. fs_h_fms_component_datapositive_source + S (fms_v_component_datapositive) = S ((S (fms_j_component_datapositive)) * pc)) /\ exists fs_q_fms_component_datapositive_source. pb = fs_q_fms_component_datapositive_source * S ((S (fms_j_component_datapositive)) * pc) + (fms_v_component_datapositive))) -> (((exists fs_h_fms_component_datapositive_target. fs_h_fms_component_datapositive_target + S (fms_v_component_datapositive) = S ((S (fms_i_component_datapositive)) * qc)) /\ exists fs_q_fms_component_datapositive_target. qb = fs_q_fms_component_datapositive_target * S ((S (fms_i_component_datapositive)) * qc) + (fms_v_component_datapositive)))) /\ (forall fms_i_component_datanegative fms_j_component_datanegative fms_v_component_datanegative. (exists fms_gap_component_datanegative. fms_gap_component_datanegative + S (fms_i_component_datanegative) = (l)) -> (((exists fs_h_fms_component_datanegative_index. fs_h_fms_component_datanegative_index + S (fms_j_component_datanegative) = S ((S (fms_i_component_datanegative)) * s)) /\ exists fs_q_fms_component_datanegative_index. r = fs_q_fms_component_datanegative_index * S ((S (fms_i_component_datanegative)) * s) + (fms_j_component_datanegative))) -> (((exists fs_h_fms_component_datanegative_source. fs_h_fms_component_datanegative_source + S (fms_v_component_datanegative) = S ((S (fms_j_component_datanegative)) * nc)) /\ exists fs_q_fms_component_datanegative_source. nb = fs_q_fms_component_datanegative_source * S ((S (fms_j_component_datanegative)) * nc) + (fms_v_component_datanegative))) -> (((exists fs_h_fms_component_datanegative_target. fs_h_fms_component_datanegative_target + S (fms_v_component_datanegative) = S ((S (fms_i_component_datanegative)) * mc)) /\ exists fs_q_fms_component_datanegative_target. mb = fs_q_fms_component_datanegative_target * S ((S (fms_i_component_datanegative)) * mc) + (fms_v_component_datanegative)))))) -> (forall dsr_index_component_result dsr_image_component_result dsr_value_component_result. (exists pvs_gap_component_resultbound. pvs_gap_component_resultbound + S (dsr_index_component_result) = (l)) -> (((exists ff_h_pvs_component_resultmap. ff_h_pvs_component_resultmap + S (dsr_image_component_result) = S ((S (dsr_index_component_result)) * s)) /\ exists ff_q_pvs_component_resultmap. r = ff_q_pvs_component_resultmap * S ((S (dsr_index_component_result)) * s) + (dsr_image_component_result))) -> (exists dst_positive_code_component_resultsource dst_positive_scale_component_resultsource dst_negative_code_component_resultsource dst_negative_scale_component_resultsource dst_positive_component_resultsource dst_negative_component_resultsource. (((F) = (((((dst_positive_code_component_resultsource) + (dst_positive_scale_component_resultsource)) * S ((dst_positive_code_component_resultsource) + (dst_positive_scale_component_resultsource)) + ((dst_positive_scale_component_resultsource) + (dst_positive_scale_component_resultsource))) + (((dst_negative_code_component_resultsource) + (dst_negative_scale_component_resultsource)) * S ((dst_negative_code_component_resultsource) + (dst_negative_scale_component_resultsource)) + ((dst_negative_scale_component_resultsource) + (dst_negative_scale_component_resultsource)))) * S ((((dst_positive_code_component_resultsource) + (dst_positive_scale_component_resultsource)) * S ((dst_positive_code_component_resultsource) + (dst_positive_scale_component_resultsource)) + ((dst_positive_scale_component_resultsource) + (dst_positive_scale_component_resultsource))) + (((dst_negative_code_component_resultsource) + (dst_negative_scale_component_resultsource)) * S ((dst_negative_code_component_resultsource) + (dst_negative_scale_component_resultsource)) + ((dst_negative_scale_component_resultsource) + (dst_negative_scale_component_resultsource)))) + ((((dst_negative_code_component_resultsource) + (dst_negative_scale_component_resultsource)) * S ((dst_negative_code_component_resultsource) + (dst_negative_scale_component_resultsource)) + ((dst_negative_scale_component_resultsource) + (dst_negative_scale_component_resultsource))) + (((dst_negative_code_component_resultsource) + (dst_negative_scale_component_resultsource)) * S ((dst_negative_code_component_resultsource) + (dst_negative_scale_component_resultsource)) + ((dst_negative_scale_component_resultsource) + (dst_negative_scale_component_resultsource)))))) /\ (((((exists ff_h_pvs_component_resultsourcepositive. ff_h_pvs_component_resultsourcepositive + S (dst_positive_component_resultsource) = S ((S (dsr_image_component_result)) * dst_positive_scale_component_resultsource)) /\ exists ff_q_pvs_component_resultsourcepositive. dst_positive_code_component_resultsource = ff_q_pvs_component_resultsourcepositive * S ((S (dsr_image_component_result)) * dst_positive_scale_component_resultsource) + (dst_positive_component_resultsource))) /\ (((((exists ff_h_pvs_component_resultsourcenegative. ff_h_pvs_component_resultsourcenegative + S (dst_negative_component_resultsource) = S ((S (dsr_image_component_result)) * dst_negative_scale_component_resultsource)) /\ exists ff_q_pvs_component_resultsourcenegative. dst_negative_code_component_resultsource = ff_q_pvs_component_resultsourcenegative * S ((S (dsr_image_component_result)) * dst_negative_scale_component_resultsource) + (dst_negative_component_resultsource))) /\ (exists ge_balance_positive_component_resultsourcevalue ge_balance_negative_component_resultsourcevalue. (((((dsr_value_component_result) = 2 * (ge_balance_positive_component_resultsourcevalue) /\ (ge_balance_negative_component_resultsourcevalue) = 0) \/ exists ge_signed_half_component_resultsourcevaluedecode. (((dsr_value_component_result) = 2 * ge_signed_half_component_resultsourcevaluedecode + 1 /\ (ge_balance_positive_component_resultsourcevalue) = 0) /\ (ge_balance_negative_component_resultsourcevalue) = S ge_signed_half_component_resultsourcevaluedecode))) /\ ((dst_positive_component_resultsource) + ge_balance_negative_component_resultsourcevalue = (dst_negative_component_resultsource) + ge_balance_positive_component_resultsourcevalue))))))))) -> (exists dst_positive_code_component_resulttarget dst_positive_scale_component_resulttarget dst_negative_code_component_resulttarget dst_negative_scale_component_resulttarget dst_positive_component_resulttarget dst_negative_component_resulttarget. (((G) = (((((dst_positive_code_component_resulttarget) + (dst_positive_scale_component_resulttarget)) * S ((dst_positive_code_component_resulttarget) + (dst_positive_scale_component_resulttarget)) + ((dst_positive_scale_component_resulttarget) + (dst_positive_scale_component_resulttarget))) + (((dst_negative_code_component_resulttarget) + (dst_negative_scale_component_resulttarget)) * S ((dst_negative_code_component_resulttarget) + (dst_negative_scale_component_resulttarget)) + ((dst_negative_scale_component_resulttarget) + (dst_negative_scale_component_resulttarget)))) * S ((((dst_positive_code_component_resulttarget) + (dst_positive_scale_component_resulttarget)) * S ((dst_positive_code_component_resulttarget) + (dst_positive_scale_component_resulttarget)) + ((dst_positive_scale_component_resulttarget) + (dst_positive_scale_component_resulttarget))) + (((dst_negative_code_component_resulttarget) + (dst_negative_scale_component_resulttarget)) * S ((dst_negative_code_component_resulttarget) + (dst_negative_scale_component_resulttarget)) + ((dst_negative_scale_component_resulttarget) + (dst_negative_scale_component_resulttarget)))) + ((((dst_negative_code_component_resulttarget) + (dst_negative_scale_component_resulttarget)) * S ((dst_negative_code_component_resulttarget) + (dst_negative_scale_component_resulttarget)) + ((dst_negative_scale_component_resulttarget) + (dst_negative_scale_component_resulttarget))) + (((dst_negative_code_component_resulttarget) + (dst_negative_scale_component_resulttarget)) * S ((dst_negative_code_component_resulttarget) + (dst_negative_scale_component_resulttarget)) + ((dst_negative_scale_component_resulttarget) + (dst_negative_scale_component_resulttarget)))))) /\ (((((exists ff_h_pvs_component_resulttargetpositive. ff_h_pvs_component_resulttargetpositive + S (dst_positive_component_resulttarget) = S ((S (dsr_index_component_result)) * dst_positive_scale_component_resulttarget)) /\ exists ff_q_pvs_component_resulttargetpositive. dst_positive_code_component_resulttarget = ff_q_pvs_component_resulttargetpositive * S ((S (dsr_index_component_result)) * dst_positive_scale_component_resulttarget) + (dst_positive_component_resulttarget))) /\ (((((exists ff_h_pvs_component_resulttargetnegative. ff_h_pvs_component_resulttargetnegative + S (dst_negative_component_resulttarget) = S ((S (dsr_index_component_result)) * dst_negative_scale_component_resulttarget)) /\ exists ff_q_pvs_component_resulttargetnegative. dst_negative_code_component_resulttarget = ff_q_pvs_component_resulttargetnegative * S ((S (dsr_index_component_result)) * dst_negative_scale_component_resulttarget) + (dst_negative_component_resulttarget))) /\ (exists ge_balance_positive_component_resulttargetvalue ge_balance_negative_component_resulttargetvalue. (((((dsr_value_component_result) = 2 * (ge_balance_positive_component_resulttargetvalue) /\ (ge_balance_negative_component_resulttargetvalue) = 0) \/ exists ge_signed_half_component_resulttargetvaluedecode. (((dsr_value_component_result) = 2 * ge_signed_half_component_resulttargetvaluedecode + 1 /\ (ge_balance_positive_component_resulttargetvalue) = 0) /\ (ge_balance_negative_component_resulttargetvalue) = S ge_signed_half_component_resulttargetvaluedecode))) /\ ((dst_positive_component_resulttarget) + ge_balance_negative_component_resulttargetvalue = (dst_negative_component_resulttarget) + ge_balance_positive_component_resulttargetvalue))))))))))

forall N F r s l. (exists dst_positive_code_constructed_source dst_positive_scale_constructed_source dst_negative_code_constructed_source dst_negative_scale_constructed_source. (((F) = (((((dst_positive_code_constructed_source) + (dst_positive_scale_constructed_source)) * S ((dst_positive_code_constructed_source) + (dst_positive_scale_constructed_source)) + ((dst_positive_scale_constructed_source) + (dst_positive_scale_constructed_source))) + (((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) * S ((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) + ((dst_negative_scale_constructed_source) + (dst_negative_scale_constructed_source)))) * S ((((dst_positive_code_constructed_source) + (dst_positive_scale_constructed_source)) * S ((dst_positive_code_constructed_source) + (dst_positive_scale_constructed_source)) + ((dst_positive_scale_constructed_source) + (dst_positive_scale_constructed_source))) + (((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) * S ((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) + ((dst_negative_scale_constructed_source) + (dst_negative_scale_constructed_source)))) + ((((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) * S ((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) + ((dst_negative_scale_constructed_source) + (dst_negative_scale_constructed_source))) + (((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) * S ((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) + ((dst_negative_scale_constructed_source) + (dst_negative_scale_constructed_source)))))) /\ (forall dst_index_constructed_source. (exists pvs_le_gap_constructed_sourcedomain. pvs_le_gap_constructed_sourcedomain + (dst_index_constructed_source) = (N)) -> exists dst_positive_constructed_source dst_negative_constructed_source dst_value_constructed_source. ((((exists ff_h_pvs_constructed_sourceentrypositive. ff_h_pvs_constructed_sourceentrypositive + S (dst_positive_constructed_source) = S ((S (dst_index_constructed_source)) * dst_positive_scale_constructed_source)) /\ exists ff_q_pvs_constructed_sourceentrypositive. dst_positive_code_constructed_source = ff_q_pvs_constructed_sourceentrypositive * S ((S (dst_index_constructed_source)) * dst_positive_scale_constructed_source) + (dst_positive_constructed_source))) /\ (((((exists ff_h_pvs_constructed_sourceentrynegative. ff_h_pvs_constructed_sourceentrynegative + S (dst_negative_constructed_source) = S ((S (dst_index_constructed_source)) * dst_negative_scale_constructed_source)) /\ exists ff_q_pvs_constructed_sourceentrynegative. dst_negative_code_constructed_source = ff_q_pvs_constructed_sourceentrynegative * S ((S (dst_index_constructed_source)) * dst_negative_scale_constructed_source) + (dst_negative_constructed_source))) /\ (exists ge_balance_positive_constructed_sourceentryvalue ge_balance_negative_constructed_sourceentryvalue. (((((dst_value_constructed_source) = 2 * (ge_balance_positive_constructed_sourceentryvalue) /\ (ge_balance_negative_constructed_sourceentryvalue) = 0) \/ exists ge_signed_half_constructed_sourceentryvaluedecode. (((dst_value_constructed_source) = 2 * ge_signed_half_constructed_sourceentryvaluedecode + 1 /\ (ge_balance_positive_constructed_sourceentryvalue) = 0) /\ (ge_balance_negative_constructed_sourceentryvalue) = S ge_signed_half_constructed_sourceentryvaluedecode))) /\ ((dst_positive_constructed_source) + ge_balance_negative_constructed_sourceentryvalue = (dst_negative_constructed_source) + ge_balance_positive_constructed_sourceentryvalue))))))))) -> exists G. (exists dst_positive_code_constructed_target dst_positive_scale_constructed_target dst_negative_code_constructed_target dst_negative_scale_constructed_target. (((G) = (((((dst_positive_code_constructed_target) + (dst_positive_scale_constructed_target)) * S ((dst_positive_code_constructed_target) + (dst_positive_scale_constructed_target)) + ((dst_positive_scale_constructed_target) + (dst_positive_scale_constructed_target))) + (((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) * S ((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) + ((dst_negative_scale_constructed_target) + (dst_negative_scale_constructed_target)))) * S ((((dst_positive_code_constructed_target) + (dst_positive_scale_constructed_target)) * S ((dst_positive_code_constructed_target) + (dst_positive_scale_constructed_target)) + ((dst_positive_scale_constructed_target) + (dst_positive_scale_constructed_target))) + (((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) * S ((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) + ((dst_negative_scale_constructed_target) + (dst_negative_scale_constructed_target)))) + ((((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) * S ((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) + ((dst_negative_scale_constructed_target) + (dst_negative_scale_constructed_target))) + (((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) * S ((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) + ((dst_negative_scale_constructed_target) + (dst_negative_scale_constructed_target)))))) /\ (forall dst_index_constructed_target. (exists pvs_le_gap_constructed_targetdomain. pvs_le_gap_constructed_targetdomain + (dst_index_constructed_target) = (l)) -> exists dst_positive_constructed_target dst_negative_constructed_target dst_value_constructed_target. ((((exists ff_h_pvs_constructed_targetentrypositive. ff_h_pvs_constructed_targetentrypositive + S (dst_positive_constructed_target) = S ((S (dst_index_constructed_target)) * dst_positive_scale_constructed_target)) /\ exists ff_q_pvs_constructed_targetentrypositive. dst_positive_code_constructed_target = ff_q_pvs_constructed_targetentrypositive * S ((S (dst_index_constructed_target)) * dst_positive_scale_constructed_target) + (dst_positive_constructed_target))) /\ (((((exists ff_h_pvs_constructed_targetentrynegative. ff_h_pvs_constructed_targetentrynegative + S (dst_negative_constructed_target) = S ((S (dst_index_constructed_target)) * dst_negative_scale_constructed_target)) /\ exists ff_q_pvs_constructed_targetentrynegative. dst_negative_code_constructed_target = ff_q_pvs_constructed_targetentrynegative * S ((S (dst_index_constructed_target)) * dst_negative_scale_constructed_target) + (dst_negative_constructed_target))) /\ (exists ge_balance_positive_constructed_targetentryvalue ge_balance_negative_constructed_targetentryvalue. (((((dst_value_constructed_target) = 2 * (ge_balance_positive_constructed_targetentryvalue) /\ (ge_balance_negative_constructed_targetentryvalue) = 0) \/ exists ge_signed_half_constructed_targetentryvaluedecode. (((dst_value_constructed_target) = 2 * ge_signed_half_constructed_targetentryvaluedecode + 1 /\ (ge_balance_positive_constructed_targetentryvalue) = 0) /\ (ge_balance_negative_constructed_targetentryvalue) = S ge_signed_half_constructed_targetentryvaluedecode))) /\ ((dst_positive_constructed_target) + ge_balance_negative_constructed_targetentryvalue = (dst_negative_constructed_target) + ge_balance_positive_constructed_targetentryvalue))))))))) /\ (forall dsr_index_constructed_reindex dsr_image_constructed_reindex dsr_value_constructed_reindex. (exists pvs_gap_constructed_reindexbound. pvs_gap_constructed_reindexbound + S (dsr_index_constructed_reindex) = (l)) -> (((exists ff_h_pvs_constructed_reindexmap. ff_h_pvs_constructed_reindexmap + S (dsr_image_constructed_reindex) = S ((S (dsr_index_constructed_reindex)) * s)) /\ exists ff_q_pvs_constructed_reindexmap. r = ff_q_pvs_constructed_reindexmap * S ((S (dsr_index_constructed_reindex)) * s) + (dsr_image_constructed_reindex))) -> (exists dst_positive_code_constructed_reindexsource dst_positive_scale_constructed_reindexsource dst_negative_code_constructed_reindexsource dst_negative_scale_constructed_reindexsource dst_positive_constructed_reindexsource dst_negative_constructed_reindexsource. (((F) = (((((dst_positive_code_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource)) * S ((dst_positive_code_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource)) + ((dst_positive_scale_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource))) + (((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) * S ((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) + ((dst_negative_scale_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)))) * S ((((dst_positive_code_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource)) * S ((dst_positive_code_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource)) + ((dst_positive_scale_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource))) + (((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) * S ((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) + ((dst_negative_scale_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)))) + ((((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) * S ((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) + ((dst_negative_scale_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource))) + (((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) * S ((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) + ((dst_negative_scale_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)))))) /\ (((((exists ff_h_pvs_constructed_reindexsourcepositive. ff_h_pvs_constructed_reindexsourcepositive + S (dst_positive_constructed_reindexsource) = S ((S (dsr_image_constructed_reindex)) * dst_positive_scale_constructed_reindexsource)) /\ exists ff_q_pvs_constructed_reindexsourcepositive. dst_positive_code_constructed_reindexsource = ff_q_pvs_constructed_reindexsourcepositive * S ((S (dsr_image_constructed_reindex)) * dst_positive_scale_constructed_reindexsource) + (dst_positive_constructed_reindexsource))) /\ (((((exists ff_h_pvs_constructed_reindexsourcenegative. ff_h_pvs_constructed_reindexsourcenegative + S (dst_negative_constructed_reindexsource) = S ((S (dsr_image_constructed_reindex)) * dst_negative_scale_constructed_reindexsource)) /\ exists ff_q_pvs_constructed_reindexsourcenegative. dst_negative_code_constructed_reindexsource = ff_q_pvs_constructed_reindexsourcenegative * S ((S (dsr_image_constructed_reindex)) * dst_negative_scale_constructed_reindexsource) + (dst_negative_constructed_reindexsource))) /\ (exists ge_balance_positive_constructed_reindexsourcevalue ge_balance_negative_constructed_reindexsourcevalue. (((((dsr_value_constructed_reindex) = 2 * (ge_balance_positive_constructed_reindexsourcevalue) /\ (ge_balance_negative_constructed_reindexsourcevalue) = 0) \/ exists ge_signed_half_constructed_reindexsourcevaluedecode. (((dsr_value_constructed_reindex) = 2 * ge_signed_half_constructed_reindexsourcevaluedecode + 1 /\ (ge_balance_positive_constructed_reindexsourcevalue) = 0) /\ (ge_balance_negative_constructed_reindexsourcevalue) = S ge_signed_half_constructed_reindexsourcevaluedecode))) /\ ((dst_positive_constructed_reindexsource) + ge_balance_negative_constructed_reindexsourcevalue = (dst_negative_constructed_reindexsource) + ge_balance_positive_constructed_reindexsourcevalue))))))))) -> (exists dst_positive_code_constructed_reindextarget dst_positive_scale_constructed_reindextarget dst_negative_code_constructed_reindextarget dst_negative_scale_constructed_reindextarget dst_positive_constructed_reindextarget dst_negative_constructed_reindextarget. (((G) = (((((dst_positive_code_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget)) * S ((dst_positive_code_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget)) + ((dst_positive_scale_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget))) + (((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) * S ((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) + ((dst_negative_scale_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)))) * S ((((dst_positive_code_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget)) * S ((dst_positive_code_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget)) + ((dst_positive_scale_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget))) + (((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) * S ((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) + ((dst_negative_scale_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)))) + ((((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) * S ((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) + ((dst_negative_scale_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget))) + (((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) * S ((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) + ((dst_negative_scale_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)))))) /\ (((((exists ff_h_pvs_constructed_reindextargetpositive. ff_h_pvs_constructed_reindextargetpositive + S (dst_positive_constructed_reindextarget) = S ((S (dsr_index_constructed_reindex)) * dst_positive_scale_constructed_reindextarget)) /\ exists ff_q_pvs_constructed_reindextargetpositive. dst_positive_code_constructed_reindextarget = ff_q_pvs_constructed_reindextargetpositive * S ((S (dsr_index_constructed_reindex)) * dst_positive_scale_constructed_reindextarget) + (dst_positive_constructed_reindextarget))) /\ (((((exists ff_h_pvs_constructed_reindextargetnegative. ff_h_pvs_constructed_reindextargetnegative + S (dst_negative_constructed_reindextarget) = S ((S (dsr_index_constructed_reindex)) * dst_negative_scale_constructed_reindextarget)) /\ exists ff_q_pvs_constructed_reindextargetnegative. dst_negative_code_constructed_reindextarget = ff_q_pvs_constructed_reindextargetnegative * S ((S (dsr_index_constructed_reindex)) * dst_negative_scale_constructed_reindextarget) + (dst_negative_constructed_reindextarget))) /\ (exists ge_balance_positive_constructed_reindextargetvalue ge_balance_negative_constructed_reindextargetvalue. (((((dsr_value_constructed_reindex) = 2 * (ge_balance_positive_constructed_reindextargetvalue) /\ (ge_balance_negative_constructed_reindextargetvalue) = 0) \/ exists ge_signed_half_constructed_reindextargetvaluedecode. (((dsr_value_constructed_reindex) = 2 * ge_signed_half_constructed_reindextargetvaluedecode + 1 /\ (ge_balance_positive_constructed_reindextargetvalue) = 0) /\ (ge_balance_negative_constructed_reindextargetvalue) = S ge_signed_half_constructed_reindextargetvaluedecode))) /\ ((dst_positive_constructed_reindextarget) + ge_balance_negative_constructed_reindextargetvalue = (dst_negative_constructed_reindextarget) + ge_balance_positive_constructed_reindextargetvalue))))))))))

forall F G H pb pc nb nc r s l. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (forall dsr_index_functional_first dsr_image_functional_first dsr_value_functional_first. (exists pvs_gap_functional_firstbound. pvs_gap_functional_firstbound + S (dsr_index_functional_first) = (l)) -> (((exists ff_h_pvs_functional_firstmap. ff_h_pvs_functional_firstmap + S (dsr_image_functional_first) = S ((S (dsr_index_functional_first)) * s)) /\ exists ff_q_pvs_functional_firstmap. r = ff_q_pvs_functional_firstmap * S ((S (dsr_index_functional_first)) * s) + (dsr_image_functional_first))) -> (exists dst_positive_code_functional_firstsource dst_positive_scale_functional_firstsource dst_negative_code_functional_firstsource dst_negative_scale_functional_firstsource dst_positive_functional_firstsource dst_negative_functional_firstsource. (((F) = (((((dst_positive_code_functional_firstsource) + (dst_positive_scale_functional_firstsource)) * S ((dst_positive_code_functional_firstsource) + (dst_positive_scale_functional_firstsource)) + ((dst_positive_scale_functional_firstsource) + (dst_positive_scale_functional_firstsource))) + (((dst_negative_code_functional_firstsource) + (dst_negative_scale_functional_firstsource)) * S ((dst_negative_code_functional_firstsource) + (dst_negative_scale_functional_firstsource)) + ((dst_negative_scale_functional_firstsource) + (dst_negative_scale_functional_firstsource)))) * S ((((dst_positive_code_functional_firstsource) + (dst_positive_scale_functional_firstsource)) * S ((dst_positive_code_functional_firstsource) + (dst_positive_scale_functional_firstsource)) + ((dst_positive_scale_functional_firstsource) + (dst_positive_scale_functional_firstsource))) + (((dst_negative_code_functional_firstsource) + (dst_negative_scale_functional_firstsource)) * S ((dst_negative_code_functional_firstsource) + (dst_negative_scale_functional_firstsource)) + ((dst_negative_scale_functional_firstsource) + (dst_negative_scale_functional_firstsource)))) + ((((dst_negative_code_functional_firstsource) + (dst_negative_scale_functional_firstsource)) * S ((dst_negative_code_functional_firstsource) + (dst_negative_scale_functional_firstsource)) + ((dst_negative_scale_functional_firstsource) + (dst_negative_scale_functional_firstsource))) + (((dst_negative_code_functional_firstsource) + (dst_negative_scale_functional_firstsource)) * S ((dst_negative_code_functional_firstsource) + (dst_negative_scale_functional_firstsource)) + ((dst_negative_scale_functional_firstsource) + (dst_negative_scale_functional_firstsource)))))) /\ (((((exists ff_h_pvs_functional_firstsourcepositive. ff_h_pvs_functional_firstsourcepositive + S (dst_positive_functional_firstsource) = S ((S (dsr_image_functional_first)) * dst_positive_scale_functional_firstsource)) /\ exists ff_q_pvs_functional_firstsourcepositive. dst_positive_code_functional_firstsource = ff_q_pvs_functional_firstsourcepositive * S ((S (dsr_image_functional_first)) * dst_positive_scale_functional_firstsource) + (dst_positive_functional_firstsource))) /\ (((((exists ff_h_pvs_functional_firstsourcenegative. ff_h_pvs_functional_firstsourcenegative + S (dst_negative_functional_firstsource) = S ((S (dsr_image_functional_first)) * dst_negative_scale_functional_firstsource)) /\ exists ff_q_pvs_functional_firstsourcenegative. dst_negative_code_functional_firstsource = ff_q_pvs_functional_firstsourcenegative * S ((S (dsr_image_functional_first)) * dst_negative_scale_functional_firstsource) + (dst_negative_functional_firstsource))) /\ (exists ge_balance_positive_functional_firstsourcevalue ge_balance_negative_functional_firstsourcevalue. (((((dsr_value_functional_first) = 2 * (ge_balance_positive_functional_firstsourcevalue) /\ (ge_balance_negative_functional_firstsourcevalue) = 0) \/ exists ge_signed_half_functional_firstsourcevaluedecode. (((dsr_value_functional_first) = 2 * ge_signed_half_functional_firstsourcevaluedecode + 1 /\ (ge_balance_positive_functional_firstsourcevalue) = 0) /\ (ge_balance_negative_functional_firstsourcevalue) = S ge_signed_half_functional_firstsourcevaluedecode))) /\ ((dst_positive_functional_firstsource) + ge_balance_negative_functional_firstsourcevalue = (dst_negative_functional_firstsource) + ge_balance_positive_functional_firstsourcevalue))))))))) -> (exists dst_positive_code_functional_firsttarget dst_positive_scale_functional_firsttarget dst_negative_code_functional_firsttarget dst_negative_scale_functional_firsttarget dst_positive_functional_firsttarget dst_negative_functional_firsttarget. (((G) = (((((dst_positive_code_functional_firsttarget) + (dst_positive_scale_functional_firsttarget)) * S ((dst_positive_code_functional_firsttarget) + (dst_positive_scale_functional_firsttarget)) + ((dst_positive_scale_functional_firsttarget) + (dst_positive_scale_functional_firsttarget))) + (((dst_negative_code_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)) * S ((dst_negative_code_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)) + ((dst_negative_scale_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)))) * S ((((dst_positive_code_functional_firsttarget) + (dst_positive_scale_functional_firsttarget)) * S ((dst_positive_code_functional_firsttarget) + (dst_positive_scale_functional_firsttarget)) + ((dst_positive_scale_functional_firsttarget) + (dst_positive_scale_functional_firsttarget))) + (((dst_negative_code_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)) * S ((dst_negative_code_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)) + ((dst_negative_scale_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)))) + ((((dst_negative_code_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)) * S ((dst_negative_code_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)) + ((dst_negative_scale_functional_firsttarget) + (dst_negative_scale_functional_firsttarget))) + (((dst_negative_code_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)) * S ((dst_negative_code_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)) + ((dst_negative_scale_functional_firsttarget) + (dst_negative_scale_functional_firsttarget)))))) /\ (((((exists ff_h_pvs_functional_firsttargetpositive. ff_h_pvs_functional_firsttargetpositive + S (dst_positive_functional_firsttarget) = S ((S (dsr_index_functional_first)) * dst_positive_scale_functional_firsttarget)) /\ exists ff_q_pvs_functional_firsttargetpositive. dst_positive_code_functional_firsttarget = ff_q_pvs_functional_firsttargetpositive * S ((S (dsr_index_functional_first)) * dst_positive_scale_functional_firsttarget) + (dst_positive_functional_firsttarget))) /\ (((((exists ff_h_pvs_functional_firsttargetnegative. ff_h_pvs_functional_firsttargetnegative + S (dst_negative_functional_firsttarget) = S ((S (dsr_index_functional_first)) * dst_negative_scale_functional_firsttarget)) /\ exists ff_q_pvs_functional_firsttargetnegative. dst_negative_code_functional_firsttarget = ff_q_pvs_functional_firsttargetnegative * S ((S (dsr_index_functional_first)) * dst_negative_scale_functional_firsttarget) + (dst_negative_functional_firsttarget))) /\ (exists ge_balance_positive_functional_firsttargetvalue ge_balance_negative_functional_firsttargetvalue. (((((dsr_value_functional_first) = 2 * (ge_balance_positive_functional_firsttargetvalue) /\ (ge_balance_negative_functional_firsttargetvalue) = 0) \/ exists ge_signed_half_functional_firsttargetvaluedecode. (((dsr_value_functional_first) = 2 * ge_signed_half_functional_firsttargetvaluedecode + 1 /\ (ge_balance_positive_functional_firsttargetvalue) = 0) /\ (ge_balance_negative_functional_firsttargetvalue) = S ge_signed_half_functional_firsttargetvaluedecode))) /\ ((dst_positive_functional_firsttarget) + ge_balance_negative_functional_firsttargetvalue = (dst_negative_functional_firsttarget) + ge_balance_positive_functional_firsttargetvalue)))))))))) -> (forall dsr_index_functional_second dsr_image_functional_second dsr_value_functional_second. (exists pvs_gap_functional_secondbound. pvs_gap_functional_secondbound + S (dsr_index_functional_second) = (l)) -> (((exists ff_h_pvs_functional_secondmap. ff_h_pvs_functional_secondmap + S (dsr_image_functional_second) = S ((S (dsr_index_functional_second)) * s)) /\ exists ff_q_pvs_functional_secondmap. r = ff_q_pvs_functional_secondmap * S ((S (dsr_index_functional_second)) * s) + (dsr_image_functional_second))) -> (exists dst_positive_code_functional_secondsource dst_positive_scale_functional_secondsource dst_negative_code_functional_secondsource dst_negative_scale_functional_secondsource dst_positive_functional_secondsource dst_negative_functional_secondsource. (((F) = (((((dst_positive_code_functional_secondsource) + (dst_positive_scale_functional_secondsource)) * S ((dst_positive_code_functional_secondsource) + (dst_positive_scale_functional_secondsource)) + ((dst_positive_scale_functional_secondsource) + (dst_positive_scale_functional_secondsource))) + (((dst_negative_code_functional_secondsource) + (dst_negative_scale_functional_secondsource)) * S ((dst_negative_code_functional_secondsource) + (dst_negative_scale_functional_secondsource)) + ((dst_negative_scale_functional_secondsource) + (dst_negative_scale_functional_secondsource)))) * S ((((dst_positive_code_functional_secondsource) + (dst_positive_scale_functional_secondsource)) * S ((dst_positive_code_functional_secondsource) + (dst_positive_scale_functional_secondsource)) + ((dst_positive_scale_functional_secondsource) + (dst_positive_scale_functional_secondsource))) + (((dst_negative_code_functional_secondsource) + (dst_negative_scale_functional_secondsource)) * S ((dst_negative_code_functional_secondsource) + (dst_negative_scale_functional_secondsource)) + ((dst_negative_scale_functional_secondsource) + (dst_negative_scale_functional_secondsource)))) + ((((dst_negative_code_functional_secondsource) + (dst_negative_scale_functional_secondsource)) * S ((dst_negative_code_functional_secondsource) + (dst_negative_scale_functional_secondsource)) + ((dst_negative_scale_functional_secondsource) + (dst_negative_scale_functional_secondsource))) + (((dst_negative_code_functional_secondsource) + (dst_negative_scale_functional_secondsource)) * S ((dst_negative_code_functional_secondsource) + (dst_negative_scale_functional_secondsource)) + ((dst_negative_scale_functional_secondsource) + (dst_negative_scale_functional_secondsource)))))) /\ (((((exists ff_h_pvs_functional_secondsourcepositive. ff_h_pvs_functional_secondsourcepositive + S (dst_positive_functional_secondsource) = S ((S (dsr_image_functional_second)) * dst_positive_scale_functional_secondsource)) /\ exists ff_q_pvs_functional_secondsourcepositive. dst_positive_code_functional_secondsource = ff_q_pvs_functional_secondsourcepositive * S ((S (dsr_image_functional_second)) * dst_positive_scale_functional_secondsource) + (dst_positive_functional_secondsource))) /\ (((((exists ff_h_pvs_functional_secondsourcenegative. ff_h_pvs_functional_secondsourcenegative + S (dst_negative_functional_secondsource) = S ((S (dsr_image_functional_second)) * dst_negative_scale_functional_secondsource)) /\ exists ff_q_pvs_functional_secondsourcenegative. dst_negative_code_functional_secondsource = ff_q_pvs_functional_secondsourcenegative * S ((S (dsr_image_functional_second)) * dst_negative_scale_functional_secondsource) + (dst_negative_functional_secondsource))) /\ (exists ge_balance_positive_functional_secondsourcevalue ge_balance_negative_functional_secondsourcevalue. (((((dsr_value_functional_second) = 2 * (ge_balance_positive_functional_secondsourcevalue) /\ (ge_balance_negative_functional_secondsourcevalue) = 0) \/ exists ge_signed_half_functional_secondsourcevaluedecode. (((dsr_value_functional_second) = 2 * ge_signed_half_functional_secondsourcevaluedecode + 1 /\ (ge_balance_positive_functional_secondsourcevalue) = 0) /\ (ge_balance_negative_functional_secondsourcevalue) = S ge_signed_half_functional_secondsourcevaluedecode))) /\ ((dst_positive_functional_secondsource) + ge_balance_negative_functional_secondsourcevalue = (dst_negative_functional_secondsource) + ge_balance_positive_functional_secondsourcevalue))))))))) -> (exists dst_positive_code_functional_secondtarget dst_positive_scale_functional_secondtarget dst_negative_code_functional_secondtarget dst_negative_scale_functional_secondtarget dst_positive_functional_secondtarget dst_negative_functional_secondtarget. (((H) = (((((dst_positive_code_functional_secondtarget) + (dst_positive_scale_functional_secondtarget)) * S ((dst_positive_code_functional_secondtarget) + (dst_positive_scale_functional_secondtarget)) + ((dst_positive_scale_functional_secondtarget) + (dst_positive_scale_functional_secondtarget))) + (((dst_negative_code_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)) * S ((dst_negative_code_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)) + ((dst_negative_scale_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)))) * S ((((dst_positive_code_functional_secondtarget) + (dst_positive_scale_functional_secondtarget)) * S ((dst_positive_code_functional_secondtarget) + (dst_positive_scale_functional_secondtarget)) + ((dst_positive_scale_functional_secondtarget) + (dst_positive_scale_functional_secondtarget))) + (((dst_negative_code_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)) * S ((dst_negative_code_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)) + ((dst_negative_scale_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)))) + ((((dst_negative_code_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)) * S ((dst_negative_code_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)) + ((dst_negative_scale_functional_secondtarget) + (dst_negative_scale_functional_secondtarget))) + (((dst_negative_code_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)) * S ((dst_negative_code_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)) + ((dst_negative_scale_functional_secondtarget) + (dst_negative_scale_functional_secondtarget)))))) /\ (((((exists ff_h_pvs_functional_secondtargetpositive. ff_h_pvs_functional_secondtargetpositive + S (dst_positive_functional_secondtarget) = S ((S (dsr_index_functional_second)) * dst_positive_scale_functional_secondtarget)) /\ exists ff_q_pvs_functional_secondtargetpositive. dst_positive_code_functional_secondtarget = ff_q_pvs_functional_secondtargetpositive * S ((S (dsr_index_functional_second)) * dst_positive_scale_functional_secondtarget) + (dst_positive_functional_secondtarget))) /\ (((((exists ff_h_pvs_functional_secondtargetnegative. ff_h_pvs_functional_secondtargetnegative + S (dst_negative_functional_secondtarget) = S ((S (dsr_index_functional_second)) * dst_negative_scale_functional_secondtarget)) /\ exists ff_q_pvs_functional_secondtargetnegative. dst_negative_code_functional_secondtarget = ff_q_pvs_functional_secondtargetnegative * S ((S (dsr_index_functional_second)) * dst_negative_scale_functional_secondtarget) + (dst_negative_functional_secondtarget))) /\ (exists ge_balance_positive_functional_secondtargetvalue ge_balance_negative_functional_secondtargetvalue. (((((dsr_value_functional_second) = 2 * (ge_balance_positive_functional_secondtargetvalue) /\ (ge_balance_negative_functional_secondtargetvalue) = 0) \/ exists ge_signed_half_functional_secondtargetvaluedecode. (((dsr_value_functional_second) = 2 * ge_signed_half_functional_secondtargetvaluedecode + 1 /\ (ge_balance_positive_functional_secondtargetvalue) = 0) /\ (ge_balance_negative_functional_secondtargetvalue) = S ge_signed_half_functional_secondtargetvaluedecode))) /\ ((dst_positive_functional_secondtarget) + ge_balance_negative_functional_secondtargetvalue = (dst_negative_functional_secondtarget) + ge_balance_positive_functional_secondtargetvalue)))))))))) -> (forall dst_index_functional_result dst_first_functional_result dst_second_functional_result. (exists pvs_gap_functional_resultbound. pvs_gap_functional_resultbound + S (dst_index_functional_result) = (l)) -> (exists dst_positive_code_functional_resultfirst dst_positive_scale_functional_resultfirst dst_negative_code_functional_resultfirst dst_negative_scale_functional_resultfirst dst_positive_functional_resultfirst dst_negative_functional_resultfirst. (((G) = (((((dst_positive_code_functional_resultfirst) + (dst_positive_scale_functional_resultfirst)) * S ((dst_positive_code_functional_resultfirst) + (dst_positive_scale_functional_resultfirst)) + ((dst_positive_scale_functional_resultfirst) + (dst_positive_scale_functional_resultfirst))) + (((dst_negative_code_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)) * S ((dst_negative_code_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)) + ((dst_negative_scale_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)))) * S ((((dst_positive_code_functional_resultfirst) + (dst_positive_scale_functional_resultfirst)) * S ((dst_positive_code_functional_resultfirst) + (dst_positive_scale_functional_resultfirst)) + ((dst_positive_scale_functional_resultfirst) + (dst_positive_scale_functional_resultfirst))) + (((dst_negative_code_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)) * S ((dst_negative_code_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)) + ((dst_negative_scale_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)))) + ((((dst_negative_code_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)) * S ((dst_negative_code_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)) + ((dst_negative_scale_functional_resultfirst) + (dst_negative_scale_functional_resultfirst))) + (((dst_negative_code_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)) * S ((dst_negative_code_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)) + ((dst_negative_scale_functional_resultfirst) + (dst_negative_scale_functional_resultfirst)))))) /\ (((((exists ff_h_pvs_functional_resultfirstpositive. ff_h_pvs_functional_resultfirstpositive + S (dst_positive_functional_resultfirst) = S ((S (dst_index_functional_result)) * dst_positive_scale_functional_resultfirst)) /\ exists ff_q_pvs_functional_resultfirstpositive. dst_positive_code_functional_resultfirst = ff_q_pvs_functional_resultfirstpositive * S ((S (dst_index_functional_result)) * dst_positive_scale_functional_resultfirst) + (dst_positive_functional_resultfirst))) /\ (((((exists ff_h_pvs_functional_resultfirstnegative. ff_h_pvs_functional_resultfirstnegative + S (dst_negative_functional_resultfirst) = S ((S (dst_index_functional_result)) * dst_negative_scale_functional_resultfirst)) /\ exists ff_q_pvs_functional_resultfirstnegative. dst_negative_code_functional_resultfirst = ff_q_pvs_functional_resultfirstnegative * S ((S (dst_index_functional_result)) * dst_negative_scale_functional_resultfirst) + (dst_negative_functional_resultfirst))) /\ (exists ge_balance_positive_functional_resultfirstvalue ge_balance_negative_functional_resultfirstvalue. (((((dst_first_functional_result) = 2 * (ge_balance_positive_functional_resultfirstvalue) /\ (ge_balance_negative_functional_resultfirstvalue) = 0) \/ exists ge_signed_half_functional_resultfirstvaluedecode. (((dst_first_functional_result) = 2 * ge_signed_half_functional_resultfirstvaluedecode + 1 /\ (ge_balance_positive_functional_resultfirstvalue) = 0) /\ (ge_balance_negative_functional_resultfirstvalue) = S ge_signed_half_functional_resultfirstvaluedecode))) /\ ((dst_positive_functional_resultfirst) + ge_balance_negative_functional_resultfirstvalue = (dst_negative_functional_resultfirst) + ge_balance_positive_functional_resultfirstvalue))))))))) -> (exists dst_positive_code_functional_resultsecond dst_positive_scale_functional_resultsecond dst_negative_code_functional_resultsecond dst_negative_scale_functional_resultsecond dst_positive_functional_resultsecond dst_negative_functional_resultsecond. (((H) = (((((dst_positive_code_functional_resultsecond) + (dst_positive_scale_functional_resultsecond)) * S ((dst_positive_code_functional_resultsecond) + (dst_positive_scale_functional_resultsecond)) + ((dst_positive_scale_functional_resultsecond) + (dst_positive_scale_functional_resultsecond))) + (((dst_negative_code_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)) * S ((dst_negative_code_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)) + ((dst_negative_scale_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)))) * S ((((dst_positive_code_functional_resultsecond) + (dst_positive_scale_functional_resultsecond)) * S ((dst_positive_code_functional_resultsecond) + (dst_positive_scale_functional_resultsecond)) + ((dst_positive_scale_functional_resultsecond) + (dst_positive_scale_functional_resultsecond))) + (((dst_negative_code_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)) * S ((dst_negative_code_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)) + ((dst_negative_scale_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)))) + ((((dst_negative_code_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)) * S ((dst_negative_code_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)) + ((dst_negative_scale_functional_resultsecond) + (dst_negative_scale_functional_resultsecond))) + (((dst_negative_code_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)) * S ((dst_negative_code_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)) + ((dst_negative_scale_functional_resultsecond) + (dst_negative_scale_functional_resultsecond)))))) /\ (((((exists ff_h_pvs_functional_resultsecondpositive. ff_h_pvs_functional_resultsecondpositive + S (dst_positive_functional_resultsecond) = S ((S (dst_index_functional_result)) * dst_positive_scale_functional_resultsecond)) /\ exists ff_q_pvs_functional_resultsecondpositive. dst_positive_code_functional_resultsecond = ff_q_pvs_functional_resultsecondpositive * S ((S (dst_index_functional_result)) * dst_positive_scale_functional_resultsecond) + (dst_positive_functional_resultsecond))) /\ (((((exists ff_h_pvs_functional_resultsecondnegative. ff_h_pvs_functional_resultsecondnegative + S (dst_negative_functional_resultsecond) = S ((S (dst_index_functional_result)) * dst_negative_scale_functional_resultsecond)) /\ exists ff_q_pvs_functional_resultsecondnegative. dst_negative_code_functional_resultsecond = ff_q_pvs_functional_resultsecondnegative * S ((S (dst_index_functional_result)) * dst_negative_scale_functional_resultsecond) + (dst_negative_functional_resultsecond))) /\ (exists ge_balance_positive_functional_resultsecondvalue ge_balance_negative_functional_resultsecondvalue. (((((dst_second_functional_result) = 2 * (ge_balance_positive_functional_resultsecondvalue) /\ (ge_balance_negative_functional_resultsecondvalue) = 0) \/ exists ge_signed_half_functional_resultsecondvaluedecode. (((dst_second_functional_result) = 2 * ge_signed_half_functional_resultsecondvaluedecode + 1 /\ (ge_balance_positive_functional_resultsecondvalue) = 0) /\ (ge_balance_negative_functional_resultsecondvalue) = S ge_signed_half_functional_resultsecondvaluedecode))) /\ ((dst_positive_functional_resultsecond) + ge_balance_negative_functional_resultsecondvalue = (dst_negative_functional_resultsecond) + ge_balance_positive_functional_resultsecondvalue))))))))) -> dst_first_functional_result = dst_second_functional_result)

forall F G pb pc nb nc qb qc mb mc r s l u v. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> ((G) = (((((qb) + (qc)) * S ((qb) + (qc)) + ((qc) + (qc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))) * S ((((qb) + (qc)) * S ((qb) + (qc)) + ((qc) + (qc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))) + ((((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))))) -> (forall pfp_i_sum_map_bounded. (exists pfp_gap_sum_map_boundedindex. pfp_gap_sum_map_boundedindex + S (pfp_i_sum_map_bounded) = (l)) -> exists pfp_a_sum_map_bounded. (((exists ff_h_pfp_sum_map_boundedentry. ff_h_pfp_sum_map_boundedentry + S (pfp_a_sum_map_bounded) = S ((S (pfp_i_sum_map_bounded)) * s)) /\ exists ff_q_pfp_sum_map_boundedentry. r = ff_q_pfp_sum_map_boundedentry * S ((S (pfp_i_sum_map_bounded)) * s) + (pfp_a_sum_map_bounded))) /\ (exists pfp_gap_sum_map_boundedvalue. pfp_gap_sum_map_boundedvalue + S (pfp_a_sum_map_bounded) = (l))) -> (forall pfp_i_sum_map_injective pfp_j_sum_map_injective pfp_a_sum_map_injective. (exists pfp_gap_sum_map_injectivefirst. pfp_gap_sum_map_injectivefirst + S (pfp_i_sum_map_injective) = (l)) -> (exists pfp_gap_sum_map_injectivesecond. pfp_gap_sum_map_injectivesecond + S (pfp_j_sum_map_injective) = (l)) -> (((exists ff_h_pfp_sum_map_injectiveleft. ff_h_pfp_sum_map_injectiveleft + S (pfp_a_sum_map_injective) = S ((S (pfp_i_sum_map_injective)) * s)) /\ exists ff_q_pfp_sum_map_injectiveleft. r = ff_q_pfp_sum_map_injectiveleft * S ((S (pfp_i_sum_map_injective)) * s) + (pfp_a_sum_map_injective))) -> (((exists ff_h_pfp_sum_map_injectiveright. ff_h_pfp_sum_map_injectiveright + S (pfp_a_sum_map_injective) = S ((S (pfp_j_sum_map_injective)) * s)) /\ exists ff_q_pfp_sum_map_injectiveright. r = ff_q_pfp_sum_map_injectiveright * S ((S (pfp_j_sum_map_injective)) * s) + (pfp_a_sum_map_injective))) -> pfp_i_sum_map_injective = pfp_j_sum_map_injective) -> (((forall fms_i_sum_component_compositionpositive fms_j_sum_component_compositionpositive fms_v_sum_component_compositionpositive. (exists fms_gap_sum_component_compositionpositive. fms_gap_sum_component_compositionpositive + S (fms_i_sum_component_compositionpositive) = (l)) -> (((exists fs_h_fms_sum_component_compositionpositive_index. fs_h_fms_sum_component_compositionpositive_index + S (fms_j_sum_component_compositionpositive) = S ((S (fms_i_sum_component_compositionpositive)) * s)) /\ exists fs_q_fms_sum_component_compositionpositive_index. r = fs_q_fms_sum_component_compositionpositive_index * S ((S (fms_i_sum_component_compositionpositive)) * s) + (fms_j_sum_component_compositionpositive))) -> (((exists fs_h_fms_sum_component_compositionpositive_source. fs_h_fms_sum_component_compositionpositive_source + S (fms_v_sum_component_compositionpositive) = S ((S (fms_j_sum_component_compositionpositive)) * pc)) /\ exists fs_q_fms_sum_component_compositionpositive_source. pb = fs_q_fms_sum_component_compositionpositive_source * S ((S (fms_j_sum_component_compositionpositive)) * pc) + (fms_v_sum_component_compositionpositive))) -> (((exists fs_h_fms_sum_component_compositionpositive_target. fs_h_fms_sum_component_compositionpositive_target + S (fms_v_sum_component_compositionpositive) = S ((S (fms_i_sum_component_compositionpositive)) * qc)) /\ exists fs_q_fms_sum_component_compositionpositive_target. qb = fs_q_fms_sum_component_compositionpositive_target * S ((S (fms_i_sum_component_compositionpositive)) * qc) + (fms_v_sum_component_compositionpositive)))) /\ (forall fms_i_sum_component_compositionnegative fms_j_sum_component_compositionnegative fms_v_sum_component_compositionnegative. (exists fms_gap_sum_component_compositionnegative. fms_gap_sum_component_compositionnegative + S (fms_i_sum_component_compositionnegative) = (l)) -> (((exists fs_h_fms_sum_component_compositionnegative_index. fs_h_fms_sum_component_compositionnegative_index + S (fms_j_sum_component_compositionnegative) = S ((S (fms_i_sum_component_compositionnegative)) * s)) /\ exists fs_q_fms_sum_component_compositionnegative_index. r = fs_q_fms_sum_component_compositionnegative_index * S ((S (fms_i_sum_component_compositionnegative)) * s) + (fms_j_sum_component_compositionnegative))) -> (((exists fs_h_fms_sum_component_compositionnegative_source. fs_h_fms_sum_component_compositionnegative_source + S (fms_v_sum_component_compositionnegative) = S ((S (fms_j_sum_component_compositionnegative)) * nc)) /\ exists fs_q_fms_sum_component_compositionnegative_source. nb = fs_q_fms_sum_component_compositionnegative_source * S ((S (fms_j_sum_component_compositionnegative)) * nc) + (fms_v_sum_component_compositionnegative))) -> (((exists fs_h_fms_sum_component_compositionnegative_target. fs_h_fms_sum_component_compositionnegative_target + S (fms_v_sum_component_compositionnegative) = S ((S (fms_i_sum_component_compositionnegative)) * mc)) /\ exists fs_q_fms_sum_component_compositionnegative_target. mb = fs_q_fms_sum_component_compositionnegative_target * S ((S (fms_i_sum_component_compositionnegative)) * mc) + (fms_v_sum_component_compositionnegative)))))) -> (exists dst_positive_code_sum_source dst_positive_scale_sum_source dst_negative_code_sum_source dst_negative_scale_sum_source dst_positive_sum_sum_source dst_negative_sum_sum_source. (((F) = (((((dst_positive_code_sum_source) + (dst_positive_scale_sum_source)) * S ((dst_positive_code_sum_source) + (dst_positive_scale_sum_source)) + ((dst_positive_scale_sum_source) + (dst_positive_scale_sum_source))) + (((dst_negative_code_sum_source) + (dst_negative_scale_sum_source)) * S ((dst_negative_code_sum_source) + (dst_negative_scale_sum_source)) + ((dst_negative_scale_sum_source) + (dst_negative_scale_sum_source)))) * S ((((dst_positive_code_sum_source) + (dst_positive_scale_sum_source)) * S ((dst_positive_code_sum_source) + (dst_positive_scale_sum_source)) + ((dst_positive_scale_sum_source) + (dst_positive_scale_sum_source))) + (((dst_negative_code_sum_source) + (dst_negative_scale_sum_source)) * S ((dst_negative_code_sum_source) + (dst_negative_scale_sum_source)) + ((dst_negative_scale_sum_source) + (dst_negative_scale_sum_source)))) + ((((dst_negative_code_sum_source) + (dst_negative_scale_sum_source)) * S ((dst_negative_code_sum_source) + (dst_negative_scale_sum_source)) + ((dst_negative_scale_sum_source) + (dst_negative_scale_sum_source))) + (((dst_negative_code_sum_source) + (dst_negative_scale_sum_source)) * S ((dst_negative_code_sum_source) + (dst_negative_scale_sum_source)) + ((dst_negative_scale_sum_source) + (dst_negative_scale_sum_source)))))) /\ (((exists fs_u_dst_sum_sourcepositive fs_v_dst_sum_sourcepositive. ((((exists fs_h_dst_sum_sourcepositive_body_start. fs_h_dst_sum_sourcepositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_sourcepositive)) /\ exists fs_q_dst_sum_sourcepositive_body_start. fs_u_dst_sum_sourcepositive = fs_q_dst_sum_sourcepositive_body_start * S ((S (0)) * fs_v_dst_sum_sourcepositive) + (0))) /\ ((((exists fs_h_dst_sum_sourcepositive_body_terminal. fs_h_dst_sum_sourcepositive_body_terminal + S (dst_positive_sum_sum_source) = S ((S (l)) * fs_v_dst_sum_sourcepositive)) /\ exists fs_q_dst_sum_sourcepositive_body_terminal. fs_u_dst_sum_sourcepositive = fs_q_dst_sum_sourcepositive_body_terminal * S ((S (l)) * fs_v_dst_sum_sourcepositive) + (dst_positive_sum_sum_source))) /\ forall fs_i_dst_sum_sourcepositive_body_steps. (exists fs_lt_dst_sum_sourcepositive_body_steps_bound. fs_lt_dst_sum_sourcepositive_body_steps_bound + S fs_i_dst_sum_sourcepositive_body_steps = l) -> exists fs_a_dst_sum_sourcepositive_body_steps fs_r_dst_sum_sourcepositive_body_steps fs_s_dst_sum_sourcepositive_body_steps. ((((exists fs_h_dst_sum_sourcepositive_body_steps_summand. fs_h_dst_sum_sourcepositive_body_steps_summand + S (fs_a_dst_sum_sourcepositive_body_steps) = S ((S (fs_i_dst_sum_sourcepositive_body_steps)) * dst_positive_scale_sum_source)) /\ exists fs_q_dst_sum_sourcepositive_body_steps_summand. dst_positive_code_sum_source = fs_q_dst_sum_sourcepositive_body_steps_summand * S ((S (fs_i_dst_sum_sourcepositive_body_steps)) * dst_positive_scale_sum_source) + (fs_a_dst_sum_sourcepositive_body_steps))) /\ ((((exists fs_h_dst_sum_sourcepositive_body_steps_partial. fs_h_dst_sum_sourcepositive_body_steps_partial + S (fs_r_dst_sum_sourcepositive_body_steps) = S ((S (fs_i_dst_sum_sourcepositive_body_steps)) * fs_v_dst_sum_sourcepositive)) /\ exists fs_q_dst_sum_sourcepositive_body_steps_partial. fs_u_dst_sum_sourcepositive = fs_q_dst_sum_sourcepositive_body_steps_partial * S ((S (fs_i_dst_sum_sourcepositive_body_steps)) * fs_v_dst_sum_sourcepositive) + (fs_r_dst_sum_sourcepositive_body_steps))) /\ ((((exists fs_h_dst_sum_sourcepositive_body_steps_successor. fs_h_dst_sum_sourcepositive_body_steps_successor + S (fs_s_dst_sum_sourcepositive_body_steps) = S ((S (S fs_i_dst_sum_sourcepositive_body_steps)) * fs_v_dst_sum_sourcepositive)) /\ exists fs_q_dst_sum_sourcepositive_body_steps_successor. fs_u_dst_sum_sourcepositive = fs_q_dst_sum_sourcepositive_body_steps_successor * S ((S (S fs_i_dst_sum_sourcepositive_body_steps)) * fs_v_dst_sum_sourcepositive) + (fs_s_dst_sum_sourcepositive_body_steps))) /\ fs_s_dst_sum_sourcepositive_body_steps = fs_r_dst_sum_sourcepositive_body_steps + fs_a_dst_sum_sourcepositive_body_steps)))))) /\ (((exists fs_u_dst_sum_sourcenegative fs_v_dst_sum_sourcenegative. ((((exists fs_h_dst_sum_sourcenegative_body_start. fs_h_dst_sum_sourcenegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_sourcenegative)) /\ exists fs_q_dst_sum_sourcenegative_body_start. fs_u_dst_sum_sourcenegative = fs_q_dst_sum_sourcenegative_body_start * S ((S (0)) * fs_v_dst_sum_sourcenegative) + (0))) /\ ((((exists fs_h_dst_sum_sourcenegative_body_terminal. fs_h_dst_sum_sourcenegative_body_terminal + S (dst_negative_sum_sum_source) = S ((S (l)) * fs_v_dst_sum_sourcenegative)) /\ exists fs_q_dst_sum_sourcenegative_body_terminal. fs_u_dst_sum_sourcenegative = fs_q_dst_sum_sourcenegative_body_terminal * S ((S (l)) * fs_v_dst_sum_sourcenegative) + (dst_negative_sum_sum_source))) /\ forall fs_i_dst_sum_sourcenegative_body_steps. (exists fs_lt_dst_sum_sourcenegative_body_steps_bound. fs_lt_dst_sum_sourcenegative_body_steps_bound + S fs_i_dst_sum_sourcenegative_body_steps = l) -> exists fs_a_dst_sum_sourcenegative_body_steps fs_r_dst_sum_sourcenegative_body_steps fs_s_dst_sum_sourcenegative_body_steps. ((((exists fs_h_dst_sum_sourcenegative_body_steps_summand. fs_h_dst_sum_sourcenegative_body_steps_summand + S (fs_a_dst_sum_sourcenegative_body_steps) = S ((S (fs_i_dst_sum_sourcenegative_body_steps)) * dst_negative_scale_sum_source)) /\ exists fs_q_dst_sum_sourcenegative_body_steps_summand. dst_negative_code_sum_source = fs_q_dst_sum_sourcenegative_body_steps_summand * S ((S (fs_i_dst_sum_sourcenegative_body_steps)) * dst_negative_scale_sum_source) + (fs_a_dst_sum_sourcenegative_body_steps))) /\ ((((exists fs_h_dst_sum_sourcenegative_body_steps_partial. fs_h_dst_sum_sourcenegative_body_steps_partial + S (fs_r_dst_sum_sourcenegative_body_steps) = S ((S (fs_i_dst_sum_sourcenegative_body_steps)) * fs_v_dst_sum_sourcenegative)) /\ exists fs_q_dst_sum_sourcenegative_body_steps_partial. fs_u_dst_sum_sourcenegative = fs_q_dst_sum_sourcenegative_body_steps_partial * S ((S (fs_i_dst_sum_sourcenegative_body_steps)) * fs_v_dst_sum_sourcenegative) + (fs_r_dst_sum_sourcenegative_body_steps))) /\ ((((exists fs_h_dst_sum_sourcenegative_body_steps_successor. fs_h_dst_sum_sourcenegative_body_steps_successor + S (fs_s_dst_sum_sourcenegative_body_steps) = S ((S (S fs_i_dst_sum_sourcenegative_body_steps)) * fs_v_dst_sum_sourcenegative)) /\ exists fs_q_dst_sum_sourcenegative_body_steps_successor. fs_u_dst_sum_sourcenegative = fs_q_dst_sum_sourcenegative_body_steps_successor * S ((S (S fs_i_dst_sum_sourcenegative_body_steps)) * fs_v_dst_sum_sourcenegative) + (fs_s_dst_sum_sourcenegative_body_steps))) /\ fs_s_dst_sum_sourcenegative_body_steps = fs_r_dst_sum_sourcenegative_body_steps + fs_a_dst_sum_sourcenegative_body_steps)))))) /\ (exists ge_balance_positive_sum_sourceresult ge_balance_negative_sum_sourceresult. (((((u) = 2 * (ge_balance_positive_sum_sourceresult) /\ (ge_balance_negative_sum_sourceresult) = 0) \/ exists ge_signed_half_sum_sourceresultdecode. (((u) = 2 * ge_signed_half_sum_sourceresultdecode + 1 /\ (ge_balance_positive_sum_sourceresult) = 0) /\ (ge_balance_negative_sum_sourceresult) = S ge_signed_half_sum_sourceresultdecode))) /\ ((dst_positive_sum_sum_source) + ge_balance_negative_sum_sourceresult = (dst_negative_sum_sum_source) + ge_balance_positive_sum_sourceresult))))))))) -> (exists dst_positive_code_sum_target dst_positive_scale_sum_target dst_negative_code_sum_target dst_negative_scale_sum_target dst_positive_sum_sum_target dst_negative_sum_sum_target. (((G) = (((((dst_positive_code_sum_target) + (dst_positive_scale_sum_target)) * S ((dst_positive_code_sum_target) + (dst_positive_scale_sum_target)) + ((dst_positive_scale_sum_target) + (dst_positive_scale_sum_target))) + (((dst_negative_code_sum_target) + (dst_negative_scale_sum_target)) * S ((dst_negative_code_sum_target) + (dst_negative_scale_sum_target)) + ((dst_negative_scale_sum_target) + (dst_negative_scale_sum_target)))) * S ((((dst_positive_code_sum_target) + (dst_positive_scale_sum_target)) * S ((dst_positive_code_sum_target) + (dst_positive_scale_sum_target)) + ((dst_positive_scale_sum_target) + (dst_positive_scale_sum_target))) + (((dst_negative_code_sum_target) + (dst_negative_scale_sum_target)) * S ((dst_negative_code_sum_target) + (dst_negative_scale_sum_target)) + ((dst_negative_scale_sum_target) + (dst_negative_scale_sum_target)))) + ((((dst_negative_code_sum_target) + (dst_negative_scale_sum_target)) * S ((dst_negative_code_sum_target) + (dst_negative_scale_sum_target)) + ((dst_negative_scale_sum_target) + (dst_negative_scale_sum_target))) + (((dst_negative_code_sum_target) + (dst_negative_scale_sum_target)) * S ((dst_negative_code_sum_target) + (dst_negative_scale_sum_target)) + ((dst_negative_scale_sum_target) + (dst_negative_scale_sum_target)))))) /\ (((exists fs_u_dst_sum_targetpositive fs_v_dst_sum_targetpositive. ((((exists fs_h_dst_sum_targetpositive_body_start. fs_h_dst_sum_targetpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_targetpositive)) /\ exists fs_q_dst_sum_targetpositive_body_start. fs_u_dst_sum_targetpositive = fs_q_dst_sum_targetpositive_body_start * S ((S (0)) * fs_v_dst_sum_targetpositive) + (0))) /\ ((((exists fs_h_dst_sum_targetpositive_body_terminal. fs_h_dst_sum_targetpositive_body_terminal + S (dst_positive_sum_sum_target) = S ((S (l)) * fs_v_dst_sum_targetpositive)) /\ exists fs_q_dst_sum_targetpositive_body_terminal. fs_u_dst_sum_targetpositive = fs_q_dst_sum_targetpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_targetpositive) + (dst_positive_sum_sum_target))) /\ forall fs_i_dst_sum_targetpositive_body_steps. (exists fs_lt_dst_sum_targetpositive_body_steps_bound. fs_lt_dst_sum_targetpositive_body_steps_bound + S fs_i_dst_sum_targetpositive_body_steps = l) -> exists fs_a_dst_sum_targetpositive_body_steps fs_r_dst_sum_targetpositive_body_steps fs_s_dst_sum_targetpositive_body_steps. ((((exists fs_h_dst_sum_targetpositive_body_steps_summand. fs_h_dst_sum_targetpositive_body_steps_summand + S (fs_a_dst_sum_targetpositive_body_steps) = S ((S (fs_i_dst_sum_targetpositive_body_steps)) * dst_positive_scale_sum_target)) /\ exists fs_q_dst_sum_targetpositive_body_steps_summand. dst_positive_code_sum_target = fs_q_dst_sum_targetpositive_body_steps_summand * S ((S (fs_i_dst_sum_targetpositive_body_steps)) * dst_positive_scale_sum_target) + (fs_a_dst_sum_targetpositive_body_steps))) /\ ((((exists fs_h_dst_sum_targetpositive_body_steps_partial. fs_h_dst_sum_targetpositive_body_steps_partial + S (fs_r_dst_sum_targetpositive_body_steps) = S ((S (fs_i_dst_sum_targetpositive_body_steps)) * fs_v_dst_sum_targetpositive)) /\ exists fs_q_dst_sum_targetpositive_body_steps_partial. fs_u_dst_sum_targetpositive = fs_q_dst_sum_targetpositive_body_steps_partial * S ((S (fs_i_dst_sum_targetpositive_body_steps)) * fs_v_dst_sum_targetpositive) + (fs_r_dst_sum_targetpositive_body_steps))) /\ ((((exists fs_h_dst_sum_targetpositive_body_steps_successor. fs_h_dst_sum_targetpositive_body_steps_successor + S (fs_s_dst_sum_targetpositive_body_steps) = S ((S (S fs_i_dst_sum_targetpositive_body_steps)) * fs_v_dst_sum_targetpositive)) /\ exists fs_q_dst_sum_targetpositive_body_steps_successor. fs_u_dst_sum_targetpositive = fs_q_dst_sum_targetpositive_body_steps_successor * S ((S (S fs_i_dst_sum_targetpositive_body_steps)) * fs_v_dst_sum_targetpositive) + (fs_s_dst_sum_targetpositive_body_steps))) /\ fs_s_dst_sum_targetpositive_body_steps = fs_r_dst_sum_targetpositive_body_steps + fs_a_dst_sum_targetpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_targetnegative fs_v_dst_sum_targetnegative. ((((exists fs_h_dst_sum_targetnegative_body_start. fs_h_dst_sum_targetnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_targetnegative)) /\ exists fs_q_dst_sum_targetnegative_body_start. fs_u_dst_sum_targetnegative = fs_q_dst_sum_targetnegative_body_start * S ((S (0)) * fs_v_dst_sum_targetnegative) + (0))) /\ ((((exists fs_h_dst_sum_targetnegative_body_terminal. fs_h_dst_sum_targetnegative_body_terminal + S (dst_negative_sum_sum_target) = S ((S (l)) * fs_v_dst_sum_targetnegative)) /\ exists fs_q_dst_sum_targetnegative_body_terminal. fs_u_dst_sum_targetnegative = fs_q_dst_sum_targetnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_targetnegative) + (dst_negative_sum_sum_target))) /\ forall fs_i_dst_sum_targetnegative_body_steps. (exists fs_lt_dst_sum_targetnegative_body_steps_bound. fs_lt_dst_sum_targetnegative_body_steps_bound + S fs_i_dst_sum_targetnegative_body_steps = l) -> exists fs_a_dst_sum_targetnegative_body_steps fs_r_dst_sum_targetnegative_body_steps fs_s_dst_sum_targetnegative_body_steps. ((((exists fs_h_dst_sum_targetnegative_body_steps_summand. fs_h_dst_sum_targetnegative_body_steps_summand + S (fs_a_dst_sum_targetnegative_body_steps) = S ((S (fs_i_dst_sum_targetnegative_body_steps)) * dst_negative_scale_sum_target)) /\ exists fs_q_dst_sum_targetnegative_body_steps_summand. dst_negative_code_sum_target = fs_q_dst_sum_targetnegative_body_steps_summand * S ((S (fs_i_dst_sum_targetnegative_body_steps)) * dst_negative_scale_sum_target) + (fs_a_dst_sum_targetnegative_body_steps))) /\ ((((exists fs_h_dst_sum_targetnegative_body_steps_partial. fs_h_dst_sum_targetnegative_body_steps_partial + S (fs_r_dst_sum_targetnegative_body_steps) = S ((S (fs_i_dst_sum_targetnegative_body_steps)) * fs_v_dst_sum_targetnegative)) /\ exists fs_q_dst_sum_targetnegative_body_steps_partial. fs_u_dst_sum_targetnegative = fs_q_dst_sum_targetnegative_body_steps_partial * S ((S (fs_i_dst_sum_targetnegative_body_steps)) * fs_v_dst_sum_targetnegative) + (fs_r_dst_sum_targetnegative_body_steps))) /\ ((((exists fs_h_dst_sum_targetnegative_body_steps_successor. fs_h_dst_sum_targetnegative_body_steps_successor + S (fs_s_dst_sum_targetnegative_body_steps) = S ((S (S fs_i_dst_sum_targetnegative_body_steps)) * fs_v_dst_sum_targetnegative)) /\ exists fs_q_dst_sum_targetnegative_body_steps_successor. fs_u_dst_sum_targetnegative = fs_q_dst_sum_targetnegative_body_steps_successor * S ((S (S fs_i_dst_sum_targetnegative_body_steps)) * fs_v_dst_sum_targetnegative) + (fs_s_dst_sum_targetnegative_body_steps))) /\ fs_s_dst_sum_targetnegative_body_steps = fs_r_dst_sum_targetnegative_body_steps + fs_a_dst_sum_targetnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_targetresult ge_balance_negative_sum_targetresult. (((((v) = 2 * (ge_balance_positive_sum_targetresult) /\ (ge_balance_negative_sum_targetresult) = 0) \/ exists ge_signed_half_sum_targetresultdecode. (((v) = 2 * ge_signed_half_sum_targetresultdecode + 1 /\ (ge_balance_positive_sum_targetresult) = 0) /\ (ge_balance_negative_sum_targetresult) = S ge_signed_half_sum_targetresultdecode))) /\ ((dst_positive_sum_sum_target) + ge_balance_negative_sum_targetresult = (dst_negative_sum_sum_target) + ge_balance_positive_sum_targetresult))))))))) -> u = v

forall F G r s l u v. (forall pfp_i_permutation_bound. (exists pfp_gap_permutation_boundindex. pfp_gap_permutation_boundindex + S (pfp_i_permutation_bound) = (l)) -> exists pfp_a_permutation_bound. (((exists ff_h_pfp_permutation_boundentry. ff_h_pfp_permutation_boundentry + S (pfp_a_permutation_bound) = S ((S (pfp_i_permutation_bound)) * s)) /\ exists ff_q_pfp_permutation_boundentry. r = ff_q_pfp_permutation_boundentry * S ((S (pfp_i_permutation_bound)) * s) + (pfp_a_permutation_bound))) /\ (exists pfp_gap_permutation_boundvalue. pfp_gap_permutation_boundvalue + S (pfp_a_permutation_bound) = (l))) -> (forall pfp_i_permutation_injective pfp_j_permutation_injective pfp_a_permutation_injective. (exists pfp_gap_permutation_injectivefirst. pfp_gap_permutation_injectivefirst + S (pfp_i_permutation_injective) = (l)) -> (exists pfp_gap_permutation_injectivesecond. pfp_gap_permutation_injectivesecond + S (pfp_j_permutation_injective) = (l)) -> (((exists ff_h_pfp_permutation_injectiveleft. ff_h_pfp_permutation_injectiveleft + S (pfp_a_permutation_injective) = S ((S (pfp_i_permutation_injective)) * s)) /\ exists ff_q_pfp_permutation_injectiveleft. r = ff_q_pfp_permutation_injectiveleft * S ((S (pfp_i_permutation_injective)) * s) + (pfp_a_permutation_injective))) -> (((exists ff_h_pfp_permutation_injectiveright. ff_h_pfp_permutation_injectiveright + S (pfp_a_permutation_injective) = S ((S (pfp_j_permutation_injective)) * s)) /\ exists ff_q_pfp_permutation_injectiveright. r = ff_q_pfp_permutation_injectiveright * S ((S (pfp_j_permutation_injective)) * s) + (pfp_a_permutation_injective))) -> pfp_i_permutation_injective = pfp_j_permutation_injective) -> (forall dsr_index_permutation_pullback dsr_image_permutation_pullback dsr_value_permutation_pullback. (exists pvs_gap_permutation_pullbackbound. pvs_gap_permutation_pullbackbound + S (dsr_index_permutation_pullback) = (l)) -> (((exists ff_h_pvs_permutation_pullbackmap. ff_h_pvs_permutation_pullbackmap + S (dsr_image_permutation_pullback) = S ((S (dsr_index_permutation_pullback)) * s)) /\ exists ff_q_pvs_permutation_pullbackmap. r = ff_q_pvs_permutation_pullbackmap * S ((S (dsr_index_permutation_pullback)) * s) + (dsr_image_permutation_pullback))) -> (exists dst_positive_code_permutation_pullbacksource dst_positive_scale_permutation_pullbacksource dst_negative_code_permutation_pullbacksource dst_negative_scale_permutation_pullbacksource dst_positive_permutation_pullbacksource dst_negative_permutation_pullbacksource. (((F) = (((((dst_positive_code_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource)) * S ((dst_positive_code_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource)) + ((dst_positive_scale_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource))) + (((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) * S ((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) + ((dst_negative_scale_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)))) * S ((((dst_positive_code_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource)) * S ((dst_positive_code_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource)) + ((dst_positive_scale_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource))) + (((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) * S ((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) + ((dst_negative_scale_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)))) + ((((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) * S ((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) + ((dst_negative_scale_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource))) + (((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) * S ((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) + ((dst_negative_scale_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)))))) /\ (((((exists ff_h_pvs_permutation_pullbacksourcepositive. ff_h_pvs_permutation_pullbacksourcepositive + S (dst_positive_permutation_pullbacksource) = S ((S (dsr_image_permutation_pullback)) * dst_positive_scale_permutation_pullbacksource)) /\ exists ff_q_pvs_permutation_pullbacksourcepositive. dst_positive_code_permutation_pullbacksource = ff_q_pvs_permutation_pullbacksourcepositive * S ((S (dsr_image_permutation_pullback)) * dst_positive_scale_permutation_pullbacksource) + (dst_positive_permutation_pullbacksource))) /\ (((((exists ff_h_pvs_permutation_pullbacksourcenegative. ff_h_pvs_permutation_pullbacksourcenegative + S (dst_negative_permutation_pullbacksource) = S ((S (dsr_image_permutation_pullback)) * dst_negative_scale_permutation_pullbacksource)) /\ exists ff_q_pvs_permutation_pullbacksourcenegative. dst_negative_code_permutation_pullbacksource = ff_q_pvs_permutation_pullbacksourcenegative * S ((S (dsr_image_permutation_pullback)) * dst_negative_scale_permutation_pullbacksource) + (dst_negative_permutation_pullbacksource))) /\ (exists ge_balance_positive_permutation_pullbacksourcevalue ge_balance_negative_permutation_pullbacksourcevalue. (((((dsr_value_permutation_pullback) = 2 * (ge_balance_positive_permutation_pullbacksourcevalue) /\ (ge_balance_negative_permutation_pullbacksourcevalue) = 0) \/ exists ge_signed_half_permutation_pullbacksourcevaluedecode. (((dsr_value_permutation_pullback) = 2 * ge_signed_half_permutation_pullbacksourcevaluedecode + 1 /\ (ge_balance_positive_permutation_pullbacksourcevalue) = 0) /\ (ge_balance_negative_permutation_pullbacksourcevalue) = S ge_signed_half_permutation_pullbacksourcevaluedecode))) /\ ((dst_positive_permutation_pullbacksource) + ge_balance_negative_permutation_pullbacksourcevalue = (dst_negative_permutation_pullbacksource) + ge_balance_positive_permutation_pullbacksourcevalue))))))))) -> (exists dst_positive_code_permutation_pullbacktarget dst_positive_scale_permutation_pullbacktarget dst_negative_code_permutation_pullbacktarget dst_negative_scale_permutation_pullbacktarget dst_positive_permutation_pullbacktarget dst_negative_permutation_pullbacktarget. (((G) = (((((dst_positive_code_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget)) * S ((dst_positive_code_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget)) + ((dst_positive_scale_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget))) + (((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) * S ((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) + ((dst_negative_scale_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)))) * S ((((dst_positive_code_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget)) * S ((dst_positive_code_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget)) + ((dst_positive_scale_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget))) + (((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) * S ((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) + ((dst_negative_scale_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)))) + ((((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) * S ((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) + ((dst_negative_scale_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget))) + (((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) * S ((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) + ((dst_negative_scale_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)))))) /\ (((((exists ff_h_pvs_permutation_pullbacktargetpositive. ff_h_pvs_permutation_pullbacktargetpositive + S (dst_positive_permutation_pullbacktarget) = S ((S (dsr_index_permutation_pullback)) * dst_positive_scale_permutation_pullbacktarget)) /\ exists ff_q_pvs_permutation_pullbacktargetpositive. dst_positive_code_permutation_pullbacktarget = ff_q_pvs_permutation_pullbacktargetpositive * S ((S (dsr_index_permutation_pullback)) * dst_positive_scale_permutation_pullbacktarget) + (dst_positive_permutation_pullbacktarget))) /\ (((((exists ff_h_pvs_permutation_pullbacktargetnegative. ff_h_pvs_permutation_pullbacktargetnegative + S (dst_negative_permutation_pullbacktarget) = S ((S (dsr_index_permutation_pullback)) * dst_negative_scale_permutation_pullbacktarget)) /\ exists ff_q_pvs_permutation_pullbacktargetnegative. dst_negative_code_permutation_pullbacktarget = ff_q_pvs_permutation_pullbacktargetnegative * S ((S (dsr_index_permutation_pullback)) * dst_negative_scale_permutation_pullbacktarget) + (dst_negative_permutation_pullbacktarget))) /\ (exists ge_balance_positive_permutation_pullbacktargetvalue ge_balance_negative_permutation_pullbacktargetvalue. (((((dsr_value_permutation_pullback) = 2 * (ge_balance_positive_permutation_pullbacktargetvalue) /\ (ge_balance_negative_permutation_pullbacktargetvalue) = 0) \/ exists ge_signed_half_permutation_pullbacktargetvaluedecode. (((dsr_value_permutation_pullback) = 2 * ge_signed_half_permutation_pullbacktargetvaluedecode + 1 /\ (ge_balance_positive_permutation_pullbacktargetvalue) = 0) /\ (ge_balance_negative_permutation_pullbacktargetvalue) = S ge_signed_half_permutation_pullbacktargetvaluedecode))) /\ ((dst_positive_permutation_pullbacktarget) + ge_balance_negative_permutation_pullbacktargetvalue = (dst_negative_permutation_pullbacktarget) + ge_balance_positive_permutation_pullbacktargetvalue)))))))))) -> (exists dst_positive_code_permutation_source dst_positive_scale_permutation_source dst_negative_code_permutation_source dst_negative_scale_permutation_source dst_positive_sum_permutation_source dst_negative_sum_permutation_source. (((F) = (((((dst_positive_code_permutation_source) + (dst_positive_scale_permutation_source)) * S ((dst_positive_code_permutation_source) + (dst_positive_scale_permutation_source)) + ((dst_positive_scale_permutation_source) + (dst_positive_scale_permutation_source))) + (((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) * S ((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) + ((dst_negative_scale_permutation_source) + (dst_negative_scale_permutation_source)))) * S ((((dst_positive_code_permutation_source) + (dst_positive_scale_permutation_source)) * S ((dst_positive_code_permutation_source) + (dst_positive_scale_permutation_source)) + ((dst_positive_scale_permutation_source) + (dst_positive_scale_permutation_source))) + (((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) * S ((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) + ((dst_negative_scale_permutation_source) + (dst_negative_scale_permutation_source)))) + ((((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) * S ((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) + ((dst_negative_scale_permutation_source) + (dst_negative_scale_permutation_source))) + (((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) * S ((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) + ((dst_negative_scale_permutation_source) + (dst_negative_scale_permutation_source)))))) /\ (((exists fs_u_dst_permutation_sourcepositive fs_v_dst_permutation_sourcepositive. ((((exists fs_h_dst_permutation_sourcepositive_body_start. fs_h_dst_permutation_sourcepositive_body_start + S (0) = S ((S (0)) * fs_v_dst_permutation_sourcepositive)) /\ exists fs_q_dst_permutation_sourcepositive_body_start. fs_u_dst_permutation_sourcepositive = fs_q_dst_permutation_sourcepositive_body_start * S ((S (0)) * fs_v_dst_permutation_sourcepositive) + (0))) /\ ((((exists fs_h_dst_permutation_sourcepositive_body_terminal. fs_h_dst_permutation_sourcepositive_body_terminal + S (dst_positive_sum_permutation_source) = S ((S (l)) * fs_v_dst_permutation_sourcepositive)) /\ exists fs_q_dst_permutation_sourcepositive_body_terminal. fs_u_dst_permutation_sourcepositive = fs_q_dst_permutation_sourcepositive_body_terminal * S ((S (l)) * fs_v_dst_permutation_sourcepositive) + (dst_positive_sum_permutation_source))) /\ forall fs_i_dst_permutation_sourcepositive_body_steps. (exists fs_lt_dst_permutation_sourcepositive_body_steps_bound. fs_lt_dst_permutation_sourcepositive_body_steps_bound + S fs_i_dst_permutation_sourcepositive_body_steps = l) -> exists fs_a_dst_permutation_sourcepositive_body_steps fs_r_dst_permutation_sourcepositive_body_steps fs_s_dst_permutation_sourcepositive_body_steps. ((((exists fs_h_dst_permutation_sourcepositive_body_steps_summand. fs_h_dst_permutation_sourcepositive_body_steps_summand + S (fs_a_dst_permutation_sourcepositive_body_steps) = S ((S (fs_i_dst_permutation_sourcepositive_body_steps)) * dst_positive_scale_permutation_source)) /\ exists fs_q_dst_permutation_sourcepositive_body_steps_summand. dst_positive_code_permutation_source = fs_q_dst_permutation_sourcepositive_body_steps_summand * S ((S (fs_i_dst_permutation_sourcepositive_body_steps)) * dst_positive_scale_permutation_source) + (fs_a_dst_permutation_sourcepositive_body_steps))) /\ ((((exists fs_h_dst_permutation_sourcepositive_body_steps_partial. fs_h_dst_permutation_sourcepositive_body_steps_partial + S (fs_r_dst_permutation_sourcepositive_body_steps) = S ((S (fs_i_dst_permutation_sourcepositive_body_steps)) * fs_v_dst_permutation_sourcepositive)) /\ exists fs_q_dst_permutation_sourcepositive_body_steps_partial. fs_u_dst_permutation_sourcepositive = fs_q_dst_permutation_sourcepositive_body_steps_partial * S ((S (fs_i_dst_permutation_sourcepositive_body_steps)) * fs_v_dst_permutation_sourcepositive) + (fs_r_dst_permutation_sourcepositive_body_steps))) /\ ((((exists fs_h_dst_permutation_sourcepositive_body_steps_successor. fs_h_dst_permutation_sourcepositive_body_steps_successor + S (fs_s_dst_permutation_sourcepositive_body_steps) = S ((S (S fs_i_dst_permutation_sourcepositive_body_steps)) * fs_v_dst_permutation_sourcepositive)) /\ exists fs_q_dst_permutation_sourcepositive_body_steps_successor. fs_u_dst_permutation_sourcepositive = fs_q_dst_permutation_sourcepositive_body_steps_successor * S ((S (S fs_i_dst_permutation_sourcepositive_body_steps)) * fs_v_dst_permutation_sourcepositive) + (fs_s_dst_permutation_sourcepositive_body_steps))) /\ fs_s_dst_permutation_sourcepositive_body_steps = fs_r_dst_permutation_sourcepositive_body_steps + fs_a_dst_permutation_sourcepositive_body_steps)))))) /\ (((exists fs_u_dst_permutation_sourcenegative fs_v_dst_permutation_sourcenegative. ((((exists fs_h_dst_permutation_sourcenegative_body_start. fs_h_dst_permutation_sourcenegative_body_start + S (0) = S ((S (0)) * fs_v_dst_permutation_sourcenegative)) /\ exists fs_q_dst_permutation_sourcenegative_body_start. fs_u_dst_permutation_sourcenegative = fs_q_dst_permutation_sourcenegative_body_start * S ((S (0)) * fs_v_dst_permutation_sourcenegative) + (0))) /\ ((((exists fs_h_dst_permutation_sourcenegative_body_terminal. fs_h_dst_permutation_sourcenegative_body_terminal + S (dst_negative_sum_permutation_source) = S ((S (l)) * fs_v_dst_permutation_sourcenegative)) /\ exists fs_q_dst_permutation_sourcenegative_body_terminal. fs_u_dst_permutation_sourcenegative = fs_q_dst_permutation_sourcenegative_body_terminal * S ((S (l)) * fs_v_dst_permutation_sourcenegative) + (dst_negative_sum_permutation_source))) /\ forall fs_i_dst_permutation_sourcenegative_body_steps. (exists fs_lt_dst_permutation_sourcenegative_body_steps_bound. fs_lt_dst_permutation_sourcenegative_body_steps_bound + S fs_i_dst_permutation_sourcenegative_body_steps = l) -> exists fs_a_dst_permutation_sourcenegative_body_steps fs_r_dst_permutation_sourcenegative_body_steps fs_s_dst_permutation_sourcenegative_body_steps. ((((exists fs_h_dst_permutation_sourcenegative_body_steps_summand. fs_h_dst_permutation_sourcenegative_body_steps_summand + S (fs_a_dst_permutation_sourcenegative_body_steps) = S ((S (fs_i_dst_permutation_sourcenegative_body_steps)) * dst_negative_scale_permutation_source)) /\ exists fs_q_dst_permutation_sourcenegative_body_steps_summand. dst_negative_code_permutation_source = fs_q_dst_permutation_sourcenegative_body_steps_summand * S ((S (fs_i_dst_permutation_sourcenegative_body_steps)) * dst_negative_scale_permutation_source) + (fs_a_dst_permutation_sourcenegative_body_steps))) /\ ((((exists fs_h_dst_permutation_sourcenegative_body_steps_partial. fs_h_dst_permutation_sourcenegative_body_steps_partial + S (fs_r_dst_permutation_sourcenegative_body_steps) = S ((S (fs_i_dst_permutation_sourcenegative_body_steps)) * fs_v_dst_permutation_sourcenegative)) /\ exists fs_q_dst_permutation_sourcenegative_body_steps_partial. fs_u_dst_permutation_sourcenegative = fs_q_dst_permutation_sourcenegative_body_steps_partial * S ((S (fs_i_dst_permutation_sourcenegative_body_steps)) * fs_v_dst_permutation_sourcenegative) + (fs_r_dst_permutation_sourcenegative_body_steps))) /\ ((((exists fs_h_dst_permutation_sourcenegative_body_steps_successor. fs_h_dst_permutation_sourcenegative_body_steps_successor + S (fs_s_dst_permutation_sourcenegative_body_steps) = S ((S (S fs_i_dst_permutation_sourcenegative_body_steps)) * fs_v_dst_permutation_sourcenegative)) /\ exists fs_q_dst_permutation_sourcenegative_body_steps_successor. fs_u_dst_permutation_sourcenegative = fs_q_dst_permutation_sourcenegative_body_steps_successor * S ((S (S fs_i_dst_permutation_sourcenegative_body_steps)) * fs_v_dst_permutation_sourcenegative) + (fs_s_dst_permutation_sourcenegative_body_steps))) /\ fs_s_dst_permutation_sourcenegative_body_steps = fs_r_dst_permutation_sourcenegative_body_steps + fs_a_dst_permutation_sourcenegative_body_steps)))))) /\ (exists ge_balance_positive_permutation_sourceresult ge_balance_negative_permutation_sourceresult. (((((u) = 2 * (ge_balance_positive_permutation_sourceresult) /\ (ge_balance_negative_permutation_sourceresult) = 0) \/ exists ge_signed_half_permutation_sourceresultdecode. (((u) = 2 * ge_signed_half_permutation_sourceresultdecode + 1 /\ (ge_balance_positive_permutation_sourceresult) = 0) /\ (ge_balance_negative_permutation_sourceresult) = S ge_signed_half_permutation_sourceresultdecode))) /\ ((dst_positive_sum_permutation_source) + ge_balance_negative_permutation_sourceresult = (dst_negative_sum_permutation_source) + ge_balance_positive_permutation_sourceresult))))))))) -> (exists dst_positive_code_permutation_target dst_positive_scale_permutation_target dst_negative_code_permutation_target dst_negative_scale_permutation_target dst_positive_sum_permutation_target dst_negative_sum_permutation_target. (((G) = (((((dst_positive_code_permutation_target) + (dst_positive_scale_permutation_target)) * S ((dst_positive_code_permutation_target) + (dst_positive_scale_permutation_target)) + ((dst_positive_scale_permutation_target) + (dst_positive_scale_permutation_target))) + (((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) * S ((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) + ((dst_negative_scale_permutation_target) + (dst_negative_scale_permutation_target)))) * S ((((dst_positive_code_permutation_target) + (dst_positive_scale_permutation_target)) * S ((dst_positive_code_permutation_target) + (dst_positive_scale_permutation_target)) + ((dst_positive_scale_permutation_target) + (dst_positive_scale_permutation_target))) + (((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) * S ((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) + ((dst_negative_scale_permutation_target) + (dst_negative_scale_permutation_target)))) + ((((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) * S ((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) + ((dst_negative_scale_permutation_target) + (dst_negative_scale_permutation_target))) + (((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) * S ((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) + ((dst_negative_scale_permutation_target) + (dst_negative_scale_permutation_target)))))) /\ (((exists fs_u_dst_permutation_targetpositive fs_v_dst_permutation_targetpositive. ((((exists fs_h_dst_permutation_targetpositive_body_start. fs_h_dst_permutation_targetpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_permutation_targetpositive)) /\ exists fs_q_dst_permutation_targetpositive_body_start. fs_u_dst_permutation_targetpositive = fs_q_dst_permutation_targetpositive_body_start * S ((S (0)) * fs_v_dst_permutation_targetpositive) + (0))) /\ ((((exists fs_h_dst_permutation_targetpositive_body_terminal. fs_h_dst_permutation_targetpositive_body_terminal + S (dst_positive_sum_permutation_target) = S ((S (l)) * fs_v_dst_permutation_targetpositive)) /\ exists fs_q_dst_permutation_targetpositive_body_terminal. fs_u_dst_permutation_targetpositive = fs_q_dst_permutation_targetpositive_body_terminal * S ((S (l)) * fs_v_dst_permutation_targetpositive) + (dst_positive_sum_permutation_target))) /\ forall fs_i_dst_permutation_targetpositive_body_steps. (exists fs_lt_dst_permutation_targetpositive_body_steps_bound. fs_lt_dst_permutation_targetpositive_body_steps_bound + S fs_i_dst_permutation_targetpositive_body_steps = l) -> exists fs_a_dst_permutation_targetpositive_body_steps fs_r_dst_permutation_targetpositive_body_steps fs_s_dst_permutation_targetpositive_body_steps. ((((exists fs_h_dst_permutation_targetpositive_body_steps_summand. fs_h_dst_permutation_targetpositive_body_steps_summand + S (fs_a_dst_permutation_targetpositive_body_steps) = S ((S (fs_i_dst_permutation_targetpositive_body_steps)) * dst_positive_scale_permutation_target)) /\ exists fs_q_dst_permutation_targetpositive_body_steps_summand. dst_positive_code_permutation_target = fs_q_dst_permutation_targetpositive_body_steps_summand * S ((S (fs_i_dst_permutation_targetpositive_body_steps)) * dst_positive_scale_permutation_target) + (fs_a_dst_permutation_targetpositive_body_steps))) /\ ((((exists fs_h_dst_permutation_targetpositive_body_steps_partial. fs_h_dst_permutation_targetpositive_body_steps_partial + S (fs_r_dst_permutation_targetpositive_body_steps) = S ((S (fs_i_dst_permutation_targetpositive_body_steps)) * fs_v_dst_permutation_targetpositive)) /\ exists fs_q_dst_permutation_targetpositive_body_steps_partial. fs_u_dst_permutation_targetpositive = fs_q_dst_permutation_targetpositive_body_steps_partial * S ((S (fs_i_dst_permutation_targetpositive_body_steps)) * fs_v_dst_permutation_targetpositive) + (fs_r_dst_permutation_targetpositive_body_steps))) /\ ((((exists fs_h_dst_permutation_targetpositive_body_steps_successor. fs_h_dst_permutation_targetpositive_body_steps_successor + S (fs_s_dst_permutation_targetpositive_body_steps) = S ((S (S fs_i_dst_permutation_targetpositive_body_steps)) * fs_v_dst_permutation_targetpositive)) /\ exists fs_q_dst_permutation_targetpositive_body_steps_successor. fs_u_dst_permutation_targetpositive = fs_q_dst_permutation_targetpositive_body_steps_successor * S ((S (S fs_i_dst_permutation_targetpositive_body_steps)) * fs_v_dst_permutation_targetpositive) + (fs_s_dst_permutation_targetpositive_body_steps))) /\ fs_s_dst_permutation_targetpositive_body_steps = fs_r_dst_permutation_targetpositive_body_steps + fs_a_dst_permutation_targetpositive_body_steps)))))) /\ (((exists fs_u_dst_permutation_targetnegative fs_v_dst_permutation_targetnegative. ((((exists fs_h_dst_permutation_targetnegative_body_start. fs_h_dst_permutation_targetnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_permutation_targetnegative)) /\ exists fs_q_dst_permutation_targetnegative_body_start. fs_u_dst_permutation_targetnegative = fs_q_dst_permutation_targetnegative_body_start * S ((S (0)) * fs_v_dst_permutation_targetnegative) + (0))) /\ ((((exists fs_h_dst_permutation_targetnegative_body_terminal. fs_h_dst_permutation_targetnegative_body_terminal + S (dst_negative_sum_permutation_target) = S ((S (l)) * fs_v_dst_permutation_targetnegative)) /\ exists fs_q_dst_permutation_targetnegative_body_terminal. fs_u_dst_permutation_targetnegative = fs_q_dst_permutation_targetnegative_body_terminal * S ((S (l)) * fs_v_dst_permutation_targetnegative) + (dst_negative_sum_permutation_target))) /\ forall fs_i_dst_permutation_targetnegative_body_steps. (exists fs_lt_dst_permutation_targetnegative_body_steps_bound. fs_lt_dst_permutation_targetnegative_body_steps_bound + S fs_i_dst_permutation_targetnegative_body_steps = l) -> exists fs_a_dst_permutation_targetnegative_body_steps fs_r_dst_permutation_targetnegative_body_steps fs_s_dst_permutation_targetnegative_body_steps. ((((exists fs_h_dst_permutation_targetnegative_body_steps_summand. fs_h_dst_permutation_targetnegative_body_steps_summand + S (fs_a_dst_permutation_targetnegative_body_steps) = S ((S (fs_i_dst_permutation_targetnegative_body_steps)) * dst_negative_scale_permutation_target)) /\ exists fs_q_dst_permutation_targetnegative_body_steps_summand. dst_negative_code_permutation_target = fs_q_dst_permutation_targetnegative_body_steps_summand * S ((S (fs_i_dst_permutation_targetnegative_body_steps)) * dst_negative_scale_permutation_target) + (fs_a_dst_permutation_targetnegative_body_steps))) /\ ((((exists fs_h_dst_permutation_targetnegative_body_steps_partial. fs_h_dst_permutation_targetnegative_body_steps_partial + S (fs_r_dst_permutation_targetnegative_body_steps) = S ((S (fs_i_dst_permutation_targetnegative_body_steps)) * fs_v_dst_permutation_targetnegative)) /\ exists fs_q_dst_permutation_targetnegative_body_steps_partial. fs_u_dst_permutation_targetnegative = fs_q_dst_permutation_targetnegative_body_steps_partial * S ((S (fs_i_dst_permutation_targetnegative_body_steps)) * fs_v_dst_permutation_targetnegative) + (fs_r_dst_permutation_targetnegative_body_steps))) /\ ((((exists fs_h_dst_permutation_targetnegative_body_steps_successor. fs_h_dst_permutation_targetnegative_body_steps_successor + S (fs_s_dst_permutation_targetnegative_body_steps) = S ((S (S fs_i_dst_permutation_targetnegative_body_steps)) * fs_v_dst_permutation_targetnegative)) /\ exists fs_q_dst_permutation_targetnegative_body_steps_successor. fs_u_dst_permutation_targetnegative = fs_q_dst_permutation_targetnegative_body_steps_successor * S ((S (S fs_i_dst_permutation_targetnegative_body_steps)) * fs_v_dst_permutation_targetnegative) + (fs_s_dst_permutation_targetnegative_body_steps))) /\ fs_s_dst_permutation_targetnegative_body_steps = fs_r_dst_permutation_targetnegative_body_steps + fs_a_dst_permutation_targetnegative_body_steps)))))) /\ (exists ge_balance_positive_permutation_targetresult ge_balance_negative_permutation_targetresult. (((((v) = 2 * (ge_balance_positive_permutation_targetresult) /\ (ge_balance_negative_permutation_targetresult) = 0) \/ exists ge_signed_half_permutation_targetresultdecode. (((v) = 2 * ge_signed_half_permutation_targetresultdecode + 1 /\ (ge_balance_positive_permutation_targetresult) = 0) /\ (ge_balance_negative_permutation_targetresult) = S ge_signed_half_permutation_targetresultdecode))) /\ ((dst_positive_sum_permutation_target) + ge_balance_negative_permutation_targetresult = (dst_negative_sum_permutation_target) + ge_balance_positive_permutation_targetresult))))))))) -> u = v

forall n m. n + m = m + n

forall b c i. exists x. ((exists h. h + S x = S ((S i) * c)) /\ exists q. b = q * S ((S i) * c) + x)

forall b c i x y. ((exists h. h + S x = S ((S i) * c)) /\ exists q. b = q * S ((S i) * c) + x) -> ((exists h. h + S y = S ((S i) * c)) /\ exists q. b = q * S ((S i) * c) + y) -> x = y

forall b c l. exists n. (exists ff_u_x ff_v_x. ((((exists ff_h_x_start. ff_h_x_start + S (0) = S ((S (0)) * ff_v_x)) /\ exists ff_q_x_start. ff_u_x = ff_q_x_start * S ((S (0)) * ff_v_x) + (0))) /\ ((((exists ff_h_x_terminal. ff_h_x_terminal + S (n) = S ((S (l)) * ff_v_x)) /\ exists ff_q_x_terminal. ff_u_x = ff_q_x_terminal * S ((S (l)) * ff_v_x) + (n))) /\ forall ff_i_x. (exists ff_lt_x_bound. ff_lt_x_bound + S ff_i_x = l) -> exists ff_a_x ff_r_x ff_s_x. ((((exists ff_h_x_summand. ff_h_x_summand + S (ff_a_x) = S ((S (ff_i_x)) * c)) /\ exists ff_q_x_summand. b = ff_q_x_summand * S ((S (ff_i_x)) * c) + (ff_a_x))) /\ ((((exists ff_h_x_partial. ff_h_x_partial + S (ff_r_x) = S ((S (ff_i_x)) * ff_v_x)) /\ exists ff_q_x_partial. ff_u_x = ff_q_x_partial * S ((S (ff_i_x)) * ff_v_x) + (ff_r_x))) /\ ((((exists ff_h_x_successor. ff_h_x_successor + S (ff_s_x) = S ((S (S ff_i_x)) * ff_v_x)) /\ exists ff_q_x_successor. ff_u_x = ff_q_x_successor * S ((S (S ff_i_x)) * ff_v_x) + (ff_s_x))) /\ ff_s_x = ff_r_x + ff_a_x))))))

forall b c l n m. (exists ff_u_l ff_v_l. ((((exists ff_h_l_start. ff_h_l_start + S (0) = S ((S (0)) * ff_v_l)) /\ exists ff_q_l_start. ff_u_l = ff_q_l_start * S ((S (0)) * ff_v_l) + (0))) /\ ((((exists ff_h_l_terminal. ff_h_l_terminal + S (n) = S ((S (l)) * ff_v_l)) /\ exists ff_q_l_terminal. ff_u_l = ff_q_l_terminal * S ((S (l)) * ff_v_l) + (n))) /\ forall ff_i_l. (exists ff_lt_l_bound. ff_lt_l_bound + S ff_i_l = l) -> exists ff_a_l ff_r_l ff_s_l. ((((exists ff_h_l_summand. ff_h_l_summand + S (ff_a_l) = S ((S (ff_i_l)) * c)) /\ exists ff_q_l_summand. b = ff_q_l_summand * S ((S (ff_i_l)) * c) + (ff_a_l))) /\ ((((exists ff_h_l_partial. ff_h_l_partial + S (ff_r_l) = S ((S (ff_i_l)) * ff_v_l)) /\ exists ff_q_l_partial. ff_u_l = ff_q_l_partial * S ((S (ff_i_l)) * ff_v_l) + (ff_r_l))) /\ ((((exists ff_h_l_successor. ff_h_l_successor + S (ff_s_l) = S ((S (S ff_i_l)) * ff_v_l)) /\ exists ff_q_l_successor. ff_u_l = ff_q_l_successor * S ((S (S ff_i_l)) * ff_v_l) + (ff_s_l))) /\ ff_s_l = ff_r_l + ff_a_l)))))) -> (exists ff_u_r ff_v_r. ((((exists ff_h_r_start. ff_h_r_start + S (0) = S ((S (0)) * ff_v_r)) /\ exists ff_q_r_start. ff_u_r = ff_q_r_start * S ((S (0)) * ff_v_r) + (0))) /\ ((((exists ff_h_r_terminal. ff_h_r_terminal + S (m) = S ((S (l)) * ff_v_r)) /\ exists ff_q_r_terminal. ff_u_r = ff_q_r_terminal * S ((S (l)) * ff_v_r) + (m))) /\ forall ff_i_r. (exists ff_lt_r_bound. ff_lt_r_bound + S ff_i_r = l) -> exists ff_a_r ff_r_r ff_s_r. ((((exists ff_h_r_summand. ff_h_r_summand + S (ff_a_r) = S ((S (ff_i_r)) * c)) /\ exists ff_q_r_summand. b = ff_q_r_summand * S ((S (ff_i_r)) * c) + (ff_a_r))) /\ ((((exists ff_h_r_partial. ff_h_r_partial + S (ff_r_r) = S ((S (ff_i_r)) * ff_v_r)) /\ exists ff_q_r_partial. ff_u_r = ff_q_r_partial * S ((S (ff_i_r)) * ff_v_r) + (ff_r_r))) /\ ((((exists ff_h_r_successor. ff_h_r_successor + S (ff_s_r) = S ((S (S ff_i_r)) * ff_v_r)) /\ exists ff_q_r_successor. ff_u_r = ff_q_r_successor * S ((S (S ff_i_r)) * ff_v_r) + (ff_s_r))) /\ ff_s_r = ff_r_r + ff_a_r)))))) -> n = m

forall l r s b c z d p q. (forall fp_i_reindex_bounded. (exists fp_gap_reindex_bounded_index. fp_gap_reindex_bounded_index + S fp_i_reindex_bounded = l) -> exists fp_value_reindex_bounded. ((((exists ff_h_reindex_bounded_entry. ff_h_reindex_bounded_entry + S (fp_value_reindex_bounded) = S ((S (fp_i_reindex_bounded)) * s)) /\ exists ff_q_reindex_bounded_entry. r = ff_q_reindex_bounded_entry * S ((S (fp_i_reindex_bounded)) * s) + (fp_value_reindex_bounded))) /\ (exists fp_gap_reindex_bounded_value. fp_gap_reindex_bounded_value + S fp_value_reindex_bounded = l))) -> (forall fp_i_reindex_injective fp_j_reindex_injective fp_value_reindex_injective. (exists fp_gap_reindex_injective_i. fp_gap_reindex_injective_i + S fp_i_reindex_injective = l) -> (exists fp_gap_reindex_injective_j. fp_gap_reindex_injective_j + S fp_j_reindex_injective = l) -> (((exists ff_h_reindex_injective_left. ff_h_reindex_injective_left + S (fp_value_reindex_injective) = S ((S (fp_i_reindex_injective)) * s)) /\ exists ff_q_reindex_injective_left. r = ff_q_reindex_injective_left * S ((S (fp_i_reindex_injective)) * s) + (fp_value_reindex_injective))) -> (((exists ff_h_reindex_injective_right. ff_h_reindex_injective_right + S (fp_value_reindex_injective) = S ((S (fp_j_reindex_injective)) * s)) /\ exists ff_q_reindex_injective_right. r = ff_q_reindex_injective_right * S ((S (fp_j_reindex_injective)) * s) + (fp_value_reindex_injective))) -> fp_i_reindex_injective = fp_j_reindex_injective) -> (forall fpr_i_reindex_aligned fpr_j_reindex_aligned fpr_x_reindex_aligned. (exists fpr_h_reindex_aligned. fpr_h_reindex_aligned + S fpr_i_reindex_aligned = l) -> (((exists ff_h_reindex_aligned_map. ff_h_reindex_aligned_map + S (fpr_j_reindex_aligned) = S ((S (fpr_i_reindex_aligned)) * s)) /\ exists ff_q_reindex_aligned_map. r = ff_q_reindex_aligned_map * S ((S (fpr_i_reindex_aligned)) * s) + (fpr_j_reindex_aligned))) -> (((exists ff_h_reindex_aligned_source. ff_h_reindex_aligned_source + S (fpr_x_reindex_aligned) = S ((S (fpr_j_reindex_aligned)) * c)) /\ exists ff_q_reindex_aligned_source. b = ff_q_reindex_aligned_source * S ((S (fpr_j_reindex_aligned)) * c) + (fpr_x_reindex_aligned))) -> (((exists ff_h_reindex_aligned_target. ff_h_reindex_aligned_target + S (fpr_x_reindex_aligned) = S ((S (fpr_i_reindex_aligned)) * d)) /\ exists ff_q_reindex_aligned_target. z = ff_q_reindex_aligned_target * S ((S (fpr_i_reindex_aligned)) * d) + (fpr_x_reindex_aligned)))) -> (exists ff_u_reindex_source_product ff_v_reindex_source_product. ((((exists ff_h_reindex_source_product_start. ff_h_reindex_source_product_start + S (0) = S ((S (0)) * ff_v_reindex_source_product)) /\ exists ff_q_reindex_source_product_start. ff_u_reindex_source_product = ff_q_reindex_source_product_start * S ((S (0)) * ff_v_reindex_source_product) + (0))) /\ ((((exists ff_h_reindex_source_product_terminal. ff_h_reindex_source_product_terminal + S (p) = S ((S (l)) * ff_v_reindex_source_product)) /\ exists ff_q_reindex_source_product_terminal. ff_u_reindex_source_product = ff_q_reindex_source_product_terminal * S ((S (l)) * ff_v_reindex_source_product) + (p))) /\ forall ff_i_reindex_source_product. (exists ff_lt_reindex_source_product_bound. ff_lt_reindex_source_product_bound + S ff_i_reindex_source_product = l) -> exists ff_a_reindex_source_product ff_r_reindex_source_product ff_s_reindex_source_product. ((((exists ff_h_reindex_source_product_summand. ff_h_reindex_source_product_summand + S (ff_a_reindex_source_product) = S ((S (ff_i_reindex_source_product)) * c)) /\ exists ff_q_reindex_source_product_summand. b = ff_q_reindex_source_product_summand * S ((S (ff_i_reindex_source_product)) * c) + (ff_a_reindex_source_product))) /\ ((((exists ff_h_reindex_source_product_partial. ff_h_reindex_source_product_partial + S (ff_r_reindex_source_product) = S ((S (ff_i_reindex_source_product)) * ff_v_reindex_source_product)) /\ exists ff_q_reindex_source_product_partial. ff_u_reindex_source_product = ff_q_reindex_source_product_partial * S ((S (ff_i_reindex_source_product)) * ff_v_reindex_source_product) + (ff_r_reindex_source_product))) /\ ((((exists ff_h_reindex_source_product_successor. ff_h_reindex_source_product_successor + S (ff_s_reindex_source_product) = S ((S (S ff_i_reindex_source_product)) * ff_v_reindex_source_product)) /\ exists ff_q_reindex_source_product_successor. ff_u_reindex_source_product = ff_q_reindex_source_product_successor * S ((S (S ff_i_reindex_source_product)) * ff_v_reindex_source_product) + (ff_s_reindex_source_product))) /\ ff_s_reindex_source_product = ff_r_reindex_source_product + ff_a_reindex_source_product)))))) -> (exists ff_u_reindex_target_product ff_v_reindex_target_product. ((((exists ff_h_reindex_target_product_start. ff_h_reindex_target_product_start + S (0) = S ((S (0)) * ff_v_reindex_target_product)) /\ exists ff_q_reindex_target_product_start. ff_u_reindex_target_product = ff_q_reindex_target_product_start * S ((S (0)) * ff_v_reindex_target_product) + (0))) /\ ((((exists ff_h_reindex_target_product_terminal. ff_h_reindex_target_product_terminal + S (q) = S ((S (l)) * ff_v_reindex_target_product)) /\ exists ff_q_reindex_target_product_terminal. ff_u_reindex_target_product = ff_q_reindex_target_product_terminal * S ((S (l)) * ff_v_reindex_target_product) + (q))) /\ forall ff_i_reindex_target_product. (exists ff_lt_reindex_target_product_bound. ff_lt_reindex_target_product_bound + S ff_i_reindex_target_product = l) -> exists ff_a_reindex_target_product ff_r_reindex_target_product ff_s_reindex_target_product. ((((exists ff_h_reindex_target_product_summand. ff_h_reindex_target_product_summand + S (ff_a_reindex_target_product) = S ((S (ff_i_reindex_target_product)) * d)) /\ exists ff_q_reindex_target_product_summand. z = ff_q_reindex_target_product_summand * S ((S (ff_i_reindex_target_product)) * d) + (ff_a_reindex_target_product))) /\ ((((exists ff_h_reindex_target_product_partial. ff_h_reindex_target_product_partial + S (ff_r_reindex_target_product) = S ((S (ff_i_reindex_target_product)) * ff_v_reindex_target_product)) /\ exists ff_q_reindex_target_product_partial. ff_u_reindex_target_product = ff_q_reindex_target_product_partial * S ((S (ff_i_reindex_target_product)) * ff_v_reindex_target_product) + (ff_r_reindex_target_product))) /\ ((((exists ff_h_reindex_target_product_successor. ff_h_reindex_target_product_successor + S (ff_s_reindex_target_product) = S ((S (S ff_i_reindex_target_product)) * ff_v_reindex_target_product)) /\ exists ff_q_reindex_target_product_successor. ff_u_reindex_target_product = ff_q_reindex_target_product_successor * S ((S (S ff_i_reindex_target_product)) * ff_v_reindex_target_product) + (ff_s_reindex_target_product))) /\ ff_s_reindex_target_product = ff_r_reindex_target_product + ff_a_reindex_target_product)))))) -> p = q

forall b c l n. (exists fs_u_succ fs_v_succ. ((((exists fs_h_succ_body_start. fs_h_succ_body_start + S (0) = S ((S (0)) * fs_v_succ)) /\ exists fs_q_succ_body_start. fs_u_succ = fs_q_succ_body_start * S ((S (0)) * fs_v_succ) + (0))) /\ ((((exists fs_h_succ_body_terminal. fs_h_succ_body_terminal + S (n) = S ((S (S l)) * fs_v_succ)) /\ exists fs_q_succ_body_terminal. fs_u_succ = fs_q_succ_body_terminal * S ((S (S l)) * fs_v_succ) + (n))) /\ forall fs_i_succ_body_steps. (exists fs_lt_succ_body_steps_bound. fs_lt_succ_body_steps_bound + S fs_i_succ_body_steps = S l) -> exists fs_a_succ_body_steps fs_r_succ_body_steps fs_s_succ_body_steps. ((((exists fs_h_succ_body_steps_summand. fs_h_succ_body_steps_summand + S (fs_a_succ_body_steps) = S ((S (fs_i_succ_body_steps)) * c)) /\ exists fs_q_succ_body_steps_summand. b = fs_q_succ_body_steps_summand * S ((S (fs_i_succ_body_steps)) * c) + (fs_a_succ_body_steps))) /\ ((((exists fs_h_succ_body_steps_partial. fs_h_succ_body_steps_partial + S (fs_r_succ_body_steps) = S ((S (fs_i_succ_body_steps)) * fs_v_succ)) /\ exists fs_q_succ_body_steps_partial. fs_u_succ = fs_q_succ_body_steps_partial * S ((S (fs_i_succ_body_steps)) * fs_v_succ) + (fs_r_succ_body_steps))) /\ ((((exists fs_h_succ_body_steps_successor. fs_h_succ_body_steps_successor + S (fs_s_succ_body_steps) = S ((S (S fs_i_succ_body_steps)) * fs_v_succ)) /\ exists fs_q_succ_body_steps_successor. fs_u_succ = fs_q_succ_body_steps_successor * S ((S (S fs_i_succ_body_steps)) * fs_v_succ) + (fs_s_succ_body_steps))) /\ fs_s_succ_body_steps = fs_r_succ_body_steps + fs_a_succ_body_steps)))))) -> exists a r. (((exists fs_h_succ_factor. fs_h_succ_factor + S (a) = S ((S (l)) * c)) /\ exists fs_q_succ_factor. b = fs_q_succ_factor * S ((S (l)) * c) + (a))) /\ ((exists ff_u_prefix ff_v_prefix. ((((exists ff_h_prefix_start. ff_h_prefix_start + S (0) = S ((S (0)) * ff_v_prefix)) /\ exists ff_q_prefix_start. ff_u_prefix = ff_q_prefix_start * S ((S (0)) * ff_v_prefix) + (0))) /\ ((((exists ff_h_prefix_terminal. ff_h_prefix_terminal + S (r) = S ((S (l)) * ff_v_prefix)) /\ exists ff_q_prefix_terminal. ff_u_prefix = ff_q_prefix_terminal * S ((S (l)) * ff_v_prefix) + (r))) /\ forall ff_i_prefix. (exists ff_lt_prefix_bound. ff_lt_prefix_bound + S ff_i_prefix = l) -> exists ff_a_prefix ff_r_prefix ff_s_prefix. ((((exists ff_h_prefix_summand. ff_h_prefix_summand + S (ff_a_prefix) = S ((S (ff_i_prefix)) * c)) /\ exists ff_q_prefix_summand. b = ff_q_prefix_summand * S ((S (ff_i_prefix)) * c) + (ff_a_prefix))) /\ ((((exists ff_h_prefix_partial. ff_h_prefix_partial + S (ff_r_prefix) = S ((S (ff_i_prefix)) * ff_v_prefix)) /\ exists ff_q_prefix_partial. ff_u_prefix = ff_q_prefix_partial * S ((S (ff_i_prefix)) * ff_v_prefix) + (ff_r_prefix))) /\ ((((exists ff_h_prefix_successor. ff_h_prefix_successor + S (ff_s_prefix) = S ((S (S ff_i_prefix)) * ff_v_prefix)) /\ exists ff_q_prefix_successor. ff_u_prefix = ff_q_prefix_successor * S ((S (S ff_i_prefix)) * ff_v_prefix) + (ff_s_prefix))) /\ ff_s_prefix = ff_r_prefix + ff_a_prefix)))))) /\ n = r + a)

forall b c n. (exists fs_u_zero fs_v_zero. ((((exists fs_h_zero_body_start. fs_h_zero_body_start + S (0) = S ((S (0)) * fs_v_zero)) /\ exists fs_q_zero_body_start. fs_u_zero = fs_q_zero_body_start * S ((S (0)) * fs_v_zero) + (0))) /\ ((((exists fs_h_zero_body_terminal. fs_h_zero_body_terminal + S (n) = S ((S (0)) * fs_v_zero)) /\ exists fs_q_zero_body_terminal. fs_u_zero = fs_q_zero_body_terminal * S ((S (0)) * fs_v_zero) + (n))) /\ forall fs_i_zero_body_steps. (exists fs_lt_zero_body_steps_bound. fs_lt_zero_body_steps_bound + S fs_i_zero_body_steps = 0) -> exists fs_a_zero_body_steps fs_r_zero_body_steps fs_s_zero_body_steps. ((((exists fs_h_zero_body_steps_summand. fs_h_zero_body_steps_summand + S (fs_a_zero_body_steps) = S ((S (fs_i_zero_body_steps)) * c)) /\ exists fs_q_zero_body_steps_summand. b = fs_q_zero_body_steps_summand * S ((S (fs_i_zero_body_steps)) * c) + (fs_a_zero_body_steps))) /\ ((((exists fs_h_zero_body_steps_partial. fs_h_zero_body_steps_partial + S (fs_r_zero_body_steps) = S ((S (fs_i_zero_body_steps)) * fs_v_zero)) /\ exists fs_q_zero_body_steps_partial. fs_u_zero = fs_q_zero_body_steps_partial * S ((S (fs_i_zero_body_steps)) * fs_v_zero) + (fs_r_zero_body_steps))) /\ ((((exists fs_h_zero_body_steps_successor. fs_h_zero_body_steps_successor + S (fs_s_zero_body_steps) = S ((S (S fs_i_zero_body_steps)) * fs_v_zero)) /\ exists fs_q_zero_body_steps_successor. fs_u_zero = fs_q_zero_body_steps_successor * S ((S (S fs_i_zero_body_steps)) * fs_v_zero) + (fs_s_zero_body_steps))) /\ fs_s_zero_body_steps = fs_r_zero_body_steps + fs_a_zero_body_steps)))))) -> n = 0

forall r s b c l. exists z d. (forall fms_i_compose fms_j_compose fms_v_compose. (exists fms_gap_compose. fms_gap_compose + S (fms_i_compose) = (l)) -> (((exists fs_h_fms_compose_index. fs_h_fms_compose_index + S (fms_j_compose) = S ((S (fms_i_compose)) * s)) /\ exists fs_q_fms_compose_index. r = fs_q_fms_compose_index * S ((S (fms_i_compose)) * s) + (fms_j_compose))) -> (((exists fs_h_fms_compose_source. fs_h_fms_compose_source + S (fms_v_compose) = S ((S (fms_j_compose)) * c)) /\ exists fs_q_fms_compose_source. b = fs_q_fms_compose_source * S ((S (fms_j_compose)) * c) + (fms_v_compose))) -> (((exists fs_h_fms_compose_target. fs_h_fms_compose_target + S (fms_v_compose) = S ((S (fms_i_compose)) * d)) /\ exists fs_q_fms_compose_target. z = fs_q_fms_compose_target * S ((S (fms_i_compose)) * d) + (fms_v_compose))))

forall ac bc cc p n q m. (exists ge_balance_positive_bridge_first_add ge_balance_negative_bridge_first_add. (((((ac) = 2 * (ge_balance_positive_bridge_first_add) /\ (ge_balance_negative_bridge_first_add) = 0) \/ exists ge_signed_half_bridge_first_adddecode. (((ac) = 2 * ge_signed_half_bridge_first_adddecode + 1 /\ (ge_balance_positive_bridge_first_add) = 0) /\ (ge_balance_negative_bridge_first_add) = S ge_signed_half_bridge_first_adddecode))) /\ ((p) + ge_balance_negative_bridge_first_add = (n) + ge_balance_positive_bridge_first_add))) -> (exists ge_balance_positive_bridge_second_add ge_balance_negative_bridge_second_add. (((((bc) = 2 * (ge_balance_positive_bridge_second_add) /\ (ge_balance_negative_bridge_second_add) = 0) \/ exists ge_signed_half_bridge_second_adddecode. (((bc) = 2 * ge_signed_half_bridge_second_adddecode + 1 /\ (ge_balance_positive_bridge_second_add) = 0) /\ (ge_balance_negative_bridge_second_add) = S ge_signed_half_bridge_second_adddecode))) /\ ((q) + ge_balance_negative_bridge_second_add = (m) + ge_balance_positive_bridge_second_add))) -> (exists ge_balance_positive_bridge_output_add ge_balance_negative_bridge_output_add. (((((cc) = 2 * (ge_balance_positive_bridge_output_add) /\ (ge_balance_negative_bridge_output_add) = 0) \/ exists ge_signed_half_bridge_output_adddecode. (((cc) = 2 * ge_signed_half_bridge_output_adddecode + 1 /\ (ge_balance_positive_bridge_output_add) = 0) /\ (ge_balance_negative_bridge_output_add) = S ge_signed_half_bridge_output_adddecode))) /\ ((((p) + (q))) + ge_balance_negative_bridge_output_add = (((n) + (m))) + ge_balance_positive_bridge_output_add))) -> (exists sa_lp_gaussian_bridge_add sa_ln_gaussian_bridge_add sa_rp_gaussian_bridge_add sa_rn_gaussian_bridge_add sa_op_gaussian_bridge_add sa_on_gaussian_bridge_add. (((ac = 2 * sa_lp_gaussian_bridge_add /\ sa_ln_gaussian_bridge_add = 0) \/ exists sd_half_gaussian_bridge_add_left. ((ac = 2 * sd_half_gaussian_bridge_add_left + 1 /\ sa_lp_gaussian_bridge_add = 0) /\ sa_ln_gaussian_bridge_add = S sd_half_gaussian_bridge_add_left)) /\ (((bc = 2 * sa_rp_gaussian_bridge_add /\ sa_rn_gaussian_bridge_add = 0) \/ exists sd_half_gaussian_bridge_add_right. ((bc = 2 * sd_half_gaussian_bridge_add_right + 1 /\ sa_rp_gaussian_bridge_add = 0) /\ sa_rn_gaussian_bridge_add = S sd_half_gaussian_bridge_add_right)) /\ (((cc = 2 * sa_op_gaussian_bridge_add /\ sa_on_gaussian_bridge_add = 0) \/ exists sd_half_gaussian_bridge_add_output. ((cc = 2 * sd_half_gaussian_bridge_add_output + 1 /\ sa_op_gaussian_bridge_add = 0) /\ sa_on_gaussian_bridge_add = S sd_half_gaussian_bridge_add_output)) /\ (sa_lp_gaussian_bridge_add + sa_rp_gaussian_bridge_add) + sa_on_gaussian_bridge_add = (sa_ln_gaussian_bridge_add + sa_rn_gaussian_bridge_add) + sa_op_gaussian_bridge_add))))

forall ac bc cc p n q m. (exists ge_balance_positive_bridge_elim_first_add ge_balance_negative_bridge_elim_first_add. (((((ac) = 2 * (ge_balance_positive_bridge_elim_first_add) /\ (ge_balance_negative_bridge_elim_first_add) = 0) \/ exists ge_signed_half_bridge_elim_first_adddecode. (((ac) = 2 * ge_signed_half_bridge_elim_first_adddecode + 1 /\ (ge_balance_positive_bridge_elim_first_add) = 0) /\ (ge_balance_negative_bridge_elim_first_add) = S ge_signed_half_bridge_elim_first_adddecode))) /\ ((p) + ge_balance_negative_bridge_elim_first_add = (n) + ge_balance_positive_bridge_elim_first_add))) -> (exists ge_balance_positive_bridge_elim_second_add ge_balance_negative_bridge_elim_second_add. (((((bc) = 2 * (ge_balance_positive_bridge_elim_second_add) /\ (ge_balance_negative_bridge_elim_second_add) = 0) \/ exists ge_signed_half_bridge_elim_second_adddecode. (((bc) = 2 * ge_signed_half_bridge_elim_second_adddecode + 1 /\ (ge_balance_positive_bridge_elim_second_add) = 0) /\ (ge_balance_negative_bridge_elim_second_add) = S ge_signed_half_bridge_elim_second_adddecode))) /\ ((q) + ge_balance_negative_bridge_elim_second_add = (m) + ge_balance_positive_bridge_elim_second_add))) -> (exists sa_lp_gaussian_bridge_elim_add sa_ln_gaussian_bridge_elim_add sa_rp_gaussian_bridge_elim_add sa_rn_gaussian_bridge_elim_add sa_op_gaussian_bridge_elim_add sa_on_gaussian_bridge_elim_add. (((ac = 2 * sa_lp_gaussian_bridge_elim_add /\ sa_ln_gaussian_bridge_elim_add = 0) \/ exists sd_half_gaussian_bridge_elim_add_left. ((ac = 2 * sd_half_gaussian_bridge_elim_add_left + 1 /\ sa_lp_gaussian_bridge_elim_add = 0) /\ sa_ln_gaussian_bridge_elim_add = S sd_half_gaussian_bridge_elim_add_left)) /\ (((bc = 2 * sa_rp_gaussian_bridge_elim_add /\ sa_rn_gaussian_bridge_elim_add = 0) \/ exists sd_half_gaussian_bridge_elim_add_right. ((bc = 2 * sd_half_gaussian_bridge_elim_add_right + 1 /\ sa_rp_gaussian_bridge_elim_add = 0) /\ sa_rn_gaussian_bridge_elim_add = S sd_half_gaussian_bridge_elim_add_right)) /\ (((cc = 2 * sa_op_gaussian_bridge_elim_add /\ sa_on_gaussian_bridge_elim_add = 0) \/ exists sd_half_gaussian_bridge_elim_add_output. ((cc = 2 * sd_half_gaussian_bridge_elim_add_output + 1 /\ sa_op_gaussian_bridge_elim_add = 0) /\ sa_on_gaussian_bridge_elim_add = S sd_half_gaussian_bridge_elim_add_output)) /\ (sa_lp_gaussian_bridge_elim_add + sa_rp_gaussian_bridge_elim_add) + sa_on_gaussian_bridge_elim_add = (sa_ln_gaussian_bridge_elim_add + sa_rn_gaussian_bridge_elim_add) + sa_op_gaussian_bridge_elim_add)))) -> (exists ge_balance_positive_signed_bridge_elimination_add ge_balance_negative_signed_bridge_elimination_add. (((((cc) = 2 * (ge_balance_positive_signed_bridge_elimination_add) /\ (ge_balance_negative_signed_bridge_elimination_add) = 0) \/ exists ge_signed_half_signed_bridge_elimination_adddecode. (((cc) = 2 * ge_signed_half_signed_bridge_elimination_adddecode + 1 /\ (ge_balance_positive_signed_bridge_elimination_add) = 0) /\ (ge_balance_negative_signed_bridge_elimination_add) = S ge_signed_half_signed_bridge_elimination_adddecode))) /\ ((((p) + (q))) + ge_balance_negative_signed_bridge_elimination_add = (((n) + (m))) + ge_balance_positive_signed_bridge_elimination_add)))

forall code p n q m. (exists ge_balance_positive_same_code_first ge_balance_negative_same_code_first. (((((code) = 2 * (ge_balance_positive_same_code_first) /\ (ge_balance_negative_same_code_first) = 0) \/ exists ge_signed_half_same_code_firstdecode. (((code) = 2 * ge_signed_half_same_code_firstdecode + 1 /\ (ge_balance_positive_same_code_first) = 0) /\ (ge_balance_negative_same_code_first) = S ge_signed_half_same_code_firstdecode))) /\ ((p) + ge_balance_negative_same_code_first = (n) + ge_balance_positive_same_code_first))) -> (exists ge_balance_positive_same_code_second ge_balance_negative_same_code_second. (((((code) = 2 * (ge_balance_positive_same_code_second) /\ (ge_balance_negative_same_code_second) = 0) \/ exists ge_signed_half_same_code_seconddecode. (((code) = 2 * ge_signed_half_same_code_seconddecode + 1 /\ (ge_balance_positive_same_code_second) = 0) /\ (ge_balance_negative_same_code_second) = S ge_signed_half_same_code_seconddecode))) /\ ((q) + ge_balance_negative_same_code_second = (m) + ge_balance_positive_same_code_second))) -> (((p) + (m)) = ((q) + (n)))

forall n. n <= n

forall ab ac bb bc eb ec fb fc l p n P N. (forall ics_index_sum_pointwise ics_value0_sum_pointwise ics_value1_sum_pointwise ics_value2_sum_pointwise ics_value3_sum_pointwise. (exists ics_gap_sum_pointwise_bound. ics_gap_sum_pointwise_bound + S (ics_index_sum_pointwise) = (l)) -> (((exists fs_h_ics_sum_pointwise_at0. fs_h_ics_sum_pointwise_at0 + S (ics_value0_sum_pointwise) = S ((S (ics_index_sum_pointwise)) * ac)) /\ exists fs_q_ics_sum_pointwise_at0. ab = fs_q_ics_sum_pointwise_at0 * S ((S (ics_index_sum_pointwise)) * ac) + (ics_value0_sum_pointwise))) -> (((exists fs_h_ics_sum_pointwise_at1. fs_h_ics_sum_pointwise_at1 + S (ics_value1_sum_pointwise) = S ((S (ics_index_sum_pointwise)) * bc)) /\ exists fs_q_ics_sum_pointwise_at1. bb = fs_q_ics_sum_pointwise_at1 * S ((S (ics_index_sum_pointwise)) * bc) + (ics_value1_sum_pointwise))) -> (((exists fs_h_ics_sum_pointwise_at2. fs_h_ics_sum_pointwise_at2 + S (ics_value2_sum_pointwise) = S ((S (ics_index_sum_pointwise)) * ec)) /\ exists fs_q_ics_sum_pointwise_at2. eb = fs_q_ics_sum_pointwise_at2 * S ((S (ics_index_sum_pointwise)) * ec) + (ics_value2_sum_pointwise))) -> (((exists fs_h_ics_sum_pointwise_at3. fs_h_ics_sum_pointwise_at3 + S (ics_value3_sum_pointwise) = S ((S (ics_index_sum_pointwise)) * fc)) /\ exists fs_q_ics_sum_pointwise_at3. fb = fs_q_ics_sum_pointwise_at3 * S ((S (ics_index_sum_pointwise)) * fc) + (ics_value3_sum_pointwise))) -> ics_value0_sum_pointwise + ics_value3_sum_pointwise = ics_value2_sum_pointwise + ics_value1_sum_pointwise) -> (exists ff_u_mce_integer_sum_ap ff_v_mce_integer_sum_ap. ((((exists ff_h_mce_integer_sum_ap_start. ff_h_mce_integer_sum_ap_start + S (0) = S ((S (0)) * ff_v_mce_integer_sum_ap)) /\ exists ff_q_mce_integer_sum_ap_start. ff_u_mce_integer_sum_ap = ff_q_mce_integer_sum_ap_start * S ((S (0)) * ff_v_mce_integer_sum_ap) + (0))) /\ ((((exists ff_h_mce_integer_sum_ap_terminal. ff_h_mce_integer_sum_ap_terminal + S (p) = S ((S (l)) * ff_v_mce_integer_sum_ap)) /\ exists ff_q_mce_integer_sum_ap_terminal. ff_u_mce_integer_sum_ap = ff_q_mce_integer_sum_ap_terminal * S ((S (l)) * ff_v_mce_integer_sum_ap) + (p))) /\ forall ff_i_mce_integer_sum_ap. (exists ff_lt_mce_integer_sum_ap_bound. ff_lt_mce_integer_sum_ap_bound + S ff_i_mce_integer_sum_ap = l) -> exists ff_a_mce_integer_sum_ap ff_r_mce_integer_sum_ap ff_s_mce_integer_sum_ap. ((((exists ff_h_mce_integer_sum_ap_summand. ff_h_mce_integer_sum_ap_summand + S (ff_a_mce_integer_sum_ap) = S ((S (ff_i_mce_integer_sum_ap)) * ac)) /\ exists ff_q_mce_integer_sum_ap_summand. ab = ff_q_mce_integer_sum_ap_summand * S ((S (ff_i_mce_integer_sum_ap)) * ac) + (ff_a_mce_integer_sum_ap))) /\ ((((exists ff_h_mce_integer_sum_ap_partial. ff_h_mce_integer_sum_ap_partial + S (ff_r_mce_integer_sum_ap) = S ((S (ff_i_mce_integer_sum_ap)) * ff_v_mce_integer_sum_ap)) /\ exists ff_q_mce_integer_sum_ap_partial. ff_u_mce_integer_sum_ap = ff_q_mce_integer_sum_ap_partial * S ((S (ff_i_mce_integer_sum_ap)) * ff_v_mce_integer_sum_ap) + (ff_r_mce_integer_sum_ap))) /\ ((((exists ff_h_mce_integer_sum_ap_successor. ff_h_mce_integer_sum_ap_successor + S (ff_s_mce_integer_sum_ap) = S ((S (S ff_i_mce_integer_sum_ap)) * ff_v_mce_integer_sum_ap)) /\ exists ff_q_mce_integer_sum_ap_successor. ff_u_mce_integer_sum_ap = ff_q_mce_integer_sum_ap_successor * S ((S (S ff_i_mce_integer_sum_ap)) * ff_v_mce_integer_sum_ap) + (ff_s_mce_integer_sum_ap))) /\ ff_s_mce_integer_sum_ap = ff_r_mce_integer_sum_ap + ff_a_mce_integer_sum_ap)))))) -> (exists ff_u_mce_integer_sum_an ff_v_mce_integer_sum_an. ((((exists ff_h_mce_integer_sum_an_start. ff_h_mce_integer_sum_an_start + S (0) = S ((S (0)) * ff_v_mce_integer_sum_an)) /\ exists ff_q_mce_integer_sum_an_start. ff_u_mce_integer_sum_an = ff_q_mce_integer_sum_an_start * S ((S (0)) * ff_v_mce_integer_sum_an) + (0))) /\ ((((exists ff_h_mce_integer_sum_an_terminal. ff_h_mce_integer_sum_an_terminal + S (n) = S ((S (l)) * ff_v_mce_integer_sum_an)) /\ exists ff_q_mce_integer_sum_an_terminal. ff_u_mce_integer_sum_an = ff_q_mce_integer_sum_an_terminal * S ((S (l)) * ff_v_mce_integer_sum_an) + (n))) /\ forall ff_i_mce_integer_sum_an. (exists ff_lt_mce_integer_sum_an_bound. ff_lt_mce_integer_sum_an_bound + S ff_i_mce_integer_sum_an = l) -> exists ff_a_mce_integer_sum_an ff_r_mce_integer_sum_an ff_s_mce_integer_sum_an. ((((exists ff_h_mce_integer_sum_an_summand. ff_h_mce_integer_sum_an_summand + S (ff_a_mce_integer_sum_an) = S ((S (ff_i_mce_integer_sum_an)) * bc)) /\ exists ff_q_mce_integer_sum_an_summand. bb = ff_q_mce_integer_sum_an_summand * S ((S (ff_i_mce_integer_sum_an)) * bc) + (ff_a_mce_integer_sum_an))) /\ ((((exists ff_h_mce_integer_sum_an_partial. ff_h_mce_integer_sum_an_partial + S (ff_r_mce_integer_sum_an) = S ((S (ff_i_mce_integer_sum_an)) * ff_v_mce_integer_sum_an)) /\ exists ff_q_mce_integer_sum_an_partial. ff_u_mce_integer_sum_an = ff_q_mce_integer_sum_an_partial * S ((S (ff_i_mce_integer_sum_an)) * ff_v_mce_integer_sum_an) + (ff_r_mce_integer_sum_an))) /\ ((((exists ff_h_mce_integer_sum_an_successor. ff_h_mce_integer_sum_an_successor + S (ff_s_mce_integer_sum_an) = S ((S (S ff_i_mce_integer_sum_an)) * ff_v_mce_integer_sum_an)) /\ exists ff_q_mce_integer_sum_an_successor. ff_u_mce_integer_sum_an = ff_q_mce_integer_sum_an_successor * S ((S (S ff_i_mce_integer_sum_an)) * ff_v_mce_integer_sum_an) + (ff_s_mce_integer_sum_an))) /\ ff_s_mce_integer_sum_an = ff_r_mce_integer_sum_an + ff_a_mce_integer_sum_an)))))) -> (exists ff_u_mce_integer_sum_bp ff_v_mce_integer_sum_bp. ((((exists ff_h_mce_integer_sum_bp_start. ff_h_mce_integer_sum_bp_start + S (0) = S ((S (0)) * ff_v_mce_integer_sum_bp)) /\ exists ff_q_mce_integer_sum_bp_start. ff_u_mce_integer_sum_bp = ff_q_mce_integer_sum_bp_start * S ((S (0)) * ff_v_mce_integer_sum_bp) + (0))) /\ ((((exists ff_h_mce_integer_sum_bp_terminal. ff_h_mce_integer_sum_bp_terminal + S (P) = S ((S (l)) * ff_v_mce_integer_sum_bp)) /\ exists ff_q_mce_integer_sum_bp_terminal. ff_u_mce_integer_sum_bp = ff_q_mce_integer_sum_bp_terminal * S ((S (l)) * ff_v_mce_integer_sum_bp) + (P))) /\ forall ff_i_mce_integer_sum_bp. (exists ff_lt_mce_integer_sum_bp_bound. ff_lt_mce_integer_sum_bp_bound + S ff_i_mce_integer_sum_bp = l) -> exists ff_a_mce_integer_sum_bp ff_r_mce_integer_sum_bp ff_s_mce_integer_sum_bp. ((((exists ff_h_mce_integer_sum_bp_summand. ff_h_mce_integer_sum_bp_summand + S (ff_a_mce_integer_sum_bp) = S ((S (ff_i_mce_integer_sum_bp)) * ec)) /\ exists ff_q_mce_integer_sum_bp_summand. eb = ff_q_mce_integer_sum_bp_summand * S ((S (ff_i_mce_integer_sum_bp)) * ec) + (ff_a_mce_integer_sum_bp))) /\ ((((exists ff_h_mce_integer_sum_bp_partial. ff_h_mce_integer_sum_bp_partial + S (ff_r_mce_integer_sum_bp) = S ((S (ff_i_mce_integer_sum_bp)) * ff_v_mce_integer_sum_bp)) /\ exists ff_q_mce_integer_sum_bp_partial. ff_u_mce_integer_sum_bp = ff_q_mce_integer_sum_bp_partial * S ((S (ff_i_mce_integer_sum_bp)) * ff_v_mce_integer_sum_bp) + (ff_r_mce_integer_sum_bp))) /\ ((((exists ff_h_mce_integer_sum_bp_successor. ff_h_mce_integer_sum_bp_successor + S (ff_s_mce_integer_sum_bp) = S ((S (S ff_i_mce_integer_sum_bp)) * ff_v_mce_integer_sum_bp)) /\ exists ff_q_mce_integer_sum_bp_successor. ff_u_mce_integer_sum_bp = ff_q_mce_integer_sum_bp_successor * S ((S (S ff_i_mce_integer_sum_bp)) * ff_v_mce_integer_sum_bp) + (ff_s_mce_integer_sum_bp))) /\ ff_s_mce_integer_sum_bp = ff_r_mce_integer_sum_bp + ff_a_mce_integer_sum_bp)))))) -> (exists ff_u_mce_integer_sum_bn ff_v_mce_integer_sum_bn. ((((exists ff_h_mce_integer_sum_bn_start. ff_h_mce_integer_sum_bn_start + S (0) = S ((S (0)) * ff_v_mce_integer_sum_bn)) /\ exists ff_q_mce_integer_sum_bn_start. ff_u_mce_integer_sum_bn = ff_q_mce_integer_sum_bn_start * S ((S (0)) * ff_v_mce_integer_sum_bn) + (0))) /\ ((((exists ff_h_mce_integer_sum_bn_terminal. ff_h_mce_integer_sum_bn_terminal + S (N) = S ((S (l)) * ff_v_mce_integer_sum_bn)) /\ exists ff_q_mce_integer_sum_bn_terminal. ff_u_mce_integer_sum_bn = ff_q_mce_integer_sum_bn_terminal * S ((S (l)) * ff_v_mce_integer_sum_bn) + (N))) /\ forall ff_i_mce_integer_sum_bn. (exists ff_lt_mce_integer_sum_bn_bound. ff_lt_mce_integer_sum_bn_bound + S ff_i_mce_integer_sum_bn = l) -> exists ff_a_mce_integer_sum_bn ff_r_mce_integer_sum_bn ff_s_mce_integer_sum_bn. ((((exists ff_h_mce_integer_sum_bn_summand. ff_h_mce_integer_sum_bn_summand + S (ff_a_mce_integer_sum_bn) = S ((S (ff_i_mce_integer_sum_bn)) * fc)) /\ exists ff_q_mce_integer_sum_bn_summand. fb = ff_q_mce_integer_sum_bn_summand * S ((S (ff_i_mce_integer_sum_bn)) * fc) + (ff_a_mce_integer_sum_bn))) /\ ((((exists ff_h_mce_integer_sum_bn_partial. ff_h_mce_integer_sum_bn_partial + S (ff_r_mce_integer_sum_bn) = S ((S (ff_i_mce_integer_sum_bn)) * ff_v_mce_integer_sum_bn)) /\ exists ff_q_mce_integer_sum_bn_partial. ff_u_mce_integer_sum_bn = ff_q_mce_integer_sum_bn_partial * S ((S (ff_i_mce_integer_sum_bn)) * ff_v_mce_integer_sum_bn) + (ff_r_mce_integer_sum_bn))) /\ ((((exists ff_h_mce_integer_sum_bn_successor. ff_h_mce_integer_sum_bn_successor + S (ff_s_mce_integer_sum_bn) = S ((S (S ff_i_mce_integer_sum_bn)) * ff_v_mce_integer_sum_bn)) /\ exists ff_q_mce_integer_sum_bn_successor. ff_u_mce_integer_sum_bn = ff_q_mce_integer_sum_bn_successor * S ((S (S ff_i_mce_integer_sum_bn)) * ff_v_mce_integer_sum_bn) + (ff_s_mce_integer_sum_bn))) /\ ff_s_mce_integer_sum_bn = ff_r_mce_integer_sum_bn + ff_a_mce_integer_sum_bn)))))) -> p + N = P + n

forall z up us un ut vp vs vn vt. z = ((((up) + (us)) * S ((up) + (us)) + ((us) + (us))) + (((un) + (ut)) * S ((un) + (ut)) + ((ut) + (ut)))) * S ((((up) + (us)) * S ((up) + (us)) + ((us) + (us))) + (((un) + (ut)) * S ((un) + (ut)) + ((ut) + (ut)))) + ((((un) + (ut)) * S ((un) + (ut)) + ((ut) + (ut))) + (((un) + (ut)) * S ((un) + (ut)) + ((ut) + (ut)))) -> z = ((((vp) + (vs)) * S ((vp) + (vs)) + ((vs) + (vs))) + (((vn) + (vt)) * S ((vn) + (vt)) + ((vt) + (vt)))) * S ((((vp) + (vs)) * S ((vp) + (vs)) + ((vs) + (vs))) + (((vn) + (vt)) * S ((vn) + (vt)) + ((vt) + (vt)))) + ((((vn) + (vt)) * S ((vn) + (vt)) + ((vt) + (vt))) + (((vn) + (vt)) * S ((vn) + (vt)) + ((vt) + (vt)))) -> (up = vp /\ (us = vs /\ (un = vn /\ ut = vt)))

forall code1 code2 left1 right1 left2 right2. (exists sb_pos_ext_left sb_neg_ext_left. (((code1 = 2 * sb_pos_ext_left /\ sb_neg_ext_left = 0) \/ exists sd_half_ext_left. ((code1 = 2 * sd_half_ext_left + 1 /\ sb_pos_ext_left = 0) /\ sb_neg_ext_left = S sd_half_ext_left)) /\ left1 + sb_neg_ext_left = right1 + sb_pos_ext_left)) -> (exists sb_pos_ext_right sb_neg_ext_right. (((code2 = 2 * sb_pos_ext_right /\ sb_neg_ext_right = 0) \/ exists sd_half_ext_right. ((code2 = 2 * sd_half_ext_right + 1 /\ sb_pos_ext_right = 0) /\ sb_neg_ext_right = S sd_half_ext_right)) /\ left2 + sb_neg_ext_right = right2 + sb_pos_ext_right)) -> left1 + right2 = right1 + left2 -> code1 = code2

forall left right code1 code2. (exists sb_pos_functional_left sb_neg_functional_left. (((code1 = 2 * sb_pos_functional_left /\ sb_neg_functional_left = 0) \/ exists sd_half_functional_left. ((code1 = 2 * sd_half_functional_left + 1 /\ sb_pos_functional_left = 0) /\ sb_neg_functional_left = S sd_half_functional_left)) /\ left + sb_neg_functional_left = right + sb_pos_functional_left)) -> (exists sb_pos_functional_right sb_neg_functional_right. (((code2 = 2 * sb_pos_functional_right /\ sb_neg_functional_right = 0) \/ exists sd_half_functional_right. ((code2 = 2 * sd_half_functional_right + 1 /\ sb_pos_functional_right = 0) /\ sb_neg_functional_right = S sd_half_functional_right)) /\ left + sb_neg_functional_right = right + sb_pos_functional_right)) -> code1 = code2

forall left right. exists code. (exists sb_pos_total sb_neg_total. (((code = 2 * sb_pos_total /\ sb_neg_total = 0) \/ exists sd_half_total. ((code = 2 * sd_half_total + 1 /\ sb_pos_total = 0) /\ sb_neg_total = S sd_half_total)) /\ left + sb_neg_total = right + sb_pos_total))

forall code left right. (exists sb_pos_zero sb_neg_zero. (((code = 2 * sb_pos_zero /\ sb_neg_zero = 0) \/ exists sd_half_zero. ((code = 2 * sd_half_zero + 1 /\ sb_pos_zero = 0) /\ sb_neg_zero = S sd_half_zero)) /\ left + sb_neg_zero = right + sb_pos_zero)) -> ((code = 0 -> left = right) /\ (left = right -> code = 0))

forall code pos1 neg1 pos2 neg2. ((code = 2 * pos1 /\ neg1 = 0) \/ exists sd_half_left. ((code = 2 * sd_half_left + 1 /\ pos1 = 0) /\ neg1 = S sd_half_left)) -> ((code = 2 * pos2 /\ neg2 = 0) \/ exists sd_half_right. ((code = 2 * sd_half_right + 1 /\ pos2 = 0) /\ neg2 = S sd_half_right)) -> pos1 = pos2 /\ neg1 = neg2

forall input output pos neg. ((input = 2 * pos /\ neg = 0) \/ exists sd_half_elim_source. ((input = 2 * sd_half_elim_source + 1 /\ pos = 0) /\ neg = S sd_half_elim_source)) -> (exists sn_pos_elim sn_neg_elim. (((input = 2 * sn_pos_elim /\ sn_neg_elim = 0) \/ exists sd_half_elim_input. ((input = 2 * sd_half_elim_input + 1 /\ sn_pos_elim = 0) /\ sn_neg_elim = S sd_half_elim_input)) /\ ((output = 2 * sn_neg_elim /\ sn_pos_elim = 0) \/ exists sd_half_elim_output. ((output = 2 * sd_half_elim_output + 1 /\ sn_neg_elim = 0) /\ sn_pos_elim = S sd_half_elim_output)))) -> ((output = 2 * neg /\ pos = 0) \/ exists sd_half_elim_target. ((output = 2 * sd_half_elim_target + 1 /\ neg = 0) /\ pos = S sd_half_elim_target))

forall input. exists output. (exists sn_pos_total sn_neg_total. (((input = 2 * sn_pos_total /\ sn_neg_total = 0) \/ exists sd_half_total_input. ((input = 2 * sd_half_total_input + 1 /\ sn_pos_total = 0) /\ sn_neg_total = S sd_half_total_input)) /\ ((output = 2 * sn_neg_total /\ sn_pos_total = 0) \/ exists sd_half_total_output. ((output = 2 * sd_half_total_output + 1 /\ sn_neg_total = 0) /\ sn_pos_total = S sd_half_total_output))))