signed_multiplicative_coprime_product

Exact expanded first-order arithmetic statement

forall N F. (((~((N)=0)) /\ (((exists dst_positive_code_project_law_sourcetable dst_positive_scale_project_law_sourcetable dst_negative_code_project_law_sourcetable dst_negative_scale_project_law_sourcetable. (((F) = (((((dst_positive_code_project_law_sourcetable) + (dst_positive_scale_project_law_sourcetable)) * S ((dst_positive_code_project_law_sourcetable) + (dst_positive_scale_project_law_sourcetable)) + ((dst_positive_scale_project_law_sourcetable) + (dst_positive_scale_project_law_sourcetable))) + (((dst_negative_code_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)) * S ((dst_negative_code_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)) + ((dst_negative_scale_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)))) * S ((((dst_positive_code_project_law_sourcetable) + (dst_positive_scale_project_law_sourcetable)) * S ((dst_positive_code_project_law_sourcetable) + (dst_positive_scale_project_law_sourcetable)) + ((dst_positive_scale_project_law_sourcetable) + (dst_positive_scale_project_law_sourcetable))) + (((dst_negative_code_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)) * S ((dst_negative_code_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)) + ((dst_negative_scale_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)))) + ((((dst_negative_code_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)) * S ((dst_negative_code_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)) + ((dst_negative_scale_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable))) + (((dst_negative_code_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)) * S ((dst_negative_code_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)) + ((dst_negative_scale_project_law_sourcetable) + (dst_negative_scale_project_law_sourcetable)))))) /\ (forall dst_index_project_law_sourcetable. (exists pvs_le_gap_project_law_sourcetabledomain. pvs_le_gap_project_law_sourcetabledomain + (dst_index_project_law_sourcetable) = (N)) -> exists dst_positive_project_law_sourcetable dst_negative_project_law_sourcetable dst_value_project_law_sourcetable. ((((exists ff_h_pvs_project_law_sourcetableentrypositive. ff_h_pvs_project_law_sourcetableentrypositive + S (dst_positive_project_law_sourcetable) = S ((S (dst_index_project_law_sourcetable)) * dst_positive_scale_project_law_sourcetable)) /\ exists ff_q_pvs_project_law_sourcetableentrypositive. dst_positive_code_project_law_sourcetable = ff_q_pvs_project_law_sourcetableentrypositive * S ((S (dst_index_project_law_sourcetable)) * dst_positive_scale_project_law_sourcetable) + (dst_positive_project_law_sourcetable))) /\ (((((exists ff_h_pvs_project_law_sourcetableentrynegative. ff_h_pvs_project_law_sourcetableentrynegative + S (dst_negative_project_law_sourcetable) = S ((S (dst_index_project_law_sourcetable)) * dst_negative_scale_project_law_sourcetable)) /\ exists ff_q_pvs_project_law_sourcetableentrynegative. dst_negative_code_project_law_sourcetable = ff_q_pvs_project_law_sourcetableentrynegative * S ((S (dst_index_project_law_sourcetable)) * dst_negative_scale_project_law_sourcetable) + (dst_negative_project_law_sourcetable))) /\ (exists ge_balance_positive_project_law_sourcetableentryvalue ge_balance_negative_project_law_sourcetableentryvalue. (((((dst_value_project_law_sourcetable) = 2 * (ge_balance_positive_project_law_sourcetableentryvalue) /\ (ge_balance_negative_project_law_sourcetableentryvalue) = 0) \/ exists ge_signed_half_project_law_sourcetableentryvaluedecode. (((dst_value_project_law_sourcetable) = 2 * ge_signed_half_project_law_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_project_law_sourcetableentryvalue) = 0) /\ (ge_balance_negative_project_law_sourcetableentryvalue) = S ge_signed_half_project_law_sourcetableentryvaluedecode))) /\ ((dst_positive_project_law_sourcetable) + ge_balance_negative_project_law_sourcetableentryvalue = (dst_negative_project_law_sourcetable) + ge_balance_positive_project_law_sourcetableentryvalue))))))))) /\ (((exists dst_positive_code_project_law_sourceone dst_positive_scale_project_law_sourceone dst_negative_code_project_law_sourceone dst_negative_scale_project_law_sourceone dst_positive_project_law_sourceone dst_negative_project_law_sourceone. (((F) = (((((dst_positive_code_project_law_sourceone) + (dst_positive_scale_project_law_sourceone)) * S ((dst_positive_code_project_law_sourceone) + (dst_positive_scale_project_law_sourceone)) + ((dst_positive_scale_project_law_sourceone) + (dst_positive_scale_project_law_sourceone))) + (((dst_negative_code_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)) * S ((dst_negative_code_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)) + ((dst_negative_scale_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)))) * S ((((dst_positive_code_project_law_sourceone) + (dst_positive_scale_project_law_sourceone)) * S ((dst_positive_code_project_law_sourceone) + (dst_positive_scale_project_law_sourceone)) + ((dst_positive_scale_project_law_sourceone) + (dst_positive_scale_project_law_sourceone))) + (((dst_negative_code_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)) * S ((dst_negative_code_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)) + ((dst_negative_scale_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)))) + ((((dst_negative_code_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)) * S ((dst_negative_code_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)) + ((dst_negative_scale_project_law_sourceone) + (dst_negative_scale_project_law_sourceone))) + (((dst_negative_code_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)) * S ((dst_negative_code_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)) + ((dst_negative_scale_project_law_sourceone) + (dst_negative_scale_project_law_sourceone)))))) /\ (((((exists ff_h_pvs_project_law_sourceonepositive. ff_h_pvs_project_law_sourceonepositive + S (dst_positive_project_law_sourceone) = S ((S (1)) * dst_positive_scale_project_law_sourceone)) /\ exists ff_q_pvs_project_law_sourceonepositive. dst_positive_code_project_law_sourceone = ff_q_pvs_project_law_sourceonepositive * S ((S (1)) * dst_positive_scale_project_law_sourceone) + (dst_positive_project_law_sourceone))) /\ (((((exists ff_h_pvs_project_law_sourceonenegative. ff_h_pvs_project_law_sourceonenegative + S (dst_negative_project_law_sourceone) = S ((S (1)) * dst_negative_scale_project_law_sourceone)) /\ exists ff_q_pvs_project_law_sourceonenegative. dst_negative_code_project_law_sourceone = ff_q_pvs_project_law_sourceonenegative * S ((S (1)) * dst_negative_scale_project_law_sourceone) + (dst_negative_project_law_sourceone))) /\ (exists ge_balance_positive_project_law_sourceonevalue ge_balance_negative_project_law_sourceonevalue. (((((2) = 2 * (ge_balance_positive_project_law_sourceonevalue) /\ (ge_balance_negative_project_law_sourceonevalue) = 0) \/ exists ge_signed_half_project_law_sourceonevaluedecode. (((2) = 2 * ge_signed_half_project_law_sourceonevaluedecode + 1 /\ (ge_balance_positive_project_law_sourceonevalue) = 0) /\ (ge_balance_negative_project_law_sourceonevalue) = S ge_signed_half_project_law_sourceonevaluedecode))) /\ ((dst_positive_project_law_sourceone) + ge_balance_negative_project_law_sourceonevalue = (dst_negative_project_law_sourceone) + ge_balance_positive_project_law_sourceonevalue))))))))) /\ (forall mp_a_project_law_source mp_b_project_law_source mp_x_project_law_source mp_y_project_law_source mp_z_project_law_source. ~(mp_a_project_law_source=0) -> ~(mp_b_project_law_source=0) -> (exists pvs_le_gap_project_law_sourcebound. pvs_le_gap_project_law_sourcebound + (mp_a_project_law_source*mp_b_project_law_source) = (N)) -> (forall frp_divisor_project_law_sourcecoprime. (exists frp_left_factor_project_law_sourcecoprime. mp_a_project_law_source = frp_divisor_project_law_sourcecoprime * frp_left_factor_project_law_sourcecoprime) -> (exists frp_right_factor_project_law_sourcecoprime. mp_b_project_law_source = frp_divisor_project_law_sourcecoprime * frp_right_factor_project_law_sourcecoprime) -> frp_divisor_project_law_sourcecoprime = 1) -> (exists dst_positive_code_project_law_sourcefirst dst_positive_scale_project_law_sourcefirst dst_negative_code_project_law_sourcefirst dst_negative_scale_project_law_sourcefirst dst_positive_project_law_sourcefirst dst_negative_project_law_sourcefirst. (((F) = (((((dst_positive_code_project_law_sourcefirst) + (dst_positive_scale_project_law_sourcefirst)) * S ((dst_positive_code_project_law_sourcefirst) + (dst_positive_scale_project_law_sourcefirst)) + ((dst_positive_scale_project_law_sourcefirst) + (dst_positive_scale_project_law_sourcefirst))) + (((dst_negative_code_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)) * S ((dst_negative_code_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)) + ((dst_negative_scale_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)))) * S ((((dst_positive_code_project_law_sourcefirst) + (dst_positive_scale_project_law_sourcefirst)) * S ((dst_positive_code_project_law_sourcefirst) + (dst_positive_scale_project_law_sourcefirst)) + ((dst_positive_scale_project_law_sourcefirst) + (dst_positive_scale_project_law_sourcefirst))) + (((dst_negative_code_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)) * S ((dst_negative_code_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)) + ((dst_negative_scale_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)))) + ((((dst_negative_code_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)) * S ((dst_negative_code_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)) + ((dst_negative_scale_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst))) + (((dst_negative_code_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)) * S ((dst_negative_code_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)) + ((dst_negative_scale_project_law_sourcefirst) + (dst_negative_scale_project_law_sourcefirst)))))) /\ (((((exists ff_h_pvs_project_law_sourcefirstpositive. ff_h_pvs_project_law_sourcefirstpositive + S (dst_positive_project_law_sourcefirst) = S ((S (mp_a_project_law_source)) * dst_positive_scale_project_law_sourcefirst)) /\ exists ff_q_pvs_project_law_sourcefirstpositive. dst_positive_code_project_law_sourcefirst = ff_q_pvs_project_law_sourcefirstpositive * S ((S (mp_a_project_law_source)) * dst_positive_scale_project_law_sourcefirst) + (dst_positive_project_law_sourcefirst))) /\ (((((exists ff_h_pvs_project_law_sourcefirstnegative. ff_h_pvs_project_law_sourcefirstnegative + S (dst_negative_project_law_sourcefirst) = S ((S (mp_a_project_law_source)) * dst_negative_scale_project_law_sourcefirst)) /\ exists ff_q_pvs_project_law_sourcefirstnegative. dst_negative_code_project_law_sourcefirst = ff_q_pvs_project_law_sourcefirstnegative * S ((S (mp_a_project_law_source)) * dst_negative_scale_project_law_sourcefirst) + (dst_negative_project_law_sourcefirst))) /\ (exists ge_balance_positive_project_law_sourcefirstvalue ge_balance_negative_project_law_sourcefirstvalue. (((((mp_x_project_law_source) = 2 * (ge_balance_positive_project_law_sourcefirstvalue) /\ (ge_balance_negative_project_law_sourcefirstvalue) = 0) \/ exists ge_signed_half_project_law_sourcefirstvaluedecode. (((mp_x_project_law_source) = 2 * ge_signed_half_project_law_sourcefirstvaluedecode + 1 /\ (ge_balance_positive_project_law_sourcefirstvalue) = 0) /\ (ge_balance_negative_project_law_sourcefirstvalue) = S ge_signed_half_project_law_sourcefirstvaluedecode))) /\ ((dst_positive_project_law_sourcefirst) + ge_balance_negative_project_law_sourcefirstvalue = (dst_negative_project_law_sourcefirst) + ge_balance_positive_project_law_sourcefirstvalue))))))))) -> (exists dst_positive_code_project_law_sourcesecond dst_positive_scale_project_law_sourcesecond dst_negative_code_project_law_sourcesecond dst_negative_scale_project_law_sourcesecond dst_positive_project_law_sourcesecond dst_negative_project_law_sourcesecond. (((F) = (((((dst_positive_code_project_law_sourcesecond) + (dst_positive_scale_project_law_sourcesecond)) * S ((dst_positive_code_project_law_sourcesecond) + (dst_positive_scale_project_law_sourcesecond)) + ((dst_positive_scale_project_law_sourcesecond) + (dst_positive_scale_project_law_sourcesecond))) + (((dst_negative_code_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)) * S ((dst_negative_code_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)) + ((dst_negative_scale_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)))) * S ((((dst_positive_code_project_law_sourcesecond) + (dst_positive_scale_project_law_sourcesecond)) * S ((dst_positive_code_project_law_sourcesecond) + (dst_positive_scale_project_law_sourcesecond)) + ((dst_positive_scale_project_law_sourcesecond) + (dst_positive_scale_project_law_sourcesecond))) + (((dst_negative_code_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)) * S ((dst_negative_code_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)) + ((dst_negative_scale_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)))) + ((((dst_negative_code_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)) * S ((dst_negative_code_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)) + ((dst_negative_scale_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond))) + (((dst_negative_code_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)) * S ((dst_negative_code_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)) + ((dst_negative_scale_project_law_sourcesecond) + (dst_negative_scale_project_law_sourcesecond)))))) /\ (((((exists ff_h_pvs_project_law_sourcesecondpositive. ff_h_pvs_project_law_sourcesecondpositive + S (dst_positive_project_law_sourcesecond) = S ((S (mp_b_project_law_source)) * dst_positive_scale_project_law_sourcesecond)) /\ exists ff_q_pvs_project_law_sourcesecondpositive. dst_positive_code_project_law_sourcesecond = ff_q_pvs_project_law_sourcesecondpositive * S ((S (mp_b_project_law_source)) * dst_positive_scale_project_law_sourcesecond) + (dst_positive_project_law_sourcesecond))) /\ (((((exists ff_h_pvs_project_law_sourcesecondnegative. ff_h_pvs_project_law_sourcesecondnegative + S (dst_negative_project_law_sourcesecond) = S ((S (mp_b_project_law_source)) * dst_negative_scale_project_law_sourcesecond)) /\ exists ff_q_pvs_project_law_sourcesecondnegative. dst_negative_code_project_law_sourcesecond = ff_q_pvs_project_law_sourcesecondnegative * S ((S (mp_b_project_law_source)) * dst_negative_scale_project_law_sourcesecond) + (dst_negative_project_law_sourcesecond))) /\ (exists ge_balance_positive_project_law_sourcesecondvalue ge_balance_negative_project_law_sourcesecondvalue. (((((mp_y_project_law_source) = 2 * (ge_balance_positive_project_law_sourcesecondvalue) /\ (ge_balance_negative_project_law_sourcesecondvalue) = 0) \/ exists ge_signed_half_project_law_sourcesecondvaluedecode. (((mp_y_project_law_source) = 2 * ge_signed_half_project_law_sourcesecondvaluedecode + 1 /\ (ge_balance_positive_project_law_sourcesecondvalue) = 0) /\ (ge_balance_negative_project_law_sourcesecondvalue) = S ge_signed_half_project_law_sourcesecondvaluedecode))) /\ ((dst_positive_project_law_sourcesecond) + ge_balance_negative_project_law_sourcesecondvalue = (dst_negative_project_law_sourcesecond) + ge_balance_positive_project_law_sourcesecondvalue))))))))) -> (exists dst_positive_code_project_law_sourceproduct dst_positive_scale_project_law_sourceproduct dst_negative_code_project_law_sourceproduct dst_negative_scale_project_law_sourceproduct dst_positive_project_law_sourceproduct dst_negative_project_law_sourceproduct. (((F) = (((((dst_positive_code_project_law_sourceproduct) + (dst_positive_scale_project_law_sourceproduct)) * S ((dst_positive_code_project_law_sourceproduct) + (dst_positive_scale_project_law_sourceproduct)) + ((dst_positive_scale_project_law_sourceproduct) + (dst_positive_scale_project_law_sourceproduct))) + (((dst_negative_code_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)) * S ((dst_negative_code_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)) + ((dst_negative_scale_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)))) * S ((((dst_positive_code_project_law_sourceproduct) + (dst_positive_scale_project_law_sourceproduct)) * S ((dst_positive_code_project_law_sourceproduct) + (dst_positive_scale_project_law_sourceproduct)) + ((dst_positive_scale_project_law_sourceproduct) + (dst_positive_scale_project_law_sourceproduct))) + (((dst_negative_code_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)) * S ((dst_negative_code_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)) + ((dst_negative_scale_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)))) + ((((dst_negative_code_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)) * S ((dst_negative_code_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)) + ((dst_negative_scale_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct))) + (((dst_negative_code_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)) * S ((dst_negative_code_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)) + ((dst_negative_scale_project_law_sourceproduct) + (dst_negative_scale_project_law_sourceproduct)))))) /\ (((((exists ff_h_pvs_project_law_sourceproductpositive. ff_h_pvs_project_law_sourceproductpositive + S (dst_positive_project_law_sourceproduct) = S ((S (mp_a_project_law_source*mp_b_project_law_source)) * dst_positive_scale_project_law_sourceproduct)) /\ exists ff_q_pvs_project_law_sourceproductpositive. dst_positive_code_project_law_sourceproduct = ff_q_pvs_project_law_sourceproductpositive * S ((S (mp_a_project_law_source*mp_b_project_law_source)) * dst_positive_scale_project_law_sourceproduct) + (dst_positive_project_law_sourceproduct))) /\ (((((exists ff_h_pvs_project_law_sourceproductnegative. ff_h_pvs_project_law_sourceproductnegative + S (dst_negative_project_law_sourceproduct) = S ((S (mp_a_project_law_source*mp_b_project_law_source)) * dst_negative_scale_project_law_sourceproduct)) /\ exists ff_q_pvs_project_law_sourceproductnegative. dst_negative_code_project_law_sourceproduct = ff_q_pvs_project_law_sourceproductnegative * S ((S (mp_a_project_law_source*mp_b_project_law_source)) * dst_negative_scale_project_law_sourceproduct) + (dst_negative_project_law_sourceproduct))) /\ (exists ge_balance_positive_project_law_sourceproductvalue ge_balance_negative_project_law_sourceproductvalue. (((((mp_z_project_law_source) = 2 * (ge_balance_positive_project_law_sourceproductvalue) /\ (ge_balance_negative_project_law_sourceproductvalue) = 0) \/ exists ge_signed_half_project_law_sourceproductvaluedecode. (((mp_z_project_law_source) = 2 * ge_signed_half_project_law_sourceproductvaluedecode + 1 /\ (ge_balance_positive_project_law_sourceproductvalue) = 0) /\ (ge_balance_negative_project_law_sourceproductvalue) = S ge_signed_half_project_law_sourceproductvaluedecode))) /\ ((dst_positive_project_law_sourceproduct) + ge_balance_negative_project_law_sourceproductvalue = (dst_negative_project_law_sourceproduct) + ge_balance_positive_project_law_sourceproductvalue))))))))) -> (exists sto_ap_project_law_sourcelaw sto_an_project_law_sourcelaw sto_bp_project_law_sourcelaw sto_bn_project_law_sourcelaw sto_cp_project_law_sourcelaw sto_cn_project_law_sourcelaw. (((((mp_x_project_law_source) = 2 * (sto_ap_project_law_sourcelaw) /\ (sto_an_project_law_sourcelaw) = 0) \/ exists ge_signed_half_project_law_sourcelawleft. (((mp_x_project_law_source) = 2 * ge_signed_half_project_law_sourcelawleft + 1 /\ (sto_ap_project_law_sourcelaw) = 0) /\ (sto_an_project_law_sourcelaw) = S ge_signed_half_project_law_sourcelawleft))) /\ ((((((mp_y_project_law_source) = 2 * (sto_bp_project_law_sourcelaw) /\ (sto_bn_project_law_sourcelaw) = 0) \/ exists ge_signed_half_project_law_sourcelawright. (((mp_y_project_law_source) = 2 * ge_signed_half_project_law_sourcelawright + 1 /\ (sto_bp_project_law_sourcelaw) = 0) /\ (sto_bn_project_law_sourcelaw) = S ge_signed_half_project_law_sourcelawright))) /\ ((((((mp_z_project_law_source) = 2 * (sto_cp_project_law_sourcelaw) /\ (sto_cn_project_law_sourcelaw) = 0) \/ exists ge_signed_half_project_law_sourcelawoutput. (((mp_z_project_law_source) = 2 * ge_signed_half_project_law_sourcelawoutput + 1 /\ (sto_cp_project_law_sourcelaw) = 0) /\ (sto_cn_project_law_sourcelaw) = S ge_signed_half_project_law_sourcelawoutput))) /\ ((sto_ap_project_law_sourcelaw * sto_bp_project_law_sourcelaw + sto_an_project_law_sourcelaw * sto_bn_project_law_sourcelaw) + sto_cn_project_law_sourcelaw = (sto_ap_project_law_sourcelaw * sto_bn_project_law_sourcelaw + sto_an_project_law_sourcelaw * sto_bp_project_law_sourcelaw) + sto_cp_project_law_sourcelaw)))))))))))))) -> (forall a b x y z. ~(a=0) -> ~(b=0) -> (exists pvs_le_gap_project_law_targetbound. pvs_le_gap_project_law_targetbound + (a*b) = (N)) -> (forall frp_divisor_project_law_targetcoprime. (exists frp_left_factor_project_law_targetcoprime. a = frp_divisor_project_law_targetcoprime * frp_left_factor_project_law_targetcoprime) -> (exists frp_right_factor_project_law_targetcoprime. b = frp_divisor_project_law_targetcoprime * frp_right_factor_project_law_targetcoprime) -> frp_divisor_project_law_targetcoprime = 1) -> (exists dst_positive_code_project_law_targetfirst dst_positive_scale_project_law_targetfirst dst_negative_code_project_law_targetfirst dst_negative_scale_project_law_targetfirst dst_positive_project_law_targetfirst dst_negative_project_law_targetfirst. (((F) = (((((dst_positive_code_project_law_targetfirst) + (dst_positive_scale_project_law_targetfirst)) * S ((dst_positive_code_project_law_targetfirst) + (dst_positive_scale_project_law_targetfirst)) + ((dst_positive_scale_project_law_targetfirst) + (dst_positive_scale_project_law_targetfirst))) + (((dst_negative_code_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)) * S ((dst_negative_code_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)) + ((dst_negative_scale_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)))) * S ((((dst_positive_code_project_law_targetfirst) + (dst_positive_scale_project_law_targetfirst)) * S ((dst_positive_code_project_law_targetfirst) + (dst_positive_scale_project_law_targetfirst)) + ((dst_positive_scale_project_law_targetfirst) + (dst_positive_scale_project_law_targetfirst))) + (((dst_negative_code_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)) * S ((dst_negative_code_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)) + ((dst_negative_scale_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)))) + ((((dst_negative_code_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)) * S ((dst_negative_code_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)) + ((dst_negative_scale_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst))) + (((dst_negative_code_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)) * S ((dst_negative_code_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)) + ((dst_negative_scale_project_law_targetfirst) + (dst_negative_scale_project_law_targetfirst)))))) /\ (((((exists ff_h_pvs_project_law_targetfirstpositive. ff_h_pvs_project_law_targetfirstpositive + S (dst_positive_project_law_targetfirst) = S ((S (a)) * dst_positive_scale_project_law_targetfirst)) /\ exists ff_q_pvs_project_law_targetfirstpositive. dst_positive_code_project_law_targetfirst = ff_q_pvs_project_law_targetfirstpositive * S ((S (a)) * dst_positive_scale_project_law_targetfirst) + (dst_positive_project_law_targetfirst))) /\ (((((exists ff_h_pvs_project_law_targetfirstnegative. ff_h_pvs_project_law_targetfirstnegative + S (dst_negative_project_law_targetfirst) = S ((S (a)) * dst_negative_scale_project_law_targetfirst)) /\ exists ff_q_pvs_project_law_targetfirstnegative. dst_negative_code_project_law_targetfirst = ff_q_pvs_project_law_targetfirstnegative * S ((S (a)) * dst_negative_scale_project_law_targetfirst) + (dst_negative_project_law_targetfirst))) /\ (exists ge_balance_positive_project_law_targetfirstvalue ge_balance_negative_project_law_targetfirstvalue. (((((x) = 2 * (ge_balance_positive_project_law_targetfirstvalue) /\ (ge_balance_negative_project_law_targetfirstvalue) = 0) \/ exists ge_signed_half_project_law_targetfirstvaluedecode. (((x) = 2 * ge_signed_half_project_law_targetfirstvaluedecode + 1 /\ (ge_balance_positive_project_law_targetfirstvalue) = 0) /\ (ge_balance_negative_project_law_targetfirstvalue) = S ge_signed_half_project_law_targetfirstvaluedecode))) /\ ((dst_positive_project_law_targetfirst) + ge_balance_negative_project_law_targetfirstvalue = (dst_negative_project_law_targetfirst) + ge_balance_positive_project_law_targetfirstvalue))))))))) -> (exists dst_positive_code_project_law_targetsecond dst_positive_scale_project_law_targetsecond dst_negative_code_project_law_targetsecond dst_negative_scale_project_law_targetsecond dst_positive_project_law_targetsecond dst_negative_project_law_targetsecond. (((F) = (((((dst_positive_code_project_law_targetsecond) + (dst_positive_scale_project_law_targetsecond)) * S ((dst_positive_code_project_law_targetsecond) + (dst_positive_scale_project_law_targetsecond)) + ((dst_positive_scale_project_law_targetsecond) + (dst_positive_scale_project_law_targetsecond))) + (((dst_negative_code_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)) * S ((dst_negative_code_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)) + ((dst_negative_scale_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)))) * S ((((dst_positive_code_project_law_targetsecond) + (dst_positive_scale_project_law_targetsecond)) * S ((dst_positive_code_project_law_targetsecond) + (dst_positive_scale_project_law_targetsecond)) + ((dst_positive_scale_project_law_targetsecond) + (dst_positive_scale_project_law_targetsecond))) + (((dst_negative_code_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)) * S ((dst_negative_code_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)) + ((dst_negative_scale_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)))) + ((((dst_negative_code_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)) * S ((dst_negative_code_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)) + ((dst_negative_scale_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond))) + (((dst_negative_code_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)) * S ((dst_negative_code_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)) + ((dst_negative_scale_project_law_targetsecond) + (dst_negative_scale_project_law_targetsecond)))))) /\ (((((exists ff_h_pvs_project_law_targetsecondpositive. ff_h_pvs_project_law_targetsecondpositive + S (dst_positive_project_law_targetsecond) = S ((S (b)) * dst_positive_scale_project_law_targetsecond)) /\ exists ff_q_pvs_project_law_targetsecondpositive. dst_positive_code_project_law_targetsecond = ff_q_pvs_project_law_targetsecondpositive * S ((S (b)) * dst_positive_scale_project_law_targetsecond) + (dst_positive_project_law_targetsecond))) /\ (((((exists ff_h_pvs_project_law_targetsecondnegative. ff_h_pvs_project_law_targetsecondnegative + S (dst_negative_project_law_targetsecond) = S ((S (b)) * dst_negative_scale_project_law_targetsecond)) /\ exists ff_q_pvs_project_law_targetsecondnegative. dst_negative_code_project_law_targetsecond = ff_q_pvs_project_law_targetsecondnegative * S ((S (b)) * dst_negative_scale_project_law_targetsecond) + (dst_negative_project_law_targetsecond))) /\ (exists ge_balance_positive_project_law_targetsecondvalue ge_balance_negative_project_law_targetsecondvalue. (((((y) = 2 * (ge_balance_positive_project_law_targetsecondvalue) /\ (ge_balance_negative_project_law_targetsecondvalue) = 0) \/ exists ge_signed_half_project_law_targetsecondvaluedecode. (((y) = 2 * ge_signed_half_project_law_targetsecondvaluedecode + 1 /\ (ge_balance_positive_project_law_targetsecondvalue) = 0) /\ (ge_balance_negative_project_law_targetsecondvalue) = S ge_signed_half_project_law_targetsecondvaluedecode))) /\ ((dst_positive_project_law_targetsecond) + ge_balance_negative_project_law_targetsecondvalue = (dst_negative_project_law_targetsecond) + ge_balance_positive_project_law_targetsecondvalue))))))))) -> (exists dst_positive_code_project_law_targetproduct dst_positive_scale_project_law_targetproduct dst_negative_code_project_law_targetproduct dst_negative_scale_project_law_targetproduct dst_positive_project_law_targetproduct dst_negative_project_law_targetproduct. (((F) = (((((dst_positive_code_project_law_targetproduct) + (dst_positive_scale_project_law_targetproduct)) * S ((dst_positive_code_project_law_targetproduct) + (dst_positive_scale_project_law_targetproduct)) + ((dst_positive_scale_project_law_targetproduct) + (dst_positive_scale_project_law_targetproduct))) + (((dst_negative_code_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)) * S ((dst_negative_code_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)) + ((dst_negative_scale_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)))) * S ((((dst_positive_code_project_law_targetproduct) + (dst_positive_scale_project_law_targetproduct)) * S ((dst_positive_code_project_law_targetproduct) + (dst_positive_scale_project_law_targetproduct)) + ((dst_positive_scale_project_law_targetproduct) + (dst_positive_scale_project_law_targetproduct))) + (((dst_negative_code_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)) * S ((dst_negative_code_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)) + ((dst_negative_scale_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)))) + ((((dst_negative_code_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)) * S ((dst_negative_code_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)) + ((dst_negative_scale_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct))) + (((dst_negative_code_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)) * S ((dst_negative_code_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)) + ((dst_negative_scale_project_law_targetproduct) + (dst_negative_scale_project_law_targetproduct)))))) /\ (((((exists ff_h_pvs_project_law_targetproductpositive. ff_h_pvs_project_law_targetproductpositive + S (dst_positive_project_law_targetproduct) = S ((S (a*b)) * dst_positive_scale_project_law_targetproduct)) /\ exists ff_q_pvs_project_law_targetproductpositive. dst_positive_code_project_law_targetproduct = ff_q_pvs_project_law_targetproductpositive * S ((S (a*b)) * dst_positive_scale_project_law_targetproduct) + (dst_positive_project_law_targetproduct))) /\ (((((exists ff_h_pvs_project_law_targetproductnegative. ff_h_pvs_project_law_targetproductnegative + S (dst_negative_project_law_targetproduct) = S ((S (a*b)) * dst_negative_scale_project_law_targetproduct)) /\ exists ff_q_pvs_project_law_targetproductnegative. dst_negative_code_project_law_targetproduct = ff_q_pvs_project_law_targetproductnegative * S ((S (a*b)) * dst_negative_scale_project_law_targetproduct) + (dst_negative_project_law_targetproduct))) /\ (exists ge_balance_positive_project_law_targetproductvalue ge_balance_negative_project_law_targetproductvalue. (((((z) = 2 * (ge_balance_positive_project_law_targetproductvalue) /\ (ge_balance_negative_project_law_targetproductvalue) = 0) \/ exists ge_signed_half_project_law_targetproductvaluedecode. (((z) = 2 * ge_signed_half_project_law_targetproductvaluedecode + 1 /\ (ge_balance_positive_project_law_targetproductvalue) = 0) /\ (ge_balance_negative_project_law_targetproductvalue) = S ge_signed_half_project_law_targetproductvaluedecode))) /\ ((dst_positive_project_law_targetproduct) + ge_balance_negative_project_law_targetproductvalue = (dst_negative_project_law_targetproduct) + ge_balance_positive_project_law_targetproductvalue))))))))) -> (exists sto_ap_project_law_targetlaw sto_an_project_law_targetlaw sto_bp_project_law_targetlaw sto_bn_project_law_targetlaw sto_cp_project_law_targetlaw sto_cn_project_law_targetlaw. (((((x) = 2 * (sto_ap_project_law_targetlaw) /\ (sto_an_project_law_targetlaw) = 0) \/ exists ge_signed_half_project_law_targetlawleft. (((x) = 2 * ge_signed_half_project_law_targetlawleft + 1 /\ (sto_ap_project_law_targetlaw) = 0) /\ (sto_an_project_law_targetlaw) = S ge_signed_half_project_law_targetlawleft))) /\ ((((((y) = 2 * (sto_bp_project_law_targetlaw) /\ (sto_bn_project_law_targetlaw) = 0) \/ exists ge_signed_half_project_law_targetlawright. (((y) = 2 * ge_signed_half_project_law_targetlawright + 1 /\ (sto_bp_project_law_targetlaw) = 0) /\ (sto_bn_project_law_targetlaw) = S ge_signed_half_project_law_targetlawright))) /\ ((((((z) = 2 * (sto_cp_project_law_targetlaw) /\ (sto_cn_project_law_targetlaw) = 0) \/ exists ge_signed_half_project_law_targetlawoutput. (((z) = 2 * ge_signed_half_project_law_targetlawoutput + 1 /\ (sto_cp_project_law_targetlaw) = 0) /\ (sto_cn_project_law_targetlaw) = S ge_signed_half_project_law_targetlawoutput))) /\ ((sto_ap_project_law_targetlaw * sto_bp_project_law_targetlaw + sto_an_project_law_targetlaw * sto_bn_project_law_targetlaw) + sto_cn_project_law_targetlaw = (sto_ap_project_law_targetlaw * sto_bn_project_law_targetlaw + sto_an_project_law_targetlaw * sto_bp_project_law_targetlaw) + sto_cp_project_law_targetlaw))))))))