Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Exact expanded first-order arithmetic statement
forall N F G m n A B T Q r s. (((((~((N)=0)) /\ (((exists dst_positive_code_cover_dataFtable dst_positive_scale_cover_dataFtable dst_negative_code_cover_dataFtable dst_negative_scale_cover_dataFtable. (((F) = (((((dst_positive_code_cover_dataFtable) + (dst_positive_scale_cover_dataFtable)) * S ((dst_positive_code_cover_dataFtable) + (dst_positive_scale_cover_dataFtable)) + ((dst_positive_scale_cover_dataFtable) + (dst_positive_scale_cover_dataFtable))) + (((dst_negative_code_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)) * S ((dst_negative_code_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)) + ((dst_negative_scale_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)))) * S ((((dst_positive_code_cover_dataFtable) + (dst_positive_scale_cover_dataFtable)) * S ((dst_positive_code_cover_dataFtable) + (dst_positive_scale_cover_dataFtable)) + ((dst_positive_scale_cover_dataFtable) + (dst_positive_scale_cover_dataFtable))) + (((dst_negative_code_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)) * S ((dst_negative_code_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)) + ((dst_negative_scale_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)))) + ((((dst_negative_code_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)) * S ((dst_negative_code_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)) + ((dst_negative_scale_cover_dataFtable) + (dst_negative_scale_cover_dataFtable))) + (((dst_negative_code_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)) * S ((dst_negative_code_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)) + ((dst_negative_scale_cover_dataFtable) + (dst_negative_scale_cover_dataFtable)))))) /\ (forall dst_index_cover_dataFtable. (exists pvs_le_gap_cover_dataFtabledomain. pvs_le_gap_cover_dataFtabledomain + (dst_index_cover_dataFtable) = (N)) -> exists dst_positive_cover_dataFtable dst_negative_cover_dataFtable dst_value_cover_dataFtable. ((((exists ff_h_pvs_cover_dataFtableentrypositive. ff_h_pvs_cover_dataFtableentrypositive + S (dst_positive_cover_dataFtable) = S ((S (dst_index_cover_dataFtable)) * dst_positive_scale_cover_dataFtable)) /\ exists ff_q_pvs_cover_dataFtableentrypositive. dst_positive_code_cover_dataFtable = ff_q_pvs_cover_dataFtableentrypositive * S ((S (dst_index_cover_dataFtable)) * dst_positive_scale_cover_dataFtable) + (dst_positive_cover_dataFtable))) /\ (((((exists ff_h_pvs_cover_dataFtableentrynegative. ff_h_pvs_cover_dataFtableentrynegative + S (dst_negative_cover_dataFtable) = S ((S (dst_index_cover_dataFtable)) * dst_negative_scale_cover_dataFtable)) /\ exists ff_q_pvs_cover_dataFtableentrynegative. dst_negative_code_cover_dataFtable = ff_q_pvs_cover_dataFtableentrynegative * S ((S (dst_index_cover_dataFtable)) * dst_negative_scale_cover_dataFtable) + (dst_negative_cover_dataFtable))) /\ (exists ge_balance_positive_cover_dataFtableentryvalue ge_balance_negative_cover_dataFtableentryvalue. (((((dst_value_cover_dataFtable) = 2 * (ge_balance_positive_cover_dataFtableentryvalue) /\ (ge_balance_negative_cover_dataFtableentryvalue) = 0) \/ exists ge_signed_half_cover_dataFtableentryvaluedecode. (((dst_value_cover_dataFtable) = 2 * ge_signed_half_cover_dataFtableentryvaluedecode + 1 /\ (ge_balance_positive_cover_dataFtableentryvalue) = 0) /\ (ge_balance_negative_cover_dataFtableentryvalue) = S ge_signed_half_cover_dataFtableentryvaluedecode))) /\ ((dst_positive_cover_dataFtable) + ge_balance_negative_cover_dataFtableentryvalue = (dst_negative_cover_dataFtable) + ge_balance_positive_cover_dataFtableentryvalue))))))))) /\ (((exists dst_positive_code_cover_dataFone dst_positive_scale_cover_dataFone dst_negative_code_cover_dataFone dst_negative_scale_cover_dataFone dst_positive_cover_dataFone dst_negative_cover_dataFone. (((F) = (((((dst_positive_code_cover_dataFone) + (dst_positive_scale_cover_dataFone)) * S ((dst_positive_code_cover_dataFone) + (dst_positive_scale_cover_dataFone)) + ((dst_positive_scale_cover_dataFone) + (dst_positive_scale_cover_dataFone))) + (((dst_negative_code_cover_dataFone) + (dst_negative_scale_cover_dataFone)) * S ((dst_negative_code_cover_dataFone) + (dst_negative_scale_cover_dataFone)) + ((dst_negative_scale_cover_dataFone) + (dst_negative_scale_cover_dataFone)))) * S ((((dst_positive_code_cover_dataFone) + (dst_positive_scale_cover_dataFone)) * S ((dst_positive_code_cover_dataFone) + (dst_positive_scale_cover_dataFone)) + ((dst_positive_scale_cover_dataFone) + (dst_positive_scale_cover_dataFone))) + (((dst_negative_code_cover_dataFone) + (dst_negative_scale_cover_dataFone)) * S ((dst_negative_code_cover_dataFone) + (dst_negative_scale_cover_dataFone)) + ((dst_negative_scale_cover_dataFone) + (dst_negative_scale_cover_dataFone)))) + ((((dst_negative_code_cover_dataFone) + (dst_negative_scale_cover_dataFone)) * S ((dst_negative_code_cover_dataFone) + (dst_negative_scale_cover_dataFone)) + ((dst_negative_scale_cover_dataFone) + (dst_negative_scale_cover_dataFone))) + (((dst_negative_code_cover_dataFone) + (dst_negative_scale_cover_dataFone)) * S ((dst_negative_code_cover_dataFone) + (dst_negative_scale_cover_dataFone)) + ((dst_negative_scale_cover_dataFone) + (dst_negative_scale_cover_dataFone)))))) /\ (((((exists ff_h_pvs_cover_dataFonepositive. ff_h_pvs_cover_dataFonepositive + S (dst_positive_cover_dataFone) = S ((S (1)) * dst_positive_scale_cover_dataFone)) /\ exists ff_q_pvs_cover_dataFonepositive. dst_positive_code_cover_dataFone = ff_q_pvs_cover_dataFonepositive * S ((S (1)) * dst_positive_scale_cover_dataFone) + (dst_positive_cover_dataFone))) /\ (((((exists ff_h_pvs_cover_dataFonenegative. ff_h_pvs_cover_dataFonenegative + S (dst_negative_cover_dataFone) = S ((S (1)) * dst_negative_scale_cover_dataFone)) /\ exists ff_q_pvs_cover_dataFonenegative. dst_negative_code_cover_dataFone = ff_q_pvs_cover_dataFonenegative * S ((S (1)) * dst_negative_scale_cover_dataFone) + (dst_negative_cover_dataFone))) /\ (exists ge_balance_positive_cover_dataFonevalue ge_balance_negative_cover_dataFonevalue. (((((2) = 2 * (ge_balance_positive_cover_dataFonevalue) /\ (ge_balance_negative_cover_dataFonevalue) = 0) \/ exists ge_signed_half_cover_dataFonevaluedecode. (((2) = 2 * ge_signed_half_cover_dataFonevaluedecode + 1 /\ (ge_balance_positive_cover_dataFonevalue) = 0) /\ (ge_balance_negative_cover_dataFonevalue) = S ge_signed_half_cover_dataFonevaluedecode))) /\ ((dst_positive_cover_dataFone) + ge_balance_negative_cover_dataFonevalue = (dst_negative_cover_dataFone) + ge_balance_positive_cover_dataFonevalue))))))))) /\ (forall mp_a_cover_dataF mp_b_cover_dataF mp_x_cover_dataF mp_y_cover_dataF mp_z_cover_dataF. ~(mp_a_cover_dataF=0) -> ~(mp_b_cover_dataF=0) -> (exists pvs_le_gap_cover_dataFbound. pvs_le_gap_cover_dataFbound + (mp_a_cover_dataF*mp_b_cover_dataF) = (N)) -> (forall frp_divisor_cover_dataFcoprime. (exists frp_left_factor_cover_dataFcoprime. mp_a_cover_dataF = frp_divisor_cover_dataFcoprime * frp_left_factor_cover_dataFcoprime) -> (exists frp_right_factor_cover_dataFcoprime. mp_b_cover_dataF = frp_divisor_cover_dataFcoprime * frp_right_factor_cover_dataFcoprime) -> frp_divisor_cover_dataFcoprime = 1) -> (exists dst_positive_code_cover_dataFfirst dst_positive_scale_cover_dataFfirst dst_negative_code_cover_dataFfirst dst_negative_scale_cover_dataFfirst dst_positive_cover_dataFfirst dst_negative_cover_dataFfirst. (((F) = (((((dst_positive_code_cover_dataFfirst) + (dst_positive_scale_cover_dataFfirst)) * S ((dst_positive_code_cover_dataFfirst) + (dst_positive_scale_cover_dataFfirst)) + ((dst_positive_scale_cover_dataFfirst) + (dst_positive_scale_cover_dataFfirst))) + (((dst_negative_code_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)) * S ((dst_negative_code_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)) + ((dst_negative_scale_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)))) * S ((((dst_positive_code_cover_dataFfirst) + (dst_positive_scale_cover_dataFfirst)) * S ((dst_positive_code_cover_dataFfirst) + (dst_positive_scale_cover_dataFfirst)) + ((dst_positive_scale_cover_dataFfirst) + (dst_positive_scale_cover_dataFfirst))) + (((dst_negative_code_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)) * S ((dst_negative_code_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)) + ((dst_negative_scale_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)))) + ((((dst_negative_code_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)) * S ((dst_negative_code_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)) + ((dst_negative_scale_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst))) + (((dst_negative_code_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)) * S ((dst_negative_code_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)) + ((dst_negative_scale_cover_dataFfirst) + (dst_negative_scale_cover_dataFfirst)))))) /\ (((((exists ff_h_pvs_cover_dataFfirstpositive. ff_h_pvs_cover_dataFfirstpositive + S (dst_positive_cover_dataFfirst) = S ((S (mp_a_cover_dataF)) * dst_positive_scale_cover_dataFfirst)) /\ exists ff_q_pvs_cover_dataFfirstpositive. dst_positive_code_cover_dataFfirst = ff_q_pvs_cover_dataFfirstpositive * S ((S (mp_a_cover_dataF)) * dst_positive_scale_cover_dataFfirst) + (dst_positive_cover_dataFfirst))) /\ (((((exists ff_h_pvs_cover_dataFfirstnegative. ff_h_pvs_cover_dataFfirstnegative + S (dst_negative_cover_dataFfirst) = S ((S (mp_a_cover_dataF)) * dst_negative_scale_cover_dataFfirst)) /\ exists ff_q_pvs_cover_dataFfirstnegative. dst_negative_code_cover_dataFfirst = ff_q_pvs_cover_dataFfirstnegative * S ((S (mp_a_cover_dataF)) * dst_negative_scale_cover_dataFfirst) + (dst_negative_cover_dataFfirst))) /\ (exists ge_balance_positive_cover_dataFfirstvalue ge_balance_negative_cover_dataFfirstvalue. (((((mp_x_cover_dataF) = 2 * (ge_balance_positive_cover_dataFfirstvalue) /\ (ge_balance_negative_cover_dataFfirstvalue) = 0) \/ exists ge_signed_half_cover_dataFfirstvaluedecode. (((mp_x_cover_dataF) = 2 * ge_signed_half_cover_dataFfirstvaluedecode + 1 /\ (ge_balance_positive_cover_dataFfirstvalue) = 0) /\ (ge_balance_negative_cover_dataFfirstvalue) = S ge_signed_half_cover_dataFfirstvaluedecode))) /\ ((dst_positive_cover_dataFfirst) + ge_balance_negative_cover_dataFfirstvalue = (dst_negative_cover_dataFfirst) + ge_balance_positive_cover_dataFfirstvalue))))))))) -> (exists dst_positive_code_cover_dataFsecond dst_positive_scale_cover_dataFsecond dst_negative_code_cover_dataFsecond dst_negative_scale_cover_dataFsecond dst_positive_cover_dataFsecond dst_negative_cover_dataFsecond. (((F) = (((((dst_positive_code_cover_dataFsecond) + (dst_positive_scale_cover_dataFsecond)) * S ((dst_positive_code_cover_dataFsecond) + (dst_positive_scale_cover_dataFsecond)) + ((dst_positive_scale_cover_dataFsecond) + (dst_positive_scale_cover_dataFsecond))) + (((dst_negative_code_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)) * S ((dst_negative_code_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)) + ((dst_negative_scale_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)))) * S ((((dst_positive_code_cover_dataFsecond) + (dst_positive_scale_cover_dataFsecond)) * S ((dst_positive_code_cover_dataFsecond) + (dst_positive_scale_cover_dataFsecond)) + ((dst_positive_scale_cover_dataFsecond) + (dst_positive_scale_cover_dataFsecond))) + (((dst_negative_code_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)) * S ((dst_negative_code_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)) + ((dst_negative_scale_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)))) + ((((dst_negative_code_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)) * S ((dst_negative_code_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)) + ((dst_negative_scale_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond))) + (((dst_negative_code_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)) * S ((dst_negative_code_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)) + ((dst_negative_scale_cover_dataFsecond) + (dst_negative_scale_cover_dataFsecond)))))) /\ (((((exists ff_h_pvs_cover_dataFsecondpositive. ff_h_pvs_cover_dataFsecondpositive + S (dst_positive_cover_dataFsecond) = S ((S (mp_b_cover_dataF)) * dst_positive_scale_cover_dataFsecond)) /\ exists ff_q_pvs_cover_dataFsecondpositive. dst_positive_code_cover_dataFsecond = ff_q_pvs_cover_dataFsecondpositive * S ((S (mp_b_cover_dataF)) * dst_positive_scale_cover_dataFsecond) + (dst_positive_cover_dataFsecond))) /\ (((((exists ff_h_pvs_cover_dataFsecondnegative. ff_h_pvs_cover_dataFsecondnegative + S (dst_negative_cover_dataFsecond) = S ((S (mp_b_cover_dataF)) * dst_negative_scale_cover_dataFsecond)) /\ exists ff_q_pvs_cover_dataFsecondnegative. dst_negative_code_cover_dataFsecond = ff_q_pvs_cover_dataFsecondnegative * S ((S (mp_b_cover_dataF)) * dst_negative_scale_cover_dataFsecond) + (dst_negative_cover_dataFsecond))) /\ (exists ge_balance_positive_cover_dataFsecondvalue ge_balance_negative_cover_dataFsecondvalue. (((((mp_y_cover_dataF) = 2 * (ge_balance_positive_cover_dataFsecondvalue) /\ (ge_balance_negative_cover_dataFsecondvalue) = 0) \/ exists ge_signed_half_cover_dataFsecondvaluedecode. (((mp_y_cover_dataF) = 2 * ge_signed_half_cover_dataFsecondvaluedecode + 1 /\ (ge_balance_positive_cover_dataFsecondvalue) = 0) /\ (ge_balance_negative_cover_dataFsecondvalue) = S ge_signed_half_cover_dataFsecondvaluedecode))) /\ ((dst_positive_cover_dataFsecond) + ge_balance_negative_cover_dataFsecondvalue = (dst_negative_cover_dataFsecond) + ge_balance_positive_cover_dataFsecondvalue))))))))) -> (exists dst_positive_code_cover_dataFproduct dst_positive_scale_cover_dataFproduct dst_negative_code_cover_dataFproduct dst_negative_scale_cover_dataFproduct dst_positive_cover_dataFproduct dst_negative_cover_dataFproduct. (((F) = (((((dst_positive_code_cover_dataFproduct) + (dst_positive_scale_cover_dataFproduct)) * S ((dst_positive_code_cover_dataFproduct) + (dst_positive_scale_cover_dataFproduct)) + ((dst_positive_scale_cover_dataFproduct) + (dst_positive_scale_cover_dataFproduct))) + (((dst_negative_code_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)) * S ((dst_negative_code_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)) + ((dst_negative_scale_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)))) * S ((((dst_positive_code_cover_dataFproduct) + (dst_positive_scale_cover_dataFproduct)) * S ((dst_positive_code_cover_dataFproduct) + (dst_positive_scale_cover_dataFproduct)) + ((dst_positive_scale_cover_dataFproduct) + (dst_positive_scale_cover_dataFproduct))) + (((dst_negative_code_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)) * S ((dst_negative_code_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)) + ((dst_negative_scale_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)))) + ((((dst_negative_code_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)) * S ((dst_negative_code_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)) + ((dst_negative_scale_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct))) + (((dst_negative_code_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)) * S ((dst_negative_code_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)) + ((dst_negative_scale_cover_dataFproduct) + (dst_negative_scale_cover_dataFproduct)))))) /\ (((((exists ff_h_pvs_cover_dataFproductpositive. ff_h_pvs_cover_dataFproductpositive + S (dst_positive_cover_dataFproduct) = S ((S (mp_a_cover_dataF*mp_b_cover_dataF)) * dst_positive_scale_cover_dataFproduct)) /\ exists ff_q_pvs_cover_dataFproductpositive. dst_positive_code_cover_dataFproduct = ff_q_pvs_cover_dataFproductpositive * S ((S (mp_a_cover_dataF*mp_b_cover_dataF)) * dst_positive_scale_cover_dataFproduct) + (dst_positive_cover_dataFproduct))) /\ (((((exists ff_h_pvs_cover_dataFproductnegative. ff_h_pvs_cover_dataFproductnegative + S (dst_negative_cover_dataFproduct) = S ((S (mp_a_cover_dataF*mp_b_cover_dataF)) * dst_negative_scale_cover_dataFproduct)) /\ exists ff_q_pvs_cover_dataFproductnegative. dst_negative_code_cover_dataFproduct = ff_q_pvs_cover_dataFproductnegative * S ((S (mp_a_cover_dataF*mp_b_cover_dataF)) * dst_negative_scale_cover_dataFproduct) + (dst_negative_cover_dataFproduct))) /\ (exists ge_balance_positive_cover_dataFproductvalue ge_balance_negative_cover_dataFproductvalue. (((((mp_z_cover_dataF) = 2 * (ge_balance_positive_cover_dataFproductvalue) /\ (ge_balance_negative_cover_dataFproductvalue) = 0) \/ exists ge_signed_half_cover_dataFproductvaluedecode. (((mp_z_cover_dataF) = 2 * ge_signed_half_cover_dataFproductvaluedecode + 1 /\ (ge_balance_positive_cover_dataFproductvalue) = 0) /\ (ge_balance_negative_cover_dataFproductvalue) = S ge_signed_half_cover_dataFproductvaluedecode))) /\ ((dst_positive_cover_dataFproduct) + ge_balance_negative_cover_dataFproductvalue = (dst_negative_cover_dataFproduct) + ge_balance_positive_cover_dataFproductvalue))))))))) -> (exists sto_ap_cover_dataFlaw sto_an_cover_dataFlaw sto_bp_cover_dataFlaw sto_bn_cover_dataFlaw sto_cp_cover_dataFlaw sto_cn_cover_dataFlaw. (((((mp_x_cover_dataF) = 2 * (sto_ap_cover_dataFlaw) /\ (sto_an_cover_dataFlaw) = 0) \/ exists ge_signed_half_cover_dataFlawleft. (((mp_x_cover_dataF) = 2 * ge_signed_half_cover_dataFlawleft + 1 /\ (sto_ap_cover_dataFlaw) = 0) /\ (sto_an_cover_dataFlaw) = S ge_signed_half_cover_dataFlawleft))) /\ ((((((mp_y_cover_dataF) = 2 * (sto_bp_cover_dataFlaw) /\ (sto_bn_cover_dataFlaw) = 0) \/ exists ge_signed_half_cover_dataFlawright. (((mp_y_cover_dataF) = 2 * ge_signed_half_cover_dataFlawright + 1 /\ (sto_bp_cover_dataFlaw) = 0) /\ (sto_bn_cover_dataFlaw) = S ge_signed_half_cover_dataFlawright))) /\ ((((((mp_z_cover_dataF) = 2 * (sto_cp_cover_dataFlaw) /\ (sto_cn_cover_dataFlaw) = 0) \/ exists ge_signed_half_cover_dataFlawoutput. (((mp_z_cover_dataF) = 2 * ge_signed_half_cover_dataFlawoutput + 1 /\ (sto_cp_cover_dataFlaw) = 0) /\ (sto_cn_cover_dataFlaw) = S ge_signed_half_cover_dataFlawoutput))) /\ ((sto_ap_cover_dataFlaw * sto_bp_cover_dataFlaw + sto_an_cover_dataFlaw * sto_bn_cover_dataFlaw) + sto_cn_cover_dataFlaw = (sto_ap_cover_dataFlaw * sto_bn_cover_dataFlaw + sto_an_cover_dataFlaw * sto_bp_cover_dataFlaw) + sto_cp_cover_dataFlaw)))))))))))))) /\ (((((~((N)=0)) /\ (((exists dst_positive_code_cover_dataGtable dst_positive_scale_cover_dataGtable dst_negative_code_cover_dataGtable dst_negative_scale_cover_dataGtable. (((G) = (((((dst_positive_code_cover_dataGtable) + (dst_positive_scale_cover_dataGtable)) * S ((dst_positive_code_cover_dataGtable) + (dst_positive_scale_cover_dataGtable)) + ((dst_positive_scale_cover_dataGtable) + (dst_positive_scale_cover_dataGtable))) + (((dst_negative_code_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)) * S ((dst_negative_code_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)) + ((dst_negative_scale_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)))) * S ((((dst_positive_code_cover_dataGtable) + (dst_positive_scale_cover_dataGtable)) * S ((dst_positive_code_cover_dataGtable) + (dst_positive_scale_cover_dataGtable)) + ((dst_positive_scale_cover_dataGtable) + (dst_positive_scale_cover_dataGtable))) + (((dst_negative_code_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)) * S ((dst_negative_code_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)) + ((dst_negative_scale_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)))) + ((((dst_negative_code_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)) * S ((dst_negative_code_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)) + ((dst_negative_scale_cover_dataGtable) + (dst_negative_scale_cover_dataGtable))) + (((dst_negative_code_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)) * S ((dst_negative_code_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)) + ((dst_negative_scale_cover_dataGtable) + (dst_negative_scale_cover_dataGtable)))))) /\ (forall dst_index_cover_dataGtable. (exists pvs_le_gap_cover_dataGtabledomain. pvs_le_gap_cover_dataGtabledomain + (dst_index_cover_dataGtable) = (N)) -> exists dst_positive_cover_dataGtable dst_negative_cover_dataGtable dst_value_cover_dataGtable. ((((exists ff_h_pvs_cover_dataGtableentrypositive. ff_h_pvs_cover_dataGtableentrypositive + S (dst_positive_cover_dataGtable) = S ((S (dst_index_cover_dataGtable)) * dst_positive_scale_cover_dataGtable)) /\ exists ff_q_pvs_cover_dataGtableentrypositive. dst_positive_code_cover_dataGtable = ff_q_pvs_cover_dataGtableentrypositive * S ((S (dst_index_cover_dataGtable)) * dst_positive_scale_cover_dataGtable) + (dst_positive_cover_dataGtable))) /\ (((((exists ff_h_pvs_cover_dataGtableentrynegative. ff_h_pvs_cover_dataGtableentrynegative + S (dst_negative_cover_dataGtable) = S ((S (dst_index_cover_dataGtable)) * dst_negative_scale_cover_dataGtable)) /\ exists ff_q_pvs_cover_dataGtableentrynegative. dst_negative_code_cover_dataGtable = ff_q_pvs_cover_dataGtableentrynegative * S ((S (dst_index_cover_dataGtable)) * dst_negative_scale_cover_dataGtable) + (dst_negative_cover_dataGtable))) /\ (exists ge_balance_positive_cover_dataGtableentryvalue ge_balance_negative_cover_dataGtableentryvalue. (((((dst_value_cover_dataGtable) = 2 * (ge_balance_positive_cover_dataGtableentryvalue) /\ (ge_balance_negative_cover_dataGtableentryvalue) = 0) \/ exists ge_signed_half_cover_dataGtableentryvaluedecode. (((dst_value_cover_dataGtable) = 2 * ge_signed_half_cover_dataGtableentryvaluedecode + 1 /\ (ge_balance_positive_cover_dataGtableentryvalue) = 0) /\ (ge_balance_negative_cover_dataGtableentryvalue) = S ge_signed_half_cover_dataGtableentryvaluedecode))) /\ ((dst_positive_cover_dataGtable) + ge_balance_negative_cover_dataGtableentryvalue = (dst_negative_cover_dataGtable) + ge_balance_positive_cover_dataGtableentryvalue))))))))) /\ (((exists dst_positive_code_cover_dataGone dst_positive_scale_cover_dataGone dst_negative_code_cover_dataGone dst_negative_scale_cover_dataGone dst_positive_cover_dataGone dst_negative_cover_dataGone. (((G) = (((((dst_positive_code_cover_dataGone) + (dst_positive_scale_cover_dataGone)) * S ((dst_positive_code_cover_dataGone) + (dst_positive_scale_cover_dataGone)) + ((dst_positive_scale_cover_dataGone) + (dst_positive_scale_cover_dataGone))) + (((dst_negative_code_cover_dataGone) + (dst_negative_scale_cover_dataGone)) * S ((dst_negative_code_cover_dataGone) + (dst_negative_scale_cover_dataGone)) + ((dst_negative_scale_cover_dataGone) + (dst_negative_scale_cover_dataGone)))) * S ((((dst_positive_code_cover_dataGone) + (dst_positive_scale_cover_dataGone)) * S ((dst_positive_code_cover_dataGone) + (dst_positive_scale_cover_dataGone)) + ((dst_positive_scale_cover_dataGone) + (dst_positive_scale_cover_dataGone))) + (((dst_negative_code_cover_dataGone) + (dst_negative_scale_cover_dataGone)) * S ((dst_negative_code_cover_dataGone) + (dst_negative_scale_cover_dataGone)) + ((dst_negative_scale_cover_dataGone) + (dst_negative_scale_cover_dataGone)))) + ((((dst_negative_code_cover_dataGone) + (dst_negative_scale_cover_dataGone)) * S ((dst_negative_code_cover_dataGone) + (dst_negative_scale_cover_dataGone)) + ((dst_negative_scale_cover_dataGone) + (dst_negative_scale_cover_dataGone))) + (((dst_negative_code_cover_dataGone) + (dst_negative_scale_cover_dataGone)) * S ((dst_negative_code_cover_dataGone) + (dst_negative_scale_cover_dataGone)) + ((dst_negative_scale_cover_dataGone) + (dst_negative_scale_cover_dataGone)))))) /\ (((((exists ff_h_pvs_cover_dataGonepositive. ff_h_pvs_cover_dataGonepositive + S (dst_positive_cover_dataGone) = S ((S (1)) * dst_positive_scale_cover_dataGone)) /\ exists ff_q_pvs_cover_dataGonepositive. dst_positive_code_cover_dataGone = ff_q_pvs_cover_dataGonepositive * S ((S (1)) * dst_positive_scale_cover_dataGone) + (dst_positive_cover_dataGone))) /\ (((((exists ff_h_pvs_cover_dataGonenegative. ff_h_pvs_cover_dataGonenegative + S (dst_negative_cover_dataGone) = S ((S (1)) * dst_negative_scale_cover_dataGone)) /\ exists ff_q_pvs_cover_dataGonenegative. dst_negative_code_cover_dataGone = ff_q_pvs_cover_dataGonenegative * S ((S (1)) * dst_negative_scale_cover_dataGone) + (dst_negative_cover_dataGone))) /\ (exists ge_balance_positive_cover_dataGonevalue ge_balance_negative_cover_dataGonevalue. (((((2) = 2 * (ge_balance_positive_cover_dataGonevalue) /\ (ge_balance_negative_cover_dataGonevalue) = 0) \/ exists ge_signed_half_cover_dataGonevaluedecode. (((2) = 2 * ge_signed_half_cover_dataGonevaluedecode + 1 /\ (ge_balance_positive_cover_dataGonevalue) = 0) /\ (ge_balance_negative_cover_dataGonevalue) = S ge_signed_half_cover_dataGonevaluedecode))) /\ ((dst_positive_cover_dataGone) + ge_balance_negative_cover_dataGonevalue = (dst_negative_cover_dataGone) + ge_balance_positive_cover_dataGonevalue))))))))) /\ (forall mp_a_cover_dataG mp_b_cover_dataG mp_x_cover_dataG mp_y_cover_dataG mp_z_cover_dataG. ~(mp_a_cover_dataG=0) -> ~(mp_b_cover_dataG=0) -> (exists pvs_le_gap_cover_dataGbound. pvs_le_gap_cover_dataGbound + (mp_a_cover_dataG*mp_b_cover_dataG) = (N)) -> (forall frp_divisor_cover_dataGcoprime. (exists frp_left_factor_cover_dataGcoprime. mp_a_cover_dataG = frp_divisor_cover_dataGcoprime * frp_left_factor_cover_dataGcoprime) -> (exists frp_right_factor_cover_dataGcoprime. mp_b_cover_dataG = frp_divisor_cover_dataGcoprime * frp_right_factor_cover_dataGcoprime) -> frp_divisor_cover_dataGcoprime = 1) -> (exists dst_positive_code_cover_dataGfirst dst_positive_scale_cover_dataGfirst dst_negative_code_cover_dataGfirst dst_negative_scale_cover_dataGfirst dst_positive_cover_dataGfirst dst_negative_cover_dataGfirst. (((G) = (((((dst_positive_code_cover_dataGfirst) + (dst_positive_scale_cover_dataGfirst)) * S ((dst_positive_code_cover_dataGfirst) + (dst_positive_scale_cover_dataGfirst)) + ((dst_positive_scale_cover_dataGfirst) + (dst_positive_scale_cover_dataGfirst))) + (((dst_negative_code_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)) * S ((dst_negative_code_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)) + ((dst_negative_scale_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)))) * S ((((dst_positive_code_cover_dataGfirst) + (dst_positive_scale_cover_dataGfirst)) * S ((dst_positive_code_cover_dataGfirst) + (dst_positive_scale_cover_dataGfirst)) + ((dst_positive_scale_cover_dataGfirst) + (dst_positive_scale_cover_dataGfirst))) + (((dst_negative_code_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)) * S ((dst_negative_code_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)) + ((dst_negative_scale_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)))) + ((((dst_negative_code_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)) * S ((dst_negative_code_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)) + ((dst_negative_scale_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst))) + (((dst_negative_code_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)) * S ((dst_negative_code_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)) + ((dst_negative_scale_cover_dataGfirst) + (dst_negative_scale_cover_dataGfirst)))))) /\ (((((exists ff_h_pvs_cover_dataGfirstpositive. ff_h_pvs_cover_dataGfirstpositive + S (dst_positive_cover_dataGfirst) = S ((S (mp_a_cover_dataG)) * dst_positive_scale_cover_dataGfirst)) /\ exists ff_q_pvs_cover_dataGfirstpositive. dst_positive_code_cover_dataGfirst = ff_q_pvs_cover_dataGfirstpositive * S ((S (mp_a_cover_dataG)) * dst_positive_scale_cover_dataGfirst) + (dst_positive_cover_dataGfirst))) /\ (((((exists ff_h_pvs_cover_dataGfirstnegative. ff_h_pvs_cover_dataGfirstnegative + S (dst_negative_cover_dataGfirst) = S ((S (mp_a_cover_dataG)) * dst_negative_scale_cover_dataGfirst)) /\ exists ff_q_pvs_cover_dataGfirstnegative. dst_negative_code_cover_dataGfirst = ff_q_pvs_cover_dataGfirstnegative * S ((S (mp_a_cover_dataG)) * dst_negative_scale_cover_dataGfirst) + (dst_negative_cover_dataGfirst))) /\ (exists ge_balance_positive_cover_dataGfirstvalue ge_balance_negative_cover_dataGfirstvalue. (((((mp_x_cover_dataG) = 2 * (ge_balance_positive_cover_dataGfirstvalue) /\ (ge_balance_negative_cover_dataGfirstvalue) = 0) \/ exists ge_signed_half_cover_dataGfirstvaluedecode. (((mp_x_cover_dataG) = 2 * ge_signed_half_cover_dataGfirstvaluedecode + 1 /\ (ge_balance_positive_cover_dataGfirstvalue) = 0) /\ (ge_balance_negative_cover_dataGfirstvalue) = S ge_signed_half_cover_dataGfirstvaluedecode))) /\ ((dst_positive_cover_dataGfirst) + ge_balance_negative_cover_dataGfirstvalue = (dst_negative_cover_dataGfirst) + ge_balance_positive_cover_dataGfirstvalue))))))))) -> (exists dst_positive_code_cover_dataGsecond dst_positive_scale_cover_dataGsecond dst_negative_code_cover_dataGsecond dst_negative_scale_cover_dataGsecond dst_positive_cover_dataGsecond dst_negative_cover_dataGsecond. (((G) = (((((dst_positive_code_cover_dataGsecond) + (dst_positive_scale_cover_dataGsecond)) * S ((dst_positive_code_cover_dataGsecond) + (dst_positive_scale_cover_dataGsecond)) + ((dst_positive_scale_cover_dataGsecond) + (dst_positive_scale_cover_dataGsecond))) + (((dst_negative_code_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)) * S ((dst_negative_code_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)) + ((dst_negative_scale_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)))) * S ((((dst_positive_code_cover_dataGsecond) + (dst_positive_scale_cover_dataGsecond)) * S ((dst_positive_code_cover_dataGsecond) + (dst_positive_scale_cover_dataGsecond)) + ((dst_positive_scale_cover_dataGsecond) + (dst_positive_scale_cover_dataGsecond))) + (((dst_negative_code_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)) * S ((dst_negative_code_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)) + ((dst_negative_scale_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)))) + ((((dst_negative_code_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)) * S ((dst_negative_code_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)) + ((dst_negative_scale_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond))) + (((dst_negative_code_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)) * S ((dst_negative_code_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)) + ((dst_negative_scale_cover_dataGsecond) + (dst_negative_scale_cover_dataGsecond)))))) /\ (((((exists ff_h_pvs_cover_dataGsecondpositive. ff_h_pvs_cover_dataGsecondpositive + S (dst_positive_cover_dataGsecond) = S ((S (mp_b_cover_dataG)) * dst_positive_scale_cover_dataGsecond)) /\ exists ff_q_pvs_cover_dataGsecondpositive. dst_positive_code_cover_dataGsecond = ff_q_pvs_cover_dataGsecondpositive * S ((S (mp_b_cover_dataG)) * dst_positive_scale_cover_dataGsecond) + (dst_positive_cover_dataGsecond))) /\ (((((exists ff_h_pvs_cover_dataGsecondnegative. ff_h_pvs_cover_dataGsecondnegative + S (dst_negative_cover_dataGsecond) = S ((S (mp_b_cover_dataG)) * dst_negative_scale_cover_dataGsecond)) /\ exists ff_q_pvs_cover_dataGsecondnegative. dst_negative_code_cover_dataGsecond = ff_q_pvs_cover_dataGsecondnegative * S ((S (mp_b_cover_dataG)) * dst_negative_scale_cover_dataGsecond) + (dst_negative_cover_dataGsecond))) /\ (exists ge_balance_positive_cover_dataGsecondvalue ge_balance_negative_cover_dataGsecondvalue. (((((mp_y_cover_dataG) = 2 * (ge_balance_positive_cover_dataGsecondvalue) /\ (ge_balance_negative_cover_dataGsecondvalue) = 0) \/ exists ge_signed_half_cover_dataGsecondvaluedecode. (((mp_y_cover_dataG) = 2 * ge_signed_half_cover_dataGsecondvaluedecode + 1 /\ (ge_balance_positive_cover_dataGsecondvalue) = 0) /\ (ge_balance_negative_cover_dataGsecondvalue) = S ge_signed_half_cover_dataGsecondvaluedecode))) /\ ((dst_positive_cover_dataGsecond) + ge_balance_negative_cover_dataGsecondvalue = (dst_negative_cover_dataGsecond) + ge_balance_positive_cover_dataGsecondvalue))))))))) -> (exists dst_positive_code_cover_dataGproduct dst_positive_scale_cover_dataGproduct dst_negative_code_cover_dataGproduct dst_negative_scale_cover_dataGproduct dst_positive_cover_dataGproduct dst_negative_cover_dataGproduct. (((G) = (((((dst_positive_code_cover_dataGproduct) + (dst_positive_scale_cover_dataGproduct)) * S ((dst_positive_code_cover_dataGproduct) + (dst_positive_scale_cover_dataGproduct)) + ((dst_positive_scale_cover_dataGproduct) + (dst_positive_scale_cover_dataGproduct))) + (((dst_negative_code_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)) * S ((dst_negative_code_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)) + ((dst_negative_scale_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)))) * S ((((dst_positive_code_cover_dataGproduct) + (dst_positive_scale_cover_dataGproduct)) * S ((dst_positive_code_cover_dataGproduct) + (dst_positive_scale_cover_dataGproduct)) + ((dst_positive_scale_cover_dataGproduct) + (dst_positive_scale_cover_dataGproduct))) + (((dst_negative_code_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)) * S ((dst_negative_code_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)) + ((dst_negative_scale_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)))) + ((((dst_negative_code_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)) * S ((dst_negative_code_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)) + ((dst_negative_scale_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct))) + (((dst_negative_code_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)) * S ((dst_negative_code_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)) + ((dst_negative_scale_cover_dataGproduct) + (dst_negative_scale_cover_dataGproduct)))))) /\ (((((exists ff_h_pvs_cover_dataGproductpositive. ff_h_pvs_cover_dataGproductpositive + S (dst_positive_cover_dataGproduct) = S ((S (mp_a_cover_dataG*mp_b_cover_dataG)) * dst_positive_scale_cover_dataGproduct)) /\ exists ff_q_pvs_cover_dataGproductpositive. dst_positive_code_cover_dataGproduct = ff_q_pvs_cover_dataGproductpositive * S ((S (mp_a_cover_dataG*mp_b_cover_dataG)) * dst_positive_scale_cover_dataGproduct) + (dst_positive_cover_dataGproduct))) /\ (((((exists ff_h_pvs_cover_dataGproductnegative. ff_h_pvs_cover_dataGproductnegative + S (dst_negative_cover_dataGproduct) = S ((S (mp_a_cover_dataG*mp_b_cover_dataG)) * dst_negative_scale_cover_dataGproduct)) /\ exists ff_q_pvs_cover_dataGproductnegative. dst_negative_code_cover_dataGproduct = ff_q_pvs_cover_dataGproductnegative * S ((S (mp_a_cover_dataG*mp_b_cover_dataG)) * dst_negative_scale_cover_dataGproduct) + (dst_negative_cover_dataGproduct))) /\ (exists ge_balance_positive_cover_dataGproductvalue ge_balance_negative_cover_dataGproductvalue. (((((mp_z_cover_dataG) = 2 * (ge_balance_positive_cover_dataGproductvalue) /\ (ge_balance_negative_cover_dataGproductvalue) = 0) \/ exists ge_signed_half_cover_dataGproductvaluedecode. (((mp_z_cover_dataG) = 2 * ge_signed_half_cover_dataGproductvaluedecode + 1 /\ (ge_balance_positive_cover_dataGproductvalue) = 0) /\ (ge_balance_negative_cover_dataGproductvalue) = S ge_signed_half_cover_dataGproductvaluedecode))) /\ ((dst_positive_cover_dataGproduct) + ge_balance_negative_cover_dataGproductvalue = (dst_negative_cover_dataGproduct) + ge_balance_positive_cover_dataGproductvalue))))))))) -> (exists sto_ap_cover_dataGlaw sto_an_cover_dataGlaw sto_bp_cover_dataGlaw sto_bn_cover_dataGlaw sto_cp_cover_dataGlaw sto_cn_cover_dataGlaw. (((((mp_x_cover_dataG) = 2 * (sto_ap_cover_dataGlaw) /\ (sto_an_cover_dataGlaw) = 0) \/ exists ge_signed_half_cover_dataGlawleft. (((mp_x_cover_dataG) = 2 * ge_signed_half_cover_dataGlawleft + 1 /\ (sto_ap_cover_dataGlaw) = 0) /\ (sto_an_cover_dataGlaw) = S ge_signed_half_cover_dataGlawleft))) /\ ((((((mp_y_cover_dataG) = 2 * (sto_bp_cover_dataGlaw) /\ (sto_bn_cover_dataGlaw) = 0) \/ exists ge_signed_half_cover_dataGlawright. (((mp_y_cover_dataG) = 2 * ge_signed_half_cover_dataGlawright + 1 /\ (sto_bp_cover_dataGlaw) = 0) /\ (sto_bn_cover_dataGlaw) = S ge_signed_half_cover_dataGlawright))) /\ ((((((mp_z_cover_dataG) = 2 * (sto_cp_cover_dataGlaw) /\ (sto_cn_cover_dataGlaw) = 0) \/ exists ge_signed_half_cover_dataGlawoutput. (((mp_z_cover_dataG) = 2 * ge_signed_half_cover_dataGlawoutput + 1 /\ (sto_cp_cover_dataGlaw) = 0) /\ (sto_cn_cover_dataGlaw) = S ge_signed_half_cover_dataGlawoutput))) /\ ((sto_ap_cover_dataGlaw * sto_bp_cover_dataGlaw + sto_an_cover_dataGlaw * sto_bn_cover_dataGlaw) + sto_cn_cover_dataGlaw = (sto_ap_cover_dataGlaw * sto_bn_cover_dataGlaw + sto_an_cover_dataGlaw * sto_bp_cover_dataGlaw) + sto_cp_cover_dataGlaw)))))))))))))) /\ (((~((m)=0)) /\ (((~((n)=0)) /\ (((exists pvs_le_gap_cover_databound. pvs_le_gap_cover_databound + ((m)*(n)) = (N)) /\ (((forall sfd_common_divisor_cover_datacoprime. (exists pvs_factor_cover_datacoprimeleft. (m) = (sfd_common_divisor_cover_datacoprime) * pvs_factor_cover_datacoprimeleft) -> (exists pvs_factor_cover_datacoprimeright. (n) = (sfd_common_divisor_cover_datacoprime) * pvs_factor_cover_datacoprimeright) -> sfd_common_divisor_cover_datacoprime = 1) /\ (((((exists dst_positive_code_cover_datalefttable dst_positive_scale_cover_datalefttable dst_negative_code_cover_datalefttable dst_negative_scale_cover_datalefttable. (((A) = (((((dst_positive_code_cover_datalefttable) + (dst_positive_scale_cover_datalefttable)) * S ((dst_positive_code_cover_datalefttable) + (dst_positive_scale_cover_datalefttable)) + ((dst_positive_scale_cover_datalefttable) + (dst_positive_scale_cover_datalefttable))) + (((dst_negative_code_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)) * S ((dst_negative_code_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)) + ((dst_negative_scale_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)))) * S ((((dst_positive_code_cover_datalefttable) + (dst_positive_scale_cover_datalefttable)) * S ((dst_positive_code_cover_datalefttable) + (dst_positive_scale_cover_datalefttable)) + ((dst_positive_scale_cover_datalefttable) + (dst_positive_scale_cover_datalefttable))) + (((dst_negative_code_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)) * S ((dst_negative_code_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)) + ((dst_negative_scale_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)))) + ((((dst_negative_code_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)) * S ((dst_negative_code_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)) + ((dst_negative_scale_cover_datalefttable) + (dst_negative_scale_cover_datalefttable))) + (((dst_negative_code_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)) * S ((dst_negative_code_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)) + ((dst_negative_scale_cover_datalefttable) + (dst_negative_scale_cover_datalefttable)))))) /\ (forall dst_index_cover_datalefttable. (exists pvs_le_gap_cover_datalefttabledomain. pvs_le_gap_cover_datalefttabledomain + (dst_index_cover_datalefttable) = (m)) -> exists dst_positive_cover_datalefttable dst_negative_cover_datalefttable dst_value_cover_datalefttable. ((((exists ff_h_pvs_cover_datalefttableentrypositive. ff_h_pvs_cover_datalefttableentrypositive + S (dst_positive_cover_datalefttable) = S ((S (dst_index_cover_datalefttable)) * dst_positive_scale_cover_datalefttable)) /\ exists ff_q_pvs_cover_datalefttableentrypositive. dst_positive_code_cover_datalefttable = ff_q_pvs_cover_datalefttableentrypositive * S ((S (dst_index_cover_datalefttable)) * dst_positive_scale_cover_datalefttable) + (dst_positive_cover_datalefttable))) /\ (((((exists ff_h_pvs_cover_datalefttableentrynegative. ff_h_pvs_cover_datalefttableentrynegative + S (dst_negative_cover_datalefttable) = S ((S (dst_index_cover_datalefttable)) * dst_negative_scale_cover_datalefttable)) /\ exists ff_q_pvs_cover_datalefttableentrynegative. dst_negative_code_cover_datalefttable = ff_q_pvs_cover_datalefttableentrynegative * S ((S (dst_index_cover_datalefttable)) * dst_negative_scale_cover_datalefttable) + (dst_negative_cover_datalefttable))) /\ (exists ge_balance_positive_cover_datalefttableentryvalue ge_balance_negative_cover_datalefttableentryvalue. (((((dst_value_cover_datalefttable) = 2 * (ge_balance_positive_cover_datalefttableentryvalue) /\ (ge_balance_negative_cover_datalefttableentryvalue) = 0) \/ exists ge_signed_half_cover_datalefttableentryvaluedecode. (((dst_value_cover_datalefttable) = 2 * ge_signed_half_cover_datalefttableentryvaluedecode + 1 /\ (ge_balance_positive_cover_datalefttableentryvalue) = 0) /\ (ge_balance_negative_cover_datalefttableentryvalue) = S ge_signed_half_cover_datalefttableentryvaluedecode))) /\ ((dst_positive_cover_datalefttable) + ge_balance_negative_cover_datalefttableentryvalue = (dst_negative_cover_datalefttable) + ge_balance_positive_cover_datalefttableentryvalue))))))))) /\ (forall dc_index_cover_dataleft dc_value_cover_dataleft. (exists pvs_le_gap_cover_dataleftdomain. pvs_le_gap_cover_dataleftdomain + (dc_index_cover_dataleft) = (m)) -> (exists dst_positive_code_cover_dataleftlookup dst_positive_scale_cover_dataleftlookup dst_negative_code_cover_dataleftlookup dst_negative_scale_cover_dataleftlookup dst_positive_cover_dataleftlookup dst_negative_cover_dataleftlookup. (((A) = (((((dst_positive_code_cover_dataleftlookup) + (dst_positive_scale_cover_dataleftlookup)) * S ((dst_positive_code_cover_dataleftlookup) + (dst_positive_scale_cover_dataleftlookup)) + ((dst_positive_scale_cover_dataleftlookup) + (dst_positive_scale_cover_dataleftlookup))) + (((dst_negative_code_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)) * S ((dst_negative_code_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)) + ((dst_negative_scale_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)))) * S ((((dst_positive_code_cover_dataleftlookup) + (dst_positive_scale_cover_dataleftlookup)) * S ((dst_positive_code_cover_dataleftlookup) + (dst_positive_scale_cover_dataleftlookup)) + ((dst_positive_scale_cover_dataleftlookup) + (dst_positive_scale_cover_dataleftlookup))) + (((dst_negative_code_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)) * S ((dst_negative_code_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)) + ((dst_negative_scale_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)))) + ((((dst_negative_code_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)) * S ((dst_negative_code_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)) + ((dst_negative_scale_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup))) + (((dst_negative_code_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)) * S ((dst_negative_code_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)) + ((dst_negative_scale_cover_dataleftlookup) + (dst_negative_scale_cover_dataleftlookup)))))) /\ (((((exists ff_h_pvs_cover_dataleftlookuppositive. ff_h_pvs_cover_dataleftlookuppositive + S (dst_positive_cover_dataleftlookup) = S ((S (dc_index_cover_dataleft)) * dst_positive_scale_cover_dataleftlookup)) /\ exists ff_q_pvs_cover_dataleftlookuppositive. dst_positive_code_cover_dataleftlookup = ff_q_pvs_cover_dataleftlookuppositive * S ((S (dc_index_cover_dataleft)) * dst_positive_scale_cover_dataleftlookup) + (dst_positive_cover_dataleftlookup))) /\ (((((exists ff_h_pvs_cover_dataleftlookupnegative. ff_h_pvs_cover_dataleftlookupnegative + S (dst_negative_cover_dataleftlookup) = S ((S (dc_index_cover_dataleft)) * dst_negative_scale_cover_dataleftlookup)) /\ exists ff_q_pvs_cover_dataleftlookupnegative. dst_negative_code_cover_dataleftlookup = ff_q_pvs_cover_dataleftlookupnegative * S ((S (dc_index_cover_dataleft)) * dst_negative_scale_cover_dataleftlookup) + (dst_negative_cover_dataleftlookup))) /\ (exists ge_balance_positive_cover_dataleftlookupvalue ge_balance_negative_cover_dataleftlookupvalue. (((((dc_value_cover_dataleft) = 2 * (ge_balance_positive_cover_dataleftlookupvalue) /\ (ge_balance_negative_cover_dataleftlookupvalue) = 0) \/ exists ge_signed_half_cover_dataleftlookupvaluedecode. (((dc_value_cover_dataleft) = 2 * ge_signed_half_cover_dataleftlookupvaluedecode + 1 /\ (ge_balance_positive_cover_dataleftlookupvalue) = 0) /\ (ge_balance_negative_cover_dataleftlookupvalue) = S ge_signed_half_cover_dataleftlookupvaluedecode))) /\ ((dst_positive_cover_dataleftlookup) + ge_balance_negative_cover_dataleftlookupvalue = (dst_negative_cover_dataleftlookup) + ge_balance_positive_cover_dataleftlookupvalue))))))))) -> ((((~((dc_index_cover_dataleft)=0)) /\ (exists dc_quotient_cover_dataleftentry dc_left_cover_dataleftentry dc_right_cover_dataleftentry. (((m)=(dc_index_cover_dataleft)*dc_quotient_cover_dataleftentry) /\ (((exists dst_positive_code_cover_dataleftentryleft dst_positive_scale_cover_dataleftentryleft dst_negative_code_cover_dataleftentryleft dst_negative_scale_cover_dataleftentryleft dst_positive_cover_dataleftentryleft dst_negative_cover_dataleftentryleft. (((F) = (((((dst_positive_code_cover_dataleftentryleft) + (dst_positive_scale_cover_dataleftentryleft)) * S ((dst_positive_code_cover_dataleftentryleft) + (dst_positive_scale_cover_dataleftentryleft)) + ((dst_positive_scale_cover_dataleftentryleft) + (dst_positive_scale_cover_dataleftentryleft))) + (((dst_negative_code_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)) * S ((dst_negative_code_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)) + ((dst_negative_scale_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)))) * S ((((dst_positive_code_cover_dataleftentryleft) + (dst_positive_scale_cover_dataleftentryleft)) * S ((dst_positive_code_cover_dataleftentryleft) + (dst_positive_scale_cover_dataleftentryleft)) + ((dst_positive_scale_cover_dataleftentryleft) + (dst_positive_scale_cover_dataleftentryleft))) + (((dst_negative_code_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)) * S ((dst_negative_code_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)) + ((dst_negative_scale_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)))) + ((((dst_negative_code_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)) * S ((dst_negative_code_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)) + ((dst_negative_scale_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft))) + (((dst_negative_code_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)) * S ((dst_negative_code_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)) + ((dst_negative_scale_cover_dataleftentryleft) + (dst_negative_scale_cover_dataleftentryleft)))))) /\ (((((exists ff_h_pvs_cover_dataleftentryleftpositive. ff_h_pvs_cover_dataleftentryleftpositive + S (dst_positive_cover_dataleftentryleft) = S ((S (dc_index_cover_dataleft)) * dst_positive_scale_cover_dataleftentryleft)) /\ exists ff_q_pvs_cover_dataleftentryleftpositive. dst_positive_code_cover_dataleftentryleft = ff_q_pvs_cover_dataleftentryleftpositive * S ((S (dc_index_cover_dataleft)) * dst_positive_scale_cover_dataleftentryleft) + (dst_positive_cover_dataleftentryleft))) /\ (((((exists ff_h_pvs_cover_dataleftentryleftnegative. ff_h_pvs_cover_dataleftentryleftnegative + S (dst_negative_cover_dataleftentryleft) = S ((S (dc_index_cover_dataleft)) * dst_negative_scale_cover_dataleftentryleft)) /\ exists ff_q_pvs_cover_dataleftentryleftnegative. dst_negative_code_cover_dataleftentryleft = ff_q_pvs_cover_dataleftentryleftnegative * S ((S (dc_index_cover_dataleft)) * dst_negative_scale_cover_dataleftentryleft) + (dst_negative_cover_dataleftentryleft))) /\ (exists ge_balance_positive_cover_dataleftentryleftvalue ge_balance_negative_cover_dataleftentryleftvalue. (((((dc_left_cover_dataleftentry) = 2 * (ge_balance_positive_cover_dataleftentryleftvalue) /\ (ge_balance_negative_cover_dataleftentryleftvalue) = 0) \/ exists ge_signed_half_cover_dataleftentryleftvaluedecode. (((dc_left_cover_dataleftentry) = 2 * ge_signed_half_cover_dataleftentryleftvaluedecode + 1 /\ (ge_balance_positive_cover_dataleftentryleftvalue) = 0) /\ (ge_balance_negative_cover_dataleftentryleftvalue) = S ge_signed_half_cover_dataleftentryleftvaluedecode))) /\ ((dst_positive_cover_dataleftentryleft) + ge_balance_negative_cover_dataleftentryleftvalue = (dst_negative_cover_dataleftentryleft) + ge_balance_positive_cover_dataleftentryleftvalue))))))))) /\ (((exists dst_positive_code_cover_dataleftentryright dst_positive_scale_cover_dataleftentryright dst_negative_code_cover_dataleftentryright dst_negative_scale_cover_dataleftentryright dst_positive_cover_dataleftentryright dst_negative_cover_dataleftentryright. (((G) = (((((dst_positive_code_cover_dataleftentryright) + (dst_positive_scale_cover_dataleftentryright)) * S ((dst_positive_code_cover_dataleftentryright) + (dst_positive_scale_cover_dataleftentryright)) + ((dst_positive_scale_cover_dataleftentryright) + (dst_positive_scale_cover_dataleftentryright))) + (((dst_negative_code_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)) * S ((dst_negative_code_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)) + ((dst_negative_scale_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)))) * S ((((dst_positive_code_cover_dataleftentryright) + (dst_positive_scale_cover_dataleftentryright)) * S ((dst_positive_code_cover_dataleftentryright) + (dst_positive_scale_cover_dataleftentryright)) + ((dst_positive_scale_cover_dataleftentryright) + (dst_positive_scale_cover_dataleftentryright))) + (((dst_negative_code_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)) * S ((dst_negative_code_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)) + ((dst_negative_scale_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)))) + ((((dst_negative_code_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)) * S ((dst_negative_code_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)) + ((dst_negative_scale_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright))) + (((dst_negative_code_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)) * S ((dst_negative_code_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)) + ((dst_negative_scale_cover_dataleftentryright) + (dst_negative_scale_cover_dataleftentryright)))))) /\ (((((exists ff_h_pvs_cover_dataleftentryrightpositive. ff_h_pvs_cover_dataleftentryrightpositive + S (dst_positive_cover_dataleftentryright) = S ((S (dc_quotient_cover_dataleftentry)) * dst_positive_scale_cover_dataleftentryright)) /\ exists ff_q_pvs_cover_dataleftentryrightpositive. dst_positive_code_cover_dataleftentryright = ff_q_pvs_cover_dataleftentryrightpositive * S ((S (dc_quotient_cover_dataleftentry)) * dst_positive_scale_cover_dataleftentryright) + (dst_positive_cover_dataleftentryright))) /\ (((((exists ff_h_pvs_cover_dataleftentryrightnegative. ff_h_pvs_cover_dataleftentryrightnegative + S (dst_negative_cover_dataleftentryright) = S ((S (dc_quotient_cover_dataleftentry)) * dst_negative_scale_cover_dataleftentryright)) /\ exists ff_q_pvs_cover_dataleftentryrightnegative. dst_negative_code_cover_dataleftentryright = ff_q_pvs_cover_dataleftentryrightnegative * S ((S (dc_quotient_cover_dataleftentry)) * dst_negative_scale_cover_dataleftentryright) + (dst_negative_cover_dataleftentryright))) /\ (exists ge_balance_positive_cover_dataleftentryrightvalue ge_balance_negative_cover_dataleftentryrightvalue. (((((dc_right_cover_dataleftentry) = 2 * (ge_balance_positive_cover_dataleftentryrightvalue) /\ (ge_balance_negative_cover_dataleftentryrightvalue) = 0) \/ exists ge_signed_half_cover_dataleftentryrightvaluedecode. (((dc_right_cover_dataleftentry) = 2 * ge_signed_half_cover_dataleftentryrightvaluedecode + 1 /\ (ge_balance_positive_cover_dataleftentryrightvalue) = 0) /\ (ge_balance_negative_cover_dataleftentryrightvalue) = S ge_signed_half_cover_dataleftentryrightvaluedecode))) /\ ((dst_positive_cover_dataleftentryright) + ge_balance_negative_cover_dataleftentryrightvalue = (dst_negative_cover_dataleftentryright) + ge_balance_positive_cover_dataleftentryrightvalue))))))))) /\ (exists sto_ap_cover_dataleftentryproduct sto_an_cover_dataleftentryproduct sto_bp_cover_dataleftentryproduct sto_bn_cover_dataleftentryproduct sto_cp_cover_dataleftentryproduct sto_cn_cover_dataleftentryproduct. (((((dc_left_cover_dataleftentry) = 2 * (sto_ap_cover_dataleftentryproduct) /\ (sto_an_cover_dataleftentryproduct) = 0) \/ exists ge_signed_half_cover_dataleftentryproductleft. (((dc_left_cover_dataleftentry) = 2 * ge_signed_half_cover_dataleftentryproductleft + 1 /\ (sto_ap_cover_dataleftentryproduct) = 0) /\ (sto_an_cover_dataleftentryproduct) = S ge_signed_half_cover_dataleftentryproductleft))) /\ ((((((dc_right_cover_dataleftentry) = 2 * (sto_bp_cover_dataleftentryproduct) /\ (sto_bn_cover_dataleftentryproduct) = 0) \/ exists ge_signed_half_cover_dataleftentryproductright. (((dc_right_cover_dataleftentry) = 2 * ge_signed_half_cover_dataleftentryproductright + 1 /\ (sto_bp_cover_dataleftentryproduct) = 0) /\ (sto_bn_cover_dataleftentryproduct) = S ge_signed_half_cover_dataleftentryproductright))) /\ ((((((dc_value_cover_dataleft) = 2 * (sto_cp_cover_dataleftentryproduct) /\ (sto_cn_cover_dataleftentryproduct) = 0) \/ exists ge_signed_half_cover_dataleftentryproductoutput. (((dc_value_cover_dataleft) = 2 * ge_signed_half_cover_dataleftentryproductoutput + 1 /\ (sto_cp_cover_dataleftentryproduct) = 0) /\ (sto_cn_cover_dataleftentryproduct) = S ge_signed_half_cover_dataleftentryproductoutput))) /\ ((sto_ap_cover_dataleftentryproduct * sto_bp_cover_dataleftentryproduct + sto_an_cover_dataleftentryproduct * sto_bn_cover_dataleftentryproduct) + sto_cn_cover_dataleftentryproduct = (sto_ap_cover_dataleftentryproduct * sto_bn_cover_dataleftentryproduct + sto_an_cover_dataleftentryproduct * sto_bp_cover_dataleftentryproduct) + sto_cp_cover_dataleftentryproduct))))))))))))))) \/ ((((dc_index_cover_dataleft)=0 \/ ~(exists pvs_factor_cover_dataleftentrynondivisor. (m) = (dc_index_cover_dataleft) * pvs_factor_cover_dataleftentrynondivisor)) /\ ((dc_value_cover_dataleft)=0))))))) /\ (((((exists dst_positive_code_cover_datarighttable dst_positive_scale_cover_datarighttable dst_negative_code_cover_datarighttable dst_negative_scale_cover_datarighttable. (((B) = (((((dst_positive_code_cover_datarighttable) + (dst_positive_scale_cover_datarighttable)) * S ((dst_positive_code_cover_datarighttable) + (dst_positive_scale_cover_datarighttable)) + ((dst_positive_scale_cover_datarighttable) + (dst_positive_scale_cover_datarighttable))) + (((dst_negative_code_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)) * S ((dst_negative_code_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)) + ((dst_negative_scale_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)))) * S ((((dst_positive_code_cover_datarighttable) + (dst_positive_scale_cover_datarighttable)) * S ((dst_positive_code_cover_datarighttable) + (dst_positive_scale_cover_datarighttable)) + ((dst_positive_scale_cover_datarighttable) + (dst_positive_scale_cover_datarighttable))) + (((dst_negative_code_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)) * S ((dst_negative_code_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)) + ((dst_negative_scale_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)))) + ((((dst_negative_code_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)) * S ((dst_negative_code_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)) + ((dst_negative_scale_cover_datarighttable) + (dst_negative_scale_cover_datarighttable))) + (((dst_negative_code_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)) * S ((dst_negative_code_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)) + ((dst_negative_scale_cover_datarighttable) + (dst_negative_scale_cover_datarighttable)))))) /\ (forall dst_index_cover_datarighttable. (exists pvs_le_gap_cover_datarighttabledomain. pvs_le_gap_cover_datarighttabledomain + (dst_index_cover_datarighttable) = (n)) -> exists dst_positive_cover_datarighttable dst_negative_cover_datarighttable dst_value_cover_datarighttable. ((((exists ff_h_pvs_cover_datarighttableentrypositive. ff_h_pvs_cover_datarighttableentrypositive + S (dst_positive_cover_datarighttable) = S ((S (dst_index_cover_datarighttable)) * dst_positive_scale_cover_datarighttable)) /\ exists ff_q_pvs_cover_datarighttableentrypositive. dst_positive_code_cover_datarighttable = ff_q_pvs_cover_datarighttableentrypositive * S ((S (dst_index_cover_datarighttable)) * dst_positive_scale_cover_datarighttable) + (dst_positive_cover_datarighttable))) /\ (((((exists ff_h_pvs_cover_datarighttableentrynegative. ff_h_pvs_cover_datarighttableentrynegative + S (dst_negative_cover_datarighttable) = S ((S (dst_index_cover_datarighttable)) * dst_negative_scale_cover_datarighttable)) /\ exists ff_q_pvs_cover_datarighttableentrynegative. dst_negative_code_cover_datarighttable = ff_q_pvs_cover_datarighttableentrynegative * S ((S (dst_index_cover_datarighttable)) * dst_negative_scale_cover_datarighttable) + (dst_negative_cover_datarighttable))) /\ (exists ge_balance_positive_cover_datarighttableentryvalue ge_balance_negative_cover_datarighttableentryvalue. (((((dst_value_cover_datarighttable) = 2 * (ge_balance_positive_cover_datarighttableentryvalue) /\ (ge_balance_negative_cover_datarighttableentryvalue) = 0) \/ exists ge_signed_half_cover_datarighttableentryvaluedecode. (((dst_value_cover_datarighttable) = 2 * ge_signed_half_cover_datarighttableentryvaluedecode + 1 /\ (ge_balance_positive_cover_datarighttableentryvalue) = 0) /\ (ge_balance_negative_cover_datarighttableentryvalue) = S ge_signed_half_cover_datarighttableentryvaluedecode))) /\ ((dst_positive_cover_datarighttable) + ge_balance_negative_cover_datarighttableentryvalue = (dst_negative_cover_datarighttable) + ge_balance_positive_cover_datarighttableentryvalue))))))))) /\ (forall dc_index_cover_dataright dc_value_cover_dataright. (exists pvs_le_gap_cover_datarightdomain. pvs_le_gap_cover_datarightdomain + (dc_index_cover_dataright) = (n)) -> (exists dst_positive_code_cover_datarightlookup dst_positive_scale_cover_datarightlookup dst_negative_code_cover_datarightlookup dst_negative_scale_cover_datarightlookup dst_positive_cover_datarightlookup dst_negative_cover_datarightlookup. (((B) = (((((dst_positive_code_cover_datarightlookup) + (dst_positive_scale_cover_datarightlookup)) * S ((dst_positive_code_cover_datarightlookup) + (dst_positive_scale_cover_datarightlookup)) + ((dst_positive_scale_cover_datarightlookup) + (dst_positive_scale_cover_datarightlookup))) + (((dst_negative_code_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)) * S ((dst_negative_code_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)) + ((dst_negative_scale_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)))) * S ((((dst_positive_code_cover_datarightlookup) + (dst_positive_scale_cover_datarightlookup)) * S ((dst_positive_code_cover_datarightlookup) + (dst_positive_scale_cover_datarightlookup)) + ((dst_positive_scale_cover_datarightlookup) + (dst_positive_scale_cover_datarightlookup))) + (((dst_negative_code_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)) * S ((dst_negative_code_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)) + ((dst_negative_scale_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)))) + ((((dst_negative_code_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)) * S ((dst_negative_code_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)) + ((dst_negative_scale_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup))) + (((dst_negative_code_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)) * S ((dst_negative_code_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)) + ((dst_negative_scale_cover_datarightlookup) + (dst_negative_scale_cover_datarightlookup)))))) /\ (((((exists ff_h_pvs_cover_datarightlookuppositive. ff_h_pvs_cover_datarightlookuppositive + S (dst_positive_cover_datarightlookup) = S ((S (dc_index_cover_dataright)) * dst_positive_scale_cover_datarightlookup)) /\ exists ff_q_pvs_cover_datarightlookuppositive. dst_positive_code_cover_datarightlookup = ff_q_pvs_cover_datarightlookuppositive * S ((S (dc_index_cover_dataright)) * dst_positive_scale_cover_datarightlookup) + (dst_positive_cover_datarightlookup))) /\ (((((exists ff_h_pvs_cover_datarightlookupnegative. ff_h_pvs_cover_datarightlookupnegative + S (dst_negative_cover_datarightlookup) = S ((S (dc_index_cover_dataright)) * dst_negative_scale_cover_datarightlookup)) /\ exists ff_q_pvs_cover_datarightlookupnegative. dst_negative_code_cover_datarightlookup = ff_q_pvs_cover_datarightlookupnegative * S ((S (dc_index_cover_dataright)) * dst_negative_scale_cover_datarightlookup) + (dst_negative_cover_datarightlookup))) /\ (exists ge_balance_positive_cover_datarightlookupvalue ge_balance_negative_cover_datarightlookupvalue. (((((dc_value_cover_dataright) = 2 * (ge_balance_positive_cover_datarightlookupvalue) /\ (ge_balance_negative_cover_datarightlookupvalue) = 0) \/ exists ge_signed_half_cover_datarightlookupvaluedecode. (((dc_value_cover_dataright) = 2 * ge_signed_half_cover_datarightlookupvaluedecode + 1 /\ (ge_balance_positive_cover_datarightlookupvalue) = 0) /\ (ge_balance_negative_cover_datarightlookupvalue) = S ge_signed_half_cover_datarightlookupvaluedecode))) /\ ((dst_positive_cover_datarightlookup) + ge_balance_negative_cover_datarightlookupvalue = (dst_negative_cover_datarightlookup) + ge_balance_positive_cover_datarightlookupvalue))))))))) -> ((((~((dc_index_cover_dataright)=0)) /\ (exists dc_quotient_cover_datarightentry dc_left_cover_datarightentry dc_right_cover_datarightentry. (((n)=(dc_index_cover_dataright)*dc_quotient_cover_datarightentry) /\ (((exists dst_positive_code_cover_datarightentryleft dst_positive_scale_cover_datarightentryleft dst_negative_code_cover_datarightentryleft dst_negative_scale_cover_datarightentryleft dst_positive_cover_datarightentryleft dst_negative_cover_datarightentryleft. (((F) = (((((dst_positive_code_cover_datarightentryleft) + (dst_positive_scale_cover_datarightentryleft)) * S ((dst_positive_code_cover_datarightentryleft) + (dst_positive_scale_cover_datarightentryleft)) + ((dst_positive_scale_cover_datarightentryleft) + (dst_positive_scale_cover_datarightentryleft))) + (((dst_negative_code_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)) * S ((dst_negative_code_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)) + ((dst_negative_scale_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)))) * S ((((dst_positive_code_cover_datarightentryleft) + (dst_positive_scale_cover_datarightentryleft)) * S ((dst_positive_code_cover_datarightentryleft) + (dst_positive_scale_cover_datarightentryleft)) + ((dst_positive_scale_cover_datarightentryleft) + (dst_positive_scale_cover_datarightentryleft))) + (((dst_negative_code_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)) * S ((dst_negative_code_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)) + ((dst_negative_scale_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)))) + ((((dst_negative_code_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)) * S ((dst_negative_code_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)) + ((dst_negative_scale_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft))) + (((dst_negative_code_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)) * S ((dst_negative_code_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)) + ((dst_negative_scale_cover_datarightentryleft) + (dst_negative_scale_cover_datarightentryleft)))))) /\ (((((exists ff_h_pvs_cover_datarightentryleftpositive. ff_h_pvs_cover_datarightentryleftpositive + S (dst_positive_cover_datarightentryleft) = S ((S (dc_index_cover_dataright)) * dst_positive_scale_cover_datarightentryleft)) /\ exists ff_q_pvs_cover_datarightentryleftpositive. dst_positive_code_cover_datarightentryleft = ff_q_pvs_cover_datarightentryleftpositive * S ((S (dc_index_cover_dataright)) * dst_positive_scale_cover_datarightentryleft) + (dst_positive_cover_datarightentryleft))) /\ (((((exists ff_h_pvs_cover_datarightentryleftnegative. ff_h_pvs_cover_datarightentryleftnegative + S (dst_negative_cover_datarightentryleft) = S ((S (dc_index_cover_dataright)) * dst_negative_scale_cover_datarightentryleft)) /\ exists ff_q_pvs_cover_datarightentryleftnegative. dst_negative_code_cover_datarightentryleft = ff_q_pvs_cover_datarightentryleftnegative * S ((S (dc_index_cover_dataright)) * dst_negative_scale_cover_datarightentryleft) + (dst_negative_cover_datarightentryleft))) /\ (exists ge_balance_positive_cover_datarightentryleftvalue ge_balance_negative_cover_datarightentryleftvalue. (((((dc_left_cover_datarightentry) = 2 * (ge_balance_positive_cover_datarightentryleftvalue) /\ (ge_balance_negative_cover_datarightentryleftvalue) = 0) \/ exists ge_signed_half_cover_datarightentryleftvaluedecode. (((dc_left_cover_datarightentry) = 2 * ge_signed_half_cover_datarightentryleftvaluedecode + 1 /\ (ge_balance_positive_cover_datarightentryleftvalue) = 0) /\ (ge_balance_negative_cover_datarightentryleftvalue) = S ge_signed_half_cover_datarightentryleftvaluedecode))) /\ ((dst_positive_cover_datarightentryleft) + ge_balance_negative_cover_datarightentryleftvalue = (dst_negative_cover_datarightentryleft) + ge_balance_positive_cover_datarightentryleftvalue))))))))) /\ (((exists dst_positive_code_cover_datarightentryright dst_positive_scale_cover_datarightentryright dst_negative_code_cover_datarightentryright dst_negative_scale_cover_datarightentryright dst_positive_cover_datarightentryright dst_negative_cover_datarightentryright. (((G) = (((((dst_positive_code_cover_datarightentryright) + (dst_positive_scale_cover_datarightentryright)) * S ((dst_positive_code_cover_datarightentryright) + (dst_positive_scale_cover_datarightentryright)) + ((dst_positive_scale_cover_datarightentryright) + (dst_positive_scale_cover_datarightentryright))) + (((dst_negative_code_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)) * S ((dst_negative_code_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)) + ((dst_negative_scale_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)))) * S ((((dst_positive_code_cover_datarightentryright) + (dst_positive_scale_cover_datarightentryright)) * S ((dst_positive_code_cover_datarightentryright) + (dst_positive_scale_cover_datarightentryright)) + ((dst_positive_scale_cover_datarightentryright) + (dst_positive_scale_cover_datarightentryright))) + (((dst_negative_code_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)) * S ((dst_negative_code_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)) + ((dst_negative_scale_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)))) + ((((dst_negative_code_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)) * S ((dst_negative_code_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)) + ((dst_negative_scale_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright))) + (((dst_negative_code_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)) * S ((dst_negative_code_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)) + ((dst_negative_scale_cover_datarightentryright) + (dst_negative_scale_cover_datarightentryright)))))) /\ (((((exists ff_h_pvs_cover_datarightentryrightpositive. ff_h_pvs_cover_datarightentryrightpositive + S (dst_positive_cover_datarightentryright) = S ((S (dc_quotient_cover_datarightentry)) * dst_positive_scale_cover_datarightentryright)) /\ exists ff_q_pvs_cover_datarightentryrightpositive. dst_positive_code_cover_datarightentryright = ff_q_pvs_cover_datarightentryrightpositive * S ((S (dc_quotient_cover_datarightentry)) * dst_positive_scale_cover_datarightentryright) + (dst_positive_cover_datarightentryright))) /\ (((((exists ff_h_pvs_cover_datarightentryrightnegative. ff_h_pvs_cover_datarightentryrightnegative + S (dst_negative_cover_datarightentryright) = S ((S (dc_quotient_cover_datarightentry)) * dst_negative_scale_cover_datarightentryright)) /\ exists ff_q_pvs_cover_datarightentryrightnegative. dst_negative_code_cover_datarightentryright = ff_q_pvs_cover_datarightentryrightnegative * S ((S (dc_quotient_cover_datarightentry)) * dst_negative_scale_cover_datarightentryright) + (dst_negative_cover_datarightentryright))) /\ (exists ge_balance_positive_cover_datarightentryrightvalue ge_balance_negative_cover_datarightentryrightvalue. (((((dc_right_cover_datarightentry) = 2 * (ge_balance_positive_cover_datarightentryrightvalue) /\ (ge_balance_negative_cover_datarightentryrightvalue) = 0) \/ exists ge_signed_half_cover_datarightentryrightvaluedecode. (((dc_right_cover_datarightentry) = 2 * ge_signed_half_cover_datarightentryrightvaluedecode + 1 /\ (ge_balance_positive_cover_datarightentryrightvalue) = 0) /\ (ge_balance_negative_cover_datarightentryrightvalue) = S ge_signed_half_cover_datarightentryrightvaluedecode))) /\ ((dst_positive_cover_datarightentryright) + ge_balance_negative_cover_datarightentryrightvalue = (dst_negative_cover_datarightentryright) + ge_balance_positive_cover_datarightentryrightvalue))))))))) /\ (exists sto_ap_cover_datarightentryproduct sto_an_cover_datarightentryproduct sto_bp_cover_datarightentryproduct sto_bn_cover_datarightentryproduct sto_cp_cover_datarightentryproduct sto_cn_cover_datarightentryproduct. (((((dc_left_cover_datarightentry) = 2 * (sto_ap_cover_datarightentryproduct) /\ (sto_an_cover_datarightentryproduct) = 0) \/ exists ge_signed_half_cover_datarightentryproductleft. (((dc_left_cover_datarightentry) = 2 * ge_signed_half_cover_datarightentryproductleft + 1 /\ (sto_ap_cover_datarightentryproduct) = 0) /\ (sto_an_cover_datarightentryproduct) = S ge_signed_half_cover_datarightentryproductleft))) /\ ((((((dc_right_cover_datarightentry) = 2 * (sto_bp_cover_datarightentryproduct) /\ (sto_bn_cover_datarightentryproduct) = 0) \/ exists ge_signed_half_cover_datarightentryproductright. (((dc_right_cover_datarightentry) = 2 * ge_signed_half_cover_datarightentryproductright + 1 /\ (sto_bp_cover_datarightentryproduct) = 0) /\ (sto_bn_cover_datarightentryproduct) = S ge_signed_half_cover_datarightentryproductright))) /\ ((((((dc_value_cover_dataright) = 2 * (sto_cp_cover_datarightentryproduct) /\ (sto_cn_cover_datarightentryproduct) = 0) \/ exists ge_signed_half_cover_datarightentryproductoutput. (((dc_value_cover_dataright) = 2 * ge_signed_half_cover_datarightentryproductoutput + 1 /\ (sto_cp_cover_datarightentryproduct) = 0) /\ (sto_cn_cover_datarightentryproduct) = S ge_signed_half_cover_datarightentryproductoutput))) /\ ((sto_ap_cover_datarightentryproduct * sto_bp_cover_datarightentryproduct + sto_an_cover_datarightentryproduct * sto_bn_cover_datarightentryproduct) + sto_cn_cover_datarightentryproduct = (sto_ap_cover_datarightentryproduct * sto_bn_cover_datarightentryproduct + sto_an_cover_datarightentryproduct * sto_bp_cover_datarightentryproduct) + sto_cp_cover_datarightentryproduct))))))))))))))) \/ ((((dc_index_cover_dataright)=0 \/ ~(exists pvs_factor_cover_datarightentrynondivisor. (n) = (dc_index_cover_dataright) * pvs_factor_cover_datarightentrynondivisor)) /\ ((dc_value_cover_dataright)=0))))))) /\ (((((exists dst_positive_code_cover_datacartesianF dst_positive_scale_cover_datacartesianF dst_negative_code_cover_datacartesianF dst_negative_scale_cover_datacartesianF. (((A) = (((((dst_positive_code_cover_datacartesianF) + (dst_positive_scale_cover_datacartesianF)) * S ((dst_positive_code_cover_datacartesianF) + (dst_positive_scale_cover_datacartesianF)) + ((dst_positive_scale_cover_datacartesianF) + (dst_positive_scale_cover_datacartesianF))) + (((dst_negative_code_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)) * S ((dst_negative_code_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)) + ((dst_negative_scale_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)))) * S ((((dst_positive_code_cover_datacartesianF) + (dst_positive_scale_cover_datacartesianF)) * S ((dst_positive_code_cover_datacartesianF) + (dst_positive_scale_cover_datacartesianF)) + ((dst_positive_scale_cover_datacartesianF) + (dst_positive_scale_cover_datacartesianF))) + (((dst_negative_code_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)) * S ((dst_negative_code_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)) + ((dst_negative_scale_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)))) + ((((dst_negative_code_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)) * S ((dst_negative_code_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)) + ((dst_negative_scale_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF))) + (((dst_negative_code_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)) * S ((dst_negative_code_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)) + ((dst_negative_scale_cover_datacartesianF) + (dst_negative_scale_cover_datacartesianF)))))) /\ (forall dst_index_cover_datacartesianF. (exists pvs_le_gap_cover_datacartesianFdomain. pvs_le_gap_cover_datacartesianFdomain + (dst_index_cover_datacartesianF) = (0)) -> exists dst_positive_cover_datacartesianF dst_negative_cover_datacartesianF dst_value_cover_datacartesianF. ((((exists ff_h_pvs_cover_datacartesianFentrypositive. ff_h_pvs_cover_datacartesianFentrypositive + S (dst_positive_cover_datacartesianF) = S ((S (dst_index_cover_datacartesianF)) * dst_positive_scale_cover_datacartesianF)) /\ exists ff_q_pvs_cover_datacartesianFentrypositive. dst_positive_code_cover_datacartesianF = ff_q_pvs_cover_datacartesianFentrypositive * S ((S (dst_index_cover_datacartesianF)) * dst_positive_scale_cover_datacartesianF) + (dst_positive_cover_datacartesianF))) /\ (((((exists ff_h_pvs_cover_datacartesianFentrynegative. ff_h_pvs_cover_datacartesianFentrynegative + S (dst_negative_cover_datacartesianF) = S ((S (dst_index_cover_datacartesianF)) * dst_negative_scale_cover_datacartesianF)) /\ exists ff_q_pvs_cover_datacartesianFentrynegative. dst_negative_code_cover_datacartesianF = ff_q_pvs_cover_datacartesianFentrynegative * S ((S (dst_index_cover_datacartesianF)) * dst_negative_scale_cover_datacartesianF) + (dst_negative_cover_datacartesianF))) /\ (exists ge_balance_positive_cover_datacartesianFentryvalue ge_balance_negative_cover_datacartesianFentryvalue. (((((dst_value_cover_datacartesianF) = 2 * (ge_balance_positive_cover_datacartesianFentryvalue) /\ (ge_balance_negative_cover_datacartesianFentryvalue) = 0) \/ exists ge_signed_half_cover_datacartesianFentryvaluedecode. (((dst_value_cover_datacartesianF) = 2 * ge_signed_half_cover_datacartesianFentryvaluedecode + 1 /\ (ge_balance_positive_cover_datacartesianFentryvalue) = 0) /\ (ge_balance_negative_cover_datacartesianFentryvalue) = S ge_signed_half_cover_datacartesianFentryvaluedecode))) /\ ((dst_positive_cover_datacartesianF) + ge_balance_negative_cover_datacartesianFentryvalue = (dst_negative_cover_datacartesianF) + ge_balance_positive_cover_datacartesianFentryvalue))))))))) /\ (((exists dst_positive_code_cover_datacartesianG dst_positive_scale_cover_datacartesianG dst_negative_code_cover_datacartesianG dst_negative_scale_cover_datacartesianG. (((B) = (((((dst_positive_code_cover_datacartesianG) + (dst_positive_scale_cover_datacartesianG)) * S ((dst_positive_code_cover_datacartesianG) + (dst_positive_scale_cover_datacartesianG)) + ((dst_positive_scale_cover_datacartesianG) + (dst_positive_scale_cover_datacartesianG))) + (((dst_negative_code_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)) * S ((dst_negative_code_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)) + ((dst_negative_scale_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)))) * S ((((dst_positive_code_cover_datacartesianG) + (dst_positive_scale_cover_datacartesianG)) * S ((dst_positive_code_cover_datacartesianG) + (dst_positive_scale_cover_datacartesianG)) + ((dst_positive_scale_cover_datacartesianG) + (dst_positive_scale_cover_datacartesianG))) + (((dst_negative_code_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)) * S ((dst_negative_code_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)) + ((dst_negative_scale_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)))) + ((((dst_negative_code_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)) * S ((dst_negative_code_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)) + ((dst_negative_scale_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG))) + (((dst_negative_code_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)) * S ((dst_negative_code_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)) + ((dst_negative_scale_cover_datacartesianG) + (dst_negative_scale_cover_datacartesianG)))))) /\ (forall dst_index_cover_datacartesianG. (exists pvs_le_gap_cover_datacartesianGdomain. pvs_le_gap_cover_datacartesianGdomain + (dst_index_cover_datacartesianG) = (0)) -> exists dst_positive_cover_datacartesianG dst_negative_cover_datacartesianG dst_value_cover_datacartesianG. ((((exists ff_h_pvs_cover_datacartesianGentrypositive. ff_h_pvs_cover_datacartesianGentrypositive + S (dst_positive_cover_datacartesianG) = S ((S (dst_index_cover_datacartesianG)) * dst_positive_scale_cover_datacartesianG)) /\ exists ff_q_pvs_cover_datacartesianGentrypositive. dst_positive_code_cover_datacartesianG = ff_q_pvs_cover_datacartesianGentrypositive * S ((S (dst_index_cover_datacartesianG)) * dst_positive_scale_cover_datacartesianG) + (dst_positive_cover_datacartesianG))) /\ (((((exists ff_h_pvs_cover_datacartesianGentrynegative. ff_h_pvs_cover_datacartesianGentrynegative + S (dst_negative_cover_datacartesianG) = S ((S (dst_index_cover_datacartesianG)) * dst_negative_scale_cover_datacartesianG)) /\ exists ff_q_pvs_cover_datacartesianGentrynegative. dst_negative_code_cover_datacartesianG = ff_q_pvs_cover_datacartesianGentrynegative * S ((S (dst_index_cover_datacartesianG)) * dst_negative_scale_cover_datacartesianG) + (dst_negative_cover_datacartesianG))) /\ (exists ge_balance_positive_cover_datacartesianGentryvalue ge_balance_negative_cover_datacartesianGentryvalue. (((((dst_value_cover_datacartesianG) = 2 * (ge_balance_positive_cover_datacartesianGentryvalue) /\ (ge_balance_negative_cover_datacartesianGentryvalue) = 0) \/ exists ge_signed_half_cover_datacartesianGentryvaluedecode. (((dst_value_cover_datacartesianG) = 2 * ge_signed_half_cover_datacartesianGentryvaluedecode + 1 /\ (ge_balance_positive_cover_datacartesianGentryvalue) = 0) /\ (ge_balance_negative_cover_datacartesianGentryvalue) = S ge_signed_half_cover_datacartesianGentryvaluedecode))) /\ ((dst_positive_cover_datacartesianG) + ge_balance_negative_cover_datacartesianGentryvalue = (dst_negative_cover_datacartesianG) + ge_balance_positive_cover_datacartesianGentryvalue))))))))) /\ (((exists dst_positive_code_cover_datacartesianT dst_positive_scale_cover_datacartesianT dst_negative_code_cover_datacartesianT dst_negative_scale_cover_datacartesianT. (((T) = (((((dst_positive_code_cover_datacartesianT) + (dst_positive_scale_cover_datacartesianT)) * S ((dst_positive_code_cover_datacartesianT) + (dst_positive_scale_cover_datacartesianT)) + ((dst_positive_scale_cover_datacartesianT) + (dst_positive_scale_cover_datacartesianT))) + (((dst_negative_code_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)) * S ((dst_negative_code_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)) + ((dst_negative_scale_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)))) * S ((((dst_positive_code_cover_datacartesianT) + (dst_positive_scale_cover_datacartesianT)) * S ((dst_positive_code_cover_datacartesianT) + (dst_positive_scale_cover_datacartesianT)) + ((dst_positive_scale_cover_datacartesianT) + (dst_positive_scale_cover_datacartesianT))) + (((dst_negative_code_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)) * S ((dst_negative_code_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)) + ((dst_negative_scale_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)))) + ((((dst_negative_code_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)) * S ((dst_negative_code_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)) + ((dst_negative_scale_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT))) + (((dst_negative_code_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)) * S ((dst_negative_code_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)) + ((dst_negative_scale_cover_datacartesianT) + (dst_negative_scale_cover_datacartesianT)))))) /\ (forall dst_index_cover_datacartesianT. (exists pvs_le_gap_cover_datacartesianTdomain. pvs_le_gap_cover_datacartesianTdomain + (dst_index_cover_datacartesianT) = ((S (m))*(S (n)))) -> exists dst_positive_cover_datacartesianT dst_negative_cover_datacartesianT dst_value_cover_datacartesianT. ((((exists ff_h_pvs_cover_datacartesianTentrypositive. ff_h_pvs_cover_datacartesianTentrypositive + S (dst_positive_cover_datacartesianT) = S ((S (dst_index_cover_datacartesianT)) * dst_positive_scale_cover_datacartesianT)) /\ exists ff_q_pvs_cover_datacartesianTentrypositive. dst_positive_code_cover_datacartesianT = ff_q_pvs_cover_datacartesianTentrypositive * S ((S (dst_index_cover_datacartesianT)) * dst_positive_scale_cover_datacartesianT) + (dst_positive_cover_datacartesianT))) /\ (((((exists ff_h_pvs_cover_datacartesianTentrynegative. ff_h_pvs_cover_datacartesianTentrynegative + S (dst_negative_cover_datacartesianT) = S ((S (dst_index_cover_datacartesianT)) * dst_negative_scale_cover_datacartesianT)) /\ exists ff_q_pvs_cover_datacartesianTentrynegative. dst_negative_code_cover_datacartesianT = ff_q_pvs_cover_datacartesianTentrynegative * S ((S (dst_index_cover_datacartesianT)) * dst_negative_scale_cover_datacartesianT) + (dst_negative_cover_datacartesianT))) /\ (exists ge_balance_positive_cover_datacartesianTentryvalue ge_balance_negative_cover_datacartesianTentryvalue. (((((dst_value_cover_datacartesianT) = 2 * (ge_balance_positive_cover_datacartesianTentryvalue) /\ (ge_balance_negative_cover_datacartesianTentryvalue) = 0) \/ exists ge_signed_half_cover_datacartesianTentryvaluedecode. (((dst_value_cover_datacartesianT) = 2 * ge_signed_half_cover_datacartesianTentryvaluedecode + 1 /\ (ge_balance_positive_cover_datacartesianTentryvalue) = 0) /\ (ge_balance_negative_cover_datacartesianTentryvalue) = S ge_signed_half_cover_datacartesianTentryvaluedecode))) /\ ((dst_positive_cover_datacartesianT) + ge_balance_negative_cover_datacartesianTentryvalue = (dst_negative_cover_datacartesianT) + ge_balance_positive_cover_datacartesianTentryvalue))))))))) /\ (forall scp_row_cover_datacartesian scp_column_cover_datacartesian scp_first_cover_datacartesian scp_second_cover_datacartesian scp_value_cover_datacartesian. (exists pvs_gap_cover_datacartesianrows. pvs_gap_cover_datacartesianrows + S (scp_row_cover_datacartesian) = (S (m))) -> (exists pvs_gap_cover_datacartesiancolumns. pvs_gap_cover_datacartesiancolumns + S (scp_column_cover_datacartesian) = (S (n))) -> (exists dst_positive_code_cover_datacartesianfirst dst_positive_scale_cover_datacartesianfirst dst_negative_code_cover_datacartesianfirst dst_negative_scale_cover_datacartesianfirst dst_positive_cover_datacartesianfirst dst_negative_cover_datacartesianfirst. (((A) = (((((dst_positive_code_cover_datacartesianfirst) + (dst_positive_scale_cover_datacartesianfirst)) * S ((dst_positive_code_cover_datacartesianfirst) + (dst_positive_scale_cover_datacartesianfirst)) + ((dst_positive_scale_cover_datacartesianfirst) + (dst_positive_scale_cover_datacartesianfirst))) + (((dst_negative_code_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)) * S ((dst_negative_code_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)) + ((dst_negative_scale_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)))) * S ((((dst_positive_code_cover_datacartesianfirst) + (dst_positive_scale_cover_datacartesianfirst)) * S ((dst_positive_code_cover_datacartesianfirst) + (dst_positive_scale_cover_datacartesianfirst)) + ((dst_positive_scale_cover_datacartesianfirst) + (dst_positive_scale_cover_datacartesianfirst))) + (((dst_negative_code_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)) * S ((dst_negative_code_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)) + ((dst_negative_scale_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)))) + ((((dst_negative_code_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)) * S ((dst_negative_code_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)) + ((dst_negative_scale_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst))) + (((dst_negative_code_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)) * S ((dst_negative_code_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)) + ((dst_negative_scale_cover_datacartesianfirst) + (dst_negative_scale_cover_datacartesianfirst)))))) /\ (((((exists ff_h_pvs_cover_datacartesianfirstpositive. ff_h_pvs_cover_datacartesianfirstpositive + S (dst_positive_cover_datacartesianfirst) = S ((S (scp_row_cover_datacartesian)) * dst_positive_scale_cover_datacartesianfirst)) /\ exists ff_q_pvs_cover_datacartesianfirstpositive. dst_positive_code_cover_datacartesianfirst = ff_q_pvs_cover_datacartesianfirstpositive * S ((S (scp_row_cover_datacartesian)) * dst_positive_scale_cover_datacartesianfirst) + (dst_positive_cover_datacartesianfirst))) /\ (((((exists ff_h_pvs_cover_datacartesianfirstnegative. ff_h_pvs_cover_datacartesianfirstnegative + S (dst_negative_cover_datacartesianfirst) = S ((S (scp_row_cover_datacartesian)) * dst_negative_scale_cover_datacartesianfirst)) /\ exists ff_q_pvs_cover_datacartesianfirstnegative. dst_negative_code_cover_datacartesianfirst = ff_q_pvs_cover_datacartesianfirstnegative * S ((S (scp_row_cover_datacartesian)) * dst_negative_scale_cover_datacartesianfirst) + (dst_negative_cover_datacartesianfirst))) /\ (exists ge_balance_positive_cover_datacartesianfirstvalue ge_balance_negative_cover_datacartesianfirstvalue. (((((scp_first_cover_datacartesian) = 2 * (ge_balance_positive_cover_datacartesianfirstvalue) /\ (ge_balance_negative_cover_datacartesianfirstvalue) = 0) \/ exists ge_signed_half_cover_datacartesianfirstvaluedecode. (((scp_first_cover_datacartesian) = 2 * ge_signed_half_cover_datacartesianfirstvaluedecode + 1 /\ (ge_balance_positive_cover_datacartesianfirstvalue) = 0) /\ (ge_balance_negative_cover_datacartesianfirstvalue) = S ge_signed_half_cover_datacartesianfirstvaluedecode))) /\ ((dst_positive_cover_datacartesianfirst) + ge_balance_negative_cover_datacartesianfirstvalue = (dst_negative_cover_datacartesianfirst) + ge_balance_positive_cover_datacartesianfirstvalue))))))))) -> (exists dst_positive_code_cover_datacartesiansecond dst_positive_scale_cover_datacartesiansecond dst_negative_code_cover_datacartesiansecond dst_negative_scale_cover_datacartesiansecond dst_positive_cover_datacartesiansecond dst_negative_cover_datacartesiansecond. (((B) = (((((dst_positive_code_cover_datacartesiansecond) + (dst_positive_scale_cover_datacartesiansecond)) * S ((dst_positive_code_cover_datacartesiansecond) + (dst_positive_scale_cover_datacartesiansecond)) + ((dst_positive_scale_cover_datacartesiansecond) + (dst_positive_scale_cover_datacartesiansecond))) + (((dst_negative_code_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)) * S ((dst_negative_code_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)) + ((dst_negative_scale_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)))) * S ((((dst_positive_code_cover_datacartesiansecond) + (dst_positive_scale_cover_datacartesiansecond)) * S ((dst_positive_code_cover_datacartesiansecond) + (dst_positive_scale_cover_datacartesiansecond)) + ((dst_positive_scale_cover_datacartesiansecond) + (dst_positive_scale_cover_datacartesiansecond))) + (((dst_negative_code_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)) * S ((dst_negative_code_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)) + ((dst_negative_scale_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)))) + ((((dst_negative_code_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)) * S ((dst_negative_code_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)) + ((dst_negative_scale_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond))) + (((dst_negative_code_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)) * S ((dst_negative_code_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)) + ((dst_negative_scale_cover_datacartesiansecond) + (dst_negative_scale_cover_datacartesiansecond)))))) /\ (((((exists ff_h_pvs_cover_datacartesiansecondpositive. ff_h_pvs_cover_datacartesiansecondpositive + S (dst_positive_cover_datacartesiansecond) = S ((S (scp_column_cover_datacartesian)) * dst_positive_scale_cover_datacartesiansecond)) /\ exists ff_q_pvs_cover_datacartesiansecondpositive. dst_positive_code_cover_datacartesiansecond = ff_q_pvs_cover_datacartesiansecondpositive * S ((S (scp_column_cover_datacartesian)) * dst_positive_scale_cover_datacartesiansecond) + (dst_positive_cover_datacartesiansecond))) /\ (((((exists ff_h_pvs_cover_datacartesiansecondnegative. ff_h_pvs_cover_datacartesiansecondnegative + S (dst_negative_cover_datacartesiansecond) = S ((S (scp_column_cover_datacartesian)) * dst_negative_scale_cover_datacartesiansecond)) /\ exists ff_q_pvs_cover_datacartesiansecondnegative. dst_negative_code_cover_datacartesiansecond = ff_q_pvs_cover_datacartesiansecondnegative * S ((S (scp_column_cover_datacartesian)) * dst_negative_scale_cover_datacartesiansecond) + (dst_negative_cover_datacartesiansecond))) /\ (exists ge_balance_positive_cover_datacartesiansecondvalue ge_balance_negative_cover_datacartesiansecondvalue. (((((scp_second_cover_datacartesian) = 2 * (ge_balance_positive_cover_datacartesiansecondvalue) /\ (ge_balance_negative_cover_datacartesiansecondvalue) = 0) \/ exists ge_signed_half_cover_datacartesiansecondvaluedecode. (((scp_second_cover_datacartesian) = 2 * ge_signed_half_cover_datacartesiansecondvaluedecode + 1 /\ (ge_balance_positive_cover_datacartesiansecondvalue) = 0) /\ (ge_balance_negative_cover_datacartesiansecondvalue) = S ge_signed_half_cover_datacartesiansecondvaluedecode))) /\ ((dst_positive_cover_datacartesiansecond) + ge_balance_negative_cover_datacartesiansecondvalue = (dst_negative_cover_datacartesiansecond) + ge_balance_positive_cover_datacartesiansecondvalue))))))))) -> (exists dst_positive_code_cover_datacartesianentry dst_positive_scale_cover_datacartesianentry dst_negative_code_cover_datacartesianentry dst_negative_scale_cover_datacartesianentry dst_positive_cover_datacartesianentry dst_negative_cover_datacartesianentry. (((T) = (((((dst_positive_code_cover_datacartesianentry) + (dst_positive_scale_cover_datacartesianentry)) * S ((dst_positive_code_cover_datacartesianentry) + (dst_positive_scale_cover_datacartesianentry)) + ((dst_positive_scale_cover_datacartesianentry) + (dst_positive_scale_cover_datacartesianentry))) + (((dst_negative_code_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)) * S ((dst_negative_code_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)) + ((dst_negative_scale_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)))) * S ((((dst_positive_code_cover_datacartesianentry) + (dst_positive_scale_cover_datacartesianentry)) * S ((dst_positive_code_cover_datacartesianentry) + (dst_positive_scale_cover_datacartesianentry)) + ((dst_positive_scale_cover_datacartesianentry) + (dst_positive_scale_cover_datacartesianentry))) + (((dst_negative_code_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)) * S ((dst_negative_code_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)) + ((dst_negative_scale_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)))) + ((((dst_negative_code_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)) * S ((dst_negative_code_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)) + ((dst_negative_scale_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry))) + (((dst_negative_code_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)) * S ((dst_negative_code_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)) + ((dst_negative_scale_cover_datacartesianentry) + (dst_negative_scale_cover_datacartesianentry)))))) /\ (((((exists ff_h_pvs_cover_datacartesianentrypositive. ff_h_pvs_cover_datacartesianentrypositive + S (dst_positive_cover_datacartesianentry) = S ((S (((S (n))*(scp_row_cover_datacartesian)+(scp_column_cover_datacartesian)))) * dst_positive_scale_cover_datacartesianentry)) /\ exists ff_q_pvs_cover_datacartesianentrypositive. dst_positive_code_cover_datacartesianentry = ff_q_pvs_cover_datacartesianentrypositive * S ((S (((S (n))*(scp_row_cover_datacartesian)+(scp_column_cover_datacartesian)))) * dst_positive_scale_cover_datacartesianentry) + (dst_positive_cover_datacartesianentry))) /\ (((((exists ff_h_pvs_cover_datacartesianentrynegative. ff_h_pvs_cover_datacartesianentrynegative + S (dst_negative_cover_datacartesianentry) = S ((S (((S (n))*(scp_row_cover_datacartesian)+(scp_column_cover_datacartesian)))) * dst_negative_scale_cover_datacartesianentry)) /\ exists ff_q_pvs_cover_datacartesianentrynegative. dst_negative_code_cover_datacartesianentry = ff_q_pvs_cover_datacartesianentrynegative * S ((S (((S (n))*(scp_row_cover_datacartesian)+(scp_column_cover_datacartesian)))) * dst_negative_scale_cover_datacartesianentry) + (dst_negative_cover_datacartesianentry))) /\ (exists ge_balance_positive_cover_datacartesianentryvalue ge_balance_negative_cover_datacartesianentryvalue. (((((scp_value_cover_datacartesian) = 2 * (ge_balance_positive_cover_datacartesianentryvalue) /\ (ge_balance_negative_cover_datacartesianentryvalue) = 0) \/ exists ge_signed_half_cover_datacartesianentryvaluedecode. (((scp_value_cover_datacartesian) = 2 * ge_signed_half_cover_datacartesianentryvaluedecode + 1 /\ (ge_balance_positive_cover_datacartesianentryvalue) = 0) /\ (ge_balance_negative_cover_datacartesianentryvalue) = S ge_signed_half_cover_datacartesianentryvaluedecode))) /\ ((dst_positive_cover_datacartesianentry) + ge_balance_negative_cover_datacartesianentryvalue = (dst_negative_cover_datacartesianentry) + ge_balance_positive_cover_datacartesianentryvalue))))))))) -> (exists sto_ap_cover_datacartesianmultiply sto_an_cover_datacartesianmultiply sto_bp_cover_datacartesianmultiply sto_bn_cover_datacartesianmultiply sto_cp_cover_datacartesianmultiply sto_cn_cover_datacartesianmultiply. (((((scp_first_cover_datacartesian) = 2 * (sto_ap_cover_datacartesianmultiply) /\ (sto_an_cover_datacartesianmultiply) = 0) \/ exists ge_signed_half_cover_datacartesianmultiplyleft. (((scp_first_cover_datacartesian) = 2 * ge_signed_half_cover_datacartesianmultiplyleft + 1 /\ (sto_ap_cover_datacartesianmultiply) = 0) /\ (sto_an_cover_datacartesianmultiply) = S ge_signed_half_cover_datacartesianmultiplyleft))) /\ ((((((scp_second_cover_datacartesian) = 2 * (sto_bp_cover_datacartesianmultiply) /\ (sto_bn_cover_datacartesianmultiply) = 0) \/ exists ge_signed_half_cover_datacartesianmultiplyright. (((scp_second_cover_datacartesian) = 2 * ge_signed_half_cover_datacartesianmultiplyright + 1 /\ (sto_bp_cover_datacartesianmultiply) = 0) /\ (sto_bn_cover_datacartesianmultiply) = S ge_signed_half_cover_datacartesianmultiplyright))) /\ ((((((scp_value_cover_datacartesian) = 2 * (sto_cp_cover_datacartesianmultiply) /\ (sto_cn_cover_datacartesianmultiply) = 0) \/ exists ge_signed_half_cover_datacartesianmultiplyoutput. (((scp_value_cover_datacartesian) = 2 * ge_signed_half_cover_datacartesianmultiplyoutput + 1 /\ (sto_cp_cover_datacartesianmultiply) = 0) /\ (sto_cn_cover_datacartesianmultiply) = S ge_signed_half_cover_datacartesianmultiplyoutput))) /\ ((sto_ap_cover_datacartesianmultiply * sto_bp_cover_datacartesianmultiply + sto_an_cover_datacartesianmultiply * sto_bn_cover_datacartesianmultiply) + sto_cn_cover_datacartesianmultiply = (sto_ap_cover_datacartesianmultiply * sto_bn_cover_datacartesianmultiply + sto_an_cover_datacartesianmultiply * sto_bp_cover_datacartesianmultiply) + sto_cp_cover_datacartesianmultiply)))))))))))))) /\ (((((exists dst_positive_code_cover_datatargettable dst_positive_scale_cover_datatargettable dst_negative_code_cover_datatargettable dst_negative_scale_cover_datatargettable. (((Q) = (((((dst_positive_code_cover_datatargettable) + (dst_positive_scale_cover_datatargettable)) * S ((dst_positive_code_cover_datatargettable) + (dst_positive_scale_cover_datatargettable)) + ((dst_positive_scale_cover_datatargettable) + (dst_positive_scale_cover_datatargettable))) + (((dst_negative_code_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)) * S ((dst_negative_code_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)) + ((dst_negative_scale_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)))) * S ((((dst_positive_code_cover_datatargettable) + (dst_positive_scale_cover_datatargettable)) * S ((dst_positive_code_cover_datatargettable) + (dst_positive_scale_cover_datatargettable)) + ((dst_positive_scale_cover_datatargettable) + (dst_positive_scale_cover_datatargettable))) + (((dst_negative_code_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)) * S ((dst_negative_code_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)) + ((dst_negative_scale_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)))) + ((((dst_negative_code_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)) * S ((dst_negative_code_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)) + ((dst_negative_scale_cover_datatargettable) + (dst_negative_scale_cover_datatargettable))) + (((dst_negative_code_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)) * S ((dst_negative_code_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)) + ((dst_negative_scale_cover_datatargettable) + (dst_negative_scale_cover_datatargettable)))))) /\ (forall dst_index_cover_datatargettable. (exists pvs_le_gap_cover_datatargettabledomain. pvs_le_gap_cover_datatargettabledomain + (dst_index_cover_datatargettable) = ((m)*(n))) -> exists dst_positive_cover_datatargettable dst_negative_cover_datatargettable dst_value_cover_datatargettable. ((((exists ff_h_pvs_cover_datatargettableentrypositive. ff_h_pvs_cover_datatargettableentrypositive + S (dst_positive_cover_datatargettable) = S ((S (dst_index_cover_datatargettable)) * dst_positive_scale_cover_datatargettable)) /\ exists ff_q_pvs_cover_datatargettableentrypositive. dst_positive_code_cover_datatargettable = ff_q_pvs_cover_datatargettableentrypositive * S ((S (dst_index_cover_datatargettable)) * dst_positive_scale_cover_datatargettable) + (dst_positive_cover_datatargettable))) /\ (((((exists ff_h_pvs_cover_datatargettableentrynegative. ff_h_pvs_cover_datatargettableentrynegative + S (dst_negative_cover_datatargettable) = S ((S (dst_index_cover_datatargettable)) * dst_negative_scale_cover_datatargettable)) /\ exists ff_q_pvs_cover_datatargettableentrynegative. dst_negative_code_cover_datatargettable = ff_q_pvs_cover_datatargettableentrynegative * S ((S (dst_index_cover_datatargettable)) * dst_negative_scale_cover_datatargettable) + (dst_negative_cover_datatargettable))) /\ (exists ge_balance_positive_cover_datatargettableentryvalue ge_balance_negative_cover_datatargettableentryvalue. (((((dst_value_cover_datatargettable) = 2 * (ge_balance_positive_cover_datatargettableentryvalue) /\ (ge_balance_negative_cover_datatargettableentryvalue) = 0) \/ exists ge_signed_half_cover_datatargettableentryvaluedecode. (((dst_value_cover_datatargettable) = 2 * ge_signed_half_cover_datatargettableentryvaluedecode + 1 /\ (ge_balance_positive_cover_datatargettableentryvalue) = 0) /\ (ge_balance_negative_cover_datatargettableentryvalue) = S ge_signed_half_cover_datatargettableentryvaluedecode))) /\ ((dst_positive_cover_datatargettable) + ge_balance_negative_cover_datatargettableentryvalue = (dst_negative_cover_datatargettable) + ge_balance_positive_cover_datatargettableentryvalue))))))))) /\ (forall dc_index_cover_datatarget dc_value_cover_datatarget. (exists pvs_le_gap_cover_datatargetdomain. pvs_le_gap_cover_datatargetdomain + (dc_index_cover_datatarget) = ((m)*(n))) -> (exists dst_positive_code_cover_datatargetlookup dst_positive_scale_cover_datatargetlookup dst_negative_code_cover_datatargetlookup dst_negative_scale_cover_datatargetlookup dst_positive_cover_datatargetlookup dst_negative_cover_datatargetlookup. (((Q) = (((((dst_positive_code_cover_datatargetlookup) + (dst_positive_scale_cover_datatargetlookup)) * S ((dst_positive_code_cover_datatargetlookup) + (dst_positive_scale_cover_datatargetlookup)) + ((dst_positive_scale_cover_datatargetlookup) + (dst_positive_scale_cover_datatargetlookup))) + (((dst_negative_code_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)) * S ((dst_negative_code_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)) + ((dst_negative_scale_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)))) * S ((((dst_positive_code_cover_datatargetlookup) + (dst_positive_scale_cover_datatargetlookup)) * S ((dst_positive_code_cover_datatargetlookup) + (dst_positive_scale_cover_datatargetlookup)) + ((dst_positive_scale_cover_datatargetlookup) + (dst_positive_scale_cover_datatargetlookup))) + (((dst_negative_code_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)) * S ((dst_negative_code_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)) + ((dst_negative_scale_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)))) + ((((dst_negative_code_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)) * S ((dst_negative_code_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)) + ((dst_negative_scale_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup))) + (((dst_negative_code_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)) * S ((dst_negative_code_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)) + ((dst_negative_scale_cover_datatargetlookup) + (dst_negative_scale_cover_datatargetlookup)))))) /\ (((((exists ff_h_pvs_cover_datatargetlookuppositive. ff_h_pvs_cover_datatargetlookuppositive + S (dst_positive_cover_datatargetlookup) = S ((S (dc_index_cover_datatarget)) * dst_positive_scale_cover_datatargetlookup)) /\ exists ff_q_pvs_cover_datatargetlookuppositive. dst_positive_code_cover_datatargetlookup = ff_q_pvs_cover_datatargetlookuppositive * S ((S (dc_index_cover_datatarget)) * dst_positive_scale_cover_datatargetlookup) + (dst_positive_cover_datatargetlookup))) /\ (((((exists ff_h_pvs_cover_datatargetlookupnegative. ff_h_pvs_cover_datatargetlookupnegative + S (dst_negative_cover_datatargetlookup) = S ((S (dc_index_cover_datatarget)) * dst_negative_scale_cover_datatargetlookup)) /\ exists ff_q_pvs_cover_datatargetlookupnegative. dst_negative_code_cover_datatargetlookup = ff_q_pvs_cover_datatargetlookupnegative * S ((S (dc_index_cover_datatarget)) * dst_negative_scale_cover_datatargetlookup) + (dst_negative_cover_datatargetlookup))) /\ (exists ge_balance_positive_cover_datatargetlookupvalue ge_balance_negative_cover_datatargetlookupvalue. (((((dc_value_cover_datatarget) = 2 * (ge_balance_positive_cover_datatargetlookupvalue) /\ (ge_balance_negative_cover_datatargetlookupvalue) = 0) \/ exists ge_signed_half_cover_datatargetlookupvaluedecode. (((dc_value_cover_datatarget) = 2 * ge_signed_half_cover_datatargetlookupvaluedecode + 1 /\ (ge_balance_positive_cover_datatargetlookupvalue) = 0) /\ (ge_balance_negative_cover_datatargetlookupvalue) = S ge_signed_half_cover_datatargetlookupvaluedecode))) /\ ((dst_positive_cover_datatargetlookup) + ge_balance_negative_cover_datatargetlookupvalue = (dst_negative_cover_datatargetlookup) + ge_balance_positive_cover_datatargetlookupvalue))))))))) -> ((((~((dc_index_cover_datatarget)=0)) /\ (exists dc_quotient_cover_datatargetentry dc_left_cover_datatargetentry dc_right_cover_datatargetentry. ((((m)*(n))=(dc_index_cover_datatarget)*dc_quotient_cover_datatargetentry) /\ (((exists dst_positive_code_cover_datatargetentryleft dst_positive_scale_cover_datatargetentryleft dst_negative_code_cover_datatargetentryleft dst_negative_scale_cover_datatargetentryleft dst_positive_cover_datatargetentryleft dst_negative_cover_datatargetentryleft. (((F) = (((((dst_positive_code_cover_datatargetentryleft) + (dst_positive_scale_cover_datatargetentryleft)) * S ((dst_positive_code_cover_datatargetentryleft) + (dst_positive_scale_cover_datatargetentryleft)) + ((dst_positive_scale_cover_datatargetentryleft) + (dst_positive_scale_cover_datatargetentryleft))) + (((dst_negative_code_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)) * S ((dst_negative_code_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)) + ((dst_negative_scale_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)))) * S ((((dst_positive_code_cover_datatargetentryleft) + (dst_positive_scale_cover_datatargetentryleft)) * S ((dst_positive_code_cover_datatargetentryleft) + (dst_positive_scale_cover_datatargetentryleft)) + ((dst_positive_scale_cover_datatargetentryleft) + (dst_positive_scale_cover_datatargetentryleft))) + (((dst_negative_code_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)) * S ((dst_negative_code_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)) + ((dst_negative_scale_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)))) + ((((dst_negative_code_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)) * S ((dst_negative_code_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)) + ((dst_negative_scale_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft))) + (((dst_negative_code_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)) * S ((dst_negative_code_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)) + ((dst_negative_scale_cover_datatargetentryleft) + (dst_negative_scale_cover_datatargetentryleft)))))) /\ (((((exists ff_h_pvs_cover_datatargetentryleftpositive. ff_h_pvs_cover_datatargetentryleftpositive + S (dst_positive_cover_datatargetentryleft) = S ((S (dc_index_cover_datatarget)) * dst_positive_scale_cover_datatargetentryleft)) /\ exists ff_q_pvs_cover_datatargetentryleftpositive. dst_positive_code_cover_datatargetentryleft = ff_q_pvs_cover_datatargetentryleftpositive * S ((S (dc_index_cover_datatarget)) * dst_positive_scale_cover_datatargetentryleft) + (dst_positive_cover_datatargetentryleft))) /\ (((((exists ff_h_pvs_cover_datatargetentryleftnegative. ff_h_pvs_cover_datatargetentryleftnegative + S (dst_negative_cover_datatargetentryleft) = S ((S (dc_index_cover_datatarget)) * dst_negative_scale_cover_datatargetentryleft)) /\ exists ff_q_pvs_cover_datatargetentryleftnegative. dst_negative_code_cover_datatargetentryleft = ff_q_pvs_cover_datatargetentryleftnegative * S ((S (dc_index_cover_datatarget)) * dst_negative_scale_cover_datatargetentryleft) + (dst_negative_cover_datatargetentryleft))) /\ (exists ge_balance_positive_cover_datatargetentryleftvalue ge_balance_negative_cover_datatargetentryleftvalue. (((((dc_left_cover_datatargetentry) = 2 * (ge_balance_positive_cover_datatargetentryleftvalue) /\ (ge_balance_negative_cover_datatargetentryleftvalue) = 0) \/ exists ge_signed_half_cover_datatargetentryleftvaluedecode. (((dc_left_cover_datatargetentry) = 2 * ge_signed_half_cover_datatargetentryleftvaluedecode + 1 /\ (ge_balance_positive_cover_datatargetentryleftvalue) = 0) /\ (ge_balance_negative_cover_datatargetentryleftvalue) = S ge_signed_half_cover_datatargetentryleftvaluedecode))) /\ ((dst_positive_cover_datatargetentryleft) + ge_balance_negative_cover_datatargetentryleftvalue = (dst_negative_cover_datatargetentryleft) + ge_balance_positive_cover_datatargetentryleftvalue))))))))) /\ (((exists dst_positive_code_cover_datatargetentryright dst_positive_scale_cover_datatargetentryright dst_negative_code_cover_datatargetentryright dst_negative_scale_cover_datatargetentryright dst_positive_cover_datatargetentryright dst_negative_cover_datatargetentryright. (((G) = (((((dst_positive_code_cover_datatargetentryright) + (dst_positive_scale_cover_datatargetentryright)) * S ((dst_positive_code_cover_datatargetentryright) + (dst_positive_scale_cover_datatargetentryright)) + ((dst_positive_scale_cover_datatargetentryright) + (dst_positive_scale_cover_datatargetentryright))) + (((dst_negative_code_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)) * S ((dst_negative_code_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)) + ((dst_negative_scale_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)))) * S ((((dst_positive_code_cover_datatargetentryright) + (dst_positive_scale_cover_datatargetentryright)) * S ((dst_positive_code_cover_datatargetentryright) + (dst_positive_scale_cover_datatargetentryright)) + ((dst_positive_scale_cover_datatargetentryright) + (dst_positive_scale_cover_datatargetentryright))) + (((dst_negative_code_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)) * S ((dst_negative_code_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)) + ((dst_negative_scale_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)))) + ((((dst_negative_code_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)) * S ((dst_negative_code_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)) + ((dst_negative_scale_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright))) + (((dst_negative_code_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)) * S ((dst_negative_code_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)) + ((dst_negative_scale_cover_datatargetentryright) + (dst_negative_scale_cover_datatargetentryright)))))) /\ (((((exists ff_h_pvs_cover_datatargetentryrightpositive. ff_h_pvs_cover_datatargetentryrightpositive + S (dst_positive_cover_datatargetentryright) = S ((S (dc_quotient_cover_datatargetentry)) * dst_positive_scale_cover_datatargetentryright)) /\ exists ff_q_pvs_cover_datatargetentryrightpositive. dst_positive_code_cover_datatargetentryright = ff_q_pvs_cover_datatargetentryrightpositive * S ((S (dc_quotient_cover_datatargetentry)) * dst_positive_scale_cover_datatargetentryright) + (dst_positive_cover_datatargetentryright))) /\ (((((exists ff_h_pvs_cover_datatargetentryrightnegative. ff_h_pvs_cover_datatargetentryrightnegative + S (dst_negative_cover_datatargetentryright) = S ((S (dc_quotient_cover_datatargetentry)) * dst_negative_scale_cover_datatargetentryright)) /\ exists ff_q_pvs_cover_datatargetentryrightnegative. dst_negative_code_cover_datatargetentryright = ff_q_pvs_cover_datatargetentryrightnegative * S ((S (dc_quotient_cover_datatargetentry)) * dst_negative_scale_cover_datatargetentryright) + (dst_negative_cover_datatargetentryright))) /\ (exists ge_balance_positive_cover_datatargetentryrightvalue ge_balance_negative_cover_datatargetentryrightvalue. (((((dc_right_cover_datatargetentry) = 2 * (ge_balance_positive_cover_datatargetentryrightvalue) /\ (ge_balance_negative_cover_datatargetentryrightvalue) = 0) \/ exists ge_signed_half_cover_datatargetentryrightvaluedecode. (((dc_right_cover_datatargetentry) = 2 * ge_signed_half_cover_datatargetentryrightvaluedecode + 1 /\ (ge_balance_positive_cover_datatargetentryrightvalue) = 0) /\ (ge_balance_negative_cover_datatargetentryrightvalue) = S ge_signed_half_cover_datatargetentryrightvaluedecode))) /\ ((dst_positive_cover_datatargetentryright) + ge_balance_negative_cover_datatargetentryrightvalue = (dst_negative_cover_datatargetentryright) + ge_balance_positive_cover_datatargetentryrightvalue))))))))) /\ (exists sto_ap_cover_datatargetentryproduct sto_an_cover_datatargetentryproduct sto_bp_cover_datatargetentryproduct sto_bn_cover_datatargetentryproduct sto_cp_cover_datatargetentryproduct sto_cn_cover_datatargetentryproduct. (((((dc_left_cover_datatargetentry) = 2 * (sto_ap_cover_datatargetentryproduct) /\ (sto_an_cover_datatargetentryproduct) = 0) \/ exists ge_signed_half_cover_datatargetentryproductleft. (((dc_left_cover_datatargetentry) = 2 * ge_signed_half_cover_datatargetentryproductleft + 1 /\ (sto_ap_cover_datatargetentryproduct) = 0) /\ (sto_an_cover_datatargetentryproduct) = S ge_signed_half_cover_datatargetentryproductleft))) /\ ((((((dc_right_cover_datatargetentry) = 2 * (sto_bp_cover_datatargetentryproduct) /\ (sto_bn_cover_datatargetentryproduct) = 0) \/ exists ge_signed_half_cover_datatargetentryproductright. (((dc_right_cover_datatargetentry) = 2 * ge_signed_half_cover_datatargetentryproductright + 1 /\ (sto_bp_cover_datatargetentryproduct) = 0) /\ (sto_bn_cover_datatargetentryproduct) = S ge_signed_half_cover_datatargetentryproductright))) /\ ((((((dc_value_cover_datatarget) = 2 * (sto_cp_cover_datatargetentryproduct) /\ (sto_cn_cover_datatargetentryproduct) = 0) \/ exists ge_signed_half_cover_datatargetentryproductoutput. (((dc_value_cover_datatarget) = 2 * ge_signed_half_cover_datatargetentryproductoutput + 1 /\ (sto_cp_cover_datatargetentryproduct) = 0) /\ (sto_cn_cover_datatargetentryproduct) = S ge_signed_half_cover_datatargetentryproductoutput))) /\ ((sto_ap_cover_datatargetentryproduct * sto_bp_cover_datatargetentryproduct + sto_an_cover_datatargetentryproduct * sto_bn_cover_datatargetentryproduct) + sto_cn_cover_datatargetentryproduct = (sto_ap_cover_datatargetentryproduct * sto_bn_cover_datatargetentryproduct + sto_an_cover_datatargetentryproduct * sto_bp_cover_datatargetentryproduct) + sto_cp_cover_datatargetentryproduct))))))))))))))) \/ ((((dc_index_cover_datatarget)=0 \/ ~(exists pvs_factor_cover_datatargetentrynondivisor. ((m)*(n)) = (dc_index_cover_datatarget) * pvs_factor_cover_datatargetentrynondivisor)) /\ ((dc_value_cover_datatarget)=0))))))) /\ (((~((S (n))=0)) /\ (forall dpi_index_cover_datamap dpi_row_cover_datamap dpi_column_cover_datamap. (exists pvs_gap_cover_datamapwindow. pvs_gap_cover_datamapwindow + S (dpi_index_cover_datamap) = ((S (m))*(S (n)))) -> (exists pvs_gap_cover_datamapremainder. pvs_gap_cover_datamapremainder + S (dpi_column_cover_datamap) = (S (n))) -> (dpi_index_cover_datamap)=(S (n))*(dpi_row_cover_datamap)+(dpi_column_cover_datamap) -> (((exists ff_h_pvs_cover_datamapvalue. ff_h_pvs_cover_datamapvalue + S ((dpi_row_cover_datamap)*(dpi_column_cover_datamap)) = S ((S (dpi_index_cover_datamap)) * s)) /\ exists ff_q_pvs_cover_datamapvalue. r = ff_q_pvs_cover_datamapvalue * S ((S (dpi_index_cover_datamap)) * s) + ((dpi_row_cover_datamap)*(dpi_column_cover_datamap))))))))))))))))))))))))))) -> (forall ssr_target_cover_result ssr_value_cover_result. (exists pvs_gap_cover_resulttarget_bound. pvs_gap_cover_resulttarget_bound + S (ssr_target_cover_result) = (S (m*n))) -> (exists dst_positive_code_cover_resulttarget_value dst_positive_scale_cover_resulttarget_value dst_negative_code_cover_resulttarget_value dst_negative_scale_cover_resulttarget_value dst_positive_cover_resulttarget_value dst_negative_cover_resulttarget_value. (((Q) = (((((dst_positive_code_cover_resulttarget_value) + (dst_positive_scale_cover_resulttarget_value)) * S ((dst_positive_code_cover_resulttarget_value) + (dst_positive_scale_cover_resulttarget_value)) + ((dst_positive_scale_cover_resulttarget_value) + (dst_positive_scale_cover_resulttarget_value))) + (((dst_negative_code_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)) * S ((dst_negative_code_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)) + ((dst_negative_scale_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)))) * S ((((dst_positive_code_cover_resulttarget_value) + (dst_positive_scale_cover_resulttarget_value)) * S ((dst_positive_code_cover_resulttarget_value) + (dst_positive_scale_cover_resulttarget_value)) + ((dst_positive_scale_cover_resulttarget_value) + (dst_positive_scale_cover_resulttarget_value))) + (((dst_negative_code_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)) * S ((dst_negative_code_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)) + ((dst_negative_scale_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)))) + ((((dst_negative_code_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)) * S ((dst_negative_code_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)) + ((dst_negative_scale_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value))) + (((dst_negative_code_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)) * S ((dst_negative_code_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)) + ((dst_negative_scale_cover_resulttarget_value) + (dst_negative_scale_cover_resulttarget_value)))))) /\ (((((exists ff_h_pvs_cover_resulttarget_valuepositive. ff_h_pvs_cover_resulttarget_valuepositive + S (dst_positive_cover_resulttarget_value) = S ((S (ssr_target_cover_result)) * dst_positive_scale_cover_resulttarget_value)) /\ exists ff_q_pvs_cover_resulttarget_valuepositive. dst_positive_code_cover_resulttarget_value = ff_q_pvs_cover_resulttarget_valuepositive * S ((S (ssr_target_cover_result)) * dst_positive_scale_cover_resulttarget_value) + (dst_positive_cover_resulttarget_value))) /\ (((((exists ff_h_pvs_cover_resulttarget_valuenegative. ff_h_pvs_cover_resulttarget_valuenegative + S (dst_negative_cover_resulttarget_value) = S ((S (ssr_target_cover_result)) * dst_negative_scale_cover_resulttarget_value)) /\ exists ff_q_pvs_cover_resulttarget_valuenegative. dst_negative_code_cover_resulttarget_value = ff_q_pvs_cover_resulttarget_valuenegative * S ((S (ssr_target_cover_result)) * dst_negative_scale_cover_resulttarget_value) + (dst_negative_cover_resulttarget_value))) /\ (exists ge_balance_positive_cover_resulttarget_valuevalue ge_balance_negative_cover_resulttarget_valuevalue. (((((ssr_value_cover_result) = 2 * (ge_balance_positive_cover_resulttarget_valuevalue) /\ (ge_balance_negative_cover_resulttarget_valuevalue) = 0) \/ exists ge_signed_half_cover_resulttarget_valuevaluedecode. (((ssr_value_cover_result) = 2 * ge_signed_half_cover_resulttarget_valuevaluedecode + 1 /\ (ge_balance_positive_cover_resulttarget_valuevalue) = 0) /\ (ge_balance_negative_cover_resulttarget_valuevalue) = S ge_signed_half_cover_resulttarget_valuevaluedecode))) /\ ((dst_positive_cover_resulttarget_value) + ge_balance_negative_cover_resulttarget_valuevalue = (dst_negative_cover_resulttarget_value) + ge_balance_positive_cover_resulttarget_valuevalue))))))))) -> ~(ssr_value_cover_result=0) -> exists ssr_source_cover_result. ((exists pvs_gap_cover_resultsource_bound. pvs_gap_cover_resultsource_bound + S (ssr_source_cover_result) = ((S (m))*(S (n)))) /\ (((((exists ff_h_pvs_cover_resultmap. ff_h_pvs_cover_resultmap + S (ssr_target_cover_result) = S ((S (ssr_source_cover_result)) * s)) /\ exists ff_q_pvs_cover_resultmap. r = ff_q_pvs_cover_resultmap * S ((S (ssr_source_cover_result)) * s) + (ssr_target_cover_result))) /\ (exists dst_positive_code_cover_resultsource_value dst_positive_scale_cover_resultsource_value dst_negative_code_cover_resultsource_value dst_negative_scale_cover_resultsource_value dst_positive_cover_resultsource_value dst_negative_cover_resultsource_value. (((T) = (((((dst_positive_code_cover_resultsource_value) + (dst_positive_scale_cover_resultsource_value)) * S ((dst_positive_code_cover_resultsource_value) + (dst_positive_scale_cover_resultsource_value)) + ((dst_positive_scale_cover_resultsource_value) + (dst_positive_scale_cover_resultsource_value))) + (((dst_negative_code_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)) * S ((dst_negative_code_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)) + ((dst_negative_scale_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)))) * S ((((dst_positive_code_cover_resultsource_value) + (dst_positive_scale_cover_resultsource_value)) * S ((dst_positive_code_cover_resultsource_value) + (dst_positive_scale_cover_resultsource_value)) + ((dst_positive_scale_cover_resultsource_value) + (dst_positive_scale_cover_resultsource_value))) + (((dst_negative_code_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)) * S ((dst_negative_code_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)) + ((dst_negative_scale_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)))) + ((((dst_negative_code_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)) * S ((dst_negative_code_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)) + ((dst_negative_scale_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value))) + (((dst_negative_code_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)) * S ((dst_negative_code_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)) + ((dst_negative_scale_cover_resultsource_value) + (dst_negative_scale_cover_resultsource_value)))))) /\ (((((exists ff_h_pvs_cover_resultsource_valuepositive. ff_h_pvs_cover_resultsource_valuepositive + S (dst_positive_cover_resultsource_value) = S ((S (ssr_source_cover_result)) * dst_positive_scale_cover_resultsource_value)) /\ exists ff_q_pvs_cover_resultsource_valuepositive. dst_positive_code_cover_resultsource_value = ff_q_pvs_cover_resultsource_valuepositive * S ((S (ssr_source_cover_result)) * dst_positive_scale_cover_resultsource_value) + (dst_positive_cover_resultsource_value))) /\ (((((exists ff_h_pvs_cover_resultsource_valuenegative. ff_h_pvs_cover_resultsource_valuenegative + S (dst_negative_cover_resultsource_value) = S ((S (ssr_source_cover_result)) * dst_negative_scale_cover_resultsource_value)) /\ exists ff_q_pvs_cover_resultsource_valuenegative. dst_negative_code_cover_resultsource_value = ff_q_pvs_cover_resultsource_valuenegative * S ((S (ssr_source_cover_result)) * dst_negative_scale_cover_resultsource_value) + (dst_negative_cover_resultsource_value))) /\ (exists ge_balance_positive_cover_resultsource_valuevalue ge_balance_negative_cover_resultsource_valuevalue. (((((ssr_value_cover_result) = 2 * (ge_balance_positive_cover_resultsource_valuevalue) /\ (ge_balance_negative_cover_resultsource_valuevalue) = 0) \/ exists ge_signed_half_cover_resultsource_valuevaluedecode. (((ssr_value_cover_result) = 2 * ge_signed_half_cover_resultsource_valuevaluedecode + 1 /\ (ge_balance_positive_cover_resultsource_valuevalue) = 0) /\ (ge_balance_negative_cover_resultsource_valuevalue) = S ge_signed_half_cover_resultsource_valuevaluedecode))) /\ ((dst_positive_cover_resultsource_value) + ge_balance_negative_cover_resultsource_valuevalue = (dst_negative_cover_resultsource_value) + ge_balance_positive_cover_resultsource_valuevalue)))))))))))))Constructive proof overview
Generated structural guide
Every nonzero target summand has a genuine bounded source slot: construct its unique positive divisor pair, both input summands and the product-table lookup, then prove exact value preservation.
The unchanged tactic script uses 12 declared prerequisites and contains 232 exact native proof lines.
Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
dirichlet_convolution_prefix_lookup Alpha theorem; checked-use authorized le_of_succ_le_succ Stable theorem; checked-use authorized MX004E dirichlet_convolution_entry_nonzero_support MX000F coprime_divisor_factor_pair_exists MX0010 coprime_divisor_factor_pair_bounds mul_comm Stable theorem; checked-use authorized matrix_integer_rectangular_index_bound Alpha theorem; checked-use authorized succ_le_succ Stable theorem; checked-use authorized signed_table_lookup_any Alpha theorem; checked-use authorized signed_mul_functional Alpha theorem; checked-use authorized MX004F dirichlet_multiplicative_pair_factorization MX0016 divisor_pair_index_map_lookupDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Named ingredients (5)
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–12
03Separate the logical casesL13–22
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L13
cases hd - L14
cases hd_right - L15
cases hd_right_right - L16
cases hd_right_right_right - L17
cases hd_right_right_right_right - L18
cases hd_right_right_right_right_right - L19
cases hd_right_right_right_right_right_right - L20
cases hd_right_right_right_right_right_right_right - L21
cases hd_right_right_right_right_right_right_right_right - L22
cases hd_right_right_right_right_right_right_right_right_right
04Separate the logical casesL23–25
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
05Fix variables and assumptionsL26–30
06Establish htL31–40
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet convolution prefix lookup.
- L31
have ht : DirichletEntry(F,G,m · n,j,z)Definitions: DirichletEntry - L32
specialize dirichlet_convolution_prefix_lookup (F) - L33
specialize dirichlet_convolution_prefix_lookup (G) - L34
specialize dirichlet_convolution_prefix_lookup (m*n) - L35
specialize dirichlet_convolution_prefix_lookup (m*n) - L36
specialize dirichlet_convolution_prefix_lookup (Q) - L37
specialize dirichlet_convolution_prefix_lookup (j) - L38
specialize dirichlet_convolution_prefix_lookup (z) - L39
apply dirichlet_convolution_prefix_lookup - L40
exact hd_right_right_right_right_right_right_right_right_right_left
07Use earlier factsL41–45
08Establish hsL46–54
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet convolution entry nonzero support.
- L46
have hs : ((~(j=0)) /\ (exists pvs_factor_cover_target_divisor. (m*n) = (j) * pvs_factor_cover_target_divisor)) - L47
specialize dirichlet_convolution_entry_nonzero_support (F) - L48
specialize dirichlet_convolution_entry_nonzero_support (G) - L49
specialize dirichlet_convolution_entry_nonzero_support (m*n) - L50
specialize dirichlet_convolution_entry_nonzero_support (j) - L51
specialize dirichlet_convolution_entry_nonzero_support (z) - L52
apply dirichlet_convolution_entry_nonzero_support - L53
exact ht - L54
exact hnz
09Separate the logical casesL55–55
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L55
cases hs
10Establish hpL56–63
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply coprime divisor factor pair exists.
- L56
have hp : exists d e. (((~((d)=0)) /\ (((~((e)=0)) /\ (((exists pvs_factor_cover_actual_pairleft. (m) = (d) * pvs_factor_cover_actual_pairleft) /\ (((exists pvs_factor_cover_actual_pairright. (n) = (e) * pvs_factor_cover_actual_pairright) /\ ((j)=(d)*(e)))))))))) - L57
specialize coprime_divisor_factor_pair_exists (m) - L58
specialize coprime_divisor_factor_pair_exists (n) - L59
specialize coprime_divisor_factor_pair_exists (j) - L60
apply coprime_divisor_factor_pair_exists - L61
exact hs_left - L62
exact hd_right_right_right_right_right_left - L63
exact hs_right
11Separate the logical casesL64–69
12Establish hbL70–79
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply coprime divisor factor pair bounds.
- L70
have hb : ((exists pvs_le_gap_cover_pair_boundsleft. pvs_le_gap_cover_pair_boundsleft + (x) = (m)) /\ (((exists pvs_le_gap_cover_pair_boundsright. pvs_le_gap_cover_pair_boundsright + (x1) = (n)) /\ (forall sfd_common_divisor_cover_pair_boundscoprime. (exists pvs_factor_cover_pair_boundscoprimeleft. (x) = (sfd_common_divisor_cover_pair_boundscoprime) * pvs_factor_cover_pair_boundscoprimeleft) -> (exists pvs_factor_cover_pair_boundscoprimeright. (x1) = (sfd_common_divisor_cover_pair_boundscoprime) * pvs_factor_cover_pair_boundscoprimeright) -> sfd_common_divisor_cover_pair_boundscoprime = 1)))) - L71
specialize coprime_divisor_factor_pair_bounds (m) - L72
specialize coprime_divisor_factor_pair_bounds (n) - L73
specialize coprime_divisor_factor_pair_bounds (j) - L74
specialize coprime_divisor_factor_pair_bounds (x) - L75
specialize coprime_divisor_factor_pair_bounds (x1) - L76
apply coprime_divisor_factor_pair_bounds - L77
exact hd_right_right_left - L78
exact hd_right_right_right_left - L79
exact hd_right_right_right_right_right_left
13Use earlier factsL80–80
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L80
exact hp_witness_witness
14Separate the logical casesL81–82
15Establish hiL83–83
Establish this local claim before using it. It is not an additional assumption.
- L83
have hi : exists pvs_gap_cover_source_bound. pvs_gap_cover_source_bound + S ((S (n))*(x)+(x1)) = ((S (m))*(S (n)))
16Establish hcommL84–93
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply mul comm.
- L84
have hcomm : (S n)*x=x*(S n) - L85
apply mul_comm - L86
rewrite hcomm - L87
specialize matrix_integer_rectangular_index_bound (S m) - L88
specialize matrix_integer_rectangular_index_bound (S n) - L89
specialize matrix_integer_rectangular_index_bound (x) - L90
specialize matrix_integer_rectangular_index_bound (x1) - L91
apply matrix_integer_rectangular_index_bound - L92
specialize succ_le_succ (x) - L93
specialize succ_le_succ (m)
17Use earlier factsL94–99
18Establish hlvL100–105
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed table lookup any.
19Separate the logical casesL106–106
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L106
cases hlv
20Establish hrvL107–112
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed table lookup any.
21Separate the logical casesL113–113
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L113
cases hrv
22Establish hwvL114–119
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed table lookup any.
- L114
have hwv : ∃ value. ArithAt(T,S n · x + x1,value)Definitions: ArithAt - L115
specialize signed_table_lookup_any ((S (m))*(S (n))) - L116
specialize signed_table_lookup_any (T) - L117
specialize signed_table_lookup_any ((S (n))*(x)+(x1)) - L118
apply signed_table_lookup_any - L119
exact hd_right_right_right_right_right_right_right_right_left_right_right_left
23Separate the logical casesL120–120
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L120
cases hwv
24Establish hlL121–130
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet convolution prefix lookup.
- L121
have hl : DirichletEntry(F,G,m,x,x2)Definitions: DirichletEntry - L122
specialize dirichlet_convolution_prefix_lookup (F) - L123
specialize dirichlet_convolution_prefix_lookup (G) - L124
specialize dirichlet_convolution_prefix_lookup (m) - L125
specialize dirichlet_convolution_prefix_lookup (m) - L126
specialize dirichlet_convolution_prefix_lookup (A) - L127
specialize dirichlet_convolution_prefix_lookup (x) - L128
specialize dirichlet_convolution_prefix_lookup (x2) - L129
apply dirichlet_convolution_prefix_lookup - L130
exact hd_right_right_right_right_right_right_left
25Use earlier factsL131–132
26Establish hrL133–142
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet convolution prefix lookup.
- L133
have hr : DirichletEntry(F,G,n,x1,x3)Definitions: DirichletEntry - L134
specialize dirichlet_convolution_prefix_lookup (F) - L135
specialize dirichlet_convolution_prefix_lookup (G) - L136
specialize dirichlet_convolution_prefix_lookup (n) - L137
specialize dirichlet_convolution_prefix_lookup (n) - L138
specialize dirichlet_convolution_prefix_lookup (B) - L139
specialize dirichlet_convolution_prefix_lookup (x1) - L140
specialize dirichlet_convolution_prefix_lookup (x3) - L141
apply dirichlet_convolution_prefix_lookup - L142
exact hd_right_right_right_right_right_right_right_left
27Use earlier factsL143–144
28Establish hproductL145–154
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply hd right right right right right right right right left right right right.
- L145
have hproduct : SignedMul(x2,x3,x4)Definitions: SignedMul - L146
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x) - L147
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x1) - L148
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x2) - L149
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x3) - L150
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x4) - L151
apply hd_right_right_right_right_right_right_right_right_left_right_right_right - L152
specialize succ_le_succ (x) - L153
specialize succ_le_succ (m) - L154
apply succ_le_succ
29Use earlier factsL155–162
30Establish hpairL163–163
Establish this local claim before using it. It is not an additional assumption.
- L163
have hpair : ((~((x)=0)) /\ (((~((x1)=0)) /\ (((exists pvs_factor_cover_pair_productleft. (m) = (x) * pvs_factor_cover_pair_productleft) /\ (((exists pvs_factor_cover_pair_productright. (n) = (x1) * pvs_factor_cover_pair_productright) /\ ((x*x1)=(x)*(x1)))))))))
31Separate the logical casesL164–164
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L164
split
32Use earlier factsL165–165
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L165
exact hp_witness_witness_left
33Separate the logical casesL166–166
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L166
split
34Use earlier factsL167–167
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L167
exact hp_witness_witness_right_left
35Separate the logical casesL168–168
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L168
split
36Use earlier factsL169–169
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L169
exact hp_witness_witness_right_right_left
37Separate the logical casesL170–170
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L170
split
38Use earlier factsL171–171
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L171
exact hp_witness_witness_right_right_right_left
39Calculate and transport equalitiesL172–180
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L172
refl - L173
rewrite hp_witness_witness_right_right_right_right at ht - L174
rewrite hp_witness_witness_right_right_right_right at ht - L175
rewrite hp_witness_witness_right_right_right_right at ht - L176
rewrite hp_witness_witness_right_right_right_right at ht - L177
rewrite hp_witness_witness_right_right_right_right at ht - L178
rewrite hp_witness_witness_right_right_right_right at ht - L179
rewrite hp_witness_witness_right_right_right_right at ht - L180
rewrite hp_witness_witness_right_right_right_right at ht
40Establish heqL181–190
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed mul functional.
- L181
have heq : x4=z - L182
specialize signed_mul_functional (x2) - L183
specialize signed_mul_functional (x3) - L184
specialize signed_mul_functional (x4) - L185
specialize signed_mul_functional (z) - L186
apply signed_mul_functional - L187
exact hproduct - L188
specialize dirichlet_multiplicative_pair_factorization (N) - L189
specialize dirichlet_multiplicative_pair_factorization (F) - L190
specialize dirichlet_multiplicative_pair_factorization (G)
41Use earlier factsL191–200
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L191
specialize dirichlet_multiplicative_pair_factorization (m) - L192
specialize dirichlet_multiplicative_pair_factorization (n) - L193
specialize dirichlet_multiplicative_pair_factorization (x) - L194
specialize dirichlet_multiplicative_pair_factorization (x1) - L195
specialize dirichlet_multiplicative_pair_factorization (x2) - L196
specialize dirichlet_multiplicative_pair_factorization (x3) - L197
specialize dirichlet_multiplicative_pair_factorization (z) - L198
apply dirichlet_multiplicative_pair_factorization - L199
exact hd_left - L200
exact hd_right_left
42Use earlier factsL201–208
43Calculate and transport equalitiesL209–210
44Construct an explicit witnessL211–211
Supply the displayed value, then prove that it has the required property.
- L211
exists (S n)*x+x1
45Separate the logical casesL212–212
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L212
split
46Use earlier factsL213–213
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L213
exact hi
47Separate the logical casesL214–214
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L214
split
48Calculate and transport equalitiesL215–216
49Use earlier factsL217–226
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L217
specialize divisor_pair_index_map_lookup (S n) - L218
specialize divisor_pair_index_map_lookup ((S (m))*(S (n))) - L219
specialize divisor_pair_index_map_lookup (r) - L220
specialize divisor_pair_index_map_lookup (s) - L221
specialize divisor_pair_index_map_lookup ((S (n))*(x)+(x1)) - L222
specialize divisor_pair_index_map_lookup (x) - L223
specialize divisor_pair_index_map_lookup (x1) - L224
apply divisor_pair_index_map_lookup - L225
exact hd_right_right_right_right_right_right_right_right_right_right - L226
exact hi
50Use earlier factsL227–230
51Calculate and transport equalitiesL231–231
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L231
refl
52Use earlier factsL232–232
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L232
exact hwv_witness
Original exact command ledger · 232 lines
- 0001
intro N - 0002
intro F - 0003
intro G - 0004
intro m - 0005
intro n - 0006
intro A - 0007
intro B - 0008
intro T - 0009
intro Q - 0010
intro r - 0011
intro s - 0012
intro hd - 0013
cases hd - 0014
cases hd_right - 0015
cases hd_right_right - 0016
cases hd_right_right_right - 0017
cases hd_right_right_right_right - 0018
cases hd_right_right_right_right_right - 0019
cases hd_right_right_right_right_right_right - 0020
cases hd_right_right_right_right_right_right_right - 0021
cases hd_right_right_right_right_right_right_right_right - 0022
cases hd_right_right_right_right_right_right_right_right_right - 0023
cases hd_right_right_right_right_right_right_right_right_left - 0024
cases hd_right_right_right_right_right_right_right_right_left_right - 0025
cases hd_right_right_right_right_right_right_right_right_left_right_right - 0026
intro j - 0027
intro z - 0028
intro hj - 0029
intro hz - 0030
intro hnz - 0031
have ht : (((~((j)=0)) /\ (exists dc_quotient_cover_target_entry dc_left_cover_target_entry dc_right_cover_target_entry. (((m*n)=(j)*dc_quotient_cover_target_entry) /\ (((exists dst_positive_code_cover_target_entryleft dst_positive_scale_cover_target_entryleft dst_negative_code_cover_target_entryleft dst_negative_scale_cover_target_entryleft dst_positive_cover_target_entryleft dst_negative_cover_target_entryleft. (((F) = (((((dst_positive_code_cover_target_entryleft) + (dst_positive_scale_cover_target_entryleft)) * S ((dst_positive_code_cover_target_entryleft) + (dst_positive_scale_cover_target_entryleft)) + ((dst_positive_scale_cover_target_entryleft) + (dst_positive_scale_cover_target_entryleft))) + (((dst_negative_code_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)) * S ((dst_negative_code_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)) + ((dst_negative_scale_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)))) * S ((((dst_positive_code_cover_target_entryleft) + (dst_positive_scale_cover_target_entryleft)) * S ((dst_positive_code_cover_target_entryleft) + (dst_positive_scale_cover_target_entryleft)) + ((dst_positive_scale_cover_target_entryleft) + (dst_positive_scale_cover_target_entryleft))) + (((dst_negative_code_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)) * S ((dst_negative_code_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)) + ((dst_negative_scale_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)))) + ((((dst_negative_code_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)) * S ((dst_negative_code_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)) + ((dst_negative_scale_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft))) + (((dst_negative_code_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)) * S ((dst_negative_code_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)) + ((dst_negative_scale_cover_target_entryleft) + (dst_negative_scale_cover_target_entryleft)))))) /\ (((((exists ff_h_pvs_cover_target_entryleftpositive. ff_h_pvs_cover_target_entryleftpositive + S (dst_positive_cover_target_entryleft) = S ((S (j)) * dst_positive_scale_cover_target_entryleft)) /\ exists ff_q_pvs_cover_target_entryleftpositive. dst_positive_code_cover_target_entryleft = ff_q_pvs_cover_target_entryleftpositive * S ((S (j)) * dst_positive_scale_cover_target_entryleft) + (dst_positive_cover_target_entryleft))) /\ (((((exists ff_h_pvs_cover_target_entryleftnegative. ff_h_pvs_cover_target_entryleftnegative + S (dst_negative_cover_target_entryleft) = S ((S (j)) * dst_negative_scale_cover_target_entryleft)) /\ exists ff_q_pvs_cover_target_entryleftnegative. dst_negative_code_cover_target_entryleft = ff_q_pvs_cover_target_entryleftnegative * S ((S (j)) * dst_negative_scale_cover_target_entryleft) + (dst_negative_cover_target_entryleft))) /\ (exists ge_balance_positive_cover_target_entryleftvalue ge_balance_negative_cover_target_entryleftvalue. (((((dc_left_cover_target_entry) = 2 * (ge_balance_positive_cover_target_entryleftvalue) /\ (ge_balance_negative_cover_target_entryleftvalue) = 0) \/ exists ge_signed_half_cover_target_entryleftvaluedecode. (((dc_left_cover_target_entry) = 2 * ge_signed_half_cover_target_entryleftvaluedecode + 1 /\ (ge_balance_positive_cover_target_entryleftvalue) = 0) /\ (ge_balance_negative_cover_target_entryleftvalue) = S ge_signed_half_cover_target_entryleftvaluedecode))) /\ ((dst_positive_cover_target_entryleft) + ge_balance_negative_cover_target_entryleftvalue = (dst_negative_cover_target_entryleft) + ge_balance_positive_cover_target_entryleftvalue))))))))) /\ (((exists dst_positive_code_cover_target_entryright dst_positive_scale_cover_target_entryright dst_negative_code_cover_target_entryright dst_negative_scale_cover_target_entryright dst_positive_cover_target_entryright dst_negative_cover_target_entryright. (((G) = (((((dst_positive_code_cover_target_entryright) + (dst_positive_scale_cover_target_entryright)) * S ((dst_positive_code_cover_target_entryright) + (dst_positive_scale_cover_target_entryright)) + ((dst_positive_scale_cover_target_entryright) + (dst_positive_scale_cover_target_entryright))) + (((dst_negative_code_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)) * S ((dst_negative_code_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)) + ((dst_negative_scale_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)))) * S ((((dst_positive_code_cover_target_entryright) + (dst_positive_scale_cover_target_entryright)) * S ((dst_positive_code_cover_target_entryright) + (dst_positive_scale_cover_target_entryright)) + ((dst_positive_scale_cover_target_entryright) + (dst_positive_scale_cover_target_entryright))) + (((dst_negative_code_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)) * S ((dst_negative_code_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)) + ((dst_negative_scale_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)))) + ((((dst_negative_code_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)) * S ((dst_negative_code_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)) + ((dst_negative_scale_cover_target_entryright) + (dst_negative_scale_cover_target_entryright))) + (((dst_negative_code_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)) * S ((dst_negative_code_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)) + ((dst_negative_scale_cover_target_entryright) + (dst_negative_scale_cover_target_entryright)))))) /\ (((((exists ff_h_pvs_cover_target_entryrightpositive. ff_h_pvs_cover_target_entryrightpositive + S (dst_positive_cover_target_entryright) = S ((S (dc_quotient_cover_target_entry)) * dst_positive_scale_cover_target_entryright)) /\ exists ff_q_pvs_cover_target_entryrightpositive. dst_positive_code_cover_target_entryright = ff_q_pvs_cover_target_entryrightpositive * S ((S (dc_quotient_cover_target_entry)) * dst_positive_scale_cover_target_entryright) + (dst_positive_cover_target_entryright))) /\ (((((exists ff_h_pvs_cover_target_entryrightnegative. ff_h_pvs_cover_target_entryrightnegative + S (dst_negative_cover_target_entryright) = S ((S (dc_quotient_cover_target_entry)) * dst_negative_scale_cover_target_entryright)) /\ exists ff_q_pvs_cover_target_entryrightnegative. dst_negative_code_cover_target_entryright = ff_q_pvs_cover_target_entryrightnegative * S ((S (dc_quotient_cover_target_entry)) * dst_negative_scale_cover_target_entryright) + (dst_negative_cover_target_entryright))) /\ (exists ge_balance_positive_cover_target_entryrightvalue ge_balance_negative_cover_target_entryrightvalue. (((((dc_right_cover_target_entry) = 2 * (ge_balance_positive_cover_target_entryrightvalue) /\ (ge_balance_negative_cover_target_entryrightvalue) = 0) \/ exists ge_signed_half_cover_target_entryrightvaluedecode. (((dc_right_cover_target_entry) = 2 * ge_signed_half_cover_target_entryrightvaluedecode + 1 /\ (ge_balance_positive_cover_target_entryrightvalue) = 0) /\ (ge_balance_negative_cover_target_entryrightvalue) = S ge_signed_half_cover_target_entryrightvaluedecode))) /\ ((dst_positive_cover_target_entryright) + ge_balance_negative_cover_target_entryrightvalue = (dst_negative_cover_target_entryright) + ge_balance_positive_cover_target_entryrightvalue))))))))) /\ (exists sto_ap_cover_target_entryproduct sto_an_cover_target_entryproduct sto_bp_cover_target_entryproduct sto_bn_cover_target_entryproduct sto_cp_cover_target_entryproduct sto_cn_cover_target_entryproduct. (((((dc_left_cover_target_entry) = 2 * (sto_ap_cover_target_entryproduct) /\ (sto_an_cover_target_entryproduct) = 0) \/ exists ge_signed_half_cover_target_entryproductleft. (((dc_left_cover_target_entry) = 2 * ge_signed_half_cover_target_entryproductleft + 1 /\ (sto_ap_cover_target_entryproduct) = 0) /\ (sto_an_cover_target_entryproduct) = S ge_signed_half_cover_target_entryproductleft))) /\ ((((((dc_right_cover_target_entry) = 2 * (sto_bp_cover_target_entryproduct) /\ (sto_bn_cover_target_entryproduct) = 0) \/ exists ge_signed_half_cover_target_entryproductright. (((dc_right_cover_target_entry) = 2 * ge_signed_half_cover_target_entryproductright + 1 /\ (sto_bp_cover_target_entryproduct) = 0) /\ (sto_bn_cover_target_entryproduct) = S ge_signed_half_cover_target_entryproductright))) /\ ((((((z) = 2 * (sto_cp_cover_target_entryproduct) /\ (sto_cn_cover_target_entryproduct) = 0) \/ exists ge_signed_half_cover_target_entryproductoutput. (((z) = 2 * ge_signed_half_cover_target_entryproductoutput + 1 /\ (sto_cp_cover_target_entryproduct) = 0) /\ (sto_cn_cover_target_entryproduct) = S ge_signed_half_cover_target_entryproductoutput))) /\ ((sto_ap_cover_target_entryproduct * sto_bp_cover_target_entryproduct + sto_an_cover_target_entryproduct * sto_bn_cover_target_entryproduct) + sto_cn_cover_target_entryproduct = (sto_ap_cover_target_entryproduct * sto_bn_cover_target_entryproduct + sto_an_cover_target_entryproduct * sto_bp_cover_target_entryproduct) + sto_cp_cover_target_entryproduct))))))))))))))) \/ ((((j)=0 \/ ~(exists pvs_factor_cover_target_entrynondivisor. (m*n) = (j) * pvs_factor_cover_target_entrynondivisor)) /\ ((z)=0))) - 0032
specialize dirichlet_convolution_prefix_lookup (F) - 0033
specialize dirichlet_convolution_prefix_lookup (G) - 0034
specialize dirichlet_convolution_prefix_lookup (m*n) - 0035
specialize dirichlet_convolution_prefix_lookup (m*n) - 0036
specialize dirichlet_convolution_prefix_lookup (Q) - 0037
specialize dirichlet_convolution_prefix_lookup (j) - 0038
specialize dirichlet_convolution_prefix_lookup (z) - 0039
apply dirichlet_convolution_prefix_lookup - 0040
exact hd_right_right_right_right_right_right_right_right_right_left - 0041
specialize le_of_succ_le_succ (j) - 0042
specialize le_of_succ_le_succ (m*n) - 0043
apply le_of_succ_le_succ - 0044
exact hj - 0045
exact hz - 0046
have hs : ((~(j=0)) /\ (exists pvs_factor_cover_target_divisor. (m*n) = (j) * pvs_factor_cover_target_divisor)) - 0047
specialize dirichlet_convolution_entry_nonzero_support (F) - 0048
specialize dirichlet_convolution_entry_nonzero_support (G) - 0049
specialize dirichlet_convolution_entry_nonzero_support (m*n) - 0050
specialize dirichlet_convolution_entry_nonzero_support (j) - 0051
specialize dirichlet_convolution_entry_nonzero_support (z) - 0052
apply dirichlet_convolution_entry_nonzero_support - 0053
exact ht - 0054
exact hnz - 0055
cases hs - 0056
have hp : exists d e. (((~((d)=0)) /\ (((~((e)=0)) /\ (((exists pvs_factor_cover_actual_pairleft. (m) = (d) * pvs_factor_cover_actual_pairleft) /\ (((exists pvs_factor_cover_actual_pairright. (n) = (e) * pvs_factor_cover_actual_pairright) /\ ((j)=(d)*(e)))))))))) - 0057
specialize coprime_divisor_factor_pair_exists (m) - 0058
specialize coprime_divisor_factor_pair_exists (n) - 0059
specialize coprime_divisor_factor_pair_exists (j) - 0060
apply coprime_divisor_factor_pair_exists - 0061
exact hs_left - 0062
exact hd_right_right_right_right_right_left - 0063
exact hs_right - 0064
cases hp - 0065
cases hp_witness - 0066
cases hp_witness_witness - 0067
cases hp_witness_witness_right - 0068
cases hp_witness_witness_right_right - 0069
cases hp_witness_witness_right_right_right - 0070
have hb : ((exists pvs_le_gap_cover_pair_boundsleft. pvs_le_gap_cover_pair_boundsleft + (x) = (m)) /\ (((exists pvs_le_gap_cover_pair_boundsright. pvs_le_gap_cover_pair_boundsright + (x1) = (n)) /\ (forall sfd_common_divisor_cover_pair_boundscoprime. (exists pvs_factor_cover_pair_boundscoprimeleft. (x) = (sfd_common_divisor_cover_pair_boundscoprime) * pvs_factor_cover_pair_boundscoprimeleft) -> (exists pvs_factor_cover_pair_boundscoprimeright. (x1) = (sfd_common_divisor_cover_pair_boundscoprime) * pvs_factor_cover_pair_boundscoprimeright) -> sfd_common_divisor_cover_pair_boundscoprime = 1)))) - 0071
specialize coprime_divisor_factor_pair_bounds (m) - 0072
specialize coprime_divisor_factor_pair_bounds (n) - 0073
specialize coprime_divisor_factor_pair_bounds (j) - 0074
specialize coprime_divisor_factor_pair_bounds (x) - 0075
specialize coprime_divisor_factor_pair_bounds (x1) - 0076
apply coprime_divisor_factor_pair_bounds - 0077
exact hd_right_right_left - 0078
exact hd_right_right_right_left - 0079
exact hd_right_right_right_right_right_left - 0080
exact hp_witness_witness - 0081
cases hb - 0082
cases hb_right - 0083
have hi : exists pvs_gap_cover_source_bound. pvs_gap_cover_source_bound + S ((S (n))*(x)+(x1)) = ((S (m))*(S (n))) - 0084
have hcomm : (S n)*x=x*(S n) - 0085
apply mul_comm - 0086
rewrite hcomm - 0087
specialize matrix_integer_rectangular_index_bound (S m) - 0088
specialize matrix_integer_rectangular_index_bound (S n) - 0089
specialize matrix_integer_rectangular_index_bound (x) - 0090
specialize matrix_integer_rectangular_index_bound (x1) - 0091
apply matrix_integer_rectangular_index_bound - 0092
specialize succ_le_succ (x) - 0093
specialize succ_le_succ (m) - 0094
apply succ_le_succ - 0095
exact hb_left - 0096
specialize succ_le_succ (x1) - 0097
specialize succ_le_succ (n) - 0098
apply succ_le_succ - 0099
exact hb_right_left - 0100
have hlv : exists value. (exists dst_positive_code_hlvactual dst_positive_scale_hlvactual dst_negative_code_hlvactual dst_negative_scale_hlvactual dst_positive_hlvactual dst_negative_hlvactual. (((A) = (((((dst_positive_code_hlvactual) + (dst_positive_scale_hlvactual)) * S ((dst_positive_code_hlvactual) + (dst_positive_scale_hlvactual)) + ((dst_positive_scale_hlvactual) + (dst_positive_scale_hlvactual))) + (((dst_negative_code_hlvactual) + (dst_negative_scale_hlvactual)) * S ((dst_negative_code_hlvactual) + (dst_negative_scale_hlvactual)) + ((dst_negative_scale_hlvactual) + (dst_negative_scale_hlvactual)))) * S ((((dst_positive_code_hlvactual) + (dst_positive_scale_hlvactual)) * S ((dst_positive_code_hlvactual) + (dst_positive_scale_hlvactual)) + ((dst_positive_scale_hlvactual) + (dst_positive_scale_hlvactual))) + (((dst_negative_code_hlvactual) + (dst_negative_scale_hlvactual)) * S ((dst_negative_code_hlvactual) + (dst_negative_scale_hlvactual)) + ((dst_negative_scale_hlvactual) + (dst_negative_scale_hlvactual)))) + ((((dst_negative_code_hlvactual) + (dst_negative_scale_hlvactual)) * S ((dst_negative_code_hlvactual) + (dst_negative_scale_hlvactual)) + ((dst_negative_scale_hlvactual) + (dst_negative_scale_hlvactual))) + (((dst_negative_code_hlvactual) + (dst_negative_scale_hlvactual)) * S ((dst_negative_code_hlvactual) + (dst_negative_scale_hlvactual)) + ((dst_negative_scale_hlvactual) + (dst_negative_scale_hlvactual)))))) /\ (((((exists ff_h_pvs_hlvactualpositive. ff_h_pvs_hlvactualpositive + S (dst_positive_hlvactual) = S ((S (x)) * dst_positive_scale_hlvactual)) /\ exists ff_q_pvs_hlvactualpositive. dst_positive_code_hlvactual = ff_q_pvs_hlvactualpositive * S ((S (x)) * dst_positive_scale_hlvactual) + (dst_positive_hlvactual))) /\ (((((exists ff_h_pvs_hlvactualnegative. ff_h_pvs_hlvactualnegative + S (dst_negative_hlvactual) = S ((S (x)) * dst_negative_scale_hlvactual)) /\ exists ff_q_pvs_hlvactualnegative. dst_negative_code_hlvactual = ff_q_pvs_hlvactualnegative * S ((S (x)) * dst_negative_scale_hlvactual) + (dst_negative_hlvactual))) /\ (exists ge_balance_positive_hlvactualvalue ge_balance_negative_hlvactualvalue. (((((value) = 2 * (ge_balance_positive_hlvactualvalue) /\ (ge_balance_negative_hlvactualvalue) = 0) \/ exists ge_signed_half_hlvactualvaluedecode. (((value) = 2 * ge_signed_half_hlvactualvaluedecode + 1 /\ (ge_balance_positive_hlvactualvalue) = 0) /\ (ge_balance_negative_hlvactualvalue) = S ge_signed_half_hlvactualvaluedecode))) /\ ((dst_positive_hlvactual) + ge_balance_negative_hlvactualvalue = (dst_negative_hlvactual) + ge_balance_positive_hlvactualvalue))))))))) - 0101
specialize signed_table_lookup_any (0) - 0102
specialize signed_table_lookup_any (A) - 0103
specialize signed_table_lookup_any (x) - 0104
apply signed_table_lookup_any - 0105
exact hd_right_right_right_right_right_right_right_right_left_left - 0106
cases hlv - 0107
have hrv : exists value. (exists dst_positive_code_hrvactual dst_positive_scale_hrvactual dst_negative_code_hrvactual dst_negative_scale_hrvactual dst_positive_hrvactual dst_negative_hrvactual. (((B) = (((((dst_positive_code_hrvactual) + (dst_positive_scale_hrvactual)) * S ((dst_positive_code_hrvactual) + (dst_positive_scale_hrvactual)) + ((dst_positive_scale_hrvactual) + (dst_positive_scale_hrvactual))) + (((dst_negative_code_hrvactual) + (dst_negative_scale_hrvactual)) * S ((dst_negative_code_hrvactual) + (dst_negative_scale_hrvactual)) + ((dst_negative_scale_hrvactual) + (dst_negative_scale_hrvactual)))) * S ((((dst_positive_code_hrvactual) + (dst_positive_scale_hrvactual)) * S ((dst_positive_code_hrvactual) + (dst_positive_scale_hrvactual)) + ((dst_positive_scale_hrvactual) + (dst_positive_scale_hrvactual))) + (((dst_negative_code_hrvactual) + (dst_negative_scale_hrvactual)) * S ((dst_negative_code_hrvactual) + (dst_negative_scale_hrvactual)) + ((dst_negative_scale_hrvactual) + (dst_negative_scale_hrvactual)))) + ((((dst_negative_code_hrvactual) + (dst_negative_scale_hrvactual)) * S ((dst_negative_code_hrvactual) + (dst_negative_scale_hrvactual)) + ((dst_negative_scale_hrvactual) + (dst_negative_scale_hrvactual))) + (((dst_negative_code_hrvactual) + (dst_negative_scale_hrvactual)) * S ((dst_negative_code_hrvactual) + (dst_negative_scale_hrvactual)) + ((dst_negative_scale_hrvactual) + (dst_negative_scale_hrvactual)))))) /\ (((((exists ff_h_pvs_hrvactualpositive. ff_h_pvs_hrvactualpositive + S (dst_positive_hrvactual) = S ((S (x1)) * dst_positive_scale_hrvactual)) /\ exists ff_q_pvs_hrvactualpositive. dst_positive_code_hrvactual = ff_q_pvs_hrvactualpositive * S ((S (x1)) * dst_positive_scale_hrvactual) + (dst_positive_hrvactual))) /\ (((((exists ff_h_pvs_hrvactualnegative. ff_h_pvs_hrvactualnegative + S (dst_negative_hrvactual) = S ((S (x1)) * dst_negative_scale_hrvactual)) /\ exists ff_q_pvs_hrvactualnegative. dst_negative_code_hrvactual = ff_q_pvs_hrvactualnegative * S ((S (x1)) * dst_negative_scale_hrvactual) + (dst_negative_hrvactual))) /\ (exists ge_balance_positive_hrvactualvalue ge_balance_negative_hrvactualvalue. (((((value) = 2 * (ge_balance_positive_hrvactualvalue) /\ (ge_balance_negative_hrvactualvalue) = 0) \/ exists ge_signed_half_hrvactualvaluedecode. (((value) = 2 * ge_signed_half_hrvactualvaluedecode + 1 /\ (ge_balance_positive_hrvactualvalue) = 0) /\ (ge_balance_negative_hrvactualvalue) = S ge_signed_half_hrvactualvaluedecode))) /\ ((dst_positive_hrvactual) + ge_balance_negative_hrvactualvalue = (dst_negative_hrvactual) + ge_balance_positive_hrvactualvalue))))))))) - 0108
specialize signed_table_lookup_any (0) - 0109
specialize signed_table_lookup_any (B) - 0110
specialize signed_table_lookup_any (x1) - 0111
apply signed_table_lookup_any - 0112
exact hd_right_right_right_right_right_right_right_right_left_right_left - 0113
cases hrv - 0114
have hwv : exists value. (exists dst_positive_code_hwvactual dst_positive_scale_hwvactual dst_negative_code_hwvactual dst_negative_scale_hwvactual dst_positive_hwvactual dst_negative_hwvactual. (((T) = (((((dst_positive_code_hwvactual) + (dst_positive_scale_hwvactual)) * S ((dst_positive_code_hwvactual) + (dst_positive_scale_hwvactual)) + ((dst_positive_scale_hwvactual) + (dst_positive_scale_hwvactual))) + (((dst_negative_code_hwvactual) + (dst_negative_scale_hwvactual)) * S ((dst_negative_code_hwvactual) + (dst_negative_scale_hwvactual)) + ((dst_negative_scale_hwvactual) + (dst_negative_scale_hwvactual)))) * S ((((dst_positive_code_hwvactual) + (dst_positive_scale_hwvactual)) * S ((dst_positive_code_hwvactual) + (dst_positive_scale_hwvactual)) + ((dst_positive_scale_hwvactual) + (dst_positive_scale_hwvactual))) + (((dst_negative_code_hwvactual) + (dst_negative_scale_hwvactual)) * S ((dst_negative_code_hwvactual) + (dst_negative_scale_hwvactual)) + ((dst_negative_scale_hwvactual) + (dst_negative_scale_hwvactual)))) + ((((dst_negative_code_hwvactual) + (dst_negative_scale_hwvactual)) * S ((dst_negative_code_hwvactual) + (dst_negative_scale_hwvactual)) + ((dst_negative_scale_hwvactual) + (dst_negative_scale_hwvactual))) + (((dst_negative_code_hwvactual) + (dst_negative_scale_hwvactual)) * S ((dst_negative_code_hwvactual) + (dst_negative_scale_hwvactual)) + ((dst_negative_scale_hwvactual) + (dst_negative_scale_hwvactual)))))) /\ (((((exists ff_h_pvs_hwvactualpositive. ff_h_pvs_hwvactualpositive + S (dst_positive_hwvactual) = S ((S ((S (n))*(x)+(x1))) * dst_positive_scale_hwvactual)) /\ exists ff_q_pvs_hwvactualpositive. dst_positive_code_hwvactual = ff_q_pvs_hwvactualpositive * S ((S ((S (n))*(x)+(x1))) * dst_positive_scale_hwvactual) + (dst_positive_hwvactual))) /\ (((((exists ff_h_pvs_hwvactualnegative. ff_h_pvs_hwvactualnegative + S (dst_negative_hwvactual) = S ((S ((S (n))*(x)+(x1))) * dst_negative_scale_hwvactual)) /\ exists ff_q_pvs_hwvactualnegative. dst_negative_code_hwvactual = ff_q_pvs_hwvactualnegative * S ((S ((S (n))*(x)+(x1))) * dst_negative_scale_hwvactual) + (dst_negative_hwvactual))) /\ (exists ge_balance_positive_hwvactualvalue ge_balance_negative_hwvactualvalue. (((((value) = 2 * (ge_balance_positive_hwvactualvalue) /\ (ge_balance_negative_hwvactualvalue) = 0) \/ exists ge_signed_half_hwvactualvaluedecode. (((value) = 2 * ge_signed_half_hwvactualvaluedecode + 1 /\ (ge_balance_positive_hwvactualvalue) = 0) /\ (ge_balance_negative_hwvactualvalue) = S ge_signed_half_hwvactualvaluedecode))) /\ ((dst_positive_hwvactual) + ge_balance_negative_hwvactualvalue = (dst_negative_hwvactual) + ge_balance_positive_hwvactualvalue))))))))) - 0115
specialize signed_table_lookup_any ((S (m))*(S (n))) - 0116
specialize signed_table_lookup_any (T) - 0117
specialize signed_table_lookup_any ((S (n))*(x)+(x1)) - 0118
apply signed_table_lookup_any - 0119
exact hd_right_right_right_right_right_right_right_right_left_right_right_left - 0120
cases hwv - 0121
have hl : (((~((x)=0)) /\ (exists dc_quotient_hlcover_entry dc_left_hlcover_entry dc_right_hlcover_entry. (((m)=(x)*dc_quotient_hlcover_entry) /\ (((exists dst_positive_code_hlcover_entryleft dst_positive_scale_hlcover_entryleft dst_negative_code_hlcover_entryleft dst_negative_scale_hlcover_entryleft dst_positive_hlcover_entryleft dst_negative_hlcover_entryleft. (((F) = (((((dst_positive_code_hlcover_entryleft) + (dst_positive_scale_hlcover_entryleft)) * S ((dst_positive_code_hlcover_entryleft) + (dst_positive_scale_hlcover_entryleft)) + ((dst_positive_scale_hlcover_entryleft) + (dst_positive_scale_hlcover_entryleft))) + (((dst_negative_code_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)) * S ((dst_negative_code_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)) + ((dst_negative_scale_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)))) * S ((((dst_positive_code_hlcover_entryleft) + (dst_positive_scale_hlcover_entryleft)) * S ((dst_positive_code_hlcover_entryleft) + (dst_positive_scale_hlcover_entryleft)) + ((dst_positive_scale_hlcover_entryleft) + (dst_positive_scale_hlcover_entryleft))) + (((dst_negative_code_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)) * S ((dst_negative_code_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)) + ((dst_negative_scale_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)))) + ((((dst_negative_code_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)) * S ((dst_negative_code_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)) + ((dst_negative_scale_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft))) + (((dst_negative_code_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)) * S ((dst_negative_code_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)) + ((dst_negative_scale_hlcover_entryleft) + (dst_negative_scale_hlcover_entryleft)))))) /\ (((((exists ff_h_pvs_hlcover_entryleftpositive. ff_h_pvs_hlcover_entryleftpositive + S (dst_positive_hlcover_entryleft) = S ((S (x)) * dst_positive_scale_hlcover_entryleft)) /\ exists ff_q_pvs_hlcover_entryleftpositive. dst_positive_code_hlcover_entryleft = ff_q_pvs_hlcover_entryleftpositive * S ((S (x)) * dst_positive_scale_hlcover_entryleft) + (dst_positive_hlcover_entryleft))) /\ (((((exists ff_h_pvs_hlcover_entryleftnegative. ff_h_pvs_hlcover_entryleftnegative + S (dst_negative_hlcover_entryleft) = S ((S (x)) * dst_negative_scale_hlcover_entryleft)) /\ exists ff_q_pvs_hlcover_entryleftnegative. dst_negative_code_hlcover_entryleft = ff_q_pvs_hlcover_entryleftnegative * S ((S (x)) * dst_negative_scale_hlcover_entryleft) + (dst_negative_hlcover_entryleft))) /\ (exists ge_balance_positive_hlcover_entryleftvalue ge_balance_negative_hlcover_entryleftvalue. (((((dc_left_hlcover_entry) = 2 * (ge_balance_positive_hlcover_entryleftvalue) /\ (ge_balance_negative_hlcover_entryleftvalue) = 0) \/ exists ge_signed_half_hlcover_entryleftvaluedecode. (((dc_left_hlcover_entry) = 2 * ge_signed_half_hlcover_entryleftvaluedecode + 1 /\ (ge_balance_positive_hlcover_entryleftvalue) = 0) /\ (ge_balance_negative_hlcover_entryleftvalue) = S ge_signed_half_hlcover_entryleftvaluedecode))) /\ ((dst_positive_hlcover_entryleft) + ge_balance_negative_hlcover_entryleftvalue = (dst_negative_hlcover_entryleft) + ge_balance_positive_hlcover_entryleftvalue))))))))) /\ (((exists dst_positive_code_hlcover_entryright dst_positive_scale_hlcover_entryright dst_negative_code_hlcover_entryright dst_negative_scale_hlcover_entryright dst_positive_hlcover_entryright dst_negative_hlcover_entryright. (((G) = (((((dst_positive_code_hlcover_entryright) + (dst_positive_scale_hlcover_entryright)) * S ((dst_positive_code_hlcover_entryright) + (dst_positive_scale_hlcover_entryright)) + ((dst_positive_scale_hlcover_entryright) + (dst_positive_scale_hlcover_entryright))) + (((dst_negative_code_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)) * S ((dst_negative_code_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)) + ((dst_negative_scale_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)))) * S ((((dst_positive_code_hlcover_entryright) + (dst_positive_scale_hlcover_entryright)) * S ((dst_positive_code_hlcover_entryright) + (dst_positive_scale_hlcover_entryright)) + ((dst_positive_scale_hlcover_entryright) + (dst_positive_scale_hlcover_entryright))) + (((dst_negative_code_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)) * S ((dst_negative_code_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)) + ((dst_negative_scale_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)))) + ((((dst_negative_code_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)) * S ((dst_negative_code_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)) + ((dst_negative_scale_hlcover_entryright) + (dst_negative_scale_hlcover_entryright))) + (((dst_negative_code_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)) * S ((dst_negative_code_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)) + ((dst_negative_scale_hlcover_entryright) + (dst_negative_scale_hlcover_entryright)))))) /\ (((((exists ff_h_pvs_hlcover_entryrightpositive. ff_h_pvs_hlcover_entryrightpositive + S (dst_positive_hlcover_entryright) = S ((S (dc_quotient_hlcover_entry)) * dst_positive_scale_hlcover_entryright)) /\ exists ff_q_pvs_hlcover_entryrightpositive. dst_positive_code_hlcover_entryright = ff_q_pvs_hlcover_entryrightpositive * S ((S (dc_quotient_hlcover_entry)) * dst_positive_scale_hlcover_entryright) + (dst_positive_hlcover_entryright))) /\ (((((exists ff_h_pvs_hlcover_entryrightnegative. ff_h_pvs_hlcover_entryrightnegative + S (dst_negative_hlcover_entryright) = S ((S (dc_quotient_hlcover_entry)) * dst_negative_scale_hlcover_entryright)) /\ exists ff_q_pvs_hlcover_entryrightnegative. dst_negative_code_hlcover_entryright = ff_q_pvs_hlcover_entryrightnegative * S ((S (dc_quotient_hlcover_entry)) * dst_negative_scale_hlcover_entryright) + (dst_negative_hlcover_entryright))) /\ (exists ge_balance_positive_hlcover_entryrightvalue ge_balance_negative_hlcover_entryrightvalue. (((((dc_right_hlcover_entry) = 2 * (ge_balance_positive_hlcover_entryrightvalue) /\ (ge_balance_negative_hlcover_entryrightvalue) = 0) \/ exists ge_signed_half_hlcover_entryrightvaluedecode. (((dc_right_hlcover_entry) = 2 * ge_signed_half_hlcover_entryrightvaluedecode + 1 /\ (ge_balance_positive_hlcover_entryrightvalue) = 0) /\ (ge_balance_negative_hlcover_entryrightvalue) = S ge_signed_half_hlcover_entryrightvaluedecode))) /\ ((dst_positive_hlcover_entryright) + ge_balance_negative_hlcover_entryrightvalue = (dst_negative_hlcover_entryright) + ge_balance_positive_hlcover_entryrightvalue))))))))) /\ (exists sto_ap_hlcover_entryproduct sto_an_hlcover_entryproduct sto_bp_hlcover_entryproduct sto_bn_hlcover_entryproduct sto_cp_hlcover_entryproduct sto_cn_hlcover_entryproduct. (((((dc_left_hlcover_entry) = 2 * (sto_ap_hlcover_entryproduct) /\ (sto_an_hlcover_entryproduct) = 0) \/ exists ge_signed_half_hlcover_entryproductleft. (((dc_left_hlcover_entry) = 2 * ge_signed_half_hlcover_entryproductleft + 1 /\ (sto_ap_hlcover_entryproduct) = 0) /\ (sto_an_hlcover_entryproduct) = S ge_signed_half_hlcover_entryproductleft))) /\ ((((((dc_right_hlcover_entry) = 2 * (sto_bp_hlcover_entryproduct) /\ (sto_bn_hlcover_entryproduct) = 0) \/ exists ge_signed_half_hlcover_entryproductright. (((dc_right_hlcover_entry) = 2 * ge_signed_half_hlcover_entryproductright + 1 /\ (sto_bp_hlcover_entryproduct) = 0) /\ (sto_bn_hlcover_entryproduct) = S ge_signed_half_hlcover_entryproductright))) /\ ((((((x2) = 2 * (sto_cp_hlcover_entryproduct) /\ (sto_cn_hlcover_entryproduct) = 0) \/ exists ge_signed_half_hlcover_entryproductoutput. (((x2) = 2 * ge_signed_half_hlcover_entryproductoutput + 1 /\ (sto_cp_hlcover_entryproduct) = 0) /\ (sto_cn_hlcover_entryproduct) = S ge_signed_half_hlcover_entryproductoutput))) /\ ((sto_ap_hlcover_entryproduct * sto_bp_hlcover_entryproduct + sto_an_hlcover_entryproduct * sto_bn_hlcover_entryproduct) + sto_cn_hlcover_entryproduct = (sto_ap_hlcover_entryproduct * sto_bn_hlcover_entryproduct + sto_an_hlcover_entryproduct * sto_bp_hlcover_entryproduct) + sto_cp_hlcover_entryproduct))))))))))))))) \/ ((((x)=0 \/ ~(exists pvs_factor_hlcover_entrynondivisor. (m) = (x) * pvs_factor_hlcover_entrynondivisor)) /\ ((x2)=0))) - 0122
specialize dirichlet_convolution_prefix_lookup (F) - 0123
specialize dirichlet_convolution_prefix_lookup (G) - 0124
specialize dirichlet_convolution_prefix_lookup (m) - 0125
specialize dirichlet_convolution_prefix_lookup (m) - 0126
specialize dirichlet_convolution_prefix_lookup (A) - 0127
specialize dirichlet_convolution_prefix_lookup (x) - 0128
specialize dirichlet_convolution_prefix_lookup (x2) - 0129
apply dirichlet_convolution_prefix_lookup - 0130
exact hd_right_right_right_right_right_right_left - 0131
exact hb_left - 0132
exact hlv_witness - 0133
have hr : (((~((x1)=0)) /\ (exists dc_quotient_hrcover_entry dc_left_hrcover_entry dc_right_hrcover_entry. (((n)=(x1)*dc_quotient_hrcover_entry) /\ (((exists dst_positive_code_hrcover_entryleft dst_positive_scale_hrcover_entryleft dst_negative_code_hrcover_entryleft dst_negative_scale_hrcover_entryleft dst_positive_hrcover_entryleft dst_negative_hrcover_entryleft. (((F) = (((((dst_positive_code_hrcover_entryleft) + (dst_positive_scale_hrcover_entryleft)) * S ((dst_positive_code_hrcover_entryleft) + (dst_positive_scale_hrcover_entryleft)) + ((dst_positive_scale_hrcover_entryleft) + (dst_positive_scale_hrcover_entryleft))) + (((dst_negative_code_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)) * S ((dst_negative_code_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)) + ((dst_negative_scale_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)))) * S ((((dst_positive_code_hrcover_entryleft) + (dst_positive_scale_hrcover_entryleft)) * S ((dst_positive_code_hrcover_entryleft) + (dst_positive_scale_hrcover_entryleft)) + ((dst_positive_scale_hrcover_entryleft) + (dst_positive_scale_hrcover_entryleft))) + (((dst_negative_code_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)) * S ((dst_negative_code_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)) + ((dst_negative_scale_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)))) + ((((dst_negative_code_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)) * S ((dst_negative_code_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)) + ((dst_negative_scale_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft))) + (((dst_negative_code_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)) * S ((dst_negative_code_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)) + ((dst_negative_scale_hrcover_entryleft) + (dst_negative_scale_hrcover_entryleft)))))) /\ (((((exists ff_h_pvs_hrcover_entryleftpositive. ff_h_pvs_hrcover_entryleftpositive + S (dst_positive_hrcover_entryleft) = S ((S (x1)) * dst_positive_scale_hrcover_entryleft)) /\ exists ff_q_pvs_hrcover_entryleftpositive. dst_positive_code_hrcover_entryleft = ff_q_pvs_hrcover_entryleftpositive * S ((S (x1)) * dst_positive_scale_hrcover_entryleft) + (dst_positive_hrcover_entryleft))) /\ (((((exists ff_h_pvs_hrcover_entryleftnegative. ff_h_pvs_hrcover_entryleftnegative + S (dst_negative_hrcover_entryleft) = S ((S (x1)) * dst_negative_scale_hrcover_entryleft)) /\ exists ff_q_pvs_hrcover_entryleftnegative. dst_negative_code_hrcover_entryleft = ff_q_pvs_hrcover_entryleftnegative * S ((S (x1)) * dst_negative_scale_hrcover_entryleft) + (dst_negative_hrcover_entryleft))) /\ (exists ge_balance_positive_hrcover_entryleftvalue ge_balance_negative_hrcover_entryleftvalue. (((((dc_left_hrcover_entry) = 2 * (ge_balance_positive_hrcover_entryleftvalue) /\ (ge_balance_negative_hrcover_entryleftvalue) = 0) \/ exists ge_signed_half_hrcover_entryleftvaluedecode. (((dc_left_hrcover_entry) = 2 * ge_signed_half_hrcover_entryleftvaluedecode + 1 /\ (ge_balance_positive_hrcover_entryleftvalue) = 0) /\ (ge_balance_negative_hrcover_entryleftvalue) = S ge_signed_half_hrcover_entryleftvaluedecode))) /\ ((dst_positive_hrcover_entryleft) + ge_balance_negative_hrcover_entryleftvalue = (dst_negative_hrcover_entryleft) + ge_balance_positive_hrcover_entryleftvalue))))))))) /\ (((exists dst_positive_code_hrcover_entryright dst_positive_scale_hrcover_entryright dst_negative_code_hrcover_entryright dst_negative_scale_hrcover_entryright dst_positive_hrcover_entryright dst_negative_hrcover_entryright. (((G) = (((((dst_positive_code_hrcover_entryright) + (dst_positive_scale_hrcover_entryright)) * S ((dst_positive_code_hrcover_entryright) + (dst_positive_scale_hrcover_entryright)) + ((dst_positive_scale_hrcover_entryright) + (dst_positive_scale_hrcover_entryright))) + (((dst_negative_code_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)) * S ((dst_negative_code_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)) + ((dst_negative_scale_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)))) * S ((((dst_positive_code_hrcover_entryright) + (dst_positive_scale_hrcover_entryright)) * S ((dst_positive_code_hrcover_entryright) + (dst_positive_scale_hrcover_entryright)) + ((dst_positive_scale_hrcover_entryright) + (dst_positive_scale_hrcover_entryright))) + (((dst_negative_code_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)) * S ((dst_negative_code_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)) + ((dst_negative_scale_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)))) + ((((dst_negative_code_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)) * S ((dst_negative_code_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)) + ((dst_negative_scale_hrcover_entryright) + (dst_negative_scale_hrcover_entryright))) + (((dst_negative_code_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)) * S ((dst_negative_code_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)) + ((dst_negative_scale_hrcover_entryright) + (dst_negative_scale_hrcover_entryright)))))) /\ (((((exists ff_h_pvs_hrcover_entryrightpositive. ff_h_pvs_hrcover_entryrightpositive + S (dst_positive_hrcover_entryright) = S ((S (dc_quotient_hrcover_entry)) * dst_positive_scale_hrcover_entryright)) /\ exists ff_q_pvs_hrcover_entryrightpositive. dst_positive_code_hrcover_entryright = ff_q_pvs_hrcover_entryrightpositive * S ((S (dc_quotient_hrcover_entry)) * dst_positive_scale_hrcover_entryright) + (dst_positive_hrcover_entryright))) /\ (((((exists ff_h_pvs_hrcover_entryrightnegative. ff_h_pvs_hrcover_entryrightnegative + S (dst_negative_hrcover_entryright) = S ((S (dc_quotient_hrcover_entry)) * dst_negative_scale_hrcover_entryright)) /\ exists ff_q_pvs_hrcover_entryrightnegative. dst_negative_code_hrcover_entryright = ff_q_pvs_hrcover_entryrightnegative * S ((S (dc_quotient_hrcover_entry)) * dst_negative_scale_hrcover_entryright) + (dst_negative_hrcover_entryright))) /\ (exists ge_balance_positive_hrcover_entryrightvalue ge_balance_negative_hrcover_entryrightvalue. (((((dc_right_hrcover_entry) = 2 * (ge_balance_positive_hrcover_entryrightvalue) /\ (ge_balance_negative_hrcover_entryrightvalue) = 0) \/ exists ge_signed_half_hrcover_entryrightvaluedecode. (((dc_right_hrcover_entry) = 2 * ge_signed_half_hrcover_entryrightvaluedecode + 1 /\ (ge_balance_positive_hrcover_entryrightvalue) = 0) /\ (ge_balance_negative_hrcover_entryrightvalue) = S ge_signed_half_hrcover_entryrightvaluedecode))) /\ ((dst_positive_hrcover_entryright) + ge_balance_negative_hrcover_entryrightvalue = (dst_negative_hrcover_entryright) + ge_balance_positive_hrcover_entryrightvalue))))))))) /\ (exists sto_ap_hrcover_entryproduct sto_an_hrcover_entryproduct sto_bp_hrcover_entryproduct sto_bn_hrcover_entryproduct sto_cp_hrcover_entryproduct sto_cn_hrcover_entryproduct. (((((dc_left_hrcover_entry) = 2 * (sto_ap_hrcover_entryproduct) /\ (sto_an_hrcover_entryproduct) = 0) \/ exists ge_signed_half_hrcover_entryproductleft. (((dc_left_hrcover_entry) = 2 * ge_signed_half_hrcover_entryproductleft + 1 /\ (sto_ap_hrcover_entryproduct) = 0) /\ (sto_an_hrcover_entryproduct) = S ge_signed_half_hrcover_entryproductleft))) /\ ((((((dc_right_hrcover_entry) = 2 * (sto_bp_hrcover_entryproduct) /\ (sto_bn_hrcover_entryproduct) = 0) \/ exists ge_signed_half_hrcover_entryproductright. (((dc_right_hrcover_entry) = 2 * ge_signed_half_hrcover_entryproductright + 1 /\ (sto_bp_hrcover_entryproduct) = 0) /\ (sto_bn_hrcover_entryproduct) = S ge_signed_half_hrcover_entryproductright))) /\ ((((((x3) = 2 * (sto_cp_hrcover_entryproduct) /\ (sto_cn_hrcover_entryproduct) = 0) \/ exists ge_signed_half_hrcover_entryproductoutput. (((x3) = 2 * ge_signed_half_hrcover_entryproductoutput + 1 /\ (sto_cp_hrcover_entryproduct) = 0) /\ (sto_cn_hrcover_entryproduct) = S ge_signed_half_hrcover_entryproductoutput))) /\ ((sto_ap_hrcover_entryproduct * sto_bp_hrcover_entryproduct + sto_an_hrcover_entryproduct * sto_bn_hrcover_entryproduct) + sto_cn_hrcover_entryproduct = (sto_ap_hrcover_entryproduct * sto_bn_hrcover_entryproduct + sto_an_hrcover_entryproduct * sto_bp_hrcover_entryproduct) + sto_cp_hrcover_entryproduct))))))))))))))) \/ ((((x1)=0 \/ ~(exists pvs_factor_hrcover_entrynondivisor. (n) = (x1) * pvs_factor_hrcover_entrynondivisor)) /\ ((x3)=0))) - 0134
specialize dirichlet_convolution_prefix_lookup (F) - 0135
specialize dirichlet_convolution_prefix_lookup (G) - 0136
specialize dirichlet_convolution_prefix_lookup (n) - 0137
specialize dirichlet_convolution_prefix_lookup (n) - 0138
specialize dirichlet_convolution_prefix_lookup (B) - 0139
specialize dirichlet_convolution_prefix_lookup (x1) - 0140
specialize dirichlet_convolution_prefix_lookup (x3) - 0141
apply dirichlet_convolution_prefix_lookup - 0142
exact hd_right_right_right_right_right_right_right_left - 0143
exact hb_right_left - 0144
exact hrv_witness - 0145
have hproduct : exists sto_ap_cover_actual_product sto_an_cover_actual_product sto_bp_cover_actual_product sto_bn_cover_actual_product sto_cp_cover_actual_product sto_cn_cover_actual_product. (((((x2) = 2 * (sto_ap_cover_actual_product) /\ (sto_an_cover_actual_product) = 0) \/ exists ge_signed_half_cover_actual_productleft. (((x2) = 2 * ge_signed_half_cover_actual_productleft + 1 /\ (sto_ap_cover_actual_product) = 0) /\ (sto_an_cover_actual_product) = S ge_signed_half_cover_actual_productleft))) /\ ((((((x3) = 2 * (sto_bp_cover_actual_product) /\ (sto_bn_cover_actual_product) = 0) \/ exists ge_signed_half_cover_actual_productright. (((x3) = 2 * ge_signed_half_cover_actual_productright + 1 /\ (sto_bp_cover_actual_product) = 0) /\ (sto_bn_cover_actual_product) = S ge_signed_half_cover_actual_productright))) /\ ((((((x4) = 2 * (sto_cp_cover_actual_product) /\ (sto_cn_cover_actual_product) = 0) \/ exists ge_signed_half_cover_actual_productoutput. (((x4) = 2 * ge_signed_half_cover_actual_productoutput + 1 /\ (sto_cp_cover_actual_product) = 0) /\ (sto_cn_cover_actual_product) = S ge_signed_half_cover_actual_productoutput))) /\ ((sto_ap_cover_actual_product * sto_bp_cover_actual_product + sto_an_cover_actual_product * sto_bn_cover_actual_product) + sto_cn_cover_actual_product = (sto_ap_cover_actual_product * sto_bn_cover_actual_product + sto_an_cover_actual_product * sto_bp_cover_actual_product) + sto_cp_cover_actual_product)))))) - 0146
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x) - 0147
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x1) - 0148
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x2) - 0149
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x3) - 0150
specialize hd_right_right_right_right_right_right_right_right_left_right_right_right (x4) - 0151
apply hd_right_right_right_right_right_right_right_right_left_right_right_right - 0152
specialize succ_le_succ (x) - 0153
specialize succ_le_succ (m) - 0154
apply succ_le_succ - 0155
exact hb_left - 0156
specialize succ_le_succ (x1) - 0157
specialize succ_le_succ (n) - 0158
apply succ_le_succ - 0159
exact hb_right_left - 0160
exact hlv_witness - 0161
exact hrv_witness - 0162
exact hwv_witness - 0163
have hpair : ((~((x)=0)) /\ (((~((x1)=0)) /\ (((exists pvs_factor_cover_pair_productleft. (m) = (x) * pvs_factor_cover_pair_productleft) /\ (((exists pvs_factor_cover_pair_productright. (n) = (x1) * pvs_factor_cover_pair_productright) /\ ((x*x1)=(x)*(x1))))))))) - 0164
split - 0165
exact hp_witness_witness_left - 0166
split - 0167
exact hp_witness_witness_right_left - 0168
split - 0169
exact hp_witness_witness_right_right_left - 0170
split - 0171
exact hp_witness_witness_right_right_right_left - 0172
refl - 0173
rewrite hp_witness_witness_right_right_right_right at ht - 0174
rewrite hp_witness_witness_right_right_right_right at ht - 0175
rewrite hp_witness_witness_right_right_right_right at ht - 0176
rewrite hp_witness_witness_right_right_right_right at ht - 0177
rewrite hp_witness_witness_right_right_right_right at ht - 0178
rewrite hp_witness_witness_right_right_right_right at ht - 0179
rewrite hp_witness_witness_right_right_right_right at ht - 0180
rewrite hp_witness_witness_right_right_right_right at ht - 0181
have heq : x4=z - 0182
specialize signed_mul_functional (x2) - 0183
specialize signed_mul_functional (x3) - 0184
specialize signed_mul_functional (x4) - 0185
specialize signed_mul_functional (z) - 0186
apply signed_mul_functional - 0187
exact hproduct - 0188
specialize dirichlet_multiplicative_pair_factorization (N) - 0189
specialize dirichlet_multiplicative_pair_factorization (F) - 0190
specialize dirichlet_multiplicative_pair_factorization (G) - 0191
specialize dirichlet_multiplicative_pair_factorization (m) - 0192
specialize dirichlet_multiplicative_pair_factorization (n) - 0193
specialize dirichlet_multiplicative_pair_factorization (x) - 0194
specialize dirichlet_multiplicative_pair_factorization (x1) - 0195
specialize dirichlet_multiplicative_pair_factorization (x2) - 0196
specialize dirichlet_multiplicative_pair_factorization (x3) - 0197
specialize dirichlet_multiplicative_pair_factorization (z) - 0198
apply dirichlet_multiplicative_pair_factorization - 0199
exact hd_left - 0200
exact hd_right_left - 0201
exact hd_right_right_left - 0202
exact hd_right_right_right_left - 0203
exact hd_right_right_right_right_left - 0204
exact hd_right_right_right_right_right_left - 0205
exact hpair - 0206
exact hl - 0207
exact hr - 0208
exact ht - 0209
rewrite heq at hwv_witness - 0210
rewrite heq at hwv_witness - 0211
exists (S n)*x+x1 - 0212
split - 0213
exact hi - 0214
split - 0215
rewrite hp_witness_witness_right_right_right_right - 0216
rewrite hp_witness_witness_right_right_right_right - 0217
specialize divisor_pair_index_map_lookup (S n) - 0218
specialize divisor_pair_index_map_lookup ((S (m))*(S (n))) - 0219
specialize divisor_pair_index_map_lookup (r) - 0220
specialize divisor_pair_index_map_lookup (s) - 0221
specialize divisor_pair_index_map_lookup ((S (n))*(x)+(x1)) - 0222
specialize divisor_pair_index_map_lookup (x) - 0223
specialize divisor_pair_index_map_lookup (x1) - 0224
apply divisor_pair_index_map_lookup - 0225
exact hd_right_right_right_right_right_right_right_right_right_right - 0226
exact hi - 0227
specialize succ_le_succ (x1) - 0228
specialize succ_le_succ (n) - 0229
apply succ_le_succ - 0230
exact hb_right_left - 0231
refl - 0232
exact hwv_witness