mobius_divisor_sum_nonunit_zero

Exact expanded first-order arithmetic statement

forall N M n. (((exists dst_positive_code_cancel_zero_tabletable dst_positive_scale_cancel_zero_tabletable dst_negative_code_cancel_zero_tabletable dst_negative_scale_cancel_zero_tabletable. (((M) = (((((dst_positive_code_cancel_zero_tabletable) + (dst_positive_scale_cancel_zero_tabletable)) * S ((dst_positive_code_cancel_zero_tabletable) + (dst_positive_scale_cancel_zero_tabletable)) + ((dst_positive_scale_cancel_zero_tabletable) + (dst_positive_scale_cancel_zero_tabletable))) + (((dst_negative_code_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)) * S ((dst_negative_code_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)) + ((dst_negative_scale_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)))) * S ((((dst_positive_code_cancel_zero_tabletable) + (dst_positive_scale_cancel_zero_tabletable)) * S ((dst_positive_code_cancel_zero_tabletable) + (dst_positive_scale_cancel_zero_tabletable)) + ((dst_positive_scale_cancel_zero_tabletable) + (dst_positive_scale_cancel_zero_tabletable))) + (((dst_negative_code_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)) * S ((dst_negative_code_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)) + ((dst_negative_scale_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)))) + ((((dst_negative_code_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)) * S ((dst_negative_code_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)) + ((dst_negative_scale_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable))) + (((dst_negative_code_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)) * S ((dst_negative_code_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)) + ((dst_negative_scale_cancel_zero_tabletable) + (dst_negative_scale_cancel_zero_tabletable)))))) /\ (forall dst_index_cancel_zero_tabletable. (exists pvs_le_gap_cancel_zero_tabletabledomain. pvs_le_gap_cancel_zero_tabletabledomain + (dst_index_cancel_zero_tabletable) = (N)) -> exists dst_positive_cancel_zero_tabletable dst_negative_cancel_zero_tabletable dst_value_cancel_zero_tabletable. ((((exists ff_h_pvs_cancel_zero_tabletableentrypositive. ff_h_pvs_cancel_zero_tabletableentrypositive + S (dst_positive_cancel_zero_tabletable) = S ((S (dst_index_cancel_zero_tabletable)) * dst_positive_scale_cancel_zero_tabletable)) /\ exists ff_q_pvs_cancel_zero_tabletableentrypositive. dst_positive_code_cancel_zero_tabletable = ff_q_pvs_cancel_zero_tabletableentrypositive * S ((S (dst_index_cancel_zero_tabletable)) * dst_positive_scale_cancel_zero_tabletable) + (dst_positive_cancel_zero_tabletable))) /\ (((((exists ff_h_pvs_cancel_zero_tabletableentrynegative. ff_h_pvs_cancel_zero_tabletableentrynegative + S (dst_negative_cancel_zero_tabletable) = S ((S (dst_index_cancel_zero_tabletable)) * dst_negative_scale_cancel_zero_tabletable)) /\ exists ff_q_pvs_cancel_zero_tabletableentrynegative. dst_negative_code_cancel_zero_tabletable = ff_q_pvs_cancel_zero_tabletableentrynegative * S ((S (dst_index_cancel_zero_tabletable)) * dst_negative_scale_cancel_zero_tabletable) + (dst_negative_cancel_zero_tabletable))) /\ (exists ge_balance_positive_cancel_zero_tabletableentryvalue ge_balance_negative_cancel_zero_tabletableentryvalue. (((((dst_value_cancel_zero_tabletable) = 2 * (ge_balance_positive_cancel_zero_tabletableentryvalue) /\ (ge_balance_negative_cancel_zero_tabletableentryvalue) = 0) \/ exists ge_signed_half_cancel_zero_tabletableentryvaluedecode. (((dst_value_cancel_zero_tabletable) = 2 * ge_signed_half_cancel_zero_tabletableentryvaluedecode + 1 /\ (ge_balance_positive_cancel_zero_tabletableentryvalue) = 0) /\ (ge_balance_negative_cancel_zero_tabletableentryvalue) = S ge_signed_half_cancel_zero_tabletableentryvaluedecode))) /\ ((dst_positive_cancel_zero_tabletable) + ge_balance_negative_cancel_zero_tabletableentryvalue = (dst_negative_cancel_zero_tabletable) + ge_balance_positive_cancel_zero_tabletableentryvalue))))))))) /\ (((exists dst_positive_code_cancel_zero_tablezero dst_positive_scale_cancel_zero_tablezero dst_negative_code_cancel_zero_tablezero dst_negative_scale_cancel_zero_tablezero dst_positive_cancel_zero_tablezero dst_negative_cancel_zero_tablezero. (((M) = (((((dst_positive_code_cancel_zero_tablezero) + (dst_positive_scale_cancel_zero_tablezero)) * S ((dst_positive_code_cancel_zero_tablezero) + (dst_positive_scale_cancel_zero_tablezero)) + ((dst_positive_scale_cancel_zero_tablezero) + (dst_positive_scale_cancel_zero_tablezero))) + (((dst_negative_code_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)) * S ((dst_negative_code_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)) + ((dst_negative_scale_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)))) * S ((((dst_positive_code_cancel_zero_tablezero) + (dst_positive_scale_cancel_zero_tablezero)) * S ((dst_positive_code_cancel_zero_tablezero) + (dst_positive_scale_cancel_zero_tablezero)) + ((dst_positive_scale_cancel_zero_tablezero) + (dst_positive_scale_cancel_zero_tablezero))) + (((dst_negative_code_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)) * S ((dst_negative_code_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)) + ((dst_negative_scale_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)))) + ((((dst_negative_code_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)) * S ((dst_negative_code_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)) + ((dst_negative_scale_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero))) + (((dst_negative_code_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)) * S ((dst_negative_code_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)) + ((dst_negative_scale_cancel_zero_tablezero) + (dst_negative_scale_cancel_zero_tablezero)))))) /\ (((((exists ff_h_pvs_cancel_zero_tablezeropositive. ff_h_pvs_cancel_zero_tablezeropositive + S (dst_positive_cancel_zero_tablezero) = S ((S (0)) * dst_positive_scale_cancel_zero_tablezero)) /\ exists ff_q_pvs_cancel_zero_tablezeropositive. dst_positive_code_cancel_zero_tablezero = ff_q_pvs_cancel_zero_tablezeropositive * S ((S (0)) * dst_positive_scale_cancel_zero_tablezero) + (dst_positive_cancel_zero_tablezero))) /\ (((((exists ff_h_pvs_cancel_zero_tablezeronegative. ff_h_pvs_cancel_zero_tablezeronegative + S (dst_negative_cancel_zero_tablezero) = S ((S (0)) * dst_negative_scale_cancel_zero_tablezero)) /\ exists ff_q_pvs_cancel_zero_tablezeronegative. dst_negative_code_cancel_zero_tablezero = ff_q_pvs_cancel_zero_tablezeronegative * S ((S (0)) * dst_negative_scale_cancel_zero_tablezero) + (dst_negative_cancel_zero_tablezero))) /\ (exists ge_balance_positive_cancel_zero_tablezerovalue ge_balance_negative_cancel_zero_tablezerovalue. (((((0) = 2 * (ge_balance_positive_cancel_zero_tablezerovalue) /\ (ge_balance_negative_cancel_zero_tablezerovalue) = 0) \/ exists ge_signed_half_cancel_zero_tablezerovaluedecode. (((0) = 2 * ge_signed_half_cancel_zero_tablezerovaluedecode + 1 /\ (ge_balance_positive_cancel_zero_tablezerovalue) = 0) /\ (ge_balance_negative_cancel_zero_tablezerovalue) = S ge_signed_half_cancel_zero_tablezerovaluedecode))) /\ ((dst_positive_cancel_zero_tablezero) + ge_balance_negative_cancel_zero_tablezerovalue = (dst_negative_cancel_zero_tablezero) + ge_balance_positive_cancel_zero_tablezerovalue))))))))) /\ (forall mt_index_cancel_zero_table mt_value_cancel_zero_table. ~(mt_index_cancel_zero_table=0) -> (exists pvs_le_gap_cancel_zero_tabledomain. pvs_le_gap_cancel_zero_tabledomain + (mt_index_cancel_zero_table) = (N)) -> (exists dst_positive_code_cancel_zero_tableentry dst_positive_scale_cancel_zero_tableentry dst_negative_code_cancel_zero_tableentry dst_negative_scale_cancel_zero_tableentry dst_positive_cancel_zero_tableentry dst_negative_cancel_zero_tableentry. (((M) = (((((dst_positive_code_cancel_zero_tableentry) + (dst_positive_scale_cancel_zero_tableentry)) * S ((dst_positive_code_cancel_zero_tableentry) + (dst_positive_scale_cancel_zero_tableentry)) + ((dst_positive_scale_cancel_zero_tableentry) + (dst_positive_scale_cancel_zero_tableentry))) + (((dst_negative_code_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)) * S ((dst_negative_code_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)) + ((dst_negative_scale_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)))) * S ((((dst_positive_code_cancel_zero_tableentry) + (dst_positive_scale_cancel_zero_tableentry)) * S ((dst_positive_code_cancel_zero_tableentry) + (dst_positive_scale_cancel_zero_tableentry)) + ((dst_positive_scale_cancel_zero_tableentry) + (dst_positive_scale_cancel_zero_tableentry))) + (((dst_negative_code_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)) * S ((dst_negative_code_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)) + ((dst_negative_scale_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)))) + ((((dst_negative_code_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)) * S ((dst_negative_code_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)) + ((dst_negative_scale_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry))) + (((dst_negative_code_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)) * S ((dst_negative_code_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)) + ((dst_negative_scale_cancel_zero_tableentry) + (dst_negative_scale_cancel_zero_tableentry)))))) /\ (((((exists ff_h_pvs_cancel_zero_tableentrypositive. ff_h_pvs_cancel_zero_tableentrypositive + S (dst_positive_cancel_zero_tableentry) = S ((S (mt_index_cancel_zero_table)) * dst_positive_scale_cancel_zero_tableentry)) /\ exists ff_q_pvs_cancel_zero_tableentrypositive. dst_positive_code_cancel_zero_tableentry = ff_q_pvs_cancel_zero_tableentrypositive * S ((S (mt_index_cancel_zero_table)) * dst_positive_scale_cancel_zero_tableentry) + (dst_positive_cancel_zero_tableentry))) /\ (((((exists ff_h_pvs_cancel_zero_tableentrynegative. ff_h_pvs_cancel_zero_tableentrynegative + S (dst_negative_cancel_zero_tableentry) = S ((S (mt_index_cancel_zero_table)) * dst_negative_scale_cancel_zero_tableentry)) /\ exists ff_q_pvs_cancel_zero_tableentrynegative. dst_negative_code_cancel_zero_tableentry = ff_q_pvs_cancel_zero_tableentrynegative * S ((S (mt_index_cancel_zero_table)) * dst_negative_scale_cancel_zero_tableentry) + (dst_negative_cancel_zero_tableentry))) /\ (exists ge_balance_positive_cancel_zero_tableentryvalue ge_balance_negative_cancel_zero_tableentryvalue. (((((mt_value_cancel_zero_table) = 2 * (ge_balance_positive_cancel_zero_tableentryvalue) /\ (ge_balance_negative_cancel_zero_tableentryvalue) = 0) \/ exists ge_signed_half_cancel_zero_tableentryvaluedecode. (((mt_value_cancel_zero_table) = 2 * ge_signed_half_cancel_zero_tableentryvaluedecode + 1 /\ (ge_balance_positive_cancel_zero_tableentryvalue) = 0) /\ (ge_balance_negative_cancel_zero_tableentryvalue) = S ge_signed_half_cancel_zero_tableentryvaluedecode))) /\ ((dst_positive_cancel_zero_tableentry) + ge_balance_negative_cancel_zero_tableentryvalue = (dst_negative_cancel_zero_tableentry) + ge_balance_positive_cancel_zero_tableentryvalue))))))))) -> (((~((mt_index_cancel_zero_table) = 0)) /\ ((((exists mv_square_prime_cancel_zero_tablevaluesquare. ((~((mv_square_prime_cancel_zero_tablevaluesquare) = 1) /\ forall pvs_left_cancel_zero_tablevaluesquareprime pvs_right_cancel_zero_tablevaluesquareprime. (mv_square_prime_cancel_zero_tablevaluesquare) = pvs_left_cancel_zero_tablevaluesquareprime * pvs_right_cancel_zero_tablevaluesquareprime -> pvs_left_cancel_zero_tablevaluesquareprime = 1 \/ pvs_right_cancel_zero_tablevaluesquareprime = 1) /\ (exists pvs_factor_cancel_zero_tablevaluesquaredivisor. (mt_index_cancel_zero_table) = (mv_square_prime_cancel_zero_tablevaluesquare * mv_square_prime_cancel_zero_tablevaluesquare) * pvs_factor_cancel_zero_tablevaluesquaredivisor))) /\ ((mt_value_cancel_zero_table) = 0))) \/ (((((~((mt_index_cancel_zero_table) = 0)) /\ (forall sfd_prime_cancel_zero_tablevaluesquarefree. (~((sfd_prime_cancel_zero_tablevaluesquarefree) = 1) /\ forall pvs_left_cancel_zero_tablevaluesquarefreedomain pvs_right_cancel_zero_tablevaluesquarefreedomain. (sfd_prime_cancel_zero_tablevaluesquarefree) = pvs_left_cancel_zero_tablevaluesquarefreedomain * pvs_right_cancel_zero_tablevaluesquarefreedomain -> pvs_left_cancel_zero_tablevaluesquarefreedomain = 1 \/ pvs_right_cancel_zero_tablevaluesquarefreedomain = 1) -> (exists pvs_le_gap_cancel_zero_tablevaluesquarefreebound. pvs_le_gap_cancel_zero_tablevaluesquarefreebound + (sfd_prime_cancel_zero_tablevaluesquarefree) = (mt_index_cancel_zero_table)) -> ~(exists pvs_factor_cancel_zero_tablevaluesquarefreesquare. (mt_index_cancel_zero_table) = (sfd_prime_cancel_zero_tablevaluesquarefree * sfd_prime_cancel_zero_tablevaluesquarefree) * pvs_factor_cancel_zero_tablevaluesquarefreesquare)))) /\ (exists mv_factor_code_cancel_zero_tablevaluefactors mv_factor_scale_cancel_zero_tablevaluefactors mv_factor_count_cancel_zero_tablevaluefactors. (((~(mt_index_cancel_zero_table = 0) /\ ((exists ff_u_fsat_cancel_zero_tablevaluefactorsfactorization_product ff_v_fsat_cancel_zero_tablevaluefactorsfactorization_product. ((((exists ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_start. ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_cancel_zero_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_start. ff_u_fsat_cancel_zero_tablevaluefactorsfactorization_product = ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_cancel_zero_tablevaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_terminal. ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_terminal + S (mt_index_cancel_zero_table) = S ((S (mv_factor_count_cancel_zero_tablevaluefactors)) * ff_v_fsat_cancel_zero_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_terminal. ff_u_fsat_cancel_zero_tablevaluefactorsfactorization_product = ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_cancel_zero_tablevaluefactors)) * ff_v_fsat_cancel_zero_tablevaluefactorsfactorization_product) + (mt_index_cancel_zero_table))) /\ forall ff_i_fsat_cancel_zero_tablevaluefactorsfactorization_product. (exists ff_lt_fsat_cancel_zero_tablevaluefactorsfactorization_product_bound. ff_lt_fsat_cancel_zero_tablevaluefactorsfactorization_product_bound + S ff_i_fsat_cancel_zero_tablevaluefactorsfactorization_product = mv_factor_count_cancel_zero_tablevaluefactors) -> exists ff_p_fsat_cancel_zero_tablevaluefactorsfactorization_product ff_r_fsat_cancel_zero_tablevaluefactorsfactorization_product ff_s_fsat_cancel_zero_tablevaluefactorsfactorization_product. ((((exists ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_factor. ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_factor + S (ff_p_fsat_cancel_zero_tablevaluefactorsfactorization_product) = S ((S (ff_i_fsat_cancel_zero_tablevaluefactorsfactorization_product)) * mv_factor_scale_cancel_zero_tablevaluefactors)) /\ exists ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_factor. mv_factor_code_cancel_zero_tablevaluefactors = ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_cancel_zero_tablevaluefactorsfactorization_product)) * mv_factor_scale_cancel_zero_tablevaluefactors) + (ff_p_fsat_cancel_zero_tablevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_partial. ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_partial + S (ff_r_fsat_cancel_zero_tablevaluefactorsfactorization_product) = S ((S (ff_i_fsat_cancel_zero_tablevaluefactorsfactorization_product)) * ff_v_fsat_cancel_zero_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_partial. ff_u_fsat_cancel_zero_tablevaluefactorsfactorization_product = ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_cancel_zero_tablevaluefactorsfactorization_product)) * ff_v_fsat_cancel_zero_tablevaluefactorsfactorization_product) + (ff_r_fsat_cancel_zero_tablevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_successor. ff_h_fsat_cancel_zero_tablevaluefactorsfactorization_product_successor + S (ff_s_fsat_cancel_zero_tablevaluefactorsfactorization_product) = S ((S (S ff_i_fsat_cancel_zero_tablevaluefactorsfactorization_product)) * ff_v_fsat_cancel_zero_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_successor. ff_u_fsat_cancel_zero_tablevaluefactorsfactorization_product = ff_q_fsat_cancel_zero_tablevaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_cancel_zero_tablevaluefactorsfactorization_product)) * ff_v_fsat_cancel_zero_tablevaluefactorsfactorization_product) + (ff_s_fsat_cancel_zero_tablevaluefactorsfactorization_product))) /\ ff_s_fsat_cancel_zero_tablevaluefactorsfactorization_product = ff_r_fsat_cancel_zero_tablevaluefactorsfactorization_product * ff_p_fsat_cancel_zero_tablevaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_cancel_zero_tablevaluefactorsfactorization_primes. (exists ftsf_gap_fsat_cancel_zero_tablevaluefactorsfactorization_primes_bound. ftsf_gap_fsat_cancel_zero_tablevaluefactorsfactorization_primes_bound + S ftsf_index_fsat_cancel_zero_tablevaluefactorsfactorization_primes = (mv_factor_count_cancel_zero_tablevaluefactors)) -> exists ftsf_factor_fsat_cancel_zero_tablevaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_cancel_zero_tablevaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_cancel_zero_tablevaluefactorsfactorization_primes)) * mv_factor_scale_cancel_zero_tablevaluefactors)) /\ exists ff_q_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_entry. mv_factor_code_cancel_zero_tablevaluefactors = ff_q_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_cancel_zero_tablevaluefactorsfactorization_primes)) * mv_factor_scale_cancel_zero_tablevaluefactors) + (ftsf_factor_fsat_cancel_zero_tablevaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_cancel_zero_tablevaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_prime. ftsf_factor_fsat_cancel_zero_tablevaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_cancel_zero_tablevaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_cancel_zero_tablevaluefactorsparityeven. (mv_factor_count_cancel_zero_tablevaluefactors) = 2 * mv_even_half_cancel_zero_tablevaluefactorsparityeven) /\ ((mt_value_cancel_zero_table) = 2))) \/ (((exists mv_odd_half_cancel_zero_tablevaluefactorsparityodd. (mv_factor_count_cancel_zero_tablevaluefactors) = 2 * mv_odd_half_cancel_zero_tablevaluefactorsparityodd + 1) /\ ((mt_value_cancel_zero_table) = 1)))))))))))))))) -> ~(n=0) -> ~(n=1) -> (exists pvs_le_gap_cancel_zero_bound. pvs_le_gap_cancel_zero_bound + (n) = (N)) -> (((~((n)=0)) /\ (exists dm_mask_table_cancel_zero_result. ((((exists dst_positive_code_cancel_zero_resultmasktable dst_positive_scale_cancel_zero_resultmasktable dst_negative_code_cancel_zero_resultmasktable dst_negative_scale_cancel_zero_resultmasktable. (((dm_mask_table_cancel_zero_result) = (((((dst_positive_code_cancel_zero_resultmasktable) + (dst_positive_scale_cancel_zero_resultmasktable)) * S ((dst_positive_code_cancel_zero_resultmasktable) + (dst_positive_scale_cancel_zero_resultmasktable)) + ((dst_positive_scale_cancel_zero_resultmasktable) + (dst_positive_scale_cancel_zero_resultmasktable))) + (((dst_negative_code_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)) * S ((dst_negative_code_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)) + ((dst_negative_scale_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)))) * S ((((dst_positive_code_cancel_zero_resultmasktable) + (dst_positive_scale_cancel_zero_resultmasktable)) * S ((dst_positive_code_cancel_zero_resultmasktable) + (dst_positive_scale_cancel_zero_resultmasktable)) + ((dst_positive_scale_cancel_zero_resultmasktable) + (dst_positive_scale_cancel_zero_resultmasktable))) + (((dst_negative_code_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)) * S ((dst_negative_code_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)) + ((dst_negative_scale_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)))) + ((((dst_negative_code_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)) * S ((dst_negative_code_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)) + ((dst_negative_scale_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable))) + (((dst_negative_code_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)) * S ((dst_negative_code_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)) + ((dst_negative_scale_cancel_zero_resultmasktable) + (dst_negative_scale_cancel_zero_resultmasktable)))))) /\ (forall dst_index_cancel_zero_resultmasktable. (exists pvs_le_gap_cancel_zero_resultmasktabledomain. pvs_le_gap_cancel_zero_resultmasktabledomain + (dst_index_cancel_zero_resultmasktable) = (n)) -> exists dst_positive_cancel_zero_resultmasktable dst_negative_cancel_zero_resultmasktable dst_value_cancel_zero_resultmasktable. ((((exists ff_h_pvs_cancel_zero_resultmasktableentrypositive. ff_h_pvs_cancel_zero_resultmasktableentrypositive + S (dst_positive_cancel_zero_resultmasktable) = S ((S (dst_index_cancel_zero_resultmasktable)) * dst_positive_scale_cancel_zero_resultmasktable)) /\ exists ff_q_pvs_cancel_zero_resultmasktableentrypositive. dst_positive_code_cancel_zero_resultmasktable = ff_q_pvs_cancel_zero_resultmasktableentrypositive * S ((S (dst_index_cancel_zero_resultmasktable)) * dst_positive_scale_cancel_zero_resultmasktable) + (dst_positive_cancel_zero_resultmasktable))) /\ (((((exists ff_h_pvs_cancel_zero_resultmasktableentrynegative. ff_h_pvs_cancel_zero_resultmasktableentrynegative + S (dst_negative_cancel_zero_resultmasktable) = S ((S (dst_index_cancel_zero_resultmasktable)) * dst_negative_scale_cancel_zero_resultmasktable)) /\ exists ff_q_pvs_cancel_zero_resultmasktableentrynegative. dst_negative_code_cancel_zero_resultmasktable = ff_q_pvs_cancel_zero_resultmasktableentrynegative * S ((S (dst_index_cancel_zero_resultmasktable)) * dst_negative_scale_cancel_zero_resultmasktable) + (dst_negative_cancel_zero_resultmasktable))) /\ (exists ge_balance_positive_cancel_zero_resultmasktableentryvalue ge_balance_negative_cancel_zero_resultmasktableentryvalue. (((((dst_value_cancel_zero_resultmasktable) = 2 * (ge_balance_positive_cancel_zero_resultmasktableentryvalue) /\ (ge_balance_negative_cancel_zero_resultmasktableentryvalue) = 0) \/ exists ge_signed_half_cancel_zero_resultmasktableentryvaluedecode. (((dst_value_cancel_zero_resultmasktable) = 2 * ge_signed_half_cancel_zero_resultmasktableentryvaluedecode + 1 /\ (ge_balance_positive_cancel_zero_resultmasktableentryvalue) = 0) /\ (ge_balance_negative_cancel_zero_resultmasktableentryvalue) = S ge_signed_half_cancel_zero_resultmasktableentryvaluedecode))) /\ ((dst_positive_cancel_zero_resultmasktable) + ge_balance_negative_cancel_zero_resultmasktableentryvalue = (dst_negative_cancel_zero_resultmasktable) + ge_balance_positive_cancel_zero_resultmasktableentryvalue))))))))) /\ (forall dm_index_cancel_zero_resultmask dm_value_cancel_zero_resultmask. (exists pvs_le_gap_cancel_zero_resultmaskdomain. pvs_le_gap_cancel_zero_resultmaskdomain + (dm_index_cancel_zero_resultmask) = (n)) -> (exists dst_positive_code_cancel_zero_resultmasklookup dst_positive_scale_cancel_zero_resultmasklookup dst_negative_code_cancel_zero_resultmasklookup dst_negative_scale_cancel_zero_resultmasklookup dst_positive_cancel_zero_resultmasklookup dst_negative_cancel_zero_resultmasklookup. (((dm_mask_table_cancel_zero_result) = (((((dst_positive_code_cancel_zero_resultmasklookup) + (dst_positive_scale_cancel_zero_resultmasklookup)) * S ((dst_positive_code_cancel_zero_resultmasklookup) + (dst_positive_scale_cancel_zero_resultmasklookup)) + ((dst_positive_scale_cancel_zero_resultmasklookup) + (dst_positive_scale_cancel_zero_resultmasklookup))) + (((dst_negative_code_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)) * S ((dst_negative_code_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)) + ((dst_negative_scale_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)))) * S ((((dst_positive_code_cancel_zero_resultmasklookup) + (dst_positive_scale_cancel_zero_resultmasklookup)) * S ((dst_positive_code_cancel_zero_resultmasklookup) + (dst_positive_scale_cancel_zero_resultmasklookup)) + ((dst_positive_scale_cancel_zero_resultmasklookup) + (dst_positive_scale_cancel_zero_resultmasklookup))) + (((dst_negative_code_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)) * S ((dst_negative_code_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)) + ((dst_negative_scale_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)))) + ((((dst_negative_code_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)) * S ((dst_negative_code_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)) + ((dst_negative_scale_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup))) + (((dst_negative_code_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)) * S ((dst_negative_code_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)) + ((dst_negative_scale_cancel_zero_resultmasklookup) + (dst_negative_scale_cancel_zero_resultmasklookup)))))) /\ (((((exists ff_h_pvs_cancel_zero_resultmasklookuppositive. ff_h_pvs_cancel_zero_resultmasklookuppositive + S (dst_positive_cancel_zero_resultmasklookup) = S ((S (dm_index_cancel_zero_resultmask)) * dst_positive_scale_cancel_zero_resultmasklookup)) /\ exists ff_q_pvs_cancel_zero_resultmasklookuppositive. dst_positive_code_cancel_zero_resultmasklookup = ff_q_pvs_cancel_zero_resultmasklookuppositive * S ((S (dm_index_cancel_zero_resultmask)) * dst_positive_scale_cancel_zero_resultmasklookup) + (dst_positive_cancel_zero_resultmasklookup))) /\ (((((exists ff_h_pvs_cancel_zero_resultmasklookupnegative. ff_h_pvs_cancel_zero_resultmasklookupnegative + S (dst_negative_cancel_zero_resultmasklookup) = S ((S (dm_index_cancel_zero_resultmask)) * dst_negative_scale_cancel_zero_resultmasklookup)) /\ exists ff_q_pvs_cancel_zero_resultmasklookupnegative. dst_negative_code_cancel_zero_resultmasklookup = ff_q_pvs_cancel_zero_resultmasklookupnegative * S ((S (dm_index_cancel_zero_resultmask)) * dst_negative_scale_cancel_zero_resultmasklookup) + (dst_negative_cancel_zero_resultmasklookup))) /\ (exists ge_balance_positive_cancel_zero_resultmasklookupvalue ge_balance_negative_cancel_zero_resultmasklookupvalue. (((((dm_value_cancel_zero_resultmask) = 2 * (ge_balance_positive_cancel_zero_resultmasklookupvalue) /\ (ge_balance_negative_cancel_zero_resultmasklookupvalue) = 0) \/ exists ge_signed_half_cancel_zero_resultmasklookupvaluedecode. (((dm_value_cancel_zero_resultmask) = 2 * ge_signed_half_cancel_zero_resultmasklookupvaluedecode + 1 /\ (ge_balance_positive_cancel_zero_resultmasklookupvalue) = 0) /\ (ge_balance_negative_cancel_zero_resultmasklookupvalue) = S ge_signed_half_cancel_zero_resultmasklookupvaluedecode))) /\ ((dst_positive_cancel_zero_resultmasklookup) + ge_balance_negative_cancel_zero_resultmasklookupvalue = (dst_negative_cancel_zero_resultmasklookup) + ge_balance_positive_cancel_zero_resultmasklookupvalue))))))))) -> ((((~((dm_index_cancel_zero_resultmask)=0)) /\ (exists dm_quotient_cancel_zero_resultmaskentry. (((n)=(dm_index_cancel_zero_resultmask)*dm_quotient_cancel_zero_resultmaskentry) /\ (exists dst_positive_code_cancel_zero_resultmaskentryinput dst_positive_scale_cancel_zero_resultmaskentryinput dst_negative_code_cancel_zero_resultmaskentryinput dst_negative_scale_cancel_zero_resultmaskentryinput dst_positive_cancel_zero_resultmaskentryinput dst_negative_cancel_zero_resultmaskentryinput. (((M) = (((((dst_positive_code_cancel_zero_resultmaskentryinput) + (dst_positive_scale_cancel_zero_resultmaskentryinput)) * S ((dst_positive_code_cancel_zero_resultmaskentryinput) + (dst_positive_scale_cancel_zero_resultmaskentryinput)) + ((dst_positive_scale_cancel_zero_resultmaskentryinput) + (dst_positive_scale_cancel_zero_resultmaskentryinput))) + (((dst_negative_code_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)) * S ((dst_negative_code_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)) + ((dst_negative_scale_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)))) * S ((((dst_positive_code_cancel_zero_resultmaskentryinput) + (dst_positive_scale_cancel_zero_resultmaskentryinput)) * S ((dst_positive_code_cancel_zero_resultmaskentryinput) + (dst_positive_scale_cancel_zero_resultmaskentryinput)) + ((dst_positive_scale_cancel_zero_resultmaskentryinput) + (dst_positive_scale_cancel_zero_resultmaskentryinput))) + (((dst_negative_code_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)) * S ((dst_negative_code_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)) + ((dst_negative_scale_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)))) + ((((dst_negative_code_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)) * S ((dst_negative_code_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)) + ((dst_negative_scale_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput))) + (((dst_negative_code_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)) * S ((dst_negative_code_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)) + ((dst_negative_scale_cancel_zero_resultmaskentryinput) + (dst_negative_scale_cancel_zero_resultmaskentryinput)))))) /\ (((((exists ff_h_pvs_cancel_zero_resultmaskentryinputpositive. ff_h_pvs_cancel_zero_resultmaskentryinputpositive + S (dst_positive_cancel_zero_resultmaskentryinput) = S ((S (dm_index_cancel_zero_resultmask)) * dst_positive_scale_cancel_zero_resultmaskentryinput)) /\ exists ff_q_pvs_cancel_zero_resultmaskentryinputpositive. dst_positive_code_cancel_zero_resultmaskentryinput = ff_q_pvs_cancel_zero_resultmaskentryinputpositive * S ((S (dm_index_cancel_zero_resultmask)) * dst_positive_scale_cancel_zero_resultmaskentryinput) + (dst_positive_cancel_zero_resultmaskentryinput))) /\ (((((exists ff_h_pvs_cancel_zero_resultmaskentryinputnegative. ff_h_pvs_cancel_zero_resultmaskentryinputnegative + S (dst_negative_cancel_zero_resultmaskentryinput) = S ((S (dm_index_cancel_zero_resultmask)) * dst_negative_scale_cancel_zero_resultmaskentryinput)) /\ exists ff_q_pvs_cancel_zero_resultmaskentryinputnegative. dst_negative_code_cancel_zero_resultmaskentryinput = ff_q_pvs_cancel_zero_resultmaskentryinputnegative * S ((S (dm_index_cancel_zero_resultmask)) * dst_negative_scale_cancel_zero_resultmaskentryinput) + (dst_negative_cancel_zero_resultmaskentryinput))) /\ (exists ge_balance_positive_cancel_zero_resultmaskentryinputvalue ge_balance_negative_cancel_zero_resultmaskentryinputvalue. (((((dm_value_cancel_zero_resultmask) = 2 * (ge_balance_positive_cancel_zero_resultmaskentryinputvalue) /\ (ge_balance_negative_cancel_zero_resultmaskentryinputvalue) = 0) \/ exists ge_signed_half_cancel_zero_resultmaskentryinputvaluedecode. (((dm_value_cancel_zero_resultmask) = 2 * ge_signed_half_cancel_zero_resultmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_cancel_zero_resultmaskentryinputvalue) = 0) /\ (ge_balance_negative_cancel_zero_resultmaskentryinputvalue) = S ge_signed_half_cancel_zero_resultmaskentryinputvaluedecode))) /\ ((dst_positive_cancel_zero_resultmaskentryinput) + ge_balance_negative_cancel_zero_resultmaskentryinputvalue = (dst_negative_cancel_zero_resultmaskentryinput) + ge_balance_positive_cancel_zero_resultmaskentryinputvalue))))))))))))) \/ ((((dm_index_cancel_zero_resultmask)=0 \/ ~(exists pvs_factor_cancel_zero_resultmaskentrynondivisor. (n) = (dm_index_cancel_zero_resultmask) * pvs_factor_cancel_zero_resultmaskentrynondivisor)) /\ ((dm_value_cancel_zero_resultmask)=0))))))) /\ (exists dst_positive_code_cancel_zero_resultfold dst_positive_scale_cancel_zero_resultfold dst_negative_code_cancel_zero_resultfold dst_negative_scale_cancel_zero_resultfold dst_positive_sum_cancel_zero_resultfold dst_negative_sum_cancel_zero_resultfold. (((dm_mask_table_cancel_zero_result) = (((((dst_positive_code_cancel_zero_resultfold) + (dst_positive_scale_cancel_zero_resultfold)) * S ((dst_positive_code_cancel_zero_resultfold) + (dst_positive_scale_cancel_zero_resultfold)) + ((dst_positive_scale_cancel_zero_resultfold) + (dst_positive_scale_cancel_zero_resultfold))) + (((dst_negative_code_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)) * S ((dst_negative_code_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)) + ((dst_negative_scale_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)))) * S ((((dst_positive_code_cancel_zero_resultfold) + (dst_positive_scale_cancel_zero_resultfold)) * S ((dst_positive_code_cancel_zero_resultfold) + (dst_positive_scale_cancel_zero_resultfold)) + ((dst_positive_scale_cancel_zero_resultfold) + (dst_positive_scale_cancel_zero_resultfold))) + (((dst_negative_code_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)) * S ((dst_negative_code_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)) + ((dst_negative_scale_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)))) + ((((dst_negative_code_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)) * S ((dst_negative_code_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)) + ((dst_negative_scale_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold))) + (((dst_negative_code_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)) * S ((dst_negative_code_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)) + ((dst_negative_scale_cancel_zero_resultfold) + (dst_negative_scale_cancel_zero_resultfold)))))) /\ (((exists fs_u_dst_cancel_zero_resultfoldpositive fs_v_dst_cancel_zero_resultfoldpositive. ((((exists fs_h_dst_cancel_zero_resultfoldpositive_body_start. fs_h_dst_cancel_zero_resultfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_cancel_zero_resultfoldpositive)) /\ exists fs_q_dst_cancel_zero_resultfoldpositive_body_start. fs_u_dst_cancel_zero_resultfoldpositive = fs_q_dst_cancel_zero_resultfoldpositive_body_start * S ((S (0)) * fs_v_dst_cancel_zero_resultfoldpositive) + (0))) /\ ((((exists fs_h_dst_cancel_zero_resultfoldpositive_body_terminal. fs_h_dst_cancel_zero_resultfoldpositive_body_terminal + S (dst_positive_sum_cancel_zero_resultfold) = S ((S (S (n))) * fs_v_dst_cancel_zero_resultfoldpositive)) /\ exists fs_q_dst_cancel_zero_resultfoldpositive_body_terminal. fs_u_dst_cancel_zero_resultfoldpositive = fs_q_dst_cancel_zero_resultfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_cancel_zero_resultfoldpositive) + (dst_positive_sum_cancel_zero_resultfold))) /\ forall fs_i_dst_cancel_zero_resultfoldpositive_body_steps. (exists fs_lt_dst_cancel_zero_resultfoldpositive_body_steps_bound. fs_lt_dst_cancel_zero_resultfoldpositive_body_steps_bound + S fs_i_dst_cancel_zero_resultfoldpositive_body_steps = S (n)) -> exists fs_a_dst_cancel_zero_resultfoldpositive_body_steps fs_r_dst_cancel_zero_resultfoldpositive_body_steps fs_s_dst_cancel_zero_resultfoldpositive_body_steps. ((((exists fs_h_dst_cancel_zero_resultfoldpositive_body_steps_summand. fs_h_dst_cancel_zero_resultfoldpositive_body_steps_summand + S (fs_a_dst_cancel_zero_resultfoldpositive_body_steps) = S ((S (fs_i_dst_cancel_zero_resultfoldpositive_body_steps)) * dst_positive_scale_cancel_zero_resultfold)) /\ exists fs_q_dst_cancel_zero_resultfoldpositive_body_steps_summand. dst_positive_code_cancel_zero_resultfold = fs_q_dst_cancel_zero_resultfoldpositive_body_steps_summand * S ((S (fs_i_dst_cancel_zero_resultfoldpositive_body_steps)) * dst_positive_scale_cancel_zero_resultfold) + (fs_a_dst_cancel_zero_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_cancel_zero_resultfoldpositive_body_steps_partial. fs_h_dst_cancel_zero_resultfoldpositive_body_steps_partial + S (fs_r_dst_cancel_zero_resultfoldpositive_body_steps) = S ((S (fs_i_dst_cancel_zero_resultfoldpositive_body_steps)) * fs_v_dst_cancel_zero_resultfoldpositive)) /\ exists fs_q_dst_cancel_zero_resultfoldpositive_body_steps_partial. fs_u_dst_cancel_zero_resultfoldpositive = fs_q_dst_cancel_zero_resultfoldpositive_body_steps_partial * S ((S (fs_i_dst_cancel_zero_resultfoldpositive_body_steps)) * fs_v_dst_cancel_zero_resultfoldpositive) + (fs_r_dst_cancel_zero_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_cancel_zero_resultfoldpositive_body_steps_successor. fs_h_dst_cancel_zero_resultfoldpositive_body_steps_successor + S (fs_s_dst_cancel_zero_resultfoldpositive_body_steps) = S ((S (S fs_i_dst_cancel_zero_resultfoldpositive_body_steps)) * fs_v_dst_cancel_zero_resultfoldpositive)) /\ exists fs_q_dst_cancel_zero_resultfoldpositive_body_steps_successor. fs_u_dst_cancel_zero_resultfoldpositive = fs_q_dst_cancel_zero_resultfoldpositive_body_steps_successor * S ((S (S fs_i_dst_cancel_zero_resultfoldpositive_body_steps)) * fs_v_dst_cancel_zero_resultfoldpositive) + (fs_s_dst_cancel_zero_resultfoldpositive_body_steps))) /\ fs_s_dst_cancel_zero_resultfoldpositive_body_steps = fs_r_dst_cancel_zero_resultfoldpositive_body_steps + fs_a_dst_cancel_zero_resultfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_cancel_zero_resultfoldnegative fs_v_dst_cancel_zero_resultfoldnegative. ((((exists fs_h_dst_cancel_zero_resultfoldnegative_body_start. fs_h_dst_cancel_zero_resultfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_cancel_zero_resultfoldnegative)) /\ exists fs_q_dst_cancel_zero_resultfoldnegative_body_start. fs_u_dst_cancel_zero_resultfoldnegative = fs_q_dst_cancel_zero_resultfoldnegative_body_start * S ((S (0)) * fs_v_dst_cancel_zero_resultfoldnegative) + (0))) /\ ((((exists fs_h_dst_cancel_zero_resultfoldnegative_body_terminal. fs_h_dst_cancel_zero_resultfoldnegative_body_terminal + S (dst_negative_sum_cancel_zero_resultfold) = S ((S (S (n))) * fs_v_dst_cancel_zero_resultfoldnegative)) /\ exists fs_q_dst_cancel_zero_resultfoldnegative_body_terminal. fs_u_dst_cancel_zero_resultfoldnegative = fs_q_dst_cancel_zero_resultfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_cancel_zero_resultfoldnegative) + (dst_negative_sum_cancel_zero_resultfold))) /\ forall fs_i_dst_cancel_zero_resultfoldnegative_body_steps. (exists fs_lt_dst_cancel_zero_resultfoldnegative_body_steps_bound. fs_lt_dst_cancel_zero_resultfoldnegative_body_steps_bound + S fs_i_dst_cancel_zero_resultfoldnegative_body_steps = S (n)) -> exists fs_a_dst_cancel_zero_resultfoldnegative_body_steps fs_r_dst_cancel_zero_resultfoldnegative_body_steps fs_s_dst_cancel_zero_resultfoldnegative_body_steps. ((((exists fs_h_dst_cancel_zero_resultfoldnegative_body_steps_summand. fs_h_dst_cancel_zero_resultfoldnegative_body_steps_summand + S (fs_a_dst_cancel_zero_resultfoldnegative_body_steps) = S ((S (fs_i_dst_cancel_zero_resultfoldnegative_body_steps)) * dst_negative_scale_cancel_zero_resultfold)) /\ exists fs_q_dst_cancel_zero_resultfoldnegative_body_steps_summand. dst_negative_code_cancel_zero_resultfold = fs_q_dst_cancel_zero_resultfoldnegative_body_steps_summand * S ((S (fs_i_dst_cancel_zero_resultfoldnegative_body_steps)) * dst_negative_scale_cancel_zero_resultfold) + (fs_a_dst_cancel_zero_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_cancel_zero_resultfoldnegative_body_steps_partial. fs_h_dst_cancel_zero_resultfoldnegative_body_steps_partial + S (fs_r_dst_cancel_zero_resultfoldnegative_body_steps) = S ((S (fs_i_dst_cancel_zero_resultfoldnegative_body_steps)) * fs_v_dst_cancel_zero_resultfoldnegative)) /\ exists fs_q_dst_cancel_zero_resultfoldnegative_body_steps_partial. fs_u_dst_cancel_zero_resultfoldnegative = fs_q_dst_cancel_zero_resultfoldnegative_body_steps_partial * S ((S (fs_i_dst_cancel_zero_resultfoldnegative_body_steps)) * fs_v_dst_cancel_zero_resultfoldnegative) + (fs_r_dst_cancel_zero_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_cancel_zero_resultfoldnegative_body_steps_successor. fs_h_dst_cancel_zero_resultfoldnegative_body_steps_successor + S (fs_s_dst_cancel_zero_resultfoldnegative_body_steps) = S ((S (S fs_i_dst_cancel_zero_resultfoldnegative_body_steps)) * fs_v_dst_cancel_zero_resultfoldnegative)) /\ exists fs_q_dst_cancel_zero_resultfoldnegative_body_steps_successor. fs_u_dst_cancel_zero_resultfoldnegative = fs_q_dst_cancel_zero_resultfoldnegative_body_steps_successor * S ((S (S fs_i_dst_cancel_zero_resultfoldnegative_body_steps)) * fs_v_dst_cancel_zero_resultfoldnegative) + (fs_s_dst_cancel_zero_resultfoldnegative_body_steps))) /\ fs_s_dst_cancel_zero_resultfoldnegative_body_steps = fs_r_dst_cancel_zero_resultfoldnegative_body_steps + fs_a_dst_cancel_zero_resultfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_cancel_zero_resultfoldresult ge_balance_negative_cancel_zero_resultfoldresult. (((((0) = 2 * (ge_balance_positive_cancel_zero_resultfoldresult) /\ (ge_balance_negative_cancel_zero_resultfoldresult) = 0) \/ exists ge_signed_half_cancel_zero_resultfoldresultdecode. (((0) = 2 * ge_signed_half_cancel_zero_resultfoldresultdecode + 1 /\ (ge_balance_positive_cancel_zero_resultfoldresult) = 0) /\ (ge_balance_negative_cancel_zero_resultfoldresult) = S ge_signed_half_cancel_zero_resultfoldresultdecode))) /\ ((dst_positive_sum_cancel_zero_resultfold) + ge_balance_negative_cancel_zero_resultfoldresult = (dst_negative_sum_cancel_zero_resultfold) + ge_balance_positive_cancel_zero_resultfoldresult)))))))))))))