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 c. (((~((N)=0)) /\ (((exists dst_positive_code_scalar_firsttable dst_positive_scale_scalar_firsttable dst_negative_code_scalar_firsttable dst_negative_scale_scalar_firsttable. (((F) = (((((dst_positive_code_scalar_firsttable) + (dst_positive_scale_scalar_firsttable)) * S ((dst_positive_code_scalar_firsttable) + (dst_positive_scale_scalar_firsttable)) + ((dst_positive_scale_scalar_firsttable) + (dst_positive_scale_scalar_firsttable))) + (((dst_negative_code_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)) * S ((dst_negative_code_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)) + ((dst_negative_scale_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)))) * S ((((dst_positive_code_scalar_firsttable) + (dst_positive_scale_scalar_firsttable)) * S ((dst_positive_code_scalar_firsttable) + (dst_positive_scale_scalar_firsttable)) + ((dst_positive_scale_scalar_firsttable) + (dst_positive_scale_scalar_firsttable))) + (((dst_negative_code_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)) * S ((dst_negative_code_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)) + ((dst_negative_scale_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)))) + ((((dst_negative_code_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)) * S ((dst_negative_code_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)) + ((dst_negative_scale_scalar_firsttable) + (dst_negative_scale_scalar_firsttable))) + (((dst_negative_code_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)) * S ((dst_negative_code_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)) + ((dst_negative_scale_scalar_firsttable) + (dst_negative_scale_scalar_firsttable)))))) /\ (forall dst_index_scalar_firsttable. (exists pvs_le_gap_scalar_firsttabledomain. pvs_le_gap_scalar_firsttabledomain + (dst_index_scalar_firsttable) = (N)) -> exists dst_positive_scalar_firsttable dst_negative_scalar_firsttable dst_value_scalar_firsttable. ((((exists ff_h_pvs_scalar_firsttableentrypositive. ff_h_pvs_scalar_firsttableentrypositive + S (dst_positive_scalar_firsttable) = S ((S (dst_index_scalar_firsttable)) * dst_positive_scale_scalar_firsttable)) /\ exists ff_q_pvs_scalar_firsttableentrypositive. dst_positive_code_scalar_firsttable = ff_q_pvs_scalar_firsttableentrypositive * S ((S (dst_index_scalar_firsttable)) * dst_positive_scale_scalar_firsttable) + (dst_positive_scalar_firsttable))) /\ (((((exists ff_h_pvs_scalar_firsttableentrynegative. ff_h_pvs_scalar_firsttableentrynegative + S (dst_negative_scalar_firsttable) = S ((S (dst_index_scalar_firsttable)) * dst_negative_scale_scalar_firsttable)) /\ exists ff_q_pvs_scalar_firsttableentrynegative. dst_negative_code_scalar_firsttable = ff_q_pvs_scalar_firsttableentrynegative * S ((S (dst_index_scalar_firsttable)) * dst_negative_scale_scalar_firsttable) + (dst_negative_scalar_firsttable))) /\ (exists ge_balance_positive_scalar_firsttableentryvalue ge_balance_negative_scalar_firsttableentryvalue. (((((dst_value_scalar_firsttable) = 2 * (ge_balance_positive_scalar_firsttableentryvalue) /\ (ge_balance_negative_scalar_firsttableentryvalue) = 0) \/ exists ge_signed_half_scalar_firsttableentryvaluedecode. (((dst_value_scalar_firsttable) = 2 * ge_signed_half_scalar_firsttableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_firsttableentryvalue) = 0) /\ (ge_balance_negative_scalar_firsttableentryvalue) = S ge_signed_half_scalar_firsttableentryvaluedecode))) /\ ((dst_positive_scalar_firsttable) + ge_balance_negative_scalar_firsttableentryvalue = (dst_negative_scalar_firsttable) + ge_balance_positive_scalar_firsttableentryvalue))))))))) /\ (((exists dst_positive_code_scalar_firstone dst_positive_scale_scalar_firstone dst_negative_code_scalar_firstone dst_negative_scale_scalar_firstone dst_positive_scalar_firstone dst_negative_scalar_firstone. (((F) = (((((dst_positive_code_scalar_firstone) + (dst_positive_scale_scalar_firstone)) * S ((dst_positive_code_scalar_firstone) + (dst_positive_scale_scalar_firstone)) + ((dst_positive_scale_scalar_firstone) + (dst_positive_scale_scalar_firstone))) + (((dst_negative_code_scalar_firstone) + (dst_negative_scale_scalar_firstone)) * S ((dst_negative_code_scalar_firstone) + (dst_negative_scale_scalar_firstone)) + ((dst_negative_scale_scalar_firstone) + (dst_negative_scale_scalar_firstone)))) * S ((((dst_positive_code_scalar_firstone) + (dst_positive_scale_scalar_firstone)) * S ((dst_positive_code_scalar_firstone) + (dst_positive_scale_scalar_firstone)) + ((dst_positive_scale_scalar_firstone) + (dst_positive_scale_scalar_firstone))) + (((dst_negative_code_scalar_firstone) + (dst_negative_scale_scalar_firstone)) * S ((dst_negative_code_scalar_firstone) + (dst_negative_scale_scalar_firstone)) + ((dst_negative_scale_scalar_firstone) + (dst_negative_scale_scalar_firstone)))) + ((((dst_negative_code_scalar_firstone) + (dst_negative_scale_scalar_firstone)) * S ((dst_negative_code_scalar_firstone) + (dst_negative_scale_scalar_firstone)) + ((dst_negative_scale_scalar_firstone) + (dst_negative_scale_scalar_firstone))) + (((dst_negative_code_scalar_firstone) + (dst_negative_scale_scalar_firstone)) * S ((dst_negative_code_scalar_firstone) + (dst_negative_scale_scalar_firstone)) + ((dst_negative_scale_scalar_firstone) + (dst_negative_scale_scalar_firstone)))))) /\ (((((exists ff_h_pvs_scalar_firstonepositive. ff_h_pvs_scalar_firstonepositive + S (dst_positive_scalar_firstone) = S ((S (1)) * dst_positive_scale_scalar_firstone)) /\ exists ff_q_pvs_scalar_firstonepositive. dst_positive_code_scalar_firstone = ff_q_pvs_scalar_firstonepositive * S ((S (1)) * dst_positive_scale_scalar_firstone) + (dst_positive_scalar_firstone))) /\ (((((exists ff_h_pvs_scalar_firstonenegative. ff_h_pvs_scalar_firstonenegative + S (dst_negative_scalar_firstone) = S ((S (1)) * dst_negative_scale_scalar_firstone)) /\ exists ff_q_pvs_scalar_firstonenegative. dst_negative_code_scalar_firstone = ff_q_pvs_scalar_firstonenegative * S ((S (1)) * dst_negative_scale_scalar_firstone) + (dst_negative_scalar_firstone))) /\ (exists ge_balance_positive_scalar_firstonevalue ge_balance_negative_scalar_firstonevalue. (((((2) = 2 * (ge_balance_positive_scalar_firstonevalue) /\ (ge_balance_negative_scalar_firstonevalue) = 0) \/ exists ge_signed_half_scalar_firstonevaluedecode. (((2) = 2 * ge_signed_half_scalar_firstonevaluedecode + 1 /\ (ge_balance_positive_scalar_firstonevalue) = 0) /\ (ge_balance_negative_scalar_firstonevalue) = S ge_signed_half_scalar_firstonevaluedecode))) /\ ((dst_positive_scalar_firstone) + ge_balance_negative_scalar_firstonevalue = (dst_negative_scalar_firstone) + ge_balance_positive_scalar_firstonevalue))))))))) /\ (forall mp_a_scalar_first mp_b_scalar_first mp_x_scalar_first mp_y_scalar_first mp_z_scalar_first. ~(mp_a_scalar_first=0) -> ~(mp_b_scalar_first=0) -> (exists pvs_le_gap_scalar_firstbound. pvs_le_gap_scalar_firstbound + (mp_a_scalar_first*mp_b_scalar_first) = (N)) -> (forall frp_divisor_scalar_firstcoprime. (exists frp_left_factor_scalar_firstcoprime. mp_a_scalar_first = frp_divisor_scalar_firstcoprime * frp_left_factor_scalar_firstcoprime) -> (exists frp_right_factor_scalar_firstcoprime. mp_b_scalar_first = frp_divisor_scalar_firstcoprime * frp_right_factor_scalar_firstcoprime) -> frp_divisor_scalar_firstcoprime = 1) -> (exists dst_positive_code_scalar_firstfirst dst_positive_scale_scalar_firstfirst dst_negative_code_scalar_firstfirst dst_negative_scale_scalar_firstfirst dst_positive_scalar_firstfirst dst_negative_scalar_firstfirst. (((F) = (((((dst_positive_code_scalar_firstfirst) + (dst_positive_scale_scalar_firstfirst)) * S ((dst_positive_code_scalar_firstfirst) + (dst_positive_scale_scalar_firstfirst)) + ((dst_positive_scale_scalar_firstfirst) + (dst_positive_scale_scalar_firstfirst))) + (((dst_negative_code_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)) * S ((dst_negative_code_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)) + ((dst_negative_scale_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)))) * S ((((dst_positive_code_scalar_firstfirst) + (dst_positive_scale_scalar_firstfirst)) * S ((dst_positive_code_scalar_firstfirst) + (dst_positive_scale_scalar_firstfirst)) + ((dst_positive_scale_scalar_firstfirst) + (dst_positive_scale_scalar_firstfirst))) + (((dst_negative_code_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)) * S ((dst_negative_code_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)) + ((dst_negative_scale_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)))) + ((((dst_negative_code_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)) * S ((dst_negative_code_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)) + ((dst_negative_scale_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst))) + (((dst_negative_code_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)) * S ((dst_negative_code_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)) + ((dst_negative_scale_scalar_firstfirst) + (dst_negative_scale_scalar_firstfirst)))))) /\ (((((exists ff_h_pvs_scalar_firstfirstpositive. ff_h_pvs_scalar_firstfirstpositive + S (dst_positive_scalar_firstfirst) = S ((S (mp_a_scalar_first)) * dst_positive_scale_scalar_firstfirst)) /\ exists ff_q_pvs_scalar_firstfirstpositive. dst_positive_code_scalar_firstfirst = ff_q_pvs_scalar_firstfirstpositive * S ((S (mp_a_scalar_first)) * dst_positive_scale_scalar_firstfirst) + (dst_positive_scalar_firstfirst))) /\ (((((exists ff_h_pvs_scalar_firstfirstnegative. ff_h_pvs_scalar_firstfirstnegative + S (dst_negative_scalar_firstfirst) = S ((S (mp_a_scalar_first)) * dst_negative_scale_scalar_firstfirst)) /\ exists ff_q_pvs_scalar_firstfirstnegative. dst_negative_code_scalar_firstfirst = ff_q_pvs_scalar_firstfirstnegative * S ((S (mp_a_scalar_first)) * dst_negative_scale_scalar_firstfirst) + (dst_negative_scalar_firstfirst))) /\ (exists ge_balance_positive_scalar_firstfirstvalue ge_balance_negative_scalar_firstfirstvalue. (((((mp_x_scalar_first) = 2 * (ge_balance_positive_scalar_firstfirstvalue) /\ (ge_balance_negative_scalar_firstfirstvalue) = 0) \/ exists ge_signed_half_scalar_firstfirstvaluedecode. (((mp_x_scalar_first) = 2 * ge_signed_half_scalar_firstfirstvaluedecode + 1 /\ (ge_balance_positive_scalar_firstfirstvalue) = 0) /\ (ge_balance_negative_scalar_firstfirstvalue) = S ge_signed_half_scalar_firstfirstvaluedecode))) /\ ((dst_positive_scalar_firstfirst) + ge_balance_negative_scalar_firstfirstvalue = (dst_negative_scalar_firstfirst) + ge_balance_positive_scalar_firstfirstvalue))))))))) -> (exists dst_positive_code_scalar_firstsecond dst_positive_scale_scalar_firstsecond dst_negative_code_scalar_firstsecond dst_negative_scale_scalar_firstsecond dst_positive_scalar_firstsecond dst_negative_scalar_firstsecond. (((F) = (((((dst_positive_code_scalar_firstsecond) + (dst_positive_scale_scalar_firstsecond)) * S ((dst_positive_code_scalar_firstsecond) + (dst_positive_scale_scalar_firstsecond)) + ((dst_positive_scale_scalar_firstsecond) + (dst_positive_scale_scalar_firstsecond))) + (((dst_negative_code_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)) * S ((dst_negative_code_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)) + ((dst_negative_scale_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)))) * S ((((dst_positive_code_scalar_firstsecond) + (dst_positive_scale_scalar_firstsecond)) * S ((dst_positive_code_scalar_firstsecond) + (dst_positive_scale_scalar_firstsecond)) + ((dst_positive_scale_scalar_firstsecond) + (dst_positive_scale_scalar_firstsecond))) + (((dst_negative_code_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)) * S ((dst_negative_code_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)) + ((dst_negative_scale_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)))) + ((((dst_negative_code_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)) * S ((dst_negative_code_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)) + ((dst_negative_scale_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond))) + (((dst_negative_code_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)) * S ((dst_negative_code_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)) + ((dst_negative_scale_scalar_firstsecond) + (dst_negative_scale_scalar_firstsecond)))))) /\ (((((exists ff_h_pvs_scalar_firstsecondpositive. ff_h_pvs_scalar_firstsecondpositive + S (dst_positive_scalar_firstsecond) = S ((S (mp_b_scalar_first)) * dst_positive_scale_scalar_firstsecond)) /\ exists ff_q_pvs_scalar_firstsecondpositive. dst_positive_code_scalar_firstsecond = ff_q_pvs_scalar_firstsecondpositive * S ((S (mp_b_scalar_first)) * dst_positive_scale_scalar_firstsecond) + (dst_positive_scalar_firstsecond))) /\ (((((exists ff_h_pvs_scalar_firstsecondnegative. ff_h_pvs_scalar_firstsecondnegative + S (dst_negative_scalar_firstsecond) = S ((S (mp_b_scalar_first)) * dst_negative_scale_scalar_firstsecond)) /\ exists ff_q_pvs_scalar_firstsecondnegative. dst_negative_code_scalar_firstsecond = ff_q_pvs_scalar_firstsecondnegative * S ((S (mp_b_scalar_first)) * dst_negative_scale_scalar_firstsecond) + (dst_negative_scalar_firstsecond))) /\ (exists ge_balance_positive_scalar_firstsecondvalue ge_balance_negative_scalar_firstsecondvalue. (((((mp_y_scalar_first) = 2 * (ge_balance_positive_scalar_firstsecondvalue) /\ (ge_balance_negative_scalar_firstsecondvalue) = 0) \/ exists ge_signed_half_scalar_firstsecondvaluedecode. (((mp_y_scalar_first) = 2 * ge_signed_half_scalar_firstsecondvaluedecode + 1 /\ (ge_balance_positive_scalar_firstsecondvalue) = 0) /\ (ge_balance_negative_scalar_firstsecondvalue) = S ge_signed_half_scalar_firstsecondvaluedecode))) /\ ((dst_positive_scalar_firstsecond) + ge_balance_negative_scalar_firstsecondvalue = (dst_negative_scalar_firstsecond) + ge_balance_positive_scalar_firstsecondvalue))))))))) -> (exists dst_positive_code_scalar_firstproduct dst_positive_scale_scalar_firstproduct dst_negative_code_scalar_firstproduct dst_negative_scale_scalar_firstproduct dst_positive_scalar_firstproduct dst_negative_scalar_firstproduct. (((F) = (((((dst_positive_code_scalar_firstproduct) + (dst_positive_scale_scalar_firstproduct)) * S ((dst_positive_code_scalar_firstproduct) + (dst_positive_scale_scalar_firstproduct)) + ((dst_positive_scale_scalar_firstproduct) + (dst_positive_scale_scalar_firstproduct))) + (((dst_negative_code_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)) * S ((dst_negative_code_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)) + ((dst_negative_scale_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)))) * S ((((dst_positive_code_scalar_firstproduct) + (dst_positive_scale_scalar_firstproduct)) * S ((dst_positive_code_scalar_firstproduct) + (dst_positive_scale_scalar_firstproduct)) + ((dst_positive_scale_scalar_firstproduct) + (dst_positive_scale_scalar_firstproduct))) + (((dst_negative_code_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)) * S ((dst_negative_code_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)) + ((dst_negative_scale_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)))) + ((((dst_negative_code_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)) * S ((dst_negative_code_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)) + ((dst_negative_scale_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct))) + (((dst_negative_code_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)) * S ((dst_negative_code_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)) + ((dst_negative_scale_scalar_firstproduct) + (dst_negative_scale_scalar_firstproduct)))))) /\ (((((exists ff_h_pvs_scalar_firstproductpositive. ff_h_pvs_scalar_firstproductpositive + S (dst_positive_scalar_firstproduct) = S ((S (mp_a_scalar_first*mp_b_scalar_first)) * dst_positive_scale_scalar_firstproduct)) /\ exists ff_q_pvs_scalar_firstproductpositive. dst_positive_code_scalar_firstproduct = ff_q_pvs_scalar_firstproductpositive * S ((S (mp_a_scalar_first*mp_b_scalar_first)) * dst_positive_scale_scalar_firstproduct) + (dst_positive_scalar_firstproduct))) /\ (((((exists ff_h_pvs_scalar_firstproductnegative. ff_h_pvs_scalar_firstproductnegative + S (dst_negative_scalar_firstproduct) = S ((S (mp_a_scalar_first*mp_b_scalar_first)) * dst_negative_scale_scalar_firstproduct)) /\ exists ff_q_pvs_scalar_firstproductnegative. dst_negative_code_scalar_firstproduct = ff_q_pvs_scalar_firstproductnegative * S ((S (mp_a_scalar_first*mp_b_scalar_first)) * dst_negative_scale_scalar_firstproduct) + (dst_negative_scalar_firstproduct))) /\ (exists ge_balance_positive_scalar_firstproductvalue ge_balance_negative_scalar_firstproductvalue. (((((mp_z_scalar_first) = 2 * (ge_balance_positive_scalar_firstproductvalue) /\ (ge_balance_negative_scalar_firstproductvalue) = 0) \/ exists ge_signed_half_scalar_firstproductvaluedecode. (((mp_z_scalar_first) = 2 * ge_signed_half_scalar_firstproductvaluedecode + 1 /\ (ge_balance_positive_scalar_firstproductvalue) = 0) /\ (ge_balance_negative_scalar_firstproductvalue) = S ge_signed_half_scalar_firstproductvaluedecode))) /\ ((dst_positive_scalar_firstproduct) + ge_balance_negative_scalar_firstproductvalue = (dst_negative_scalar_firstproduct) + ge_balance_positive_scalar_firstproductvalue))))))))) -> (exists sto_ap_scalar_firstlaw sto_an_scalar_firstlaw sto_bp_scalar_firstlaw sto_bn_scalar_firstlaw sto_cp_scalar_firstlaw sto_cn_scalar_firstlaw. (((((mp_x_scalar_first) = 2 * (sto_ap_scalar_firstlaw) /\ (sto_an_scalar_firstlaw) = 0) \/ exists ge_signed_half_scalar_firstlawleft. (((mp_x_scalar_first) = 2 * ge_signed_half_scalar_firstlawleft + 1 /\ (sto_ap_scalar_firstlaw) = 0) /\ (sto_an_scalar_firstlaw) = S ge_signed_half_scalar_firstlawleft))) /\ ((((((mp_y_scalar_first) = 2 * (sto_bp_scalar_firstlaw) /\ (sto_bn_scalar_firstlaw) = 0) \/ exists ge_signed_half_scalar_firstlawright. (((mp_y_scalar_first) = 2 * ge_signed_half_scalar_firstlawright + 1 /\ (sto_bp_scalar_firstlaw) = 0) /\ (sto_bn_scalar_firstlaw) = S ge_signed_half_scalar_firstlawright))) /\ ((((((mp_z_scalar_first) = 2 * (sto_cp_scalar_firstlaw) /\ (sto_cn_scalar_firstlaw) = 0) \/ exists ge_signed_half_scalar_firstlawoutput. (((mp_z_scalar_first) = 2 * ge_signed_half_scalar_firstlawoutput + 1 /\ (sto_cp_scalar_firstlaw) = 0) /\ (sto_cn_scalar_firstlaw) = S ge_signed_half_scalar_firstlawoutput))) /\ ((sto_ap_scalar_firstlaw * sto_bp_scalar_firstlaw + sto_an_scalar_firstlaw * sto_bn_scalar_firstlaw) + sto_cn_scalar_firstlaw = (sto_ap_scalar_firstlaw * sto_bn_scalar_firstlaw + sto_an_scalar_firstlaw * sto_bp_scalar_firstlaw) + sto_cp_scalar_firstlaw)))))))))))))) -> (((~((N)=0)) /\ (((exists dst_positive_code_scalar_secondtable dst_positive_scale_scalar_secondtable dst_negative_code_scalar_secondtable dst_negative_scale_scalar_secondtable. (((G) = (((((dst_positive_code_scalar_secondtable) + (dst_positive_scale_scalar_secondtable)) * S ((dst_positive_code_scalar_secondtable) + (dst_positive_scale_scalar_secondtable)) + ((dst_positive_scale_scalar_secondtable) + (dst_positive_scale_scalar_secondtable))) + (((dst_negative_code_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)) * S ((dst_negative_code_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)) + ((dst_negative_scale_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)))) * S ((((dst_positive_code_scalar_secondtable) + (dst_positive_scale_scalar_secondtable)) * S ((dst_positive_code_scalar_secondtable) + (dst_positive_scale_scalar_secondtable)) + ((dst_positive_scale_scalar_secondtable) + (dst_positive_scale_scalar_secondtable))) + (((dst_negative_code_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)) * S ((dst_negative_code_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)) + ((dst_negative_scale_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)))) + ((((dst_negative_code_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)) * S ((dst_negative_code_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)) + ((dst_negative_scale_scalar_secondtable) + (dst_negative_scale_scalar_secondtable))) + (((dst_negative_code_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)) * S ((dst_negative_code_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)) + ((dst_negative_scale_scalar_secondtable) + (dst_negative_scale_scalar_secondtable)))))) /\ (forall dst_index_scalar_secondtable. (exists pvs_le_gap_scalar_secondtabledomain. pvs_le_gap_scalar_secondtabledomain + (dst_index_scalar_secondtable) = (N)) -> exists dst_positive_scalar_secondtable dst_negative_scalar_secondtable dst_value_scalar_secondtable. ((((exists ff_h_pvs_scalar_secondtableentrypositive. ff_h_pvs_scalar_secondtableentrypositive + S (dst_positive_scalar_secondtable) = S ((S (dst_index_scalar_secondtable)) * dst_positive_scale_scalar_secondtable)) /\ exists ff_q_pvs_scalar_secondtableentrypositive. dst_positive_code_scalar_secondtable = ff_q_pvs_scalar_secondtableentrypositive * S ((S (dst_index_scalar_secondtable)) * dst_positive_scale_scalar_secondtable) + (dst_positive_scalar_secondtable))) /\ (((((exists ff_h_pvs_scalar_secondtableentrynegative. ff_h_pvs_scalar_secondtableentrynegative + S (dst_negative_scalar_secondtable) = S ((S (dst_index_scalar_secondtable)) * dst_negative_scale_scalar_secondtable)) /\ exists ff_q_pvs_scalar_secondtableentrynegative. dst_negative_code_scalar_secondtable = ff_q_pvs_scalar_secondtableentrynegative * S ((S (dst_index_scalar_secondtable)) * dst_negative_scale_scalar_secondtable) + (dst_negative_scalar_secondtable))) /\ (exists ge_balance_positive_scalar_secondtableentryvalue ge_balance_negative_scalar_secondtableentryvalue. (((((dst_value_scalar_secondtable) = 2 * (ge_balance_positive_scalar_secondtableentryvalue) /\ (ge_balance_negative_scalar_secondtableentryvalue) = 0) \/ exists ge_signed_half_scalar_secondtableentryvaluedecode. (((dst_value_scalar_secondtable) = 2 * ge_signed_half_scalar_secondtableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_secondtableentryvalue) = 0) /\ (ge_balance_negative_scalar_secondtableentryvalue) = S ge_signed_half_scalar_secondtableentryvaluedecode))) /\ ((dst_positive_scalar_secondtable) + ge_balance_negative_scalar_secondtableentryvalue = (dst_negative_scalar_secondtable) + ge_balance_positive_scalar_secondtableentryvalue))))))))) /\ (((exists dst_positive_code_scalar_secondone dst_positive_scale_scalar_secondone dst_negative_code_scalar_secondone dst_negative_scale_scalar_secondone dst_positive_scalar_secondone dst_negative_scalar_secondone. (((G) = (((((dst_positive_code_scalar_secondone) + (dst_positive_scale_scalar_secondone)) * S ((dst_positive_code_scalar_secondone) + (dst_positive_scale_scalar_secondone)) + ((dst_positive_scale_scalar_secondone) + (dst_positive_scale_scalar_secondone))) + (((dst_negative_code_scalar_secondone) + (dst_negative_scale_scalar_secondone)) * S ((dst_negative_code_scalar_secondone) + (dst_negative_scale_scalar_secondone)) + ((dst_negative_scale_scalar_secondone) + (dst_negative_scale_scalar_secondone)))) * S ((((dst_positive_code_scalar_secondone) + (dst_positive_scale_scalar_secondone)) * S ((dst_positive_code_scalar_secondone) + (dst_positive_scale_scalar_secondone)) + ((dst_positive_scale_scalar_secondone) + (dst_positive_scale_scalar_secondone))) + (((dst_negative_code_scalar_secondone) + (dst_negative_scale_scalar_secondone)) * S ((dst_negative_code_scalar_secondone) + (dst_negative_scale_scalar_secondone)) + ((dst_negative_scale_scalar_secondone) + (dst_negative_scale_scalar_secondone)))) + ((((dst_negative_code_scalar_secondone) + (dst_negative_scale_scalar_secondone)) * S ((dst_negative_code_scalar_secondone) + (dst_negative_scale_scalar_secondone)) + ((dst_negative_scale_scalar_secondone) + (dst_negative_scale_scalar_secondone))) + (((dst_negative_code_scalar_secondone) + (dst_negative_scale_scalar_secondone)) * S ((dst_negative_code_scalar_secondone) + (dst_negative_scale_scalar_secondone)) + ((dst_negative_scale_scalar_secondone) + (dst_negative_scale_scalar_secondone)))))) /\ (((((exists ff_h_pvs_scalar_secondonepositive. ff_h_pvs_scalar_secondonepositive + S (dst_positive_scalar_secondone) = S ((S (1)) * dst_positive_scale_scalar_secondone)) /\ exists ff_q_pvs_scalar_secondonepositive. dst_positive_code_scalar_secondone = ff_q_pvs_scalar_secondonepositive * S ((S (1)) * dst_positive_scale_scalar_secondone) + (dst_positive_scalar_secondone))) /\ (((((exists ff_h_pvs_scalar_secondonenegative. ff_h_pvs_scalar_secondonenegative + S (dst_negative_scalar_secondone) = S ((S (1)) * dst_negative_scale_scalar_secondone)) /\ exists ff_q_pvs_scalar_secondonenegative. dst_negative_code_scalar_secondone = ff_q_pvs_scalar_secondonenegative * S ((S (1)) * dst_negative_scale_scalar_secondone) + (dst_negative_scalar_secondone))) /\ (exists ge_balance_positive_scalar_secondonevalue ge_balance_negative_scalar_secondonevalue. (((((2) = 2 * (ge_balance_positive_scalar_secondonevalue) /\ (ge_balance_negative_scalar_secondonevalue) = 0) \/ exists ge_signed_half_scalar_secondonevaluedecode. (((2) = 2 * ge_signed_half_scalar_secondonevaluedecode + 1 /\ (ge_balance_positive_scalar_secondonevalue) = 0) /\ (ge_balance_negative_scalar_secondonevalue) = S ge_signed_half_scalar_secondonevaluedecode))) /\ ((dst_positive_scalar_secondone) + ge_balance_negative_scalar_secondonevalue = (dst_negative_scalar_secondone) + ge_balance_positive_scalar_secondonevalue))))))))) /\ (forall mp_a_scalar_second mp_b_scalar_second mp_x_scalar_second mp_y_scalar_second mp_z_scalar_second. ~(mp_a_scalar_second=0) -> ~(mp_b_scalar_second=0) -> (exists pvs_le_gap_scalar_secondbound. pvs_le_gap_scalar_secondbound + (mp_a_scalar_second*mp_b_scalar_second) = (N)) -> (forall frp_divisor_scalar_secondcoprime. (exists frp_left_factor_scalar_secondcoprime. mp_a_scalar_second = frp_divisor_scalar_secondcoprime * frp_left_factor_scalar_secondcoprime) -> (exists frp_right_factor_scalar_secondcoprime. mp_b_scalar_second = frp_divisor_scalar_secondcoprime * frp_right_factor_scalar_secondcoprime) -> frp_divisor_scalar_secondcoprime = 1) -> (exists dst_positive_code_scalar_secondfirst dst_positive_scale_scalar_secondfirst dst_negative_code_scalar_secondfirst dst_negative_scale_scalar_secondfirst dst_positive_scalar_secondfirst dst_negative_scalar_secondfirst. (((G) = (((((dst_positive_code_scalar_secondfirst) + (dst_positive_scale_scalar_secondfirst)) * S ((dst_positive_code_scalar_secondfirst) + (dst_positive_scale_scalar_secondfirst)) + ((dst_positive_scale_scalar_secondfirst) + (dst_positive_scale_scalar_secondfirst))) + (((dst_negative_code_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)) * S ((dst_negative_code_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)) + ((dst_negative_scale_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)))) * S ((((dst_positive_code_scalar_secondfirst) + (dst_positive_scale_scalar_secondfirst)) * S ((dst_positive_code_scalar_secondfirst) + (dst_positive_scale_scalar_secondfirst)) + ((dst_positive_scale_scalar_secondfirst) + (dst_positive_scale_scalar_secondfirst))) + (((dst_negative_code_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)) * S ((dst_negative_code_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)) + ((dst_negative_scale_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)))) + ((((dst_negative_code_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)) * S ((dst_negative_code_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)) + ((dst_negative_scale_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst))) + (((dst_negative_code_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)) * S ((dst_negative_code_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)) + ((dst_negative_scale_scalar_secondfirst) + (dst_negative_scale_scalar_secondfirst)))))) /\ (((((exists ff_h_pvs_scalar_secondfirstpositive. ff_h_pvs_scalar_secondfirstpositive + S (dst_positive_scalar_secondfirst) = S ((S (mp_a_scalar_second)) * dst_positive_scale_scalar_secondfirst)) /\ exists ff_q_pvs_scalar_secondfirstpositive. dst_positive_code_scalar_secondfirst = ff_q_pvs_scalar_secondfirstpositive * S ((S (mp_a_scalar_second)) * dst_positive_scale_scalar_secondfirst) + (dst_positive_scalar_secondfirst))) /\ (((((exists ff_h_pvs_scalar_secondfirstnegative. ff_h_pvs_scalar_secondfirstnegative + S (dst_negative_scalar_secondfirst) = S ((S (mp_a_scalar_second)) * dst_negative_scale_scalar_secondfirst)) /\ exists ff_q_pvs_scalar_secondfirstnegative. dst_negative_code_scalar_secondfirst = ff_q_pvs_scalar_secondfirstnegative * S ((S (mp_a_scalar_second)) * dst_negative_scale_scalar_secondfirst) + (dst_negative_scalar_secondfirst))) /\ (exists ge_balance_positive_scalar_secondfirstvalue ge_balance_negative_scalar_secondfirstvalue. (((((mp_x_scalar_second) = 2 * (ge_balance_positive_scalar_secondfirstvalue) /\ (ge_balance_negative_scalar_secondfirstvalue) = 0) \/ exists ge_signed_half_scalar_secondfirstvaluedecode. (((mp_x_scalar_second) = 2 * ge_signed_half_scalar_secondfirstvaluedecode + 1 /\ (ge_balance_positive_scalar_secondfirstvalue) = 0) /\ (ge_balance_negative_scalar_secondfirstvalue) = S ge_signed_half_scalar_secondfirstvaluedecode))) /\ ((dst_positive_scalar_secondfirst) + ge_balance_negative_scalar_secondfirstvalue = (dst_negative_scalar_secondfirst) + ge_balance_positive_scalar_secondfirstvalue))))))))) -> (exists dst_positive_code_scalar_secondsecond dst_positive_scale_scalar_secondsecond dst_negative_code_scalar_secondsecond dst_negative_scale_scalar_secondsecond dst_positive_scalar_secondsecond dst_negative_scalar_secondsecond. (((G) = (((((dst_positive_code_scalar_secondsecond) + (dst_positive_scale_scalar_secondsecond)) * S ((dst_positive_code_scalar_secondsecond) + (dst_positive_scale_scalar_secondsecond)) + ((dst_positive_scale_scalar_secondsecond) + (dst_positive_scale_scalar_secondsecond))) + (((dst_negative_code_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)) * S ((dst_negative_code_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)) + ((dst_negative_scale_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)))) * S ((((dst_positive_code_scalar_secondsecond) + (dst_positive_scale_scalar_secondsecond)) * S ((dst_positive_code_scalar_secondsecond) + (dst_positive_scale_scalar_secondsecond)) + ((dst_positive_scale_scalar_secondsecond) + (dst_positive_scale_scalar_secondsecond))) + (((dst_negative_code_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)) * S ((dst_negative_code_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)) + ((dst_negative_scale_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)))) + ((((dst_negative_code_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)) * S ((dst_negative_code_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)) + ((dst_negative_scale_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond))) + (((dst_negative_code_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)) * S ((dst_negative_code_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)) + ((dst_negative_scale_scalar_secondsecond) + (dst_negative_scale_scalar_secondsecond)))))) /\ (((((exists ff_h_pvs_scalar_secondsecondpositive. ff_h_pvs_scalar_secondsecondpositive + S (dst_positive_scalar_secondsecond) = S ((S (mp_b_scalar_second)) * dst_positive_scale_scalar_secondsecond)) /\ exists ff_q_pvs_scalar_secondsecondpositive. dst_positive_code_scalar_secondsecond = ff_q_pvs_scalar_secondsecondpositive * S ((S (mp_b_scalar_second)) * dst_positive_scale_scalar_secondsecond) + (dst_positive_scalar_secondsecond))) /\ (((((exists ff_h_pvs_scalar_secondsecondnegative. ff_h_pvs_scalar_secondsecondnegative + S (dst_negative_scalar_secondsecond) = S ((S (mp_b_scalar_second)) * dst_negative_scale_scalar_secondsecond)) /\ exists ff_q_pvs_scalar_secondsecondnegative. dst_negative_code_scalar_secondsecond = ff_q_pvs_scalar_secondsecondnegative * S ((S (mp_b_scalar_second)) * dst_negative_scale_scalar_secondsecond) + (dst_negative_scalar_secondsecond))) /\ (exists ge_balance_positive_scalar_secondsecondvalue ge_balance_negative_scalar_secondsecondvalue. (((((mp_y_scalar_second) = 2 * (ge_balance_positive_scalar_secondsecondvalue) /\ (ge_balance_negative_scalar_secondsecondvalue) = 0) \/ exists ge_signed_half_scalar_secondsecondvaluedecode. (((mp_y_scalar_second) = 2 * ge_signed_half_scalar_secondsecondvaluedecode + 1 /\ (ge_balance_positive_scalar_secondsecondvalue) = 0) /\ (ge_balance_negative_scalar_secondsecondvalue) = S ge_signed_half_scalar_secondsecondvaluedecode))) /\ ((dst_positive_scalar_secondsecond) + ge_balance_negative_scalar_secondsecondvalue = (dst_negative_scalar_secondsecond) + ge_balance_positive_scalar_secondsecondvalue))))))))) -> (exists dst_positive_code_scalar_secondproduct dst_positive_scale_scalar_secondproduct dst_negative_code_scalar_secondproduct dst_negative_scale_scalar_secondproduct dst_positive_scalar_secondproduct dst_negative_scalar_secondproduct. (((G) = (((((dst_positive_code_scalar_secondproduct) + (dst_positive_scale_scalar_secondproduct)) * S ((dst_positive_code_scalar_secondproduct) + (dst_positive_scale_scalar_secondproduct)) + ((dst_positive_scale_scalar_secondproduct) + (dst_positive_scale_scalar_secondproduct))) + (((dst_negative_code_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)) * S ((dst_negative_code_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)) + ((dst_negative_scale_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)))) * S ((((dst_positive_code_scalar_secondproduct) + (dst_positive_scale_scalar_secondproduct)) * S ((dst_positive_code_scalar_secondproduct) + (dst_positive_scale_scalar_secondproduct)) + ((dst_positive_scale_scalar_secondproduct) + (dst_positive_scale_scalar_secondproduct))) + (((dst_negative_code_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)) * S ((dst_negative_code_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)) + ((dst_negative_scale_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)))) + ((((dst_negative_code_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)) * S ((dst_negative_code_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)) + ((dst_negative_scale_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct))) + (((dst_negative_code_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)) * S ((dst_negative_code_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)) + ((dst_negative_scale_scalar_secondproduct) + (dst_negative_scale_scalar_secondproduct)))))) /\ (((((exists ff_h_pvs_scalar_secondproductpositive. ff_h_pvs_scalar_secondproductpositive + S (dst_positive_scalar_secondproduct) = S ((S (mp_a_scalar_second*mp_b_scalar_second)) * dst_positive_scale_scalar_secondproduct)) /\ exists ff_q_pvs_scalar_secondproductpositive. dst_positive_code_scalar_secondproduct = ff_q_pvs_scalar_secondproductpositive * S ((S (mp_a_scalar_second*mp_b_scalar_second)) * dst_positive_scale_scalar_secondproduct) + (dst_positive_scalar_secondproduct))) /\ (((((exists ff_h_pvs_scalar_secondproductnegative. ff_h_pvs_scalar_secondproductnegative + S (dst_negative_scalar_secondproduct) = S ((S (mp_a_scalar_second*mp_b_scalar_second)) * dst_negative_scale_scalar_secondproduct)) /\ exists ff_q_pvs_scalar_secondproductnegative. dst_negative_code_scalar_secondproduct = ff_q_pvs_scalar_secondproductnegative * S ((S (mp_a_scalar_second*mp_b_scalar_second)) * dst_negative_scale_scalar_secondproduct) + (dst_negative_scalar_secondproduct))) /\ (exists ge_balance_positive_scalar_secondproductvalue ge_balance_negative_scalar_secondproductvalue. (((((mp_z_scalar_second) = 2 * (ge_balance_positive_scalar_secondproductvalue) /\ (ge_balance_negative_scalar_secondproductvalue) = 0) \/ exists ge_signed_half_scalar_secondproductvaluedecode. (((mp_z_scalar_second) = 2 * ge_signed_half_scalar_secondproductvaluedecode + 1 /\ (ge_balance_positive_scalar_secondproductvalue) = 0) /\ (ge_balance_negative_scalar_secondproductvalue) = S ge_signed_half_scalar_secondproductvaluedecode))) /\ ((dst_positive_scalar_secondproduct) + ge_balance_negative_scalar_secondproductvalue = (dst_negative_scalar_secondproduct) + ge_balance_positive_scalar_secondproductvalue))))))))) -> (exists sto_ap_scalar_secondlaw sto_an_scalar_secondlaw sto_bp_scalar_secondlaw sto_bn_scalar_secondlaw sto_cp_scalar_secondlaw sto_cn_scalar_secondlaw. (((((mp_x_scalar_second) = 2 * (sto_ap_scalar_secondlaw) /\ (sto_an_scalar_secondlaw) = 0) \/ exists ge_signed_half_scalar_secondlawleft. (((mp_x_scalar_second) = 2 * ge_signed_half_scalar_secondlawleft + 1 /\ (sto_ap_scalar_secondlaw) = 0) /\ (sto_an_scalar_secondlaw) = S ge_signed_half_scalar_secondlawleft))) /\ ((((((mp_y_scalar_second) = 2 * (sto_bp_scalar_secondlaw) /\ (sto_bn_scalar_secondlaw) = 0) \/ exists ge_signed_half_scalar_secondlawright. (((mp_y_scalar_second) = 2 * ge_signed_half_scalar_secondlawright + 1 /\ (sto_bp_scalar_secondlaw) = 0) /\ (sto_bn_scalar_secondlaw) = S ge_signed_half_scalar_secondlawright))) /\ ((((((mp_z_scalar_second) = 2 * (sto_cp_scalar_secondlaw) /\ (sto_cn_scalar_secondlaw) = 0) \/ exists ge_signed_half_scalar_secondlawoutput. (((mp_z_scalar_second) = 2 * ge_signed_half_scalar_secondlawoutput + 1 /\ (sto_cp_scalar_secondlaw) = 0) /\ (sto_cn_scalar_secondlaw) = S ge_signed_half_scalar_secondlawoutput))) /\ ((sto_ap_scalar_secondlaw * sto_bp_scalar_secondlaw + sto_an_scalar_secondlaw * sto_bn_scalar_secondlaw) + sto_cn_scalar_secondlaw = (sto_ap_scalar_secondlaw * sto_bn_scalar_secondlaw + sto_an_scalar_secondlaw * sto_bp_scalar_secondlaw) + sto_cp_scalar_secondlaw)))))))))))))) -> (~(m=0)) -> (~(n=0)) -> (exists pvs_le_gap_scalar_bound. pvs_le_gap_scalar_bound + (m*n) = (N)) -> (forall sfd_common_divisor_scalar_coprime. (exists pvs_factor_scalar_coprimeleft. (m) = (sfd_common_divisor_scalar_coprime) * pvs_factor_scalar_coprimeleft) -> (exists pvs_factor_scalar_coprimeright. (n) = (sfd_common_divisor_scalar_coprime) * pvs_factor_scalar_coprimeright) -> sfd_common_divisor_scalar_coprime = 1) -> (((~((m)=0)) /\ (exists dc_mask_scalar_left_sum. ((((exists dst_positive_code_scalar_left_summasktable dst_positive_scale_scalar_left_summasktable dst_negative_code_scalar_left_summasktable dst_negative_scale_scalar_left_summasktable. (((dc_mask_scalar_left_sum) = (((((dst_positive_code_scalar_left_summasktable) + (dst_positive_scale_scalar_left_summasktable)) * S ((dst_positive_code_scalar_left_summasktable) + (dst_positive_scale_scalar_left_summasktable)) + ((dst_positive_scale_scalar_left_summasktable) + (dst_positive_scale_scalar_left_summasktable))) + (((dst_negative_code_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)) * S ((dst_negative_code_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)) + ((dst_negative_scale_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)))) * S ((((dst_positive_code_scalar_left_summasktable) + (dst_positive_scale_scalar_left_summasktable)) * S ((dst_positive_code_scalar_left_summasktable) + (dst_positive_scale_scalar_left_summasktable)) + ((dst_positive_scale_scalar_left_summasktable) + (dst_positive_scale_scalar_left_summasktable))) + (((dst_negative_code_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)) * S ((dst_negative_code_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)) + ((dst_negative_scale_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)))) + ((((dst_negative_code_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)) * S ((dst_negative_code_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)) + ((dst_negative_scale_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable))) + (((dst_negative_code_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)) * S ((dst_negative_code_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)) + ((dst_negative_scale_scalar_left_summasktable) + (dst_negative_scale_scalar_left_summasktable)))))) /\ (forall dst_index_scalar_left_summasktable. (exists pvs_le_gap_scalar_left_summasktabledomain. pvs_le_gap_scalar_left_summasktabledomain + (dst_index_scalar_left_summasktable) = (m)) -> exists dst_positive_scalar_left_summasktable dst_negative_scalar_left_summasktable dst_value_scalar_left_summasktable. ((((exists ff_h_pvs_scalar_left_summasktableentrypositive. ff_h_pvs_scalar_left_summasktableentrypositive + S (dst_positive_scalar_left_summasktable) = S ((S (dst_index_scalar_left_summasktable)) * dst_positive_scale_scalar_left_summasktable)) /\ exists ff_q_pvs_scalar_left_summasktableentrypositive. dst_positive_code_scalar_left_summasktable = ff_q_pvs_scalar_left_summasktableentrypositive * S ((S (dst_index_scalar_left_summasktable)) * dst_positive_scale_scalar_left_summasktable) + (dst_positive_scalar_left_summasktable))) /\ (((((exists ff_h_pvs_scalar_left_summasktableentrynegative. ff_h_pvs_scalar_left_summasktableentrynegative + S (dst_negative_scalar_left_summasktable) = S ((S (dst_index_scalar_left_summasktable)) * dst_negative_scale_scalar_left_summasktable)) /\ exists ff_q_pvs_scalar_left_summasktableentrynegative. dst_negative_code_scalar_left_summasktable = ff_q_pvs_scalar_left_summasktableentrynegative * S ((S (dst_index_scalar_left_summasktable)) * dst_negative_scale_scalar_left_summasktable) + (dst_negative_scalar_left_summasktable))) /\ (exists ge_balance_positive_scalar_left_summasktableentryvalue ge_balance_negative_scalar_left_summasktableentryvalue. (((((dst_value_scalar_left_summasktable) = 2 * (ge_balance_positive_scalar_left_summasktableentryvalue) /\ (ge_balance_negative_scalar_left_summasktableentryvalue) = 0) \/ exists ge_signed_half_scalar_left_summasktableentryvaluedecode. (((dst_value_scalar_left_summasktable) = 2 * ge_signed_half_scalar_left_summasktableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_left_summasktableentryvalue) = 0) /\ (ge_balance_negative_scalar_left_summasktableentryvalue) = S ge_signed_half_scalar_left_summasktableentryvaluedecode))) /\ ((dst_positive_scalar_left_summasktable) + ge_balance_negative_scalar_left_summasktableentryvalue = (dst_negative_scalar_left_summasktable) + ge_balance_positive_scalar_left_summasktableentryvalue))))))))) /\ (forall dc_index_scalar_left_summask dc_value_scalar_left_summask. (exists pvs_le_gap_scalar_left_summaskdomain. pvs_le_gap_scalar_left_summaskdomain + (dc_index_scalar_left_summask) = (m)) -> (exists dst_positive_code_scalar_left_summasklookup dst_positive_scale_scalar_left_summasklookup dst_negative_code_scalar_left_summasklookup dst_negative_scale_scalar_left_summasklookup dst_positive_scalar_left_summasklookup dst_negative_scalar_left_summasklookup. (((dc_mask_scalar_left_sum) = (((((dst_positive_code_scalar_left_summasklookup) + (dst_positive_scale_scalar_left_summasklookup)) * S ((dst_positive_code_scalar_left_summasklookup) + (dst_positive_scale_scalar_left_summasklookup)) + ((dst_positive_scale_scalar_left_summasklookup) + (dst_positive_scale_scalar_left_summasklookup))) + (((dst_negative_code_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)) * S ((dst_negative_code_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)) + ((dst_negative_scale_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)))) * S ((((dst_positive_code_scalar_left_summasklookup) + (dst_positive_scale_scalar_left_summasklookup)) * S ((dst_positive_code_scalar_left_summasklookup) + (dst_positive_scale_scalar_left_summasklookup)) + ((dst_positive_scale_scalar_left_summasklookup) + (dst_positive_scale_scalar_left_summasklookup))) + (((dst_negative_code_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)) * S ((dst_negative_code_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)) + ((dst_negative_scale_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)))) + ((((dst_negative_code_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)) * S ((dst_negative_code_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)) + ((dst_negative_scale_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup))) + (((dst_negative_code_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)) * S ((dst_negative_code_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)) + ((dst_negative_scale_scalar_left_summasklookup) + (dst_negative_scale_scalar_left_summasklookup)))))) /\ (((((exists ff_h_pvs_scalar_left_summasklookuppositive. ff_h_pvs_scalar_left_summasklookuppositive + S (dst_positive_scalar_left_summasklookup) = S ((S (dc_index_scalar_left_summask)) * dst_positive_scale_scalar_left_summasklookup)) /\ exists ff_q_pvs_scalar_left_summasklookuppositive. dst_positive_code_scalar_left_summasklookup = ff_q_pvs_scalar_left_summasklookuppositive * S ((S (dc_index_scalar_left_summask)) * dst_positive_scale_scalar_left_summasklookup) + (dst_positive_scalar_left_summasklookup))) /\ (((((exists ff_h_pvs_scalar_left_summasklookupnegative. ff_h_pvs_scalar_left_summasklookupnegative + S (dst_negative_scalar_left_summasklookup) = S ((S (dc_index_scalar_left_summask)) * dst_negative_scale_scalar_left_summasklookup)) /\ exists ff_q_pvs_scalar_left_summasklookupnegative. dst_negative_code_scalar_left_summasklookup = ff_q_pvs_scalar_left_summasklookupnegative * S ((S (dc_index_scalar_left_summask)) * dst_negative_scale_scalar_left_summasklookup) + (dst_negative_scalar_left_summasklookup))) /\ (exists ge_balance_positive_scalar_left_summasklookupvalue ge_balance_negative_scalar_left_summasklookupvalue. (((((dc_value_scalar_left_summask) = 2 * (ge_balance_positive_scalar_left_summasklookupvalue) /\ (ge_balance_negative_scalar_left_summasklookupvalue) = 0) \/ exists ge_signed_half_scalar_left_summasklookupvaluedecode. (((dc_value_scalar_left_summask) = 2 * ge_signed_half_scalar_left_summasklookupvaluedecode + 1 /\ (ge_balance_positive_scalar_left_summasklookupvalue) = 0) /\ (ge_balance_negative_scalar_left_summasklookupvalue) = S ge_signed_half_scalar_left_summasklookupvaluedecode))) /\ ((dst_positive_scalar_left_summasklookup) + ge_balance_negative_scalar_left_summasklookupvalue = (dst_negative_scalar_left_summasklookup) + ge_balance_positive_scalar_left_summasklookupvalue))))))))) -> ((((~((dc_index_scalar_left_summask)=0)) /\ (exists dc_quotient_scalar_left_summaskentry dc_left_scalar_left_summaskentry dc_right_scalar_left_summaskentry. (((m)=(dc_index_scalar_left_summask)*dc_quotient_scalar_left_summaskentry) /\ (((exists dst_positive_code_scalar_left_summaskentryleft dst_positive_scale_scalar_left_summaskentryleft dst_negative_code_scalar_left_summaskentryleft dst_negative_scale_scalar_left_summaskentryleft dst_positive_scalar_left_summaskentryleft dst_negative_scalar_left_summaskentryleft. (((F) = (((((dst_positive_code_scalar_left_summaskentryleft) + (dst_positive_scale_scalar_left_summaskentryleft)) * S ((dst_positive_code_scalar_left_summaskentryleft) + (dst_positive_scale_scalar_left_summaskentryleft)) + ((dst_positive_scale_scalar_left_summaskentryleft) + (dst_positive_scale_scalar_left_summaskentryleft))) + (((dst_negative_code_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)) * S ((dst_negative_code_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)) + ((dst_negative_scale_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)))) * S ((((dst_positive_code_scalar_left_summaskentryleft) + (dst_positive_scale_scalar_left_summaskentryleft)) * S ((dst_positive_code_scalar_left_summaskentryleft) + (dst_positive_scale_scalar_left_summaskentryleft)) + ((dst_positive_scale_scalar_left_summaskentryleft) + (dst_positive_scale_scalar_left_summaskentryleft))) + (((dst_negative_code_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)) * S ((dst_negative_code_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)) + ((dst_negative_scale_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)))) + ((((dst_negative_code_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)) * S ((dst_negative_code_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)) + ((dst_negative_scale_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft))) + (((dst_negative_code_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)) * S ((dst_negative_code_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)) + ((dst_negative_scale_scalar_left_summaskentryleft) + (dst_negative_scale_scalar_left_summaskentryleft)))))) /\ (((((exists ff_h_pvs_scalar_left_summaskentryleftpositive. ff_h_pvs_scalar_left_summaskentryleftpositive + S (dst_positive_scalar_left_summaskentryleft) = S ((S (dc_index_scalar_left_summask)) * dst_positive_scale_scalar_left_summaskentryleft)) /\ exists ff_q_pvs_scalar_left_summaskentryleftpositive. dst_positive_code_scalar_left_summaskentryleft = ff_q_pvs_scalar_left_summaskentryleftpositive * S ((S (dc_index_scalar_left_summask)) * dst_positive_scale_scalar_left_summaskentryleft) + (dst_positive_scalar_left_summaskentryleft))) /\ (((((exists ff_h_pvs_scalar_left_summaskentryleftnegative. ff_h_pvs_scalar_left_summaskentryleftnegative + S (dst_negative_scalar_left_summaskentryleft) = S ((S (dc_index_scalar_left_summask)) * dst_negative_scale_scalar_left_summaskentryleft)) /\ exists ff_q_pvs_scalar_left_summaskentryleftnegative. dst_negative_code_scalar_left_summaskentryleft = ff_q_pvs_scalar_left_summaskentryleftnegative * S ((S (dc_index_scalar_left_summask)) * dst_negative_scale_scalar_left_summaskentryleft) + (dst_negative_scalar_left_summaskentryleft))) /\ (exists ge_balance_positive_scalar_left_summaskentryleftvalue ge_balance_negative_scalar_left_summaskentryleftvalue. (((((dc_left_scalar_left_summaskentry) = 2 * (ge_balance_positive_scalar_left_summaskentryleftvalue) /\ (ge_balance_negative_scalar_left_summaskentryleftvalue) = 0) \/ exists ge_signed_half_scalar_left_summaskentryleftvaluedecode. (((dc_left_scalar_left_summaskentry) = 2 * ge_signed_half_scalar_left_summaskentryleftvaluedecode + 1 /\ (ge_balance_positive_scalar_left_summaskentryleftvalue) = 0) /\ (ge_balance_negative_scalar_left_summaskentryleftvalue) = S ge_signed_half_scalar_left_summaskentryleftvaluedecode))) /\ ((dst_positive_scalar_left_summaskentryleft) + ge_balance_negative_scalar_left_summaskentryleftvalue = (dst_negative_scalar_left_summaskentryleft) + ge_balance_positive_scalar_left_summaskentryleftvalue))))))))) /\ (((exists dst_positive_code_scalar_left_summaskentryright dst_positive_scale_scalar_left_summaskentryright dst_negative_code_scalar_left_summaskentryright dst_negative_scale_scalar_left_summaskentryright dst_positive_scalar_left_summaskentryright dst_negative_scalar_left_summaskentryright. (((G) = (((((dst_positive_code_scalar_left_summaskentryright) + (dst_positive_scale_scalar_left_summaskentryright)) * S ((dst_positive_code_scalar_left_summaskentryright) + (dst_positive_scale_scalar_left_summaskentryright)) + ((dst_positive_scale_scalar_left_summaskentryright) + (dst_positive_scale_scalar_left_summaskentryright))) + (((dst_negative_code_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)) * S ((dst_negative_code_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)) + ((dst_negative_scale_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)))) * S ((((dst_positive_code_scalar_left_summaskentryright) + (dst_positive_scale_scalar_left_summaskentryright)) * S ((dst_positive_code_scalar_left_summaskentryright) + (dst_positive_scale_scalar_left_summaskentryright)) + ((dst_positive_scale_scalar_left_summaskentryright) + (dst_positive_scale_scalar_left_summaskentryright))) + (((dst_negative_code_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)) * S ((dst_negative_code_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)) + ((dst_negative_scale_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)))) + ((((dst_negative_code_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)) * S ((dst_negative_code_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)) + ((dst_negative_scale_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright))) + (((dst_negative_code_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)) * S ((dst_negative_code_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)) + ((dst_negative_scale_scalar_left_summaskentryright) + (dst_negative_scale_scalar_left_summaskentryright)))))) /\ (((((exists ff_h_pvs_scalar_left_summaskentryrightpositive. ff_h_pvs_scalar_left_summaskentryrightpositive + S (dst_positive_scalar_left_summaskentryright) = S ((S (dc_quotient_scalar_left_summaskentry)) * dst_positive_scale_scalar_left_summaskentryright)) /\ exists ff_q_pvs_scalar_left_summaskentryrightpositive. dst_positive_code_scalar_left_summaskentryright = ff_q_pvs_scalar_left_summaskentryrightpositive * S ((S (dc_quotient_scalar_left_summaskentry)) * dst_positive_scale_scalar_left_summaskentryright) + (dst_positive_scalar_left_summaskentryright))) /\ (((((exists ff_h_pvs_scalar_left_summaskentryrightnegative. ff_h_pvs_scalar_left_summaskentryrightnegative + S (dst_negative_scalar_left_summaskentryright) = S ((S (dc_quotient_scalar_left_summaskentry)) * dst_negative_scale_scalar_left_summaskentryright)) /\ exists ff_q_pvs_scalar_left_summaskentryrightnegative. dst_negative_code_scalar_left_summaskentryright = ff_q_pvs_scalar_left_summaskentryrightnegative * S ((S (dc_quotient_scalar_left_summaskentry)) * dst_negative_scale_scalar_left_summaskentryright) + (dst_negative_scalar_left_summaskentryright))) /\ (exists ge_balance_positive_scalar_left_summaskentryrightvalue ge_balance_negative_scalar_left_summaskentryrightvalue. (((((dc_right_scalar_left_summaskentry) = 2 * (ge_balance_positive_scalar_left_summaskentryrightvalue) /\ (ge_balance_negative_scalar_left_summaskentryrightvalue) = 0) \/ exists ge_signed_half_scalar_left_summaskentryrightvaluedecode. (((dc_right_scalar_left_summaskentry) = 2 * ge_signed_half_scalar_left_summaskentryrightvaluedecode + 1 /\ (ge_balance_positive_scalar_left_summaskentryrightvalue) = 0) /\ (ge_balance_negative_scalar_left_summaskentryrightvalue) = S ge_signed_half_scalar_left_summaskentryrightvaluedecode))) /\ ((dst_positive_scalar_left_summaskentryright) + ge_balance_negative_scalar_left_summaskentryrightvalue = (dst_negative_scalar_left_summaskentryright) + ge_balance_positive_scalar_left_summaskentryrightvalue))))))))) /\ (exists sto_ap_scalar_left_summaskentryproduct sto_an_scalar_left_summaskentryproduct sto_bp_scalar_left_summaskentryproduct sto_bn_scalar_left_summaskentryproduct sto_cp_scalar_left_summaskentryproduct sto_cn_scalar_left_summaskentryproduct. (((((dc_left_scalar_left_summaskentry) = 2 * (sto_ap_scalar_left_summaskentryproduct) /\ (sto_an_scalar_left_summaskentryproduct) = 0) \/ exists ge_signed_half_scalar_left_summaskentryproductleft. (((dc_left_scalar_left_summaskentry) = 2 * ge_signed_half_scalar_left_summaskentryproductleft + 1 /\ (sto_ap_scalar_left_summaskentryproduct) = 0) /\ (sto_an_scalar_left_summaskentryproduct) = S ge_signed_half_scalar_left_summaskentryproductleft))) /\ ((((((dc_right_scalar_left_summaskentry) = 2 * (sto_bp_scalar_left_summaskentryproduct) /\ (sto_bn_scalar_left_summaskentryproduct) = 0) \/ exists ge_signed_half_scalar_left_summaskentryproductright. (((dc_right_scalar_left_summaskentry) = 2 * ge_signed_half_scalar_left_summaskentryproductright + 1 /\ (sto_bp_scalar_left_summaskentryproduct) = 0) /\ (sto_bn_scalar_left_summaskentryproduct) = S ge_signed_half_scalar_left_summaskentryproductright))) /\ ((((((dc_value_scalar_left_summask) = 2 * (sto_cp_scalar_left_summaskentryproduct) /\ (sto_cn_scalar_left_summaskentryproduct) = 0) \/ exists ge_signed_half_scalar_left_summaskentryproductoutput. (((dc_value_scalar_left_summask) = 2 * ge_signed_half_scalar_left_summaskentryproductoutput + 1 /\ (sto_cp_scalar_left_summaskentryproduct) = 0) /\ (sto_cn_scalar_left_summaskentryproduct) = S ge_signed_half_scalar_left_summaskentryproductoutput))) /\ ((sto_ap_scalar_left_summaskentryproduct * sto_bp_scalar_left_summaskentryproduct + sto_an_scalar_left_summaskentryproduct * sto_bn_scalar_left_summaskentryproduct) + sto_cn_scalar_left_summaskentryproduct = (sto_ap_scalar_left_summaskentryproduct * sto_bn_scalar_left_summaskentryproduct + sto_an_scalar_left_summaskentryproduct * sto_bp_scalar_left_summaskentryproduct) + sto_cp_scalar_left_summaskentryproduct))))))))))))))) \/ ((((dc_index_scalar_left_summask)=0 \/ ~(exists pvs_factor_scalar_left_summaskentrynondivisor. (m) = (dc_index_scalar_left_summask) * pvs_factor_scalar_left_summaskentrynondivisor)) /\ ((dc_value_scalar_left_summask)=0))))))) /\ (exists dst_positive_code_scalar_left_sumfold dst_positive_scale_scalar_left_sumfold dst_negative_code_scalar_left_sumfold dst_negative_scale_scalar_left_sumfold dst_positive_sum_scalar_left_sumfold dst_negative_sum_scalar_left_sumfold. (((dc_mask_scalar_left_sum) = (((((dst_positive_code_scalar_left_sumfold) + (dst_positive_scale_scalar_left_sumfold)) * S ((dst_positive_code_scalar_left_sumfold) + (dst_positive_scale_scalar_left_sumfold)) + ((dst_positive_scale_scalar_left_sumfold) + (dst_positive_scale_scalar_left_sumfold))) + (((dst_negative_code_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)) * S ((dst_negative_code_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)) + ((dst_negative_scale_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)))) * S ((((dst_positive_code_scalar_left_sumfold) + (dst_positive_scale_scalar_left_sumfold)) * S ((dst_positive_code_scalar_left_sumfold) + (dst_positive_scale_scalar_left_sumfold)) + ((dst_positive_scale_scalar_left_sumfold) + (dst_positive_scale_scalar_left_sumfold))) + (((dst_negative_code_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)) * S ((dst_negative_code_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)) + ((dst_negative_scale_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)))) + ((((dst_negative_code_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)) * S ((dst_negative_code_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)) + ((dst_negative_scale_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold))) + (((dst_negative_code_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)) * S ((dst_negative_code_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)) + ((dst_negative_scale_scalar_left_sumfold) + (dst_negative_scale_scalar_left_sumfold)))))) /\ (((exists fs_u_dst_scalar_left_sumfoldpositive fs_v_dst_scalar_left_sumfoldpositive. ((((exists fs_h_dst_scalar_left_sumfoldpositive_body_start. fs_h_dst_scalar_left_sumfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_left_sumfoldpositive)) /\ exists fs_q_dst_scalar_left_sumfoldpositive_body_start. fs_u_dst_scalar_left_sumfoldpositive = fs_q_dst_scalar_left_sumfoldpositive_body_start * S ((S (0)) * fs_v_dst_scalar_left_sumfoldpositive) + (0))) /\ ((((exists fs_h_dst_scalar_left_sumfoldpositive_body_terminal. fs_h_dst_scalar_left_sumfoldpositive_body_terminal + S (dst_positive_sum_scalar_left_sumfold) = S ((S (S (m))) * fs_v_dst_scalar_left_sumfoldpositive)) /\ exists fs_q_dst_scalar_left_sumfoldpositive_body_terminal. fs_u_dst_scalar_left_sumfoldpositive = fs_q_dst_scalar_left_sumfoldpositive_body_terminal * S ((S (S (m))) * fs_v_dst_scalar_left_sumfoldpositive) + (dst_positive_sum_scalar_left_sumfold))) /\ forall fs_i_dst_scalar_left_sumfoldpositive_body_steps. (exists fs_lt_dst_scalar_left_sumfoldpositive_body_steps_bound. fs_lt_dst_scalar_left_sumfoldpositive_body_steps_bound + S fs_i_dst_scalar_left_sumfoldpositive_body_steps = S (m)) -> exists fs_a_dst_scalar_left_sumfoldpositive_body_steps fs_r_dst_scalar_left_sumfoldpositive_body_steps fs_s_dst_scalar_left_sumfoldpositive_body_steps. ((((exists fs_h_dst_scalar_left_sumfoldpositive_body_steps_summand. fs_h_dst_scalar_left_sumfoldpositive_body_steps_summand + S (fs_a_dst_scalar_left_sumfoldpositive_body_steps) = S ((S (fs_i_dst_scalar_left_sumfoldpositive_body_steps)) * dst_positive_scale_scalar_left_sumfold)) /\ exists fs_q_dst_scalar_left_sumfoldpositive_body_steps_summand. dst_positive_code_scalar_left_sumfold = fs_q_dst_scalar_left_sumfoldpositive_body_steps_summand * S ((S (fs_i_dst_scalar_left_sumfoldpositive_body_steps)) * dst_positive_scale_scalar_left_sumfold) + (fs_a_dst_scalar_left_sumfoldpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_left_sumfoldpositive_body_steps_partial. fs_h_dst_scalar_left_sumfoldpositive_body_steps_partial + S (fs_r_dst_scalar_left_sumfoldpositive_body_steps) = S ((S (fs_i_dst_scalar_left_sumfoldpositive_body_steps)) * fs_v_dst_scalar_left_sumfoldpositive)) /\ exists fs_q_dst_scalar_left_sumfoldpositive_body_steps_partial. fs_u_dst_scalar_left_sumfoldpositive = fs_q_dst_scalar_left_sumfoldpositive_body_steps_partial * S ((S (fs_i_dst_scalar_left_sumfoldpositive_body_steps)) * fs_v_dst_scalar_left_sumfoldpositive) + (fs_r_dst_scalar_left_sumfoldpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_left_sumfoldpositive_body_steps_successor. fs_h_dst_scalar_left_sumfoldpositive_body_steps_successor + S (fs_s_dst_scalar_left_sumfoldpositive_body_steps) = S ((S (S fs_i_dst_scalar_left_sumfoldpositive_body_steps)) * fs_v_dst_scalar_left_sumfoldpositive)) /\ exists fs_q_dst_scalar_left_sumfoldpositive_body_steps_successor. fs_u_dst_scalar_left_sumfoldpositive = fs_q_dst_scalar_left_sumfoldpositive_body_steps_successor * S ((S (S fs_i_dst_scalar_left_sumfoldpositive_body_steps)) * fs_v_dst_scalar_left_sumfoldpositive) + (fs_s_dst_scalar_left_sumfoldpositive_body_steps))) /\ fs_s_dst_scalar_left_sumfoldpositive_body_steps = fs_r_dst_scalar_left_sumfoldpositive_body_steps + fs_a_dst_scalar_left_sumfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_scalar_left_sumfoldnegative fs_v_dst_scalar_left_sumfoldnegative. ((((exists fs_h_dst_scalar_left_sumfoldnegative_body_start. fs_h_dst_scalar_left_sumfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_left_sumfoldnegative)) /\ exists fs_q_dst_scalar_left_sumfoldnegative_body_start. fs_u_dst_scalar_left_sumfoldnegative = fs_q_dst_scalar_left_sumfoldnegative_body_start * S ((S (0)) * fs_v_dst_scalar_left_sumfoldnegative) + (0))) /\ ((((exists fs_h_dst_scalar_left_sumfoldnegative_body_terminal. fs_h_dst_scalar_left_sumfoldnegative_body_terminal + S (dst_negative_sum_scalar_left_sumfold) = S ((S (S (m))) * fs_v_dst_scalar_left_sumfoldnegative)) /\ exists fs_q_dst_scalar_left_sumfoldnegative_body_terminal. fs_u_dst_scalar_left_sumfoldnegative = fs_q_dst_scalar_left_sumfoldnegative_body_terminal * S ((S (S (m))) * fs_v_dst_scalar_left_sumfoldnegative) + (dst_negative_sum_scalar_left_sumfold))) /\ forall fs_i_dst_scalar_left_sumfoldnegative_body_steps. (exists fs_lt_dst_scalar_left_sumfoldnegative_body_steps_bound. fs_lt_dst_scalar_left_sumfoldnegative_body_steps_bound + S fs_i_dst_scalar_left_sumfoldnegative_body_steps = S (m)) -> exists fs_a_dst_scalar_left_sumfoldnegative_body_steps fs_r_dst_scalar_left_sumfoldnegative_body_steps fs_s_dst_scalar_left_sumfoldnegative_body_steps. ((((exists fs_h_dst_scalar_left_sumfoldnegative_body_steps_summand. fs_h_dst_scalar_left_sumfoldnegative_body_steps_summand + S (fs_a_dst_scalar_left_sumfoldnegative_body_steps) = S ((S (fs_i_dst_scalar_left_sumfoldnegative_body_steps)) * dst_negative_scale_scalar_left_sumfold)) /\ exists fs_q_dst_scalar_left_sumfoldnegative_body_steps_summand. dst_negative_code_scalar_left_sumfold = fs_q_dst_scalar_left_sumfoldnegative_body_steps_summand * S ((S (fs_i_dst_scalar_left_sumfoldnegative_body_steps)) * dst_negative_scale_scalar_left_sumfold) + (fs_a_dst_scalar_left_sumfoldnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_left_sumfoldnegative_body_steps_partial. fs_h_dst_scalar_left_sumfoldnegative_body_steps_partial + S (fs_r_dst_scalar_left_sumfoldnegative_body_steps) = S ((S (fs_i_dst_scalar_left_sumfoldnegative_body_steps)) * fs_v_dst_scalar_left_sumfoldnegative)) /\ exists fs_q_dst_scalar_left_sumfoldnegative_body_steps_partial. fs_u_dst_scalar_left_sumfoldnegative = fs_q_dst_scalar_left_sumfoldnegative_body_steps_partial * S ((S (fs_i_dst_scalar_left_sumfoldnegative_body_steps)) * fs_v_dst_scalar_left_sumfoldnegative) + (fs_r_dst_scalar_left_sumfoldnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_left_sumfoldnegative_body_steps_successor. fs_h_dst_scalar_left_sumfoldnegative_body_steps_successor + S (fs_s_dst_scalar_left_sumfoldnegative_body_steps) = S ((S (S fs_i_dst_scalar_left_sumfoldnegative_body_steps)) * fs_v_dst_scalar_left_sumfoldnegative)) /\ exists fs_q_dst_scalar_left_sumfoldnegative_body_steps_successor. fs_u_dst_scalar_left_sumfoldnegative = fs_q_dst_scalar_left_sumfoldnegative_body_steps_successor * S ((S (S fs_i_dst_scalar_left_sumfoldnegative_body_steps)) * fs_v_dst_scalar_left_sumfoldnegative) + (fs_s_dst_scalar_left_sumfoldnegative_body_steps))) /\ fs_s_dst_scalar_left_sumfoldnegative_body_steps = fs_r_dst_scalar_left_sumfoldnegative_body_steps + fs_a_dst_scalar_left_sumfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_scalar_left_sumfoldresult ge_balance_negative_scalar_left_sumfoldresult. (((((a) = 2 * (ge_balance_positive_scalar_left_sumfoldresult) /\ (ge_balance_negative_scalar_left_sumfoldresult) = 0) \/ exists ge_signed_half_scalar_left_sumfoldresultdecode. (((a) = 2 * ge_signed_half_scalar_left_sumfoldresultdecode + 1 /\ (ge_balance_positive_scalar_left_sumfoldresult) = 0) /\ (ge_balance_negative_scalar_left_sumfoldresult) = S ge_signed_half_scalar_left_sumfoldresultdecode))) /\ ((dst_positive_sum_scalar_left_sumfold) + ge_balance_negative_scalar_left_sumfoldresult = (dst_negative_sum_scalar_left_sumfold) + ge_balance_positive_scalar_left_sumfoldresult))))))))))))) -> (((~((n)=0)) /\ (exists dc_mask_scalar_right_sum. ((((exists dst_positive_code_scalar_right_summasktable dst_positive_scale_scalar_right_summasktable dst_negative_code_scalar_right_summasktable dst_negative_scale_scalar_right_summasktable. (((dc_mask_scalar_right_sum) = (((((dst_positive_code_scalar_right_summasktable) + (dst_positive_scale_scalar_right_summasktable)) * S ((dst_positive_code_scalar_right_summasktable) + (dst_positive_scale_scalar_right_summasktable)) + ((dst_positive_scale_scalar_right_summasktable) + (dst_positive_scale_scalar_right_summasktable))) + (((dst_negative_code_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)) * S ((dst_negative_code_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)) + ((dst_negative_scale_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)))) * S ((((dst_positive_code_scalar_right_summasktable) + (dst_positive_scale_scalar_right_summasktable)) * S ((dst_positive_code_scalar_right_summasktable) + (dst_positive_scale_scalar_right_summasktable)) + ((dst_positive_scale_scalar_right_summasktable) + (dst_positive_scale_scalar_right_summasktable))) + (((dst_negative_code_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)) * S ((dst_negative_code_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)) + ((dst_negative_scale_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)))) + ((((dst_negative_code_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)) * S ((dst_negative_code_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)) + ((dst_negative_scale_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable))) + (((dst_negative_code_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)) * S ((dst_negative_code_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)) + ((dst_negative_scale_scalar_right_summasktable) + (dst_negative_scale_scalar_right_summasktable)))))) /\ (forall dst_index_scalar_right_summasktable. (exists pvs_le_gap_scalar_right_summasktabledomain. pvs_le_gap_scalar_right_summasktabledomain + (dst_index_scalar_right_summasktable) = (n)) -> exists dst_positive_scalar_right_summasktable dst_negative_scalar_right_summasktable dst_value_scalar_right_summasktable. ((((exists ff_h_pvs_scalar_right_summasktableentrypositive. ff_h_pvs_scalar_right_summasktableentrypositive + S (dst_positive_scalar_right_summasktable) = S ((S (dst_index_scalar_right_summasktable)) * dst_positive_scale_scalar_right_summasktable)) /\ exists ff_q_pvs_scalar_right_summasktableentrypositive. dst_positive_code_scalar_right_summasktable = ff_q_pvs_scalar_right_summasktableentrypositive * S ((S (dst_index_scalar_right_summasktable)) * dst_positive_scale_scalar_right_summasktable) + (dst_positive_scalar_right_summasktable))) /\ (((((exists ff_h_pvs_scalar_right_summasktableentrynegative. ff_h_pvs_scalar_right_summasktableentrynegative + S (dst_negative_scalar_right_summasktable) = S ((S (dst_index_scalar_right_summasktable)) * dst_negative_scale_scalar_right_summasktable)) /\ exists ff_q_pvs_scalar_right_summasktableentrynegative. dst_negative_code_scalar_right_summasktable = ff_q_pvs_scalar_right_summasktableentrynegative * S ((S (dst_index_scalar_right_summasktable)) * dst_negative_scale_scalar_right_summasktable) + (dst_negative_scalar_right_summasktable))) /\ (exists ge_balance_positive_scalar_right_summasktableentryvalue ge_balance_negative_scalar_right_summasktableentryvalue. (((((dst_value_scalar_right_summasktable) = 2 * (ge_balance_positive_scalar_right_summasktableentryvalue) /\ (ge_balance_negative_scalar_right_summasktableentryvalue) = 0) \/ exists ge_signed_half_scalar_right_summasktableentryvaluedecode. (((dst_value_scalar_right_summasktable) = 2 * ge_signed_half_scalar_right_summasktableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_right_summasktableentryvalue) = 0) /\ (ge_balance_negative_scalar_right_summasktableentryvalue) = S ge_signed_half_scalar_right_summasktableentryvaluedecode))) /\ ((dst_positive_scalar_right_summasktable) + ge_balance_negative_scalar_right_summasktableentryvalue = (dst_negative_scalar_right_summasktable) + ge_balance_positive_scalar_right_summasktableentryvalue))))))))) /\ (forall dc_index_scalar_right_summask dc_value_scalar_right_summask. (exists pvs_le_gap_scalar_right_summaskdomain. pvs_le_gap_scalar_right_summaskdomain + (dc_index_scalar_right_summask) = (n)) -> (exists dst_positive_code_scalar_right_summasklookup dst_positive_scale_scalar_right_summasklookup dst_negative_code_scalar_right_summasklookup dst_negative_scale_scalar_right_summasklookup dst_positive_scalar_right_summasklookup dst_negative_scalar_right_summasklookup. (((dc_mask_scalar_right_sum) = (((((dst_positive_code_scalar_right_summasklookup) + (dst_positive_scale_scalar_right_summasklookup)) * S ((dst_positive_code_scalar_right_summasklookup) + (dst_positive_scale_scalar_right_summasklookup)) + ((dst_positive_scale_scalar_right_summasklookup) + (dst_positive_scale_scalar_right_summasklookup))) + (((dst_negative_code_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)) * S ((dst_negative_code_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)) + ((dst_negative_scale_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)))) * S ((((dst_positive_code_scalar_right_summasklookup) + (dst_positive_scale_scalar_right_summasklookup)) * S ((dst_positive_code_scalar_right_summasklookup) + (dst_positive_scale_scalar_right_summasklookup)) + ((dst_positive_scale_scalar_right_summasklookup) + (dst_positive_scale_scalar_right_summasklookup))) + (((dst_negative_code_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)) * S ((dst_negative_code_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)) + ((dst_negative_scale_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)))) + ((((dst_negative_code_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)) * S ((dst_negative_code_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)) + ((dst_negative_scale_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup))) + (((dst_negative_code_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)) * S ((dst_negative_code_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)) + ((dst_negative_scale_scalar_right_summasklookup) + (dst_negative_scale_scalar_right_summasklookup)))))) /\ (((((exists ff_h_pvs_scalar_right_summasklookuppositive. ff_h_pvs_scalar_right_summasklookuppositive + S (dst_positive_scalar_right_summasklookup) = S ((S (dc_index_scalar_right_summask)) * dst_positive_scale_scalar_right_summasklookup)) /\ exists ff_q_pvs_scalar_right_summasklookuppositive. dst_positive_code_scalar_right_summasklookup = ff_q_pvs_scalar_right_summasklookuppositive * S ((S (dc_index_scalar_right_summask)) * dst_positive_scale_scalar_right_summasklookup) + (dst_positive_scalar_right_summasklookup))) /\ (((((exists ff_h_pvs_scalar_right_summasklookupnegative. ff_h_pvs_scalar_right_summasklookupnegative + S (dst_negative_scalar_right_summasklookup) = S ((S (dc_index_scalar_right_summask)) * dst_negative_scale_scalar_right_summasklookup)) /\ exists ff_q_pvs_scalar_right_summasklookupnegative. dst_negative_code_scalar_right_summasklookup = ff_q_pvs_scalar_right_summasklookupnegative * S ((S (dc_index_scalar_right_summask)) * dst_negative_scale_scalar_right_summasklookup) + (dst_negative_scalar_right_summasklookup))) /\ (exists ge_balance_positive_scalar_right_summasklookupvalue ge_balance_negative_scalar_right_summasklookupvalue. (((((dc_value_scalar_right_summask) = 2 * (ge_balance_positive_scalar_right_summasklookupvalue) /\ (ge_balance_negative_scalar_right_summasklookupvalue) = 0) \/ exists ge_signed_half_scalar_right_summasklookupvaluedecode. (((dc_value_scalar_right_summask) = 2 * ge_signed_half_scalar_right_summasklookupvaluedecode + 1 /\ (ge_balance_positive_scalar_right_summasklookupvalue) = 0) /\ (ge_balance_negative_scalar_right_summasklookupvalue) = S ge_signed_half_scalar_right_summasklookupvaluedecode))) /\ ((dst_positive_scalar_right_summasklookup) + ge_balance_negative_scalar_right_summasklookupvalue = (dst_negative_scalar_right_summasklookup) + ge_balance_positive_scalar_right_summasklookupvalue))))))))) -> ((((~((dc_index_scalar_right_summask)=0)) /\ (exists dc_quotient_scalar_right_summaskentry dc_left_scalar_right_summaskentry dc_right_scalar_right_summaskentry. (((n)=(dc_index_scalar_right_summask)*dc_quotient_scalar_right_summaskentry) /\ (((exists dst_positive_code_scalar_right_summaskentryleft dst_positive_scale_scalar_right_summaskentryleft dst_negative_code_scalar_right_summaskentryleft dst_negative_scale_scalar_right_summaskentryleft dst_positive_scalar_right_summaskentryleft dst_negative_scalar_right_summaskentryleft. (((F) = (((((dst_positive_code_scalar_right_summaskentryleft) + (dst_positive_scale_scalar_right_summaskentryleft)) * S ((dst_positive_code_scalar_right_summaskentryleft) + (dst_positive_scale_scalar_right_summaskentryleft)) + ((dst_positive_scale_scalar_right_summaskentryleft) + (dst_positive_scale_scalar_right_summaskentryleft))) + (((dst_negative_code_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)) * S ((dst_negative_code_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)) + ((dst_negative_scale_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)))) * S ((((dst_positive_code_scalar_right_summaskentryleft) + (dst_positive_scale_scalar_right_summaskentryleft)) * S ((dst_positive_code_scalar_right_summaskentryleft) + (dst_positive_scale_scalar_right_summaskentryleft)) + ((dst_positive_scale_scalar_right_summaskentryleft) + (dst_positive_scale_scalar_right_summaskentryleft))) + (((dst_negative_code_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)) * S ((dst_negative_code_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)) + ((dst_negative_scale_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)))) + ((((dst_negative_code_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)) * S ((dst_negative_code_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)) + ((dst_negative_scale_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft))) + (((dst_negative_code_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)) * S ((dst_negative_code_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)) + ((dst_negative_scale_scalar_right_summaskentryleft) + (dst_negative_scale_scalar_right_summaskentryleft)))))) /\ (((((exists ff_h_pvs_scalar_right_summaskentryleftpositive. ff_h_pvs_scalar_right_summaskentryleftpositive + S (dst_positive_scalar_right_summaskentryleft) = S ((S (dc_index_scalar_right_summask)) * dst_positive_scale_scalar_right_summaskentryleft)) /\ exists ff_q_pvs_scalar_right_summaskentryleftpositive. dst_positive_code_scalar_right_summaskentryleft = ff_q_pvs_scalar_right_summaskentryleftpositive * S ((S (dc_index_scalar_right_summask)) * dst_positive_scale_scalar_right_summaskentryleft) + (dst_positive_scalar_right_summaskentryleft))) /\ (((((exists ff_h_pvs_scalar_right_summaskentryleftnegative. ff_h_pvs_scalar_right_summaskentryleftnegative + S (dst_negative_scalar_right_summaskentryleft) = S ((S (dc_index_scalar_right_summask)) * dst_negative_scale_scalar_right_summaskentryleft)) /\ exists ff_q_pvs_scalar_right_summaskentryleftnegative. dst_negative_code_scalar_right_summaskentryleft = ff_q_pvs_scalar_right_summaskentryleftnegative * S ((S (dc_index_scalar_right_summask)) * dst_negative_scale_scalar_right_summaskentryleft) + (dst_negative_scalar_right_summaskentryleft))) /\ (exists ge_balance_positive_scalar_right_summaskentryleftvalue ge_balance_negative_scalar_right_summaskentryleftvalue. (((((dc_left_scalar_right_summaskentry) = 2 * (ge_balance_positive_scalar_right_summaskentryleftvalue) /\ (ge_balance_negative_scalar_right_summaskentryleftvalue) = 0) \/ exists ge_signed_half_scalar_right_summaskentryleftvaluedecode. (((dc_left_scalar_right_summaskentry) = 2 * ge_signed_half_scalar_right_summaskentryleftvaluedecode + 1 /\ (ge_balance_positive_scalar_right_summaskentryleftvalue) = 0) /\ (ge_balance_negative_scalar_right_summaskentryleftvalue) = S ge_signed_half_scalar_right_summaskentryleftvaluedecode))) /\ ((dst_positive_scalar_right_summaskentryleft) + ge_balance_negative_scalar_right_summaskentryleftvalue = (dst_negative_scalar_right_summaskentryleft) + ge_balance_positive_scalar_right_summaskentryleftvalue))))))))) /\ (((exists dst_positive_code_scalar_right_summaskentryright dst_positive_scale_scalar_right_summaskentryright dst_negative_code_scalar_right_summaskentryright dst_negative_scale_scalar_right_summaskentryright dst_positive_scalar_right_summaskentryright dst_negative_scalar_right_summaskentryright. (((G) = (((((dst_positive_code_scalar_right_summaskentryright) + (dst_positive_scale_scalar_right_summaskentryright)) * S ((dst_positive_code_scalar_right_summaskentryright) + (dst_positive_scale_scalar_right_summaskentryright)) + ((dst_positive_scale_scalar_right_summaskentryright) + (dst_positive_scale_scalar_right_summaskentryright))) + (((dst_negative_code_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)) * S ((dst_negative_code_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)) + ((dst_negative_scale_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)))) * S ((((dst_positive_code_scalar_right_summaskentryright) + (dst_positive_scale_scalar_right_summaskentryright)) * S ((dst_positive_code_scalar_right_summaskentryright) + (dst_positive_scale_scalar_right_summaskentryright)) + ((dst_positive_scale_scalar_right_summaskentryright) + (dst_positive_scale_scalar_right_summaskentryright))) + (((dst_negative_code_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)) * S ((dst_negative_code_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)) + ((dst_negative_scale_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)))) + ((((dst_negative_code_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)) * S ((dst_negative_code_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)) + ((dst_negative_scale_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright))) + (((dst_negative_code_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)) * S ((dst_negative_code_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)) + ((dst_negative_scale_scalar_right_summaskentryright) + (dst_negative_scale_scalar_right_summaskentryright)))))) /\ (((((exists ff_h_pvs_scalar_right_summaskentryrightpositive. ff_h_pvs_scalar_right_summaskentryrightpositive + S (dst_positive_scalar_right_summaskentryright) = S ((S (dc_quotient_scalar_right_summaskentry)) * dst_positive_scale_scalar_right_summaskentryright)) /\ exists ff_q_pvs_scalar_right_summaskentryrightpositive. dst_positive_code_scalar_right_summaskentryright = ff_q_pvs_scalar_right_summaskentryrightpositive * S ((S (dc_quotient_scalar_right_summaskentry)) * dst_positive_scale_scalar_right_summaskentryright) + (dst_positive_scalar_right_summaskentryright))) /\ (((((exists ff_h_pvs_scalar_right_summaskentryrightnegative. ff_h_pvs_scalar_right_summaskentryrightnegative + S (dst_negative_scalar_right_summaskentryright) = S ((S (dc_quotient_scalar_right_summaskentry)) * dst_negative_scale_scalar_right_summaskentryright)) /\ exists ff_q_pvs_scalar_right_summaskentryrightnegative. dst_negative_code_scalar_right_summaskentryright = ff_q_pvs_scalar_right_summaskentryrightnegative * S ((S (dc_quotient_scalar_right_summaskentry)) * dst_negative_scale_scalar_right_summaskentryright) + (dst_negative_scalar_right_summaskentryright))) /\ (exists ge_balance_positive_scalar_right_summaskentryrightvalue ge_balance_negative_scalar_right_summaskentryrightvalue. (((((dc_right_scalar_right_summaskentry) = 2 * (ge_balance_positive_scalar_right_summaskentryrightvalue) /\ (ge_balance_negative_scalar_right_summaskentryrightvalue) = 0) \/ exists ge_signed_half_scalar_right_summaskentryrightvaluedecode. (((dc_right_scalar_right_summaskentry) = 2 * ge_signed_half_scalar_right_summaskentryrightvaluedecode + 1 /\ (ge_balance_positive_scalar_right_summaskentryrightvalue) = 0) /\ (ge_balance_negative_scalar_right_summaskentryrightvalue) = S ge_signed_half_scalar_right_summaskentryrightvaluedecode))) /\ ((dst_positive_scalar_right_summaskentryright) + ge_balance_negative_scalar_right_summaskentryrightvalue = (dst_negative_scalar_right_summaskentryright) + ge_balance_positive_scalar_right_summaskentryrightvalue))))))))) /\ (exists sto_ap_scalar_right_summaskentryproduct sto_an_scalar_right_summaskentryproduct sto_bp_scalar_right_summaskentryproduct sto_bn_scalar_right_summaskentryproduct sto_cp_scalar_right_summaskentryproduct sto_cn_scalar_right_summaskentryproduct. (((((dc_left_scalar_right_summaskentry) = 2 * (sto_ap_scalar_right_summaskentryproduct) /\ (sto_an_scalar_right_summaskentryproduct) = 0) \/ exists ge_signed_half_scalar_right_summaskentryproductleft. (((dc_left_scalar_right_summaskentry) = 2 * ge_signed_half_scalar_right_summaskentryproductleft + 1 /\ (sto_ap_scalar_right_summaskentryproduct) = 0) /\ (sto_an_scalar_right_summaskentryproduct) = S ge_signed_half_scalar_right_summaskentryproductleft))) /\ ((((((dc_right_scalar_right_summaskentry) = 2 * (sto_bp_scalar_right_summaskentryproduct) /\ (sto_bn_scalar_right_summaskentryproduct) = 0) \/ exists ge_signed_half_scalar_right_summaskentryproductright. (((dc_right_scalar_right_summaskentry) = 2 * ge_signed_half_scalar_right_summaskentryproductright + 1 /\ (sto_bp_scalar_right_summaskentryproduct) = 0) /\ (sto_bn_scalar_right_summaskentryproduct) = S ge_signed_half_scalar_right_summaskentryproductright))) /\ ((((((dc_value_scalar_right_summask) = 2 * (sto_cp_scalar_right_summaskentryproduct) /\ (sto_cn_scalar_right_summaskentryproduct) = 0) \/ exists ge_signed_half_scalar_right_summaskentryproductoutput. (((dc_value_scalar_right_summask) = 2 * ge_signed_half_scalar_right_summaskentryproductoutput + 1 /\ (sto_cp_scalar_right_summaskentryproduct) = 0) /\ (sto_cn_scalar_right_summaskentryproduct) = S ge_signed_half_scalar_right_summaskentryproductoutput))) /\ ((sto_ap_scalar_right_summaskentryproduct * sto_bp_scalar_right_summaskentryproduct + sto_an_scalar_right_summaskentryproduct * sto_bn_scalar_right_summaskentryproduct) + sto_cn_scalar_right_summaskentryproduct = (sto_ap_scalar_right_summaskentryproduct * sto_bn_scalar_right_summaskentryproduct + sto_an_scalar_right_summaskentryproduct * sto_bp_scalar_right_summaskentryproduct) + sto_cp_scalar_right_summaskentryproduct))))))))))))))) \/ ((((dc_index_scalar_right_summask)=0 \/ ~(exists pvs_factor_scalar_right_summaskentrynondivisor. (n) = (dc_index_scalar_right_summask) * pvs_factor_scalar_right_summaskentrynondivisor)) /\ ((dc_value_scalar_right_summask)=0))))))) /\ (exists dst_positive_code_scalar_right_sumfold dst_positive_scale_scalar_right_sumfold dst_negative_code_scalar_right_sumfold dst_negative_scale_scalar_right_sumfold dst_positive_sum_scalar_right_sumfold dst_negative_sum_scalar_right_sumfold. (((dc_mask_scalar_right_sum) = (((((dst_positive_code_scalar_right_sumfold) + (dst_positive_scale_scalar_right_sumfold)) * S ((dst_positive_code_scalar_right_sumfold) + (dst_positive_scale_scalar_right_sumfold)) + ((dst_positive_scale_scalar_right_sumfold) + (dst_positive_scale_scalar_right_sumfold))) + (((dst_negative_code_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)) * S ((dst_negative_code_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)) + ((dst_negative_scale_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)))) * S ((((dst_positive_code_scalar_right_sumfold) + (dst_positive_scale_scalar_right_sumfold)) * S ((dst_positive_code_scalar_right_sumfold) + (dst_positive_scale_scalar_right_sumfold)) + ((dst_positive_scale_scalar_right_sumfold) + (dst_positive_scale_scalar_right_sumfold))) + (((dst_negative_code_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)) * S ((dst_negative_code_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)) + ((dst_negative_scale_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)))) + ((((dst_negative_code_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)) * S ((dst_negative_code_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)) + ((dst_negative_scale_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold))) + (((dst_negative_code_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)) * S ((dst_negative_code_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)) + ((dst_negative_scale_scalar_right_sumfold) + (dst_negative_scale_scalar_right_sumfold)))))) /\ (((exists fs_u_dst_scalar_right_sumfoldpositive fs_v_dst_scalar_right_sumfoldpositive. ((((exists fs_h_dst_scalar_right_sumfoldpositive_body_start. fs_h_dst_scalar_right_sumfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_right_sumfoldpositive)) /\ exists fs_q_dst_scalar_right_sumfoldpositive_body_start. fs_u_dst_scalar_right_sumfoldpositive = fs_q_dst_scalar_right_sumfoldpositive_body_start * S ((S (0)) * fs_v_dst_scalar_right_sumfoldpositive) + (0))) /\ ((((exists fs_h_dst_scalar_right_sumfoldpositive_body_terminal. fs_h_dst_scalar_right_sumfoldpositive_body_terminal + S (dst_positive_sum_scalar_right_sumfold) = S ((S (S (n))) * fs_v_dst_scalar_right_sumfoldpositive)) /\ exists fs_q_dst_scalar_right_sumfoldpositive_body_terminal. fs_u_dst_scalar_right_sumfoldpositive = fs_q_dst_scalar_right_sumfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_scalar_right_sumfoldpositive) + (dst_positive_sum_scalar_right_sumfold))) /\ forall fs_i_dst_scalar_right_sumfoldpositive_body_steps. (exists fs_lt_dst_scalar_right_sumfoldpositive_body_steps_bound. fs_lt_dst_scalar_right_sumfoldpositive_body_steps_bound + S fs_i_dst_scalar_right_sumfoldpositive_body_steps = S (n)) -> exists fs_a_dst_scalar_right_sumfoldpositive_body_steps fs_r_dst_scalar_right_sumfoldpositive_body_steps fs_s_dst_scalar_right_sumfoldpositive_body_steps. ((((exists fs_h_dst_scalar_right_sumfoldpositive_body_steps_summand. fs_h_dst_scalar_right_sumfoldpositive_body_steps_summand + S (fs_a_dst_scalar_right_sumfoldpositive_body_steps) = S ((S (fs_i_dst_scalar_right_sumfoldpositive_body_steps)) * dst_positive_scale_scalar_right_sumfold)) /\ exists fs_q_dst_scalar_right_sumfoldpositive_body_steps_summand. dst_positive_code_scalar_right_sumfold = fs_q_dst_scalar_right_sumfoldpositive_body_steps_summand * S ((S (fs_i_dst_scalar_right_sumfoldpositive_body_steps)) * dst_positive_scale_scalar_right_sumfold) + (fs_a_dst_scalar_right_sumfoldpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_right_sumfoldpositive_body_steps_partial. fs_h_dst_scalar_right_sumfoldpositive_body_steps_partial + S (fs_r_dst_scalar_right_sumfoldpositive_body_steps) = S ((S (fs_i_dst_scalar_right_sumfoldpositive_body_steps)) * fs_v_dst_scalar_right_sumfoldpositive)) /\ exists fs_q_dst_scalar_right_sumfoldpositive_body_steps_partial. fs_u_dst_scalar_right_sumfoldpositive = fs_q_dst_scalar_right_sumfoldpositive_body_steps_partial * S ((S (fs_i_dst_scalar_right_sumfoldpositive_body_steps)) * fs_v_dst_scalar_right_sumfoldpositive) + (fs_r_dst_scalar_right_sumfoldpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_right_sumfoldpositive_body_steps_successor. fs_h_dst_scalar_right_sumfoldpositive_body_steps_successor + S (fs_s_dst_scalar_right_sumfoldpositive_body_steps) = S ((S (S fs_i_dst_scalar_right_sumfoldpositive_body_steps)) * fs_v_dst_scalar_right_sumfoldpositive)) /\ exists fs_q_dst_scalar_right_sumfoldpositive_body_steps_successor. fs_u_dst_scalar_right_sumfoldpositive = fs_q_dst_scalar_right_sumfoldpositive_body_steps_successor * S ((S (S fs_i_dst_scalar_right_sumfoldpositive_body_steps)) * fs_v_dst_scalar_right_sumfoldpositive) + (fs_s_dst_scalar_right_sumfoldpositive_body_steps))) /\ fs_s_dst_scalar_right_sumfoldpositive_body_steps = fs_r_dst_scalar_right_sumfoldpositive_body_steps + fs_a_dst_scalar_right_sumfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_scalar_right_sumfoldnegative fs_v_dst_scalar_right_sumfoldnegative. ((((exists fs_h_dst_scalar_right_sumfoldnegative_body_start. fs_h_dst_scalar_right_sumfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_right_sumfoldnegative)) /\ exists fs_q_dst_scalar_right_sumfoldnegative_body_start. fs_u_dst_scalar_right_sumfoldnegative = fs_q_dst_scalar_right_sumfoldnegative_body_start * S ((S (0)) * fs_v_dst_scalar_right_sumfoldnegative) + (0))) /\ ((((exists fs_h_dst_scalar_right_sumfoldnegative_body_terminal. fs_h_dst_scalar_right_sumfoldnegative_body_terminal + S (dst_negative_sum_scalar_right_sumfold) = S ((S (S (n))) * fs_v_dst_scalar_right_sumfoldnegative)) /\ exists fs_q_dst_scalar_right_sumfoldnegative_body_terminal. fs_u_dst_scalar_right_sumfoldnegative = fs_q_dst_scalar_right_sumfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_scalar_right_sumfoldnegative) + (dst_negative_sum_scalar_right_sumfold))) /\ forall fs_i_dst_scalar_right_sumfoldnegative_body_steps. (exists fs_lt_dst_scalar_right_sumfoldnegative_body_steps_bound. fs_lt_dst_scalar_right_sumfoldnegative_body_steps_bound + S fs_i_dst_scalar_right_sumfoldnegative_body_steps = S (n)) -> exists fs_a_dst_scalar_right_sumfoldnegative_body_steps fs_r_dst_scalar_right_sumfoldnegative_body_steps fs_s_dst_scalar_right_sumfoldnegative_body_steps. ((((exists fs_h_dst_scalar_right_sumfoldnegative_body_steps_summand. fs_h_dst_scalar_right_sumfoldnegative_body_steps_summand + S (fs_a_dst_scalar_right_sumfoldnegative_body_steps) = S ((S (fs_i_dst_scalar_right_sumfoldnegative_body_steps)) * dst_negative_scale_scalar_right_sumfold)) /\ exists fs_q_dst_scalar_right_sumfoldnegative_body_steps_summand. dst_negative_code_scalar_right_sumfold = fs_q_dst_scalar_right_sumfoldnegative_body_steps_summand * S ((S (fs_i_dst_scalar_right_sumfoldnegative_body_steps)) * dst_negative_scale_scalar_right_sumfold) + (fs_a_dst_scalar_right_sumfoldnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_right_sumfoldnegative_body_steps_partial. fs_h_dst_scalar_right_sumfoldnegative_body_steps_partial + S (fs_r_dst_scalar_right_sumfoldnegative_body_steps) = S ((S (fs_i_dst_scalar_right_sumfoldnegative_body_steps)) * fs_v_dst_scalar_right_sumfoldnegative)) /\ exists fs_q_dst_scalar_right_sumfoldnegative_body_steps_partial. fs_u_dst_scalar_right_sumfoldnegative = fs_q_dst_scalar_right_sumfoldnegative_body_steps_partial * S ((S (fs_i_dst_scalar_right_sumfoldnegative_body_steps)) * fs_v_dst_scalar_right_sumfoldnegative) + (fs_r_dst_scalar_right_sumfoldnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_right_sumfoldnegative_body_steps_successor. fs_h_dst_scalar_right_sumfoldnegative_body_steps_successor + S (fs_s_dst_scalar_right_sumfoldnegative_body_steps) = S ((S (S fs_i_dst_scalar_right_sumfoldnegative_body_steps)) * fs_v_dst_scalar_right_sumfoldnegative)) /\ exists fs_q_dst_scalar_right_sumfoldnegative_body_steps_successor. fs_u_dst_scalar_right_sumfoldnegative = fs_q_dst_scalar_right_sumfoldnegative_body_steps_successor * S ((S (S fs_i_dst_scalar_right_sumfoldnegative_body_steps)) * fs_v_dst_scalar_right_sumfoldnegative) + (fs_s_dst_scalar_right_sumfoldnegative_body_steps))) /\ fs_s_dst_scalar_right_sumfoldnegative_body_steps = fs_r_dst_scalar_right_sumfoldnegative_body_steps + fs_a_dst_scalar_right_sumfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_scalar_right_sumfoldresult ge_balance_negative_scalar_right_sumfoldresult. (((((b) = 2 * (ge_balance_positive_scalar_right_sumfoldresult) /\ (ge_balance_negative_scalar_right_sumfoldresult) = 0) \/ exists ge_signed_half_scalar_right_sumfoldresultdecode. (((b) = 2 * ge_signed_half_scalar_right_sumfoldresultdecode + 1 /\ (ge_balance_positive_scalar_right_sumfoldresult) = 0) /\ (ge_balance_negative_scalar_right_sumfoldresult) = S ge_signed_half_scalar_right_sumfoldresultdecode))) /\ ((dst_positive_sum_scalar_right_sumfold) + ge_balance_negative_scalar_right_sumfoldresult = (dst_negative_sum_scalar_right_sumfold) + ge_balance_positive_scalar_right_sumfoldresult))))))))))))) -> (((~((m*n)=0)) /\ (exists dc_mask_scalar_target_sum. ((((exists dst_positive_code_scalar_target_summasktable dst_positive_scale_scalar_target_summasktable dst_negative_code_scalar_target_summasktable dst_negative_scale_scalar_target_summasktable. (((dc_mask_scalar_target_sum) = (((((dst_positive_code_scalar_target_summasktable) + (dst_positive_scale_scalar_target_summasktable)) * S ((dst_positive_code_scalar_target_summasktable) + (dst_positive_scale_scalar_target_summasktable)) + ((dst_positive_scale_scalar_target_summasktable) + (dst_positive_scale_scalar_target_summasktable))) + (((dst_negative_code_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)) * S ((dst_negative_code_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)) + ((dst_negative_scale_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)))) * S ((((dst_positive_code_scalar_target_summasktable) + (dst_positive_scale_scalar_target_summasktable)) * S ((dst_positive_code_scalar_target_summasktable) + (dst_positive_scale_scalar_target_summasktable)) + ((dst_positive_scale_scalar_target_summasktable) + (dst_positive_scale_scalar_target_summasktable))) + (((dst_negative_code_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)) * S ((dst_negative_code_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)) + ((dst_negative_scale_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)))) + ((((dst_negative_code_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)) * S ((dst_negative_code_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)) + ((dst_negative_scale_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable))) + (((dst_negative_code_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)) * S ((dst_negative_code_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)) + ((dst_negative_scale_scalar_target_summasktable) + (dst_negative_scale_scalar_target_summasktable)))))) /\ (forall dst_index_scalar_target_summasktable. (exists pvs_le_gap_scalar_target_summasktabledomain. pvs_le_gap_scalar_target_summasktabledomain + (dst_index_scalar_target_summasktable) = (m*n)) -> exists dst_positive_scalar_target_summasktable dst_negative_scalar_target_summasktable dst_value_scalar_target_summasktable. ((((exists ff_h_pvs_scalar_target_summasktableentrypositive. ff_h_pvs_scalar_target_summasktableentrypositive + S (dst_positive_scalar_target_summasktable) = S ((S (dst_index_scalar_target_summasktable)) * dst_positive_scale_scalar_target_summasktable)) /\ exists ff_q_pvs_scalar_target_summasktableentrypositive. dst_positive_code_scalar_target_summasktable = ff_q_pvs_scalar_target_summasktableentrypositive * S ((S (dst_index_scalar_target_summasktable)) * dst_positive_scale_scalar_target_summasktable) + (dst_positive_scalar_target_summasktable))) /\ (((((exists ff_h_pvs_scalar_target_summasktableentrynegative. ff_h_pvs_scalar_target_summasktableentrynegative + S (dst_negative_scalar_target_summasktable) = S ((S (dst_index_scalar_target_summasktable)) * dst_negative_scale_scalar_target_summasktable)) /\ exists ff_q_pvs_scalar_target_summasktableentrynegative. dst_negative_code_scalar_target_summasktable = ff_q_pvs_scalar_target_summasktableentrynegative * S ((S (dst_index_scalar_target_summasktable)) * dst_negative_scale_scalar_target_summasktable) + (dst_negative_scalar_target_summasktable))) /\ (exists ge_balance_positive_scalar_target_summasktableentryvalue ge_balance_negative_scalar_target_summasktableentryvalue. (((((dst_value_scalar_target_summasktable) = 2 * (ge_balance_positive_scalar_target_summasktableentryvalue) /\ (ge_balance_negative_scalar_target_summasktableentryvalue) = 0) \/ exists ge_signed_half_scalar_target_summasktableentryvaluedecode. (((dst_value_scalar_target_summasktable) = 2 * ge_signed_half_scalar_target_summasktableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_target_summasktableentryvalue) = 0) /\ (ge_balance_negative_scalar_target_summasktableentryvalue) = S ge_signed_half_scalar_target_summasktableentryvaluedecode))) /\ ((dst_positive_scalar_target_summasktable) + ge_balance_negative_scalar_target_summasktableentryvalue = (dst_negative_scalar_target_summasktable) + ge_balance_positive_scalar_target_summasktableentryvalue))))))))) /\ (forall dc_index_scalar_target_summask dc_value_scalar_target_summask. (exists pvs_le_gap_scalar_target_summaskdomain. pvs_le_gap_scalar_target_summaskdomain + (dc_index_scalar_target_summask) = (m*n)) -> (exists dst_positive_code_scalar_target_summasklookup dst_positive_scale_scalar_target_summasklookup dst_negative_code_scalar_target_summasklookup dst_negative_scale_scalar_target_summasklookup dst_positive_scalar_target_summasklookup dst_negative_scalar_target_summasklookup. (((dc_mask_scalar_target_sum) = (((((dst_positive_code_scalar_target_summasklookup) + (dst_positive_scale_scalar_target_summasklookup)) * S ((dst_positive_code_scalar_target_summasklookup) + (dst_positive_scale_scalar_target_summasklookup)) + ((dst_positive_scale_scalar_target_summasklookup) + (dst_positive_scale_scalar_target_summasklookup))) + (((dst_negative_code_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)) * S ((dst_negative_code_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)) + ((dst_negative_scale_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)))) * S ((((dst_positive_code_scalar_target_summasklookup) + (dst_positive_scale_scalar_target_summasklookup)) * S ((dst_positive_code_scalar_target_summasklookup) + (dst_positive_scale_scalar_target_summasklookup)) + ((dst_positive_scale_scalar_target_summasklookup) + (dst_positive_scale_scalar_target_summasklookup))) + (((dst_negative_code_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)) * S ((dst_negative_code_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)) + ((dst_negative_scale_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)))) + ((((dst_negative_code_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)) * S ((dst_negative_code_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)) + ((dst_negative_scale_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup))) + (((dst_negative_code_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)) * S ((dst_negative_code_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)) + ((dst_negative_scale_scalar_target_summasklookup) + (dst_negative_scale_scalar_target_summasklookup)))))) /\ (((((exists ff_h_pvs_scalar_target_summasklookuppositive. ff_h_pvs_scalar_target_summasklookuppositive + S (dst_positive_scalar_target_summasklookup) = S ((S (dc_index_scalar_target_summask)) * dst_positive_scale_scalar_target_summasklookup)) /\ exists ff_q_pvs_scalar_target_summasklookuppositive. dst_positive_code_scalar_target_summasklookup = ff_q_pvs_scalar_target_summasklookuppositive * S ((S (dc_index_scalar_target_summask)) * dst_positive_scale_scalar_target_summasklookup) + (dst_positive_scalar_target_summasklookup))) /\ (((((exists ff_h_pvs_scalar_target_summasklookupnegative. ff_h_pvs_scalar_target_summasklookupnegative + S (dst_negative_scalar_target_summasklookup) = S ((S (dc_index_scalar_target_summask)) * dst_negative_scale_scalar_target_summasklookup)) /\ exists ff_q_pvs_scalar_target_summasklookupnegative. dst_negative_code_scalar_target_summasklookup = ff_q_pvs_scalar_target_summasklookupnegative * S ((S (dc_index_scalar_target_summask)) * dst_negative_scale_scalar_target_summasklookup) + (dst_negative_scalar_target_summasklookup))) /\ (exists ge_balance_positive_scalar_target_summasklookupvalue ge_balance_negative_scalar_target_summasklookupvalue. (((((dc_value_scalar_target_summask) = 2 * (ge_balance_positive_scalar_target_summasklookupvalue) /\ (ge_balance_negative_scalar_target_summasklookupvalue) = 0) \/ exists ge_signed_half_scalar_target_summasklookupvaluedecode. (((dc_value_scalar_target_summask) = 2 * ge_signed_half_scalar_target_summasklookupvaluedecode + 1 /\ (ge_balance_positive_scalar_target_summasklookupvalue) = 0) /\ (ge_balance_negative_scalar_target_summasklookupvalue) = S ge_signed_half_scalar_target_summasklookupvaluedecode))) /\ ((dst_positive_scalar_target_summasklookup) + ge_balance_negative_scalar_target_summasklookupvalue = (dst_negative_scalar_target_summasklookup) + ge_balance_positive_scalar_target_summasklookupvalue))))))))) -> ((((~((dc_index_scalar_target_summask)=0)) /\ (exists dc_quotient_scalar_target_summaskentry dc_left_scalar_target_summaskentry dc_right_scalar_target_summaskentry. (((m*n)=(dc_index_scalar_target_summask)*dc_quotient_scalar_target_summaskentry) /\ (((exists dst_positive_code_scalar_target_summaskentryleft dst_positive_scale_scalar_target_summaskentryleft dst_negative_code_scalar_target_summaskentryleft dst_negative_scale_scalar_target_summaskentryleft dst_positive_scalar_target_summaskentryleft dst_negative_scalar_target_summaskentryleft. (((F) = (((((dst_positive_code_scalar_target_summaskentryleft) + (dst_positive_scale_scalar_target_summaskentryleft)) * S ((dst_positive_code_scalar_target_summaskentryleft) + (dst_positive_scale_scalar_target_summaskentryleft)) + ((dst_positive_scale_scalar_target_summaskentryleft) + (dst_positive_scale_scalar_target_summaskentryleft))) + (((dst_negative_code_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)) * S ((dst_negative_code_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)) + ((dst_negative_scale_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)))) * S ((((dst_positive_code_scalar_target_summaskentryleft) + (dst_positive_scale_scalar_target_summaskentryleft)) * S ((dst_positive_code_scalar_target_summaskentryleft) + (dst_positive_scale_scalar_target_summaskentryleft)) + ((dst_positive_scale_scalar_target_summaskentryleft) + (dst_positive_scale_scalar_target_summaskentryleft))) + (((dst_negative_code_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)) * S ((dst_negative_code_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)) + ((dst_negative_scale_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)))) + ((((dst_negative_code_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)) * S ((dst_negative_code_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)) + ((dst_negative_scale_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft))) + (((dst_negative_code_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)) * S ((dst_negative_code_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)) + ((dst_negative_scale_scalar_target_summaskentryleft) + (dst_negative_scale_scalar_target_summaskentryleft)))))) /\ (((((exists ff_h_pvs_scalar_target_summaskentryleftpositive. ff_h_pvs_scalar_target_summaskentryleftpositive + S (dst_positive_scalar_target_summaskentryleft) = S ((S (dc_index_scalar_target_summask)) * dst_positive_scale_scalar_target_summaskentryleft)) /\ exists ff_q_pvs_scalar_target_summaskentryleftpositive. dst_positive_code_scalar_target_summaskentryleft = ff_q_pvs_scalar_target_summaskentryleftpositive * S ((S (dc_index_scalar_target_summask)) * dst_positive_scale_scalar_target_summaskentryleft) + (dst_positive_scalar_target_summaskentryleft))) /\ (((((exists ff_h_pvs_scalar_target_summaskentryleftnegative. ff_h_pvs_scalar_target_summaskentryleftnegative + S (dst_negative_scalar_target_summaskentryleft) = S ((S (dc_index_scalar_target_summask)) * dst_negative_scale_scalar_target_summaskentryleft)) /\ exists ff_q_pvs_scalar_target_summaskentryleftnegative. dst_negative_code_scalar_target_summaskentryleft = ff_q_pvs_scalar_target_summaskentryleftnegative * S ((S (dc_index_scalar_target_summask)) * dst_negative_scale_scalar_target_summaskentryleft) + (dst_negative_scalar_target_summaskentryleft))) /\ (exists ge_balance_positive_scalar_target_summaskentryleftvalue ge_balance_negative_scalar_target_summaskentryleftvalue. (((((dc_left_scalar_target_summaskentry) = 2 * (ge_balance_positive_scalar_target_summaskentryleftvalue) /\ (ge_balance_negative_scalar_target_summaskentryleftvalue) = 0) \/ exists ge_signed_half_scalar_target_summaskentryleftvaluedecode. (((dc_left_scalar_target_summaskentry) = 2 * ge_signed_half_scalar_target_summaskentryleftvaluedecode + 1 /\ (ge_balance_positive_scalar_target_summaskentryleftvalue) = 0) /\ (ge_balance_negative_scalar_target_summaskentryleftvalue) = S ge_signed_half_scalar_target_summaskentryleftvaluedecode))) /\ ((dst_positive_scalar_target_summaskentryleft) + ge_balance_negative_scalar_target_summaskentryleftvalue = (dst_negative_scalar_target_summaskentryleft) + ge_balance_positive_scalar_target_summaskentryleftvalue))))))))) /\ (((exists dst_positive_code_scalar_target_summaskentryright dst_positive_scale_scalar_target_summaskentryright dst_negative_code_scalar_target_summaskentryright dst_negative_scale_scalar_target_summaskentryright dst_positive_scalar_target_summaskentryright dst_negative_scalar_target_summaskentryright. (((G) = (((((dst_positive_code_scalar_target_summaskentryright) + (dst_positive_scale_scalar_target_summaskentryright)) * S ((dst_positive_code_scalar_target_summaskentryright) + (dst_positive_scale_scalar_target_summaskentryright)) + ((dst_positive_scale_scalar_target_summaskentryright) + (dst_positive_scale_scalar_target_summaskentryright))) + (((dst_negative_code_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)) * S ((dst_negative_code_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)) + ((dst_negative_scale_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)))) * S ((((dst_positive_code_scalar_target_summaskentryright) + (dst_positive_scale_scalar_target_summaskentryright)) * S ((dst_positive_code_scalar_target_summaskentryright) + (dst_positive_scale_scalar_target_summaskentryright)) + ((dst_positive_scale_scalar_target_summaskentryright) + (dst_positive_scale_scalar_target_summaskentryright))) + (((dst_negative_code_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)) * S ((dst_negative_code_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)) + ((dst_negative_scale_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)))) + ((((dst_negative_code_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)) * S ((dst_negative_code_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)) + ((dst_negative_scale_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright))) + (((dst_negative_code_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)) * S ((dst_negative_code_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)) + ((dst_negative_scale_scalar_target_summaskentryright) + (dst_negative_scale_scalar_target_summaskentryright)))))) /\ (((((exists ff_h_pvs_scalar_target_summaskentryrightpositive. ff_h_pvs_scalar_target_summaskentryrightpositive + S (dst_positive_scalar_target_summaskentryright) = S ((S (dc_quotient_scalar_target_summaskentry)) * dst_positive_scale_scalar_target_summaskentryright)) /\ exists ff_q_pvs_scalar_target_summaskentryrightpositive. dst_positive_code_scalar_target_summaskentryright = ff_q_pvs_scalar_target_summaskentryrightpositive * S ((S (dc_quotient_scalar_target_summaskentry)) * dst_positive_scale_scalar_target_summaskentryright) + (dst_positive_scalar_target_summaskentryright))) /\ (((((exists ff_h_pvs_scalar_target_summaskentryrightnegative. ff_h_pvs_scalar_target_summaskentryrightnegative + S (dst_negative_scalar_target_summaskentryright) = S ((S (dc_quotient_scalar_target_summaskentry)) * dst_negative_scale_scalar_target_summaskentryright)) /\ exists ff_q_pvs_scalar_target_summaskentryrightnegative. dst_negative_code_scalar_target_summaskentryright = ff_q_pvs_scalar_target_summaskentryrightnegative * S ((S (dc_quotient_scalar_target_summaskentry)) * dst_negative_scale_scalar_target_summaskentryright) + (dst_negative_scalar_target_summaskentryright))) /\ (exists ge_balance_positive_scalar_target_summaskentryrightvalue ge_balance_negative_scalar_target_summaskentryrightvalue. (((((dc_right_scalar_target_summaskentry) = 2 * (ge_balance_positive_scalar_target_summaskentryrightvalue) /\ (ge_balance_negative_scalar_target_summaskentryrightvalue) = 0) \/ exists ge_signed_half_scalar_target_summaskentryrightvaluedecode. (((dc_right_scalar_target_summaskentry) = 2 * ge_signed_half_scalar_target_summaskentryrightvaluedecode + 1 /\ (ge_balance_positive_scalar_target_summaskentryrightvalue) = 0) /\ (ge_balance_negative_scalar_target_summaskentryrightvalue) = S ge_signed_half_scalar_target_summaskentryrightvaluedecode))) /\ ((dst_positive_scalar_target_summaskentryright) + ge_balance_negative_scalar_target_summaskentryrightvalue = (dst_negative_scalar_target_summaskentryright) + ge_balance_positive_scalar_target_summaskentryrightvalue))))))))) /\ (exists sto_ap_scalar_target_summaskentryproduct sto_an_scalar_target_summaskentryproduct sto_bp_scalar_target_summaskentryproduct sto_bn_scalar_target_summaskentryproduct sto_cp_scalar_target_summaskentryproduct sto_cn_scalar_target_summaskentryproduct. (((((dc_left_scalar_target_summaskentry) = 2 * (sto_ap_scalar_target_summaskentryproduct) /\ (sto_an_scalar_target_summaskentryproduct) = 0) \/ exists ge_signed_half_scalar_target_summaskentryproductleft. (((dc_left_scalar_target_summaskentry) = 2 * ge_signed_half_scalar_target_summaskentryproductleft + 1 /\ (sto_ap_scalar_target_summaskentryproduct) = 0) /\ (sto_an_scalar_target_summaskentryproduct) = S ge_signed_half_scalar_target_summaskentryproductleft))) /\ ((((((dc_right_scalar_target_summaskentry) = 2 * (sto_bp_scalar_target_summaskentryproduct) /\ (sto_bn_scalar_target_summaskentryproduct) = 0) \/ exists ge_signed_half_scalar_target_summaskentryproductright. (((dc_right_scalar_target_summaskentry) = 2 * ge_signed_half_scalar_target_summaskentryproductright + 1 /\ (sto_bp_scalar_target_summaskentryproduct) = 0) /\ (sto_bn_scalar_target_summaskentryproduct) = S ge_signed_half_scalar_target_summaskentryproductright))) /\ ((((((dc_value_scalar_target_summask) = 2 * (sto_cp_scalar_target_summaskentryproduct) /\ (sto_cn_scalar_target_summaskentryproduct) = 0) \/ exists ge_signed_half_scalar_target_summaskentryproductoutput. (((dc_value_scalar_target_summask) = 2 * ge_signed_half_scalar_target_summaskentryproductoutput + 1 /\ (sto_cp_scalar_target_summaskentryproduct) = 0) /\ (sto_cn_scalar_target_summaskentryproduct) = S ge_signed_half_scalar_target_summaskentryproductoutput))) /\ ((sto_ap_scalar_target_summaskentryproduct * sto_bp_scalar_target_summaskentryproduct + sto_an_scalar_target_summaskentryproduct * sto_bn_scalar_target_summaskentryproduct) + sto_cn_scalar_target_summaskentryproduct = (sto_ap_scalar_target_summaskentryproduct * sto_bn_scalar_target_summaskentryproduct + sto_an_scalar_target_summaskentryproduct * sto_bp_scalar_target_summaskentryproduct) + sto_cp_scalar_target_summaskentryproduct))))))))))))))) \/ ((((dc_index_scalar_target_summask)=0 \/ ~(exists pvs_factor_scalar_target_summaskentrynondivisor. (m*n) = (dc_index_scalar_target_summask) * pvs_factor_scalar_target_summaskentrynondivisor)) /\ ((dc_value_scalar_target_summask)=0))))))) /\ (exists dst_positive_code_scalar_target_sumfold dst_positive_scale_scalar_target_sumfold dst_negative_code_scalar_target_sumfold dst_negative_scale_scalar_target_sumfold dst_positive_sum_scalar_target_sumfold dst_negative_sum_scalar_target_sumfold. (((dc_mask_scalar_target_sum) = (((((dst_positive_code_scalar_target_sumfold) + (dst_positive_scale_scalar_target_sumfold)) * S ((dst_positive_code_scalar_target_sumfold) + (dst_positive_scale_scalar_target_sumfold)) + ((dst_positive_scale_scalar_target_sumfold) + (dst_positive_scale_scalar_target_sumfold))) + (((dst_negative_code_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)) * S ((dst_negative_code_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)) + ((dst_negative_scale_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)))) * S ((((dst_positive_code_scalar_target_sumfold) + (dst_positive_scale_scalar_target_sumfold)) * S ((dst_positive_code_scalar_target_sumfold) + (dst_positive_scale_scalar_target_sumfold)) + ((dst_positive_scale_scalar_target_sumfold) + (dst_positive_scale_scalar_target_sumfold))) + (((dst_negative_code_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)) * S ((dst_negative_code_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)) + ((dst_negative_scale_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)))) + ((((dst_negative_code_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)) * S ((dst_negative_code_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)) + ((dst_negative_scale_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold))) + (((dst_negative_code_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)) * S ((dst_negative_code_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)) + ((dst_negative_scale_scalar_target_sumfold) + (dst_negative_scale_scalar_target_sumfold)))))) /\ (((exists fs_u_dst_scalar_target_sumfoldpositive fs_v_dst_scalar_target_sumfoldpositive. ((((exists fs_h_dst_scalar_target_sumfoldpositive_body_start. fs_h_dst_scalar_target_sumfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_target_sumfoldpositive)) /\ exists fs_q_dst_scalar_target_sumfoldpositive_body_start. fs_u_dst_scalar_target_sumfoldpositive = fs_q_dst_scalar_target_sumfoldpositive_body_start * S ((S (0)) * fs_v_dst_scalar_target_sumfoldpositive) + (0))) /\ ((((exists fs_h_dst_scalar_target_sumfoldpositive_body_terminal. fs_h_dst_scalar_target_sumfoldpositive_body_terminal + S (dst_positive_sum_scalar_target_sumfold) = S ((S (S (m*n))) * fs_v_dst_scalar_target_sumfoldpositive)) /\ exists fs_q_dst_scalar_target_sumfoldpositive_body_terminal. fs_u_dst_scalar_target_sumfoldpositive = fs_q_dst_scalar_target_sumfoldpositive_body_terminal * S ((S (S (m*n))) * fs_v_dst_scalar_target_sumfoldpositive) + (dst_positive_sum_scalar_target_sumfold))) /\ forall fs_i_dst_scalar_target_sumfoldpositive_body_steps. (exists fs_lt_dst_scalar_target_sumfoldpositive_body_steps_bound. fs_lt_dst_scalar_target_sumfoldpositive_body_steps_bound + S fs_i_dst_scalar_target_sumfoldpositive_body_steps = S (m*n)) -> exists fs_a_dst_scalar_target_sumfoldpositive_body_steps fs_r_dst_scalar_target_sumfoldpositive_body_steps fs_s_dst_scalar_target_sumfoldpositive_body_steps. ((((exists fs_h_dst_scalar_target_sumfoldpositive_body_steps_summand. fs_h_dst_scalar_target_sumfoldpositive_body_steps_summand + S (fs_a_dst_scalar_target_sumfoldpositive_body_steps) = S ((S (fs_i_dst_scalar_target_sumfoldpositive_body_steps)) * dst_positive_scale_scalar_target_sumfold)) /\ exists fs_q_dst_scalar_target_sumfoldpositive_body_steps_summand. dst_positive_code_scalar_target_sumfold = fs_q_dst_scalar_target_sumfoldpositive_body_steps_summand * S ((S (fs_i_dst_scalar_target_sumfoldpositive_body_steps)) * dst_positive_scale_scalar_target_sumfold) + (fs_a_dst_scalar_target_sumfoldpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_target_sumfoldpositive_body_steps_partial. fs_h_dst_scalar_target_sumfoldpositive_body_steps_partial + S (fs_r_dst_scalar_target_sumfoldpositive_body_steps) = S ((S (fs_i_dst_scalar_target_sumfoldpositive_body_steps)) * fs_v_dst_scalar_target_sumfoldpositive)) /\ exists fs_q_dst_scalar_target_sumfoldpositive_body_steps_partial. fs_u_dst_scalar_target_sumfoldpositive = fs_q_dst_scalar_target_sumfoldpositive_body_steps_partial * S ((S (fs_i_dst_scalar_target_sumfoldpositive_body_steps)) * fs_v_dst_scalar_target_sumfoldpositive) + (fs_r_dst_scalar_target_sumfoldpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_target_sumfoldpositive_body_steps_successor. fs_h_dst_scalar_target_sumfoldpositive_body_steps_successor + S (fs_s_dst_scalar_target_sumfoldpositive_body_steps) = S ((S (S fs_i_dst_scalar_target_sumfoldpositive_body_steps)) * fs_v_dst_scalar_target_sumfoldpositive)) /\ exists fs_q_dst_scalar_target_sumfoldpositive_body_steps_successor. fs_u_dst_scalar_target_sumfoldpositive = fs_q_dst_scalar_target_sumfoldpositive_body_steps_successor * S ((S (S fs_i_dst_scalar_target_sumfoldpositive_body_steps)) * fs_v_dst_scalar_target_sumfoldpositive) + (fs_s_dst_scalar_target_sumfoldpositive_body_steps))) /\ fs_s_dst_scalar_target_sumfoldpositive_body_steps = fs_r_dst_scalar_target_sumfoldpositive_body_steps + fs_a_dst_scalar_target_sumfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_scalar_target_sumfoldnegative fs_v_dst_scalar_target_sumfoldnegative. ((((exists fs_h_dst_scalar_target_sumfoldnegative_body_start. fs_h_dst_scalar_target_sumfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_target_sumfoldnegative)) /\ exists fs_q_dst_scalar_target_sumfoldnegative_body_start. fs_u_dst_scalar_target_sumfoldnegative = fs_q_dst_scalar_target_sumfoldnegative_body_start * S ((S (0)) * fs_v_dst_scalar_target_sumfoldnegative) + (0))) /\ ((((exists fs_h_dst_scalar_target_sumfoldnegative_body_terminal. fs_h_dst_scalar_target_sumfoldnegative_body_terminal + S (dst_negative_sum_scalar_target_sumfold) = S ((S (S (m*n))) * fs_v_dst_scalar_target_sumfoldnegative)) /\ exists fs_q_dst_scalar_target_sumfoldnegative_body_terminal. fs_u_dst_scalar_target_sumfoldnegative = fs_q_dst_scalar_target_sumfoldnegative_body_terminal * S ((S (S (m*n))) * fs_v_dst_scalar_target_sumfoldnegative) + (dst_negative_sum_scalar_target_sumfold))) /\ forall fs_i_dst_scalar_target_sumfoldnegative_body_steps. (exists fs_lt_dst_scalar_target_sumfoldnegative_body_steps_bound. fs_lt_dst_scalar_target_sumfoldnegative_body_steps_bound + S fs_i_dst_scalar_target_sumfoldnegative_body_steps = S (m*n)) -> exists fs_a_dst_scalar_target_sumfoldnegative_body_steps fs_r_dst_scalar_target_sumfoldnegative_body_steps fs_s_dst_scalar_target_sumfoldnegative_body_steps. ((((exists fs_h_dst_scalar_target_sumfoldnegative_body_steps_summand. fs_h_dst_scalar_target_sumfoldnegative_body_steps_summand + S (fs_a_dst_scalar_target_sumfoldnegative_body_steps) = S ((S (fs_i_dst_scalar_target_sumfoldnegative_body_steps)) * dst_negative_scale_scalar_target_sumfold)) /\ exists fs_q_dst_scalar_target_sumfoldnegative_body_steps_summand. dst_negative_code_scalar_target_sumfold = fs_q_dst_scalar_target_sumfoldnegative_body_steps_summand * S ((S (fs_i_dst_scalar_target_sumfoldnegative_body_steps)) * dst_negative_scale_scalar_target_sumfold) + (fs_a_dst_scalar_target_sumfoldnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_target_sumfoldnegative_body_steps_partial. fs_h_dst_scalar_target_sumfoldnegative_body_steps_partial + S (fs_r_dst_scalar_target_sumfoldnegative_body_steps) = S ((S (fs_i_dst_scalar_target_sumfoldnegative_body_steps)) * fs_v_dst_scalar_target_sumfoldnegative)) /\ exists fs_q_dst_scalar_target_sumfoldnegative_body_steps_partial. fs_u_dst_scalar_target_sumfoldnegative = fs_q_dst_scalar_target_sumfoldnegative_body_steps_partial * S ((S (fs_i_dst_scalar_target_sumfoldnegative_body_steps)) * fs_v_dst_scalar_target_sumfoldnegative) + (fs_r_dst_scalar_target_sumfoldnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_target_sumfoldnegative_body_steps_successor. fs_h_dst_scalar_target_sumfoldnegative_body_steps_successor + S (fs_s_dst_scalar_target_sumfoldnegative_body_steps) = S ((S (S fs_i_dst_scalar_target_sumfoldnegative_body_steps)) * fs_v_dst_scalar_target_sumfoldnegative)) /\ exists fs_q_dst_scalar_target_sumfoldnegative_body_steps_successor. fs_u_dst_scalar_target_sumfoldnegative = fs_q_dst_scalar_target_sumfoldnegative_body_steps_successor * S ((S (S fs_i_dst_scalar_target_sumfoldnegative_body_steps)) * fs_v_dst_scalar_target_sumfoldnegative) + (fs_s_dst_scalar_target_sumfoldnegative_body_steps))) /\ fs_s_dst_scalar_target_sumfoldnegative_body_steps = fs_r_dst_scalar_target_sumfoldnegative_body_steps + fs_a_dst_scalar_target_sumfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_scalar_target_sumfoldresult ge_balance_negative_scalar_target_sumfoldresult. (((((c) = 2 * (ge_balance_positive_scalar_target_sumfoldresult) /\ (ge_balance_negative_scalar_target_sumfoldresult) = 0) \/ exists ge_signed_half_scalar_target_sumfoldresultdecode. (((c) = 2 * ge_signed_half_scalar_target_sumfoldresultdecode + 1 /\ (ge_balance_positive_scalar_target_sumfoldresult) = 0) /\ (ge_balance_negative_scalar_target_sumfoldresult) = S ge_signed_half_scalar_target_sumfoldresultdecode))) /\ ((dst_positive_sum_scalar_target_sumfold) + ge_balance_negative_scalar_target_sumfoldresult = (dst_negative_sum_scalar_target_sumfold) + ge_balance_positive_scalar_target_sumfoldresult))))))))))))) -> (exists sto_ap_scalar_result sto_an_scalar_result sto_bp_scalar_result sto_bn_scalar_result sto_cp_scalar_result sto_cn_scalar_result. (((((a) = 2 * (sto_ap_scalar_result) /\ (sto_an_scalar_result) = 0) \/ exists ge_signed_half_scalar_resultleft. (((a) = 2 * ge_signed_half_scalar_resultleft + 1 /\ (sto_ap_scalar_result) = 0) /\ (sto_an_scalar_result) = S ge_signed_half_scalar_resultleft))) /\ ((((((b) = 2 * (sto_bp_scalar_result) /\ (sto_bn_scalar_result) = 0) \/ exists ge_signed_half_scalar_resultright. (((b) = 2 * ge_signed_half_scalar_resultright + 1 /\ (sto_bp_scalar_result) = 0) /\ (sto_bn_scalar_result) = S ge_signed_half_scalar_resultright))) /\ ((((((c) = 2 * (sto_cp_scalar_result) /\ (sto_cn_scalar_result) = 0) \/ exists ge_signed_half_scalar_resultoutput. (((c) = 2 * ge_signed_half_scalar_resultoutput + 1 /\ (sto_cp_scalar_result) = 0) /\ (sto_cn_scalar_result) = S ge_signed_half_scalar_resultoutput))) /\ ((sto_ap_scalar_result * sto_bp_scalar_result + sto_an_scalar_result * sto_bn_scalar_result) + sto_cn_scalar_result = (sto_ap_scalar_result * sto_bn_scalar_result + sto_an_scalar_result * sto_bp_scalar_result) + sto_cp_scalar_result)))))))Constructive proof overview
Generated structural guide
The actual convolution values at positive coprime m,n multiply to the actual value at mn, using genuine divisor-pair support reindexing and only in-prefix multiplicativity.
The unchanged tactic script uses 5 declared prerequisites and contains 110 exact native proof lines.
Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
MX0056 dirichlet_coprime_product_data_construct arithmetic_signed_sum_exists Alpha theorem; checked-use authorized MX004A signed_support_reindex_sum_equal MX0055 dirichlet_coprime_grid_support_reindex MX002B signed_cartesian_product_prefix_sumDirect 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 (4)
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–17
03Separate the logical casesL18–26
04Establish hdL27–36
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet coprime product data construct.
- L27
have hd : ∃ T. ∃ r. ∃ s. DirichletCoprimeProductData(N,F,G,m,n,x,x1,T,x2,r,s)Definitions: DirichletCoprimeProductData - L28
specialize dirichlet_coprime_product_data_construct (N) - L29
specialize dirichlet_coprime_product_data_construct (F) - L30
specialize dirichlet_coprime_product_data_construct (G) - L31
specialize dirichlet_coprime_product_data_construct (m) - L32
specialize dirichlet_coprime_product_data_construct (n) - L33
specialize dirichlet_coprime_product_data_construct (x) - L34
specialize dirichlet_coprime_product_data_construct (x1) - L35
specialize dirichlet_coprime_product_data_construct (x2) - L36
apply dirichlet_coprime_product_data_construct
05Use earlier factsL37–45
06Separate the logical casesL46–55
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L46
cases hd - L47
cases hd_witness - L48
cases hd_witness_witness - L49
cases hd_witness_witness_witness - L50
cases hd_witness_witness_witness_right - L51
cases hd_witness_witness_witness_right_right - L52
cases hd_witness_witness_witness_right_right_right - L53
cases hd_witness_witness_witness_right_right_right_right - L54
cases hd_witness_witness_witness_right_right_right_right_right - L55
cases hd_witness_witness_witness_right_right_right_right_right_right
07Separate the logical casesL56–61
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L56
cases hd_witness_witness_witness_right_right_right_right_right_right_right - L57
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right - L58
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right_right - L59
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right_left - L60
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right_left_right - L61
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right_left_right_right
08Establish hvL62–67
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply arithmetic signed sum exists.
- L62
have hv : ∃ value. SignedPrefixSum(x3,S m · S n,value)Definitions: SignedPrefixSum - L63
specialize arithmetic_signed_sum_exists ((S (m))*(S (n))) - L64
specialize arithmetic_signed_sum_exists (x3) - L65
specialize arithmetic_signed_sum_exists ((S (m))*(S (n))) - L66
apply arithmetic_signed_sum_exists - L67
exact hd_witness_witness_witness_right_right_right_right_right_right_right_right_left_right_right_left
09Separate the logical casesL68–68
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L68
cases hv
10Establish heqL69–78
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed support reindex sum equal.
- L69
have heq : x6=c - L70
specialize signed_support_reindex_sum_equal (x3) - L71
specialize signed_support_reindex_sum_equal (x2) - L72
specialize signed_support_reindex_sum_equal (x4) - L73
specialize signed_support_reindex_sum_equal (x5) - L74
specialize signed_support_reindex_sum_equal ((S (m))*(S (n))) - L75
specialize signed_support_reindex_sum_equal (S (m*n)) - L76
specialize signed_support_reindex_sum_equal (x6) - L77
specialize signed_support_reindex_sum_equal (c) - L78
apply signed_support_reindex_sum_equal
11Use earlier factsL79–88
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L79
specialize dirichlet_coprime_grid_support_reindex (N) - L80
specialize dirichlet_coprime_grid_support_reindex (F) - L81
specialize dirichlet_coprime_grid_support_reindex (G) - L82
specialize dirichlet_coprime_grid_support_reindex (m) - L83
specialize dirichlet_coprime_grid_support_reindex (n) - L84
specialize dirichlet_coprime_grid_support_reindex (x) - L85
specialize dirichlet_coprime_grid_support_reindex (x1) - L86
specialize dirichlet_coprime_grid_support_reindex (x3) - L87
specialize dirichlet_coprime_grid_support_reindex (x2) - L88
specialize dirichlet_coprime_grid_support_reindex (x4)
12Use earlier factsL89–93
13Establish hpL94–103
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed cartesian product prefix sum.
- L94
have hp : SignedMul(a,b,x6)Definitions: SignedMul - L95
specialize signed_cartesian_product_prefix_sum (x) - L96
specialize signed_cartesian_product_prefix_sum (x1) - L97
specialize signed_cartesian_product_prefix_sum (x3) - L98
specialize signed_cartesian_product_prefix_sum (S m) - L99
specialize signed_cartesian_product_prefix_sum (S n) - L100
specialize signed_cartesian_product_prefix_sum (a) - L101
specialize signed_cartesian_product_prefix_sum (b) - L102
specialize signed_cartesian_product_prefix_sum (x6) - L103
apply signed_cartesian_product_prefix_sum
14Use earlier factsL104–107
15Calculate and transport equalitiesL108–109
16Use earlier factsL110–110
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L110
exact hp
Original exact command ledger · 110 lines
- 0001
intro N - 0002
intro F - 0003
intro G - 0004
intro m - 0005
intro n - 0006
intro a - 0007
intro b - 0008
intro c - 0009
intro hF - 0010
intro hG - 0011
intro hm - 0012
intro hn - 0013
intro hb - 0014
intro hc - 0015
intro hsm - 0016
intro hsn - 0017
intro hsc - 0018
cases hsm - 0019
cases hsm_right - 0020
cases hsm_right_witness - 0021
cases hsn - 0022
cases hsn_right - 0023
cases hsn_right_witness - 0024
cases hsc - 0025
cases hsc_right - 0026
cases hsc_right_witness - 0027
have hd : exists T r s. (((((~((N)=0)) /\ (((exists dst_positive_code_scalar_actual_dataFtable dst_positive_scale_scalar_actual_dataFtable dst_negative_code_scalar_actual_dataFtable dst_negative_scale_scalar_actual_dataFtable. (((F) = (((((dst_positive_code_scalar_actual_dataFtable) + (dst_positive_scale_scalar_actual_dataFtable)) * S ((dst_positive_code_scalar_actual_dataFtable) + (dst_positive_scale_scalar_actual_dataFtable)) + ((dst_positive_scale_scalar_actual_dataFtable) + (dst_positive_scale_scalar_actual_dataFtable))) + (((dst_negative_code_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)) * S ((dst_negative_code_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)) + ((dst_negative_scale_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)))) * S ((((dst_positive_code_scalar_actual_dataFtable) + (dst_positive_scale_scalar_actual_dataFtable)) * S ((dst_positive_code_scalar_actual_dataFtable) + (dst_positive_scale_scalar_actual_dataFtable)) + ((dst_positive_scale_scalar_actual_dataFtable) + (dst_positive_scale_scalar_actual_dataFtable))) + (((dst_negative_code_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)) * S ((dst_negative_code_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)) + ((dst_negative_scale_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)))) + ((((dst_negative_code_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)) * S ((dst_negative_code_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)) + ((dst_negative_scale_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable))) + (((dst_negative_code_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)) * S ((dst_negative_code_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)) + ((dst_negative_scale_scalar_actual_dataFtable) + (dst_negative_scale_scalar_actual_dataFtable)))))) /\ (forall dst_index_scalar_actual_dataFtable. (exists pvs_le_gap_scalar_actual_dataFtabledomain. pvs_le_gap_scalar_actual_dataFtabledomain + (dst_index_scalar_actual_dataFtable) = (N)) -> exists dst_positive_scalar_actual_dataFtable dst_negative_scalar_actual_dataFtable dst_value_scalar_actual_dataFtable. ((((exists ff_h_pvs_scalar_actual_dataFtableentrypositive. ff_h_pvs_scalar_actual_dataFtableentrypositive + S (dst_positive_scalar_actual_dataFtable) = S ((S (dst_index_scalar_actual_dataFtable)) * dst_positive_scale_scalar_actual_dataFtable)) /\ exists ff_q_pvs_scalar_actual_dataFtableentrypositive. dst_positive_code_scalar_actual_dataFtable = ff_q_pvs_scalar_actual_dataFtableentrypositive * S ((S (dst_index_scalar_actual_dataFtable)) * dst_positive_scale_scalar_actual_dataFtable) + (dst_positive_scalar_actual_dataFtable))) /\ (((((exists ff_h_pvs_scalar_actual_dataFtableentrynegative. ff_h_pvs_scalar_actual_dataFtableentrynegative + S (dst_negative_scalar_actual_dataFtable) = S ((S (dst_index_scalar_actual_dataFtable)) * dst_negative_scale_scalar_actual_dataFtable)) /\ exists ff_q_pvs_scalar_actual_dataFtableentrynegative. dst_negative_code_scalar_actual_dataFtable = ff_q_pvs_scalar_actual_dataFtableentrynegative * S ((S (dst_index_scalar_actual_dataFtable)) * dst_negative_scale_scalar_actual_dataFtable) + (dst_negative_scalar_actual_dataFtable))) /\ (exists ge_balance_positive_scalar_actual_dataFtableentryvalue ge_balance_negative_scalar_actual_dataFtableentryvalue. (((((dst_value_scalar_actual_dataFtable) = 2 * (ge_balance_positive_scalar_actual_dataFtableentryvalue) /\ (ge_balance_negative_scalar_actual_dataFtableentryvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataFtableentryvaluedecode. (((dst_value_scalar_actual_dataFtable) = 2 * ge_signed_half_scalar_actual_dataFtableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataFtableentryvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataFtableentryvalue) = S ge_signed_half_scalar_actual_dataFtableentryvaluedecode))) /\ ((dst_positive_scalar_actual_dataFtable) + ge_balance_negative_scalar_actual_dataFtableentryvalue = (dst_negative_scalar_actual_dataFtable) + ge_balance_positive_scalar_actual_dataFtableentryvalue))))))))) /\ (((exists dst_positive_code_scalar_actual_dataFone dst_positive_scale_scalar_actual_dataFone dst_negative_code_scalar_actual_dataFone dst_negative_scale_scalar_actual_dataFone dst_positive_scalar_actual_dataFone dst_negative_scalar_actual_dataFone. (((F) = (((((dst_positive_code_scalar_actual_dataFone) + (dst_positive_scale_scalar_actual_dataFone)) * S ((dst_positive_code_scalar_actual_dataFone) + (dst_positive_scale_scalar_actual_dataFone)) + ((dst_positive_scale_scalar_actual_dataFone) + (dst_positive_scale_scalar_actual_dataFone))) + (((dst_negative_code_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)) * S ((dst_negative_code_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)) + ((dst_negative_scale_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)))) * S ((((dst_positive_code_scalar_actual_dataFone) + (dst_positive_scale_scalar_actual_dataFone)) * S ((dst_positive_code_scalar_actual_dataFone) + (dst_positive_scale_scalar_actual_dataFone)) + ((dst_positive_scale_scalar_actual_dataFone) + (dst_positive_scale_scalar_actual_dataFone))) + (((dst_negative_code_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)) * S ((dst_negative_code_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)) + ((dst_negative_scale_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)))) + ((((dst_negative_code_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)) * S ((dst_negative_code_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)) + ((dst_negative_scale_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone))) + (((dst_negative_code_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)) * S ((dst_negative_code_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)) + ((dst_negative_scale_scalar_actual_dataFone) + (dst_negative_scale_scalar_actual_dataFone)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataFonepositive. ff_h_pvs_scalar_actual_dataFonepositive + S (dst_positive_scalar_actual_dataFone) = S ((S (1)) * dst_positive_scale_scalar_actual_dataFone)) /\ exists ff_q_pvs_scalar_actual_dataFonepositive. dst_positive_code_scalar_actual_dataFone = ff_q_pvs_scalar_actual_dataFonepositive * S ((S (1)) * dst_positive_scale_scalar_actual_dataFone) + (dst_positive_scalar_actual_dataFone))) /\ (((((exists ff_h_pvs_scalar_actual_dataFonenegative. ff_h_pvs_scalar_actual_dataFonenegative + S (dst_negative_scalar_actual_dataFone) = S ((S (1)) * dst_negative_scale_scalar_actual_dataFone)) /\ exists ff_q_pvs_scalar_actual_dataFonenegative. dst_negative_code_scalar_actual_dataFone = ff_q_pvs_scalar_actual_dataFonenegative * S ((S (1)) * dst_negative_scale_scalar_actual_dataFone) + (dst_negative_scalar_actual_dataFone))) /\ (exists ge_balance_positive_scalar_actual_dataFonevalue ge_balance_negative_scalar_actual_dataFonevalue. (((((2) = 2 * (ge_balance_positive_scalar_actual_dataFonevalue) /\ (ge_balance_negative_scalar_actual_dataFonevalue) = 0) \/ exists ge_signed_half_scalar_actual_dataFonevaluedecode. (((2) = 2 * ge_signed_half_scalar_actual_dataFonevaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataFonevalue) = 0) /\ (ge_balance_negative_scalar_actual_dataFonevalue) = S ge_signed_half_scalar_actual_dataFonevaluedecode))) /\ ((dst_positive_scalar_actual_dataFone) + ge_balance_negative_scalar_actual_dataFonevalue = (dst_negative_scalar_actual_dataFone) + ge_balance_positive_scalar_actual_dataFonevalue))))))))) /\ (forall mp_a_scalar_actual_dataF mp_b_scalar_actual_dataF mp_x_scalar_actual_dataF mp_y_scalar_actual_dataF mp_z_scalar_actual_dataF. ~(mp_a_scalar_actual_dataF=0) -> ~(mp_b_scalar_actual_dataF=0) -> (exists pvs_le_gap_scalar_actual_dataFbound. pvs_le_gap_scalar_actual_dataFbound + (mp_a_scalar_actual_dataF*mp_b_scalar_actual_dataF) = (N)) -> (forall frp_divisor_scalar_actual_dataFcoprime. (exists frp_left_factor_scalar_actual_dataFcoprime. mp_a_scalar_actual_dataF = frp_divisor_scalar_actual_dataFcoprime * frp_left_factor_scalar_actual_dataFcoprime) -> (exists frp_right_factor_scalar_actual_dataFcoprime. mp_b_scalar_actual_dataF = frp_divisor_scalar_actual_dataFcoprime * frp_right_factor_scalar_actual_dataFcoprime) -> frp_divisor_scalar_actual_dataFcoprime = 1) -> (exists dst_positive_code_scalar_actual_dataFfirst dst_positive_scale_scalar_actual_dataFfirst dst_negative_code_scalar_actual_dataFfirst dst_negative_scale_scalar_actual_dataFfirst dst_positive_scalar_actual_dataFfirst dst_negative_scalar_actual_dataFfirst. (((F) = (((((dst_positive_code_scalar_actual_dataFfirst) + (dst_positive_scale_scalar_actual_dataFfirst)) * S ((dst_positive_code_scalar_actual_dataFfirst) + (dst_positive_scale_scalar_actual_dataFfirst)) + ((dst_positive_scale_scalar_actual_dataFfirst) + (dst_positive_scale_scalar_actual_dataFfirst))) + (((dst_negative_code_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)) * S ((dst_negative_code_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)) + ((dst_negative_scale_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)))) * S ((((dst_positive_code_scalar_actual_dataFfirst) + (dst_positive_scale_scalar_actual_dataFfirst)) * S ((dst_positive_code_scalar_actual_dataFfirst) + (dst_positive_scale_scalar_actual_dataFfirst)) + ((dst_positive_scale_scalar_actual_dataFfirst) + (dst_positive_scale_scalar_actual_dataFfirst))) + (((dst_negative_code_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)) * S ((dst_negative_code_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)) + ((dst_negative_scale_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)))) + ((((dst_negative_code_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)) * S ((dst_negative_code_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)) + ((dst_negative_scale_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst))) + (((dst_negative_code_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)) * S ((dst_negative_code_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)) + ((dst_negative_scale_scalar_actual_dataFfirst) + (dst_negative_scale_scalar_actual_dataFfirst)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataFfirstpositive. ff_h_pvs_scalar_actual_dataFfirstpositive + S (dst_positive_scalar_actual_dataFfirst) = S ((S (mp_a_scalar_actual_dataF)) * dst_positive_scale_scalar_actual_dataFfirst)) /\ exists ff_q_pvs_scalar_actual_dataFfirstpositive. dst_positive_code_scalar_actual_dataFfirst = ff_q_pvs_scalar_actual_dataFfirstpositive * S ((S (mp_a_scalar_actual_dataF)) * dst_positive_scale_scalar_actual_dataFfirst) + (dst_positive_scalar_actual_dataFfirst))) /\ (((((exists ff_h_pvs_scalar_actual_dataFfirstnegative. ff_h_pvs_scalar_actual_dataFfirstnegative + S (dst_negative_scalar_actual_dataFfirst) = S ((S (mp_a_scalar_actual_dataF)) * dst_negative_scale_scalar_actual_dataFfirst)) /\ exists ff_q_pvs_scalar_actual_dataFfirstnegative. dst_negative_code_scalar_actual_dataFfirst = ff_q_pvs_scalar_actual_dataFfirstnegative * S ((S (mp_a_scalar_actual_dataF)) * dst_negative_scale_scalar_actual_dataFfirst) + (dst_negative_scalar_actual_dataFfirst))) /\ (exists ge_balance_positive_scalar_actual_dataFfirstvalue ge_balance_negative_scalar_actual_dataFfirstvalue. (((((mp_x_scalar_actual_dataF) = 2 * (ge_balance_positive_scalar_actual_dataFfirstvalue) /\ (ge_balance_negative_scalar_actual_dataFfirstvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataFfirstvaluedecode. (((mp_x_scalar_actual_dataF) = 2 * ge_signed_half_scalar_actual_dataFfirstvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataFfirstvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataFfirstvalue) = S ge_signed_half_scalar_actual_dataFfirstvaluedecode))) /\ ((dst_positive_scalar_actual_dataFfirst) + ge_balance_negative_scalar_actual_dataFfirstvalue = (dst_negative_scalar_actual_dataFfirst) + ge_balance_positive_scalar_actual_dataFfirstvalue))))))))) -> (exists dst_positive_code_scalar_actual_dataFsecond dst_positive_scale_scalar_actual_dataFsecond dst_negative_code_scalar_actual_dataFsecond dst_negative_scale_scalar_actual_dataFsecond dst_positive_scalar_actual_dataFsecond dst_negative_scalar_actual_dataFsecond. (((F) = (((((dst_positive_code_scalar_actual_dataFsecond) + (dst_positive_scale_scalar_actual_dataFsecond)) * S ((dst_positive_code_scalar_actual_dataFsecond) + (dst_positive_scale_scalar_actual_dataFsecond)) + ((dst_positive_scale_scalar_actual_dataFsecond) + (dst_positive_scale_scalar_actual_dataFsecond))) + (((dst_negative_code_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)) * S ((dst_negative_code_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)) + ((dst_negative_scale_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)))) * S ((((dst_positive_code_scalar_actual_dataFsecond) + (dst_positive_scale_scalar_actual_dataFsecond)) * S ((dst_positive_code_scalar_actual_dataFsecond) + (dst_positive_scale_scalar_actual_dataFsecond)) + ((dst_positive_scale_scalar_actual_dataFsecond) + (dst_positive_scale_scalar_actual_dataFsecond))) + (((dst_negative_code_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)) * S ((dst_negative_code_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)) + ((dst_negative_scale_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)))) + ((((dst_negative_code_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)) * S ((dst_negative_code_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)) + ((dst_negative_scale_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond))) + (((dst_negative_code_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)) * S ((dst_negative_code_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)) + ((dst_negative_scale_scalar_actual_dataFsecond) + (dst_negative_scale_scalar_actual_dataFsecond)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataFsecondpositive. ff_h_pvs_scalar_actual_dataFsecondpositive + S (dst_positive_scalar_actual_dataFsecond) = S ((S (mp_b_scalar_actual_dataF)) * dst_positive_scale_scalar_actual_dataFsecond)) /\ exists ff_q_pvs_scalar_actual_dataFsecondpositive. dst_positive_code_scalar_actual_dataFsecond = ff_q_pvs_scalar_actual_dataFsecondpositive * S ((S (mp_b_scalar_actual_dataF)) * dst_positive_scale_scalar_actual_dataFsecond) + (dst_positive_scalar_actual_dataFsecond))) /\ (((((exists ff_h_pvs_scalar_actual_dataFsecondnegative. ff_h_pvs_scalar_actual_dataFsecondnegative + S (dst_negative_scalar_actual_dataFsecond) = S ((S (mp_b_scalar_actual_dataF)) * dst_negative_scale_scalar_actual_dataFsecond)) /\ exists ff_q_pvs_scalar_actual_dataFsecondnegative. dst_negative_code_scalar_actual_dataFsecond = ff_q_pvs_scalar_actual_dataFsecondnegative * S ((S (mp_b_scalar_actual_dataF)) * dst_negative_scale_scalar_actual_dataFsecond) + (dst_negative_scalar_actual_dataFsecond))) /\ (exists ge_balance_positive_scalar_actual_dataFsecondvalue ge_balance_negative_scalar_actual_dataFsecondvalue. (((((mp_y_scalar_actual_dataF) = 2 * (ge_balance_positive_scalar_actual_dataFsecondvalue) /\ (ge_balance_negative_scalar_actual_dataFsecondvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataFsecondvaluedecode. (((mp_y_scalar_actual_dataF) = 2 * ge_signed_half_scalar_actual_dataFsecondvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataFsecondvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataFsecondvalue) = S ge_signed_half_scalar_actual_dataFsecondvaluedecode))) /\ ((dst_positive_scalar_actual_dataFsecond) + ge_balance_negative_scalar_actual_dataFsecondvalue = (dst_negative_scalar_actual_dataFsecond) + ge_balance_positive_scalar_actual_dataFsecondvalue))))))))) -> (exists dst_positive_code_scalar_actual_dataFproduct dst_positive_scale_scalar_actual_dataFproduct dst_negative_code_scalar_actual_dataFproduct dst_negative_scale_scalar_actual_dataFproduct dst_positive_scalar_actual_dataFproduct dst_negative_scalar_actual_dataFproduct. (((F) = (((((dst_positive_code_scalar_actual_dataFproduct) + (dst_positive_scale_scalar_actual_dataFproduct)) * S ((dst_positive_code_scalar_actual_dataFproduct) + (dst_positive_scale_scalar_actual_dataFproduct)) + ((dst_positive_scale_scalar_actual_dataFproduct) + (dst_positive_scale_scalar_actual_dataFproduct))) + (((dst_negative_code_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)) * S ((dst_negative_code_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)) + ((dst_negative_scale_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)))) * S ((((dst_positive_code_scalar_actual_dataFproduct) + (dst_positive_scale_scalar_actual_dataFproduct)) * S ((dst_positive_code_scalar_actual_dataFproduct) + (dst_positive_scale_scalar_actual_dataFproduct)) + ((dst_positive_scale_scalar_actual_dataFproduct) + (dst_positive_scale_scalar_actual_dataFproduct))) + (((dst_negative_code_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)) * S ((dst_negative_code_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)) + ((dst_negative_scale_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)))) + ((((dst_negative_code_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)) * S ((dst_negative_code_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)) + ((dst_negative_scale_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct))) + (((dst_negative_code_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)) * S ((dst_negative_code_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)) + ((dst_negative_scale_scalar_actual_dataFproduct) + (dst_negative_scale_scalar_actual_dataFproduct)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataFproductpositive. ff_h_pvs_scalar_actual_dataFproductpositive + S (dst_positive_scalar_actual_dataFproduct) = S ((S (mp_a_scalar_actual_dataF*mp_b_scalar_actual_dataF)) * dst_positive_scale_scalar_actual_dataFproduct)) /\ exists ff_q_pvs_scalar_actual_dataFproductpositive. dst_positive_code_scalar_actual_dataFproduct = ff_q_pvs_scalar_actual_dataFproductpositive * S ((S (mp_a_scalar_actual_dataF*mp_b_scalar_actual_dataF)) * dst_positive_scale_scalar_actual_dataFproduct) + (dst_positive_scalar_actual_dataFproduct))) /\ (((((exists ff_h_pvs_scalar_actual_dataFproductnegative. ff_h_pvs_scalar_actual_dataFproductnegative + S (dst_negative_scalar_actual_dataFproduct) = S ((S (mp_a_scalar_actual_dataF*mp_b_scalar_actual_dataF)) * dst_negative_scale_scalar_actual_dataFproduct)) /\ exists ff_q_pvs_scalar_actual_dataFproductnegative. dst_negative_code_scalar_actual_dataFproduct = ff_q_pvs_scalar_actual_dataFproductnegative * S ((S (mp_a_scalar_actual_dataF*mp_b_scalar_actual_dataF)) * dst_negative_scale_scalar_actual_dataFproduct) + (dst_negative_scalar_actual_dataFproduct))) /\ (exists ge_balance_positive_scalar_actual_dataFproductvalue ge_balance_negative_scalar_actual_dataFproductvalue. (((((mp_z_scalar_actual_dataF) = 2 * (ge_balance_positive_scalar_actual_dataFproductvalue) /\ (ge_balance_negative_scalar_actual_dataFproductvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataFproductvaluedecode. (((mp_z_scalar_actual_dataF) = 2 * ge_signed_half_scalar_actual_dataFproductvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataFproductvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataFproductvalue) = S ge_signed_half_scalar_actual_dataFproductvaluedecode))) /\ ((dst_positive_scalar_actual_dataFproduct) + ge_balance_negative_scalar_actual_dataFproductvalue = (dst_negative_scalar_actual_dataFproduct) + ge_balance_positive_scalar_actual_dataFproductvalue))))))))) -> (exists sto_ap_scalar_actual_dataFlaw sto_an_scalar_actual_dataFlaw sto_bp_scalar_actual_dataFlaw sto_bn_scalar_actual_dataFlaw sto_cp_scalar_actual_dataFlaw sto_cn_scalar_actual_dataFlaw. (((((mp_x_scalar_actual_dataF) = 2 * (sto_ap_scalar_actual_dataFlaw) /\ (sto_an_scalar_actual_dataFlaw) = 0) \/ exists ge_signed_half_scalar_actual_dataFlawleft. (((mp_x_scalar_actual_dataF) = 2 * ge_signed_half_scalar_actual_dataFlawleft + 1 /\ (sto_ap_scalar_actual_dataFlaw) = 0) /\ (sto_an_scalar_actual_dataFlaw) = S ge_signed_half_scalar_actual_dataFlawleft))) /\ ((((((mp_y_scalar_actual_dataF) = 2 * (sto_bp_scalar_actual_dataFlaw) /\ (sto_bn_scalar_actual_dataFlaw) = 0) \/ exists ge_signed_half_scalar_actual_dataFlawright. (((mp_y_scalar_actual_dataF) = 2 * ge_signed_half_scalar_actual_dataFlawright + 1 /\ (sto_bp_scalar_actual_dataFlaw) = 0) /\ (sto_bn_scalar_actual_dataFlaw) = S ge_signed_half_scalar_actual_dataFlawright))) /\ ((((((mp_z_scalar_actual_dataF) = 2 * (sto_cp_scalar_actual_dataFlaw) /\ (sto_cn_scalar_actual_dataFlaw) = 0) \/ exists ge_signed_half_scalar_actual_dataFlawoutput. (((mp_z_scalar_actual_dataF) = 2 * ge_signed_half_scalar_actual_dataFlawoutput + 1 /\ (sto_cp_scalar_actual_dataFlaw) = 0) /\ (sto_cn_scalar_actual_dataFlaw) = S ge_signed_half_scalar_actual_dataFlawoutput))) /\ ((sto_ap_scalar_actual_dataFlaw * sto_bp_scalar_actual_dataFlaw + sto_an_scalar_actual_dataFlaw * sto_bn_scalar_actual_dataFlaw) + sto_cn_scalar_actual_dataFlaw = (sto_ap_scalar_actual_dataFlaw * sto_bn_scalar_actual_dataFlaw + sto_an_scalar_actual_dataFlaw * sto_bp_scalar_actual_dataFlaw) + sto_cp_scalar_actual_dataFlaw)))))))))))))) /\ (((((~((N)=0)) /\ (((exists dst_positive_code_scalar_actual_dataGtable dst_positive_scale_scalar_actual_dataGtable dst_negative_code_scalar_actual_dataGtable dst_negative_scale_scalar_actual_dataGtable. (((G) = (((((dst_positive_code_scalar_actual_dataGtable) + (dst_positive_scale_scalar_actual_dataGtable)) * S ((dst_positive_code_scalar_actual_dataGtable) + (dst_positive_scale_scalar_actual_dataGtable)) + ((dst_positive_scale_scalar_actual_dataGtable) + (dst_positive_scale_scalar_actual_dataGtable))) + (((dst_negative_code_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)) * S ((dst_negative_code_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)) + ((dst_negative_scale_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)))) * S ((((dst_positive_code_scalar_actual_dataGtable) + (dst_positive_scale_scalar_actual_dataGtable)) * S ((dst_positive_code_scalar_actual_dataGtable) + (dst_positive_scale_scalar_actual_dataGtable)) + ((dst_positive_scale_scalar_actual_dataGtable) + (dst_positive_scale_scalar_actual_dataGtable))) + (((dst_negative_code_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)) * S ((dst_negative_code_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)) + ((dst_negative_scale_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)))) + ((((dst_negative_code_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)) * S ((dst_negative_code_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)) + ((dst_negative_scale_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable))) + (((dst_negative_code_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)) * S ((dst_negative_code_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)) + ((dst_negative_scale_scalar_actual_dataGtable) + (dst_negative_scale_scalar_actual_dataGtable)))))) /\ (forall dst_index_scalar_actual_dataGtable. (exists pvs_le_gap_scalar_actual_dataGtabledomain. pvs_le_gap_scalar_actual_dataGtabledomain + (dst_index_scalar_actual_dataGtable) = (N)) -> exists dst_positive_scalar_actual_dataGtable dst_negative_scalar_actual_dataGtable dst_value_scalar_actual_dataGtable. ((((exists ff_h_pvs_scalar_actual_dataGtableentrypositive. ff_h_pvs_scalar_actual_dataGtableentrypositive + S (dst_positive_scalar_actual_dataGtable) = S ((S (dst_index_scalar_actual_dataGtable)) * dst_positive_scale_scalar_actual_dataGtable)) /\ exists ff_q_pvs_scalar_actual_dataGtableentrypositive. dst_positive_code_scalar_actual_dataGtable = ff_q_pvs_scalar_actual_dataGtableentrypositive * S ((S (dst_index_scalar_actual_dataGtable)) * dst_positive_scale_scalar_actual_dataGtable) + (dst_positive_scalar_actual_dataGtable))) /\ (((((exists ff_h_pvs_scalar_actual_dataGtableentrynegative. ff_h_pvs_scalar_actual_dataGtableentrynegative + S (dst_negative_scalar_actual_dataGtable) = S ((S (dst_index_scalar_actual_dataGtable)) * dst_negative_scale_scalar_actual_dataGtable)) /\ exists ff_q_pvs_scalar_actual_dataGtableentrynegative. dst_negative_code_scalar_actual_dataGtable = ff_q_pvs_scalar_actual_dataGtableentrynegative * S ((S (dst_index_scalar_actual_dataGtable)) * dst_negative_scale_scalar_actual_dataGtable) + (dst_negative_scalar_actual_dataGtable))) /\ (exists ge_balance_positive_scalar_actual_dataGtableentryvalue ge_balance_negative_scalar_actual_dataGtableentryvalue. (((((dst_value_scalar_actual_dataGtable) = 2 * (ge_balance_positive_scalar_actual_dataGtableentryvalue) /\ (ge_balance_negative_scalar_actual_dataGtableentryvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataGtableentryvaluedecode. (((dst_value_scalar_actual_dataGtable) = 2 * ge_signed_half_scalar_actual_dataGtableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataGtableentryvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataGtableentryvalue) = S ge_signed_half_scalar_actual_dataGtableentryvaluedecode))) /\ ((dst_positive_scalar_actual_dataGtable) + ge_balance_negative_scalar_actual_dataGtableentryvalue = (dst_negative_scalar_actual_dataGtable) + ge_balance_positive_scalar_actual_dataGtableentryvalue))))))))) /\ (((exists dst_positive_code_scalar_actual_dataGone dst_positive_scale_scalar_actual_dataGone dst_negative_code_scalar_actual_dataGone dst_negative_scale_scalar_actual_dataGone dst_positive_scalar_actual_dataGone dst_negative_scalar_actual_dataGone. (((G) = (((((dst_positive_code_scalar_actual_dataGone) + (dst_positive_scale_scalar_actual_dataGone)) * S ((dst_positive_code_scalar_actual_dataGone) + (dst_positive_scale_scalar_actual_dataGone)) + ((dst_positive_scale_scalar_actual_dataGone) + (dst_positive_scale_scalar_actual_dataGone))) + (((dst_negative_code_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)) * S ((dst_negative_code_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)) + ((dst_negative_scale_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)))) * S ((((dst_positive_code_scalar_actual_dataGone) + (dst_positive_scale_scalar_actual_dataGone)) * S ((dst_positive_code_scalar_actual_dataGone) + (dst_positive_scale_scalar_actual_dataGone)) + ((dst_positive_scale_scalar_actual_dataGone) + (dst_positive_scale_scalar_actual_dataGone))) + (((dst_negative_code_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)) * S ((dst_negative_code_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)) + ((dst_negative_scale_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)))) + ((((dst_negative_code_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)) * S ((dst_negative_code_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)) + ((dst_negative_scale_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone))) + (((dst_negative_code_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)) * S ((dst_negative_code_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)) + ((dst_negative_scale_scalar_actual_dataGone) + (dst_negative_scale_scalar_actual_dataGone)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataGonepositive. ff_h_pvs_scalar_actual_dataGonepositive + S (dst_positive_scalar_actual_dataGone) = S ((S (1)) * dst_positive_scale_scalar_actual_dataGone)) /\ exists ff_q_pvs_scalar_actual_dataGonepositive. dst_positive_code_scalar_actual_dataGone = ff_q_pvs_scalar_actual_dataGonepositive * S ((S (1)) * dst_positive_scale_scalar_actual_dataGone) + (dst_positive_scalar_actual_dataGone))) /\ (((((exists ff_h_pvs_scalar_actual_dataGonenegative. ff_h_pvs_scalar_actual_dataGonenegative + S (dst_negative_scalar_actual_dataGone) = S ((S (1)) * dst_negative_scale_scalar_actual_dataGone)) /\ exists ff_q_pvs_scalar_actual_dataGonenegative. dst_negative_code_scalar_actual_dataGone = ff_q_pvs_scalar_actual_dataGonenegative * S ((S (1)) * dst_negative_scale_scalar_actual_dataGone) + (dst_negative_scalar_actual_dataGone))) /\ (exists ge_balance_positive_scalar_actual_dataGonevalue ge_balance_negative_scalar_actual_dataGonevalue. (((((2) = 2 * (ge_balance_positive_scalar_actual_dataGonevalue) /\ (ge_balance_negative_scalar_actual_dataGonevalue) = 0) \/ exists ge_signed_half_scalar_actual_dataGonevaluedecode. (((2) = 2 * ge_signed_half_scalar_actual_dataGonevaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataGonevalue) = 0) /\ (ge_balance_negative_scalar_actual_dataGonevalue) = S ge_signed_half_scalar_actual_dataGonevaluedecode))) /\ ((dst_positive_scalar_actual_dataGone) + ge_balance_negative_scalar_actual_dataGonevalue = (dst_negative_scalar_actual_dataGone) + ge_balance_positive_scalar_actual_dataGonevalue))))))))) /\ (forall mp_a_scalar_actual_dataG mp_b_scalar_actual_dataG mp_x_scalar_actual_dataG mp_y_scalar_actual_dataG mp_z_scalar_actual_dataG. ~(mp_a_scalar_actual_dataG=0) -> ~(mp_b_scalar_actual_dataG=0) -> (exists pvs_le_gap_scalar_actual_dataGbound. pvs_le_gap_scalar_actual_dataGbound + (mp_a_scalar_actual_dataG*mp_b_scalar_actual_dataG) = (N)) -> (forall frp_divisor_scalar_actual_dataGcoprime. (exists frp_left_factor_scalar_actual_dataGcoprime. mp_a_scalar_actual_dataG = frp_divisor_scalar_actual_dataGcoprime * frp_left_factor_scalar_actual_dataGcoprime) -> (exists frp_right_factor_scalar_actual_dataGcoprime. mp_b_scalar_actual_dataG = frp_divisor_scalar_actual_dataGcoprime * frp_right_factor_scalar_actual_dataGcoprime) -> frp_divisor_scalar_actual_dataGcoprime = 1) -> (exists dst_positive_code_scalar_actual_dataGfirst dst_positive_scale_scalar_actual_dataGfirst dst_negative_code_scalar_actual_dataGfirst dst_negative_scale_scalar_actual_dataGfirst dst_positive_scalar_actual_dataGfirst dst_negative_scalar_actual_dataGfirst. (((G) = (((((dst_positive_code_scalar_actual_dataGfirst) + (dst_positive_scale_scalar_actual_dataGfirst)) * S ((dst_positive_code_scalar_actual_dataGfirst) + (dst_positive_scale_scalar_actual_dataGfirst)) + ((dst_positive_scale_scalar_actual_dataGfirst) + (dst_positive_scale_scalar_actual_dataGfirst))) + (((dst_negative_code_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)) * S ((dst_negative_code_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)) + ((dst_negative_scale_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)))) * S ((((dst_positive_code_scalar_actual_dataGfirst) + (dst_positive_scale_scalar_actual_dataGfirst)) * S ((dst_positive_code_scalar_actual_dataGfirst) + (dst_positive_scale_scalar_actual_dataGfirst)) + ((dst_positive_scale_scalar_actual_dataGfirst) + (dst_positive_scale_scalar_actual_dataGfirst))) + (((dst_negative_code_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)) * S ((dst_negative_code_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)) + ((dst_negative_scale_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)))) + ((((dst_negative_code_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)) * S ((dst_negative_code_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)) + ((dst_negative_scale_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst))) + (((dst_negative_code_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)) * S ((dst_negative_code_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)) + ((dst_negative_scale_scalar_actual_dataGfirst) + (dst_negative_scale_scalar_actual_dataGfirst)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataGfirstpositive. ff_h_pvs_scalar_actual_dataGfirstpositive + S (dst_positive_scalar_actual_dataGfirst) = S ((S (mp_a_scalar_actual_dataG)) * dst_positive_scale_scalar_actual_dataGfirst)) /\ exists ff_q_pvs_scalar_actual_dataGfirstpositive. dst_positive_code_scalar_actual_dataGfirst = ff_q_pvs_scalar_actual_dataGfirstpositive * S ((S (mp_a_scalar_actual_dataG)) * dst_positive_scale_scalar_actual_dataGfirst) + (dst_positive_scalar_actual_dataGfirst))) /\ (((((exists ff_h_pvs_scalar_actual_dataGfirstnegative. ff_h_pvs_scalar_actual_dataGfirstnegative + S (dst_negative_scalar_actual_dataGfirst) = S ((S (mp_a_scalar_actual_dataG)) * dst_negative_scale_scalar_actual_dataGfirst)) /\ exists ff_q_pvs_scalar_actual_dataGfirstnegative. dst_negative_code_scalar_actual_dataGfirst = ff_q_pvs_scalar_actual_dataGfirstnegative * S ((S (mp_a_scalar_actual_dataG)) * dst_negative_scale_scalar_actual_dataGfirst) + (dst_negative_scalar_actual_dataGfirst))) /\ (exists ge_balance_positive_scalar_actual_dataGfirstvalue ge_balance_negative_scalar_actual_dataGfirstvalue. (((((mp_x_scalar_actual_dataG) = 2 * (ge_balance_positive_scalar_actual_dataGfirstvalue) /\ (ge_balance_negative_scalar_actual_dataGfirstvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataGfirstvaluedecode. (((mp_x_scalar_actual_dataG) = 2 * ge_signed_half_scalar_actual_dataGfirstvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataGfirstvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataGfirstvalue) = S ge_signed_half_scalar_actual_dataGfirstvaluedecode))) /\ ((dst_positive_scalar_actual_dataGfirst) + ge_balance_negative_scalar_actual_dataGfirstvalue = (dst_negative_scalar_actual_dataGfirst) + ge_balance_positive_scalar_actual_dataGfirstvalue))))))))) -> (exists dst_positive_code_scalar_actual_dataGsecond dst_positive_scale_scalar_actual_dataGsecond dst_negative_code_scalar_actual_dataGsecond dst_negative_scale_scalar_actual_dataGsecond dst_positive_scalar_actual_dataGsecond dst_negative_scalar_actual_dataGsecond. (((G) = (((((dst_positive_code_scalar_actual_dataGsecond) + (dst_positive_scale_scalar_actual_dataGsecond)) * S ((dst_positive_code_scalar_actual_dataGsecond) + (dst_positive_scale_scalar_actual_dataGsecond)) + ((dst_positive_scale_scalar_actual_dataGsecond) + (dst_positive_scale_scalar_actual_dataGsecond))) + (((dst_negative_code_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)) * S ((dst_negative_code_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)) + ((dst_negative_scale_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)))) * S ((((dst_positive_code_scalar_actual_dataGsecond) + (dst_positive_scale_scalar_actual_dataGsecond)) * S ((dst_positive_code_scalar_actual_dataGsecond) + (dst_positive_scale_scalar_actual_dataGsecond)) + ((dst_positive_scale_scalar_actual_dataGsecond) + (dst_positive_scale_scalar_actual_dataGsecond))) + (((dst_negative_code_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)) * S ((dst_negative_code_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)) + ((dst_negative_scale_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)))) + ((((dst_negative_code_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)) * S ((dst_negative_code_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)) + ((dst_negative_scale_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond))) + (((dst_negative_code_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)) * S ((dst_negative_code_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)) + ((dst_negative_scale_scalar_actual_dataGsecond) + (dst_negative_scale_scalar_actual_dataGsecond)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataGsecondpositive. ff_h_pvs_scalar_actual_dataGsecondpositive + S (dst_positive_scalar_actual_dataGsecond) = S ((S (mp_b_scalar_actual_dataG)) * dst_positive_scale_scalar_actual_dataGsecond)) /\ exists ff_q_pvs_scalar_actual_dataGsecondpositive. dst_positive_code_scalar_actual_dataGsecond = ff_q_pvs_scalar_actual_dataGsecondpositive * S ((S (mp_b_scalar_actual_dataG)) * dst_positive_scale_scalar_actual_dataGsecond) + (dst_positive_scalar_actual_dataGsecond))) /\ (((((exists ff_h_pvs_scalar_actual_dataGsecondnegative. ff_h_pvs_scalar_actual_dataGsecondnegative + S (dst_negative_scalar_actual_dataGsecond) = S ((S (mp_b_scalar_actual_dataG)) * dst_negative_scale_scalar_actual_dataGsecond)) /\ exists ff_q_pvs_scalar_actual_dataGsecondnegative. dst_negative_code_scalar_actual_dataGsecond = ff_q_pvs_scalar_actual_dataGsecondnegative * S ((S (mp_b_scalar_actual_dataG)) * dst_negative_scale_scalar_actual_dataGsecond) + (dst_negative_scalar_actual_dataGsecond))) /\ (exists ge_balance_positive_scalar_actual_dataGsecondvalue ge_balance_negative_scalar_actual_dataGsecondvalue. (((((mp_y_scalar_actual_dataG) = 2 * (ge_balance_positive_scalar_actual_dataGsecondvalue) /\ (ge_balance_negative_scalar_actual_dataGsecondvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataGsecondvaluedecode. (((mp_y_scalar_actual_dataG) = 2 * ge_signed_half_scalar_actual_dataGsecondvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataGsecondvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataGsecondvalue) = S ge_signed_half_scalar_actual_dataGsecondvaluedecode))) /\ ((dst_positive_scalar_actual_dataGsecond) + ge_balance_negative_scalar_actual_dataGsecondvalue = (dst_negative_scalar_actual_dataGsecond) + ge_balance_positive_scalar_actual_dataGsecondvalue))))))))) -> (exists dst_positive_code_scalar_actual_dataGproduct dst_positive_scale_scalar_actual_dataGproduct dst_negative_code_scalar_actual_dataGproduct dst_negative_scale_scalar_actual_dataGproduct dst_positive_scalar_actual_dataGproduct dst_negative_scalar_actual_dataGproduct. (((G) = (((((dst_positive_code_scalar_actual_dataGproduct) + (dst_positive_scale_scalar_actual_dataGproduct)) * S ((dst_positive_code_scalar_actual_dataGproduct) + (dst_positive_scale_scalar_actual_dataGproduct)) + ((dst_positive_scale_scalar_actual_dataGproduct) + (dst_positive_scale_scalar_actual_dataGproduct))) + (((dst_negative_code_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)) * S ((dst_negative_code_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)) + ((dst_negative_scale_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)))) * S ((((dst_positive_code_scalar_actual_dataGproduct) + (dst_positive_scale_scalar_actual_dataGproduct)) * S ((dst_positive_code_scalar_actual_dataGproduct) + (dst_positive_scale_scalar_actual_dataGproduct)) + ((dst_positive_scale_scalar_actual_dataGproduct) + (dst_positive_scale_scalar_actual_dataGproduct))) + (((dst_negative_code_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)) * S ((dst_negative_code_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)) + ((dst_negative_scale_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)))) + ((((dst_negative_code_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)) * S ((dst_negative_code_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)) + ((dst_negative_scale_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct))) + (((dst_negative_code_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)) * S ((dst_negative_code_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)) + ((dst_negative_scale_scalar_actual_dataGproduct) + (dst_negative_scale_scalar_actual_dataGproduct)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataGproductpositive. ff_h_pvs_scalar_actual_dataGproductpositive + S (dst_positive_scalar_actual_dataGproduct) = S ((S (mp_a_scalar_actual_dataG*mp_b_scalar_actual_dataG)) * dst_positive_scale_scalar_actual_dataGproduct)) /\ exists ff_q_pvs_scalar_actual_dataGproductpositive. dst_positive_code_scalar_actual_dataGproduct = ff_q_pvs_scalar_actual_dataGproductpositive * S ((S (mp_a_scalar_actual_dataG*mp_b_scalar_actual_dataG)) * dst_positive_scale_scalar_actual_dataGproduct) + (dst_positive_scalar_actual_dataGproduct))) /\ (((((exists ff_h_pvs_scalar_actual_dataGproductnegative. ff_h_pvs_scalar_actual_dataGproductnegative + S (dst_negative_scalar_actual_dataGproduct) = S ((S (mp_a_scalar_actual_dataG*mp_b_scalar_actual_dataG)) * dst_negative_scale_scalar_actual_dataGproduct)) /\ exists ff_q_pvs_scalar_actual_dataGproductnegative. dst_negative_code_scalar_actual_dataGproduct = ff_q_pvs_scalar_actual_dataGproductnegative * S ((S (mp_a_scalar_actual_dataG*mp_b_scalar_actual_dataG)) * dst_negative_scale_scalar_actual_dataGproduct) + (dst_negative_scalar_actual_dataGproduct))) /\ (exists ge_balance_positive_scalar_actual_dataGproductvalue ge_balance_negative_scalar_actual_dataGproductvalue. (((((mp_z_scalar_actual_dataG) = 2 * (ge_balance_positive_scalar_actual_dataGproductvalue) /\ (ge_balance_negative_scalar_actual_dataGproductvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataGproductvaluedecode. (((mp_z_scalar_actual_dataG) = 2 * ge_signed_half_scalar_actual_dataGproductvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataGproductvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataGproductvalue) = S ge_signed_half_scalar_actual_dataGproductvaluedecode))) /\ ((dst_positive_scalar_actual_dataGproduct) + ge_balance_negative_scalar_actual_dataGproductvalue = (dst_negative_scalar_actual_dataGproduct) + ge_balance_positive_scalar_actual_dataGproductvalue))))))))) -> (exists sto_ap_scalar_actual_dataGlaw sto_an_scalar_actual_dataGlaw sto_bp_scalar_actual_dataGlaw sto_bn_scalar_actual_dataGlaw sto_cp_scalar_actual_dataGlaw sto_cn_scalar_actual_dataGlaw. (((((mp_x_scalar_actual_dataG) = 2 * (sto_ap_scalar_actual_dataGlaw) /\ (sto_an_scalar_actual_dataGlaw) = 0) \/ exists ge_signed_half_scalar_actual_dataGlawleft. (((mp_x_scalar_actual_dataG) = 2 * ge_signed_half_scalar_actual_dataGlawleft + 1 /\ (sto_ap_scalar_actual_dataGlaw) = 0) /\ (sto_an_scalar_actual_dataGlaw) = S ge_signed_half_scalar_actual_dataGlawleft))) /\ ((((((mp_y_scalar_actual_dataG) = 2 * (sto_bp_scalar_actual_dataGlaw) /\ (sto_bn_scalar_actual_dataGlaw) = 0) \/ exists ge_signed_half_scalar_actual_dataGlawright. (((mp_y_scalar_actual_dataG) = 2 * ge_signed_half_scalar_actual_dataGlawright + 1 /\ (sto_bp_scalar_actual_dataGlaw) = 0) /\ (sto_bn_scalar_actual_dataGlaw) = S ge_signed_half_scalar_actual_dataGlawright))) /\ ((((((mp_z_scalar_actual_dataG) = 2 * (sto_cp_scalar_actual_dataGlaw) /\ (sto_cn_scalar_actual_dataGlaw) = 0) \/ exists ge_signed_half_scalar_actual_dataGlawoutput. (((mp_z_scalar_actual_dataG) = 2 * ge_signed_half_scalar_actual_dataGlawoutput + 1 /\ (sto_cp_scalar_actual_dataGlaw) = 0) /\ (sto_cn_scalar_actual_dataGlaw) = S ge_signed_half_scalar_actual_dataGlawoutput))) /\ ((sto_ap_scalar_actual_dataGlaw * sto_bp_scalar_actual_dataGlaw + sto_an_scalar_actual_dataGlaw * sto_bn_scalar_actual_dataGlaw) + sto_cn_scalar_actual_dataGlaw = (sto_ap_scalar_actual_dataGlaw * sto_bn_scalar_actual_dataGlaw + sto_an_scalar_actual_dataGlaw * sto_bp_scalar_actual_dataGlaw) + sto_cp_scalar_actual_dataGlaw)))))))))))))) /\ (((~((m)=0)) /\ (((~((n)=0)) /\ (((exists pvs_le_gap_scalar_actual_databound. pvs_le_gap_scalar_actual_databound + ((m)*(n)) = (N)) /\ (((forall sfd_common_divisor_scalar_actual_datacoprime. (exists pvs_factor_scalar_actual_datacoprimeleft. (m) = (sfd_common_divisor_scalar_actual_datacoprime) * pvs_factor_scalar_actual_datacoprimeleft) -> (exists pvs_factor_scalar_actual_datacoprimeright. (n) = (sfd_common_divisor_scalar_actual_datacoprime) * pvs_factor_scalar_actual_datacoprimeright) -> sfd_common_divisor_scalar_actual_datacoprime = 1) /\ (((((exists dst_positive_code_scalar_actual_datalefttable dst_positive_scale_scalar_actual_datalefttable dst_negative_code_scalar_actual_datalefttable dst_negative_scale_scalar_actual_datalefttable. (((x) = (((((dst_positive_code_scalar_actual_datalefttable) + (dst_positive_scale_scalar_actual_datalefttable)) * S ((dst_positive_code_scalar_actual_datalefttable) + (dst_positive_scale_scalar_actual_datalefttable)) + ((dst_positive_scale_scalar_actual_datalefttable) + (dst_positive_scale_scalar_actual_datalefttable))) + (((dst_negative_code_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)) * S ((dst_negative_code_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)) + ((dst_negative_scale_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)))) * S ((((dst_positive_code_scalar_actual_datalefttable) + (dst_positive_scale_scalar_actual_datalefttable)) * S ((dst_positive_code_scalar_actual_datalefttable) + (dst_positive_scale_scalar_actual_datalefttable)) + ((dst_positive_scale_scalar_actual_datalefttable) + (dst_positive_scale_scalar_actual_datalefttable))) + (((dst_negative_code_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)) * S ((dst_negative_code_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)) + ((dst_negative_scale_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)))) + ((((dst_negative_code_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)) * S ((dst_negative_code_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)) + ((dst_negative_scale_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable))) + (((dst_negative_code_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)) * S ((dst_negative_code_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)) + ((dst_negative_scale_scalar_actual_datalefttable) + (dst_negative_scale_scalar_actual_datalefttable)))))) /\ (forall dst_index_scalar_actual_datalefttable. (exists pvs_le_gap_scalar_actual_datalefttabledomain. pvs_le_gap_scalar_actual_datalefttabledomain + (dst_index_scalar_actual_datalefttable) = (m)) -> exists dst_positive_scalar_actual_datalefttable dst_negative_scalar_actual_datalefttable dst_value_scalar_actual_datalefttable. ((((exists ff_h_pvs_scalar_actual_datalefttableentrypositive. ff_h_pvs_scalar_actual_datalefttableentrypositive + S (dst_positive_scalar_actual_datalefttable) = S ((S (dst_index_scalar_actual_datalefttable)) * dst_positive_scale_scalar_actual_datalefttable)) /\ exists ff_q_pvs_scalar_actual_datalefttableentrypositive. dst_positive_code_scalar_actual_datalefttable = ff_q_pvs_scalar_actual_datalefttableentrypositive * S ((S (dst_index_scalar_actual_datalefttable)) * dst_positive_scale_scalar_actual_datalefttable) + (dst_positive_scalar_actual_datalefttable))) /\ (((((exists ff_h_pvs_scalar_actual_datalefttableentrynegative. ff_h_pvs_scalar_actual_datalefttableentrynegative + S (dst_negative_scalar_actual_datalefttable) = S ((S (dst_index_scalar_actual_datalefttable)) * dst_negative_scale_scalar_actual_datalefttable)) /\ exists ff_q_pvs_scalar_actual_datalefttableentrynegative. dst_negative_code_scalar_actual_datalefttable = ff_q_pvs_scalar_actual_datalefttableentrynegative * S ((S (dst_index_scalar_actual_datalefttable)) * dst_negative_scale_scalar_actual_datalefttable) + (dst_negative_scalar_actual_datalefttable))) /\ (exists ge_balance_positive_scalar_actual_datalefttableentryvalue ge_balance_negative_scalar_actual_datalefttableentryvalue. (((((dst_value_scalar_actual_datalefttable) = 2 * (ge_balance_positive_scalar_actual_datalefttableentryvalue) /\ (ge_balance_negative_scalar_actual_datalefttableentryvalue) = 0) \/ exists ge_signed_half_scalar_actual_datalefttableentryvaluedecode. (((dst_value_scalar_actual_datalefttable) = 2 * ge_signed_half_scalar_actual_datalefttableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datalefttableentryvalue) = 0) /\ (ge_balance_negative_scalar_actual_datalefttableentryvalue) = S ge_signed_half_scalar_actual_datalefttableentryvaluedecode))) /\ ((dst_positive_scalar_actual_datalefttable) + ge_balance_negative_scalar_actual_datalefttableentryvalue = (dst_negative_scalar_actual_datalefttable) + ge_balance_positive_scalar_actual_datalefttableentryvalue))))))))) /\ (forall dc_index_scalar_actual_dataleft dc_value_scalar_actual_dataleft. (exists pvs_le_gap_scalar_actual_dataleftdomain. pvs_le_gap_scalar_actual_dataleftdomain + (dc_index_scalar_actual_dataleft) = (m)) -> (exists dst_positive_code_scalar_actual_dataleftlookup dst_positive_scale_scalar_actual_dataleftlookup dst_negative_code_scalar_actual_dataleftlookup dst_negative_scale_scalar_actual_dataleftlookup dst_positive_scalar_actual_dataleftlookup dst_negative_scalar_actual_dataleftlookup. (((x) = (((((dst_positive_code_scalar_actual_dataleftlookup) + (dst_positive_scale_scalar_actual_dataleftlookup)) * S ((dst_positive_code_scalar_actual_dataleftlookup) + (dst_positive_scale_scalar_actual_dataleftlookup)) + ((dst_positive_scale_scalar_actual_dataleftlookup) + (dst_positive_scale_scalar_actual_dataleftlookup))) + (((dst_negative_code_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)) * S ((dst_negative_code_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)) + ((dst_negative_scale_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)))) * S ((((dst_positive_code_scalar_actual_dataleftlookup) + (dst_positive_scale_scalar_actual_dataleftlookup)) * S ((dst_positive_code_scalar_actual_dataleftlookup) + (dst_positive_scale_scalar_actual_dataleftlookup)) + ((dst_positive_scale_scalar_actual_dataleftlookup) + (dst_positive_scale_scalar_actual_dataleftlookup))) + (((dst_negative_code_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)) * S ((dst_negative_code_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)) + ((dst_negative_scale_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)))) + ((((dst_negative_code_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)) * S ((dst_negative_code_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)) + ((dst_negative_scale_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup))) + (((dst_negative_code_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)) * S ((dst_negative_code_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)) + ((dst_negative_scale_scalar_actual_dataleftlookup) + (dst_negative_scale_scalar_actual_dataleftlookup)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataleftlookuppositive. ff_h_pvs_scalar_actual_dataleftlookuppositive + S (dst_positive_scalar_actual_dataleftlookup) = S ((S (dc_index_scalar_actual_dataleft)) * dst_positive_scale_scalar_actual_dataleftlookup)) /\ exists ff_q_pvs_scalar_actual_dataleftlookuppositive. dst_positive_code_scalar_actual_dataleftlookup = ff_q_pvs_scalar_actual_dataleftlookuppositive * S ((S (dc_index_scalar_actual_dataleft)) * dst_positive_scale_scalar_actual_dataleftlookup) + (dst_positive_scalar_actual_dataleftlookup))) /\ (((((exists ff_h_pvs_scalar_actual_dataleftlookupnegative. ff_h_pvs_scalar_actual_dataleftlookupnegative + S (dst_negative_scalar_actual_dataleftlookup) = S ((S (dc_index_scalar_actual_dataleft)) * dst_negative_scale_scalar_actual_dataleftlookup)) /\ exists ff_q_pvs_scalar_actual_dataleftlookupnegative. dst_negative_code_scalar_actual_dataleftlookup = ff_q_pvs_scalar_actual_dataleftlookupnegative * S ((S (dc_index_scalar_actual_dataleft)) * dst_negative_scale_scalar_actual_dataleftlookup) + (dst_negative_scalar_actual_dataleftlookup))) /\ (exists ge_balance_positive_scalar_actual_dataleftlookupvalue ge_balance_negative_scalar_actual_dataleftlookupvalue. (((((dc_value_scalar_actual_dataleft) = 2 * (ge_balance_positive_scalar_actual_dataleftlookupvalue) /\ (ge_balance_negative_scalar_actual_dataleftlookupvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataleftlookupvaluedecode. (((dc_value_scalar_actual_dataleft) = 2 * ge_signed_half_scalar_actual_dataleftlookupvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataleftlookupvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataleftlookupvalue) = S ge_signed_half_scalar_actual_dataleftlookupvaluedecode))) /\ ((dst_positive_scalar_actual_dataleftlookup) + ge_balance_negative_scalar_actual_dataleftlookupvalue = (dst_negative_scalar_actual_dataleftlookup) + ge_balance_positive_scalar_actual_dataleftlookupvalue))))))))) -> ((((~((dc_index_scalar_actual_dataleft)=0)) /\ (exists dc_quotient_scalar_actual_dataleftentry dc_left_scalar_actual_dataleftentry dc_right_scalar_actual_dataleftentry. (((m)=(dc_index_scalar_actual_dataleft)*dc_quotient_scalar_actual_dataleftentry) /\ (((exists dst_positive_code_scalar_actual_dataleftentryleft dst_positive_scale_scalar_actual_dataleftentryleft dst_negative_code_scalar_actual_dataleftentryleft dst_negative_scale_scalar_actual_dataleftentryleft dst_positive_scalar_actual_dataleftentryleft dst_negative_scalar_actual_dataleftentryleft. (((F) = (((((dst_positive_code_scalar_actual_dataleftentryleft) + (dst_positive_scale_scalar_actual_dataleftentryleft)) * S ((dst_positive_code_scalar_actual_dataleftentryleft) + (dst_positive_scale_scalar_actual_dataleftentryleft)) + ((dst_positive_scale_scalar_actual_dataleftentryleft) + (dst_positive_scale_scalar_actual_dataleftentryleft))) + (((dst_negative_code_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)) * S ((dst_negative_code_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)) + ((dst_negative_scale_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)))) * S ((((dst_positive_code_scalar_actual_dataleftentryleft) + (dst_positive_scale_scalar_actual_dataleftentryleft)) * S ((dst_positive_code_scalar_actual_dataleftentryleft) + (dst_positive_scale_scalar_actual_dataleftentryleft)) + ((dst_positive_scale_scalar_actual_dataleftentryleft) + (dst_positive_scale_scalar_actual_dataleftentryleft))) + (((dst_negative_code_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)) * S ((dst_negative_code_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)) + ((dst_negative_scale_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)))) + ((((dst_negative_code_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)) * S ((dst_negative_code_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)) + ((dst_negative_scale_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft))) + (((dst_negative_code_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)) * S ((dst_negative_code_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)) + ((dst_negative_scale_scalar_actual_dataleftentryleft) + (dst_negative_scale_scalar_actual_dataleftentryleft)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataleftentryleftpositive. ff_h_pvs_scalar_actual_dataleftentryleftpositive + S (dst_positive_scalar_actual_dataleftentryleft) = S ((S (dc_index_scalar_actual_dataleft)) * dst_positive_scale_scalar_actual_dataleftentryleft)) /\ exists ff_q_pvs_scalar_actual_dataleftentryleftpositive. dst_positive_code_scalar_actual_dataleftentryleft = ff_q_pvs_scalar_actual_dataleftentryleftpositive * S ((S (dc_index_scalar_actual_dataleft)) * dst_positive_scale_scalar_actual_dataleftentryleft) + (dst_positive_scalar_actual_dataleftentryleft))) /\ (((((exists ff_h_pvs_scalar_actual_dataleftentryleftnegative. ff_h_pvs_scalar_actual_dataleftentryleftnegative + S (dst_negative_scalar_actual_dataleftentryleft) = S ((S (dc_index_scalar_actual_dataleft)) * dst_negative_scale_scalar_actual_dataleftentryleft)) /\ exists ff_q_pvs_scalar_actual_dataleftentryleftnegative. dst_negative_code_scalar_actual_dataleftentryleft = ff_q_pvs_scalar_actual_dataleftentryleftnegative * S ((S (dc_index_scalar_actual_dataleft)) * dst_negative_scale_scalar_actual_dataleftentryleft) + (dst_negative_scalar_actual_dataleftentryleft))) /\ (exists ge_balance_positive_scalar_actual_dataleftentryleftvalue ge_balance_negative_scalar_actual_dataleftentryleftvalue. (((((dc_left_scalar_actual_dataleftentry) = 2 * (ge_balance_positive_scalar_actual_dataleftentryleftvalue) /\ (ge_balance_negative_scalar_actual_dataleftentryleftvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataleftentryleftvaluedecode. (((dc_left_scalar_actual_dataleftentry) = 2 * ge_signed_half_scalar_actual_dataleftentryleftvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataleftentryleftvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataleftentryleftvalue) = S ge_signed_half_scalar_actual_dataleftentryleftvaluedecode))) /\ ((dst_positive_scalar_actual_dataleftentryleft) + ge_balance_negative_scalar_actual_dataleftentryleftvalue = (dst_negative_scalar_actual_dataleftentryleft) + ge_balance_positive_scalar_actual_dataleftentryleftvalue))))))))) /\ (((exists dst_positive_code_scalar_actual_dataleftentryright dst_positive_scale_scalar_actual_dataleftentryright dst_negative_code_scalar_actual_dataleftentryright dst_negative_scale_scalar_actual_dataleftentryright dst_positive_scalar_actual_dataleftentryright dst_negative_scalar_actual_dataleftentryright. (((G) = (((((dst_positive_code_scalar_actual_dataleftentryright) + (dst_positive_scale_scalar_actual_dataleftentryright)) * S ((dst_positive_code_scalar_actual_dataleftentryright) + (dst_positive_scale_scalar_actual_dataleftentryright)) + ((dst_positive_scale_scalar_actual_dataleftentryright) + (dst_positive_scale_scalar_actual_dataleftentryright))) + (((dst_negative_code_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)) * S ((dst_negative_code_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)) + ((dst_negative_scale_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)))) * S ((((dst_positive_code_scalar_actual_dataleftentryright) + (dst_positive_scale_scalar_actual_dataleftentryright)) * S ((dst_positive_code_scalar_actual_dataleftentryright) + (dst_positive_scale_scalar_actual_dataleftentryright)) + ((dst_positive_scale_scalar_actual_dataleftentryright) + (dst_positive_scale_scalar_actual_dataleftentryright))) + (((dst_negative_code_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)) * S ((dst_negative_code_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)) + ((dst_negative_scale_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)))) + ((((dst_negative_code_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)) * S ((dst_negative_code_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)) + ((dst_negative_scale_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright))) + (((dst_negative_code_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)) * S ((dst_negative_code_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)) + ((dst_negative_scale_scalar_actual_dataleftentryright) + (dst_negative_scale_scalar_actual_dataleftentryright)))))) /\ (((((exists ff_h_pvs_scalar_actual_dataleftentryrightpositive. ff_h_pvs_scalar_actual_dataleftentryrightpositive + S (dst_positive_scalar_actual_dataleftentryright) = S ((S (dc_quotient_scalar_actual_dataleftentry)) * dst_positive_scale_scalar_actual_dataleftentryright)) /\ exists ff_q_pvs_scalar_actual_dataleftentryrightpositive. dst_positive_code_scalar_actual_dataleftentryright = ff_q_pvs_scalar_actual_dataleftentryrightpositive * S ((S (dc_quotient_scalar_actual_dataleftentry)) * dst_positive_scale_scalar_actual_dataleftentryright) + (dst_positive_scalar_actual_dataleftentryright))) /\ (((((exists ff_h_pvs_scalar_actual_dataleftentryrightnegative. ff_h_pvs_scalar_actual_dataleftentryrightnegative + S (dst_negative_scalar_actual_dataleftentryright) = S ((S (dc_quotient_scalar_actual_dataleftentry)) * dst_negative_scale_scalar_actual_dataleftentryright)) /\ exists ff_q_pvs_scalar_actual_dataleftentryrightnegative. dst_negative_code_scalar_actual_dataleftentryright = ff_q_pvs_scalar_actual_dataleftentryrightnegative * S ((S (dc_quotient_scalar_actual_dataleftentry)) * dst_negative_scale_scalar_actual_dataleftentryright) + (dst_negative_scalar_actual_dataleftentryright))) /\ (exists ge_balance_positive_scalar_actual_dataleftentryrightvalue ge_balance_negative_scalar_actual_dataleftentryrightvalue. (((((dc_right_scalar_actual_dataleftentry) = 2 * (ge_balance_positive_scalar_actual_dataleftentryrightvalue) /\ (ge_balance_negative_scalar_actual_dataleftentryrightvalue) = 0) \/ exists ge_signed_half_scalar_actual_dataleftentryrightvaluedecode. (((dc_right_scalar_actual_dataleftentry) = 2 * ge_signed_half_scalar_actual_dataleftentryrightvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_dataleftentryrightvalue) = 0) /\ (ge_balance_negative_scalar_actual_dataleftentryrightvalue) = S ge_signed_half_scalar_actual_dataleftentryrightvaluedecode))) /\ ((dst_positive_scalar_actual_dataleftentryright) + ge_balance_negative_scalar_actual_dataleftentryrightvalue = (dst_negative_scalar_actual_dataleftentryright) + ge_balance_positive_scalar_actual_dataleftentryrightvalue))))))))) /\ (exists sto_ap_scalar_actual_dataleftentryproduct sto_an_scalar_actual_dataleftentryproduct sto_bp_scalar_actual_dataleftentryproduct sto_bn_scalar_actual_dataleftentryproduct sto_cp_scalar_actual_dataleftentryproduct sto_cn_scalar_actual_dataleftentryproduct. (((((dc_left_scalar_actual_dataleftentry) = 2 * (sto_ap_scalar_actual_dataleftentryproduct) /\ (sto_an_scalar_actual_dataleftentryproduct) = 0) \/ exists ge_signed_half_scalar_actual_dataleftentryproductleft. (((dc_left_scalar_actual_dataleftentry) = 2 * ge_signed_half_scalar_actual_dataleftentryproductleft + 1 /\ (sto_ap_scalar_actual_dataleftentryproduct) = 0) /\ (sto_an_scalar_actual_dataleftentryproduct) = S ge_signed_half_scalar_actual_dataleftentryproductleft))) /\ ((((((dc_right_scalar_actual_dataleftentry) = 2 * (sto_bp_scalar_actual_dataleftentryproduct) /\ (sto_bn_scalar_actual_dataleftentryproduct) = 0) \/ exists ge_signed_half_scalar_actual_dataleftentryproductright. (((dc_right_scalar_actual_dataleftentry) = 2 * ge_signed_half_scalar_actual_dataleftentryproductright + 1 /\ (sto_bp_scalar_actual_dataleftentryproduct) = 0) /\ (sto_bn_scalar_actual_dataleftentryproduct) = S ge_signed_half_scalar_actual_dataleftentryproductright))) /\ ((((((dc_value_scalar_actual_dataleft) = 2 * (sto_cp_scalar_actual_dataleftentryproduct) /\ (sto_cn_scalar_actual_dataleftentryproduct) = 0) \/ exists ge_signed_half_scalar_actual_dataleftentryproductoutput. (((dc_value_scalar_actual_dataleft) = 2 * ge_signed_half_scalar_actual_dataleftentryproductoutput + 1 /\ (sto_cp_scalar_actual_dataleftentryproduct) = 0) /\ (sto_cn_scalar_actual_dataleftentryproduct) = S ge_signed_half_scalar_actual_dataleftentryproductoutput))) /\ ((sto_ap_scalar_actual_dataleftentryproduct * sto_bp_scalar_actual_dataleftentryproduct + sto_an_scalar_actual_dataleftentryproduct * sto_bn_scalar_actual_dataleftentryproduct) + sto_cn_scalar_actual_dataleftentryproduct = (sto_ap_scalar_actual_dataleftentryproduct * sto_bn_scalar_actual_dataleftentryproduct + sto_an_scalar_actual_dataleftentryproduct * sto_bp_scalar_actual_dataleftentryproduct) + sto_cp_scalar_actual_dataleftentryproduct))))))))))))))) \/ ((((dc_index_scalar_actual_dataleft)=0 \/ ~(exists pvs_factor_scalar_actual_dataleftentrynondivisor. (m) = (dc_index_scalar_actual_dataleft) * pvs_factor_scalar_actual_dataleftentrynondivisor)) /\ ((dc_value_scalar_actual_dataleft)=0))))))) /\ (((((exists dst_positive_code_scalar_actual_datarighttable dst_positive_scale_scalar_actual_datarighttable dst_negative_code_scalar_actual_datarighttable dst_negative_scale_scalar_actual_datarighttable. (((x1) = (((((dst_positive_code_scalar_actual_datarighttable) + (dst_positive_scale_scalar_actual_datarighttable)) * S ((dst_positive_code_scalar_actual_datarighttable) + (dst_positive_scale_scalar_actual_datarighttable)) + ((dst_positive_scale_scalar_actual_datarighttable) + (dst_positive_scale_scalar_actual_datarighttable))) + (((dst_negative_code_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)) * S ((dst_negative_code_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)) + ((dst_negative_scale_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)))) * S ((((dst_positive_code_scalar_actual_datarighttable) + (dst_positive_scale_scalar_actual_datarighttable)) * S ((dst_positive_code_scalar_actual_datarighttable) + (dst_positive_scale_scalar_actual_datarighttable)) + ((dst_positive_scale_scalar_actual_datarighttable) + (dst_positive_scale_scalar_actual_datarighttable))) + (((dst_negative_code_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)) * S ((dst_negative_code_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)) + ((dst_negative_scale_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)))) + ((((dst_negative_code_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)) * S ((dst_negative_code_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)) + ((dst_negative_scale_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable))) + (((dst_negative_code_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)) * S ((dst_negative_code_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)) + ((dst_negative_scale_scalar_actual_datarighttable) + (dst_negative_scale_scalar_actual_datarighttable)))))) /\ (forall dst_index_scalar_actual_datarighttable. (exists pvs_le_gap_scalar_actual_datarighttabledomain. pvs_le_gap_scalar_actual_datarighttabledomain + (dst_index_scalar_actual_datarighttable) = (n)) -> exists dst_positive_scalar_actual_datarighttable dst_negative_scalar_actual_datarighttable dst_value_scalar_actual_datarighttable. ((((exists ff_h_pvs_scalar_actual_datarighttableentrypositive. ff_h_pvs_scalar_actual_datarighttableentrypositive + S (dst_positive_scalar_actual_datarighttable) = S ((S (dst_index_scalar_actual_datarighttable)) * dst_positive_scale_scalar_actual_datarighttable)) /\ exists ff_q_pvs_scalar_actual_datarighttableentrypositive. dst_positive_code_scalar_actual_datarighttable = ff_q_pvs_scalar_actual_datarighttableentrypositive * S ((S (dst_index_scalar_actual_datarighttable)) * dst_positive_scale_scalar_actual_datarighttable) + (dst_positive_scalar_actual_datarighttable))) /\ (((((exists ff_h_pvs_scalar_actual_datarighttableentrynegative. ff_h_pvs_scalar_actual_datarighttableentrynegative + S (dst_negative_scalar_actual_datarighttable) = S ((S (dst_index_scalar_actual_datarighttable)) * dst_negative_scale_scalar_actual_datarighttable)) /\ exists ff_q_pvs_scalar_actual_datarighttableentrynegative. dst_negative_code_scalar_actual_datarighttable = ff_q_pvs_scalar_actual_datarighttableentrynegative * S ((S (dst_index_scalar_actual_datarighttable)) * dst_negative_scale_scalar_actual_datarighttable) + (dst_negative_scalar_actual_datarighttable))) /\ (exists ge_balance_positive_scalar_actual_datarighttableentryvalue ge_balance_negative_scalar_actual_datarighttableentryvalue. (((((dst_value_scalar_actual_datarighttable) = 2 * (ge_balance_positive_scalar_actual_datarighttableentryvalue) /\ (ge_balance_negative_scalar_actual_datarighttableentryvalue) = 0) \/ exists ge_signed_half_scalar_actual_datarighttableentryvaluedecode. (((dst_value_scalar_actual_datarighttable) = 2 * ge_signed_half_scalar_actual_datarighttableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datarighttableentryvalue) = 0) /\ (ge_balance_negative_scalar_actual_datarighttableentryvalue) = S ge_signed_half_scalar_actual_datarighttableentryvaluedecode))) /\ ((dst_positive_scalar_actual_datarighttable) + ge_balance_negative_scalar_actual_datarighttableentryvalue = (dst_negative_scalar_actual_datarighttable) + ge_balance_positive_scalar_actual_datarighttableentryvalue))))))))) /\ (forall dc_index_scalar_actual_dataright dc_value_scalar_actual_dataright. (exists pvs_le_gap_scalar_actual_datarightdomain. pvs_le_gap_scalar_actual_datarightdomain + (dc_index_scalar_actual_dataright) = (n)) -> (exists dst_positive_code_scalar_actual_datarightlookup dst_positive_scale_scalar_actual_datarightlookup dst_negative_code_scalar_actual_datarightlookup dst_negative_scale_scalar_actual_datarightlookup dst_positive_scalar_actual_datarightlookup dst_negative_scalar_actual_datarightlookup. (((x1) = (((((dst_positive_code_scalar_actual_datarightlookup) + (dst_positive_scale_scalar_actual_datarightlookup)) * S ((dst_positive_code_scalar_actual_datarightlookup) + (dst_positive_scale_scalar_actual_datarightlookup)) + ((dst_positive_scale_scalar_actual_datarightlookup) + (dst_positive_scale_scalar_actual_datarightlookup))) + (((dst_negative_code_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)) * S ((dst_negative_code_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)) + ((dst_negative_scale_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)))) * S ((((dst_positive_code_scalar_actual_datarightlookup) + (dst_positive_scale_scalar_actual_datarightlookup)) * S ((dst_positive_code_scalar_actual_datarightlookup) + (dst_positive_scale_scalar_actual_datarightlookup)) + ((dst_positive_scale_scalar_actual_datarightlookup) + (dst_positive_scale_scalar_actual_datarightlookup))) + (((dst_negative_code_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)) * S ((dst_negative_code_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)) + ((dst_negative_scale_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)))) + ((((dst_negative_code_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)) * S ((dst_negative_code_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)) + ((dst_negative_scale_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup))) + (((dst_negative_code_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)) * S ((dst_negative_code_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)) + ((dst_negative_scale_scalar_actual_datarightlookup) + (dst_negative_scale_scalar_actual_datarightlookup)))))) /\ (((((exists ff_h_pvs_scalar_actual_datarightlookuppositive. ff_h_pvs_scalar_actual_datarightlookuppositive + S (dst_positive_scalar_actual_datarightlookup) = S ((S (dc_index_scalar_actual_dataright)) * dst_positive_scale_scalar_actual_datarightlookup)) /\ exists ff_q_pvs_scalar_actual_datarightlookuppositive. dst_positive_code_scalar_actual_datarightlookup = ff_q_pvs_scalar_actual_datarightlookuppositive * S ((S (dc_index_scalar_actual_dataright)) * dst_positive_scale_scalar_actual_datarightlookup) + (dst_positive_scalar_actual_datarightlookup))) /\ (((((exists ff_h_pvs_scalar_actual_datarightlookupnegative. ff_h_pvs_scalar_actual_datarightlookupnegative + S (dst_negative_scalar_actual_datarightlookup) = S ((S (dc_index_scalar_actual_dataright)) * dst_negative_scale_scalar_actual_datarightlookup)) /\ exists ff_q_pvs_scalar_actual_datarightlookupnegative. dst_negative_code_scalar_actual_datarightlookup = ff_q_pvs_scalar_actual_datarightlookupnegative * S ((S (dc_index_scalar_actual_dataright)) * dst_negative_scale_scalar_actual_datarightlookup) + (dst_negative_scalar_actual_datarightlookup))) /\ (exists ge_balance_positive_scalar_actual_datarightlookupvalue ge_balance_negative_scalar_actual_datarightlookupvalue. (((((dc_value_scalar_actual_dataright) = 2 * (ge_balance_positive_scalar_actual_datarightlookupvalue) /\ (ge_balance_negative_scalar_actual_datarightlookupvalue) = 0) \/ exists ge_signed_half_scalar_actual_datarightlookupvaluedecode. (((dc_value_scalar_actual_dataright) = 2 * ge_signed_half_scalar_actual_datarightlookupvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datarightlookupvalue) = 0) /\ (ge_balance_negative_scalar_actual_datarightlookupvalue) = S ge_signed_half_scalar_actual_datarightlookupvaluedecode))) /\ ((dst_positive_scalar_actual_datarightlookup) + ge_balance_negative_scalar_actual_datarightlookupvalue = (dst_negative_scalar_actual_datarightlookup) + ge_balance_positive_scalar_actual_datarightlookupvalue))))))))) -> ((((~((dc_index_scalar_actual_dataright)=0)) /\ (exists dc_quotient_scalar_actual_datarightentry dc_left_scalar_actual_datarightentry dc_right_scalar_actual_datarightentry. (((n)=(dc_index_scalar_actual_dataright)*dc_quotient_scalar_actual_datarightentry) /\ (((exists dst_positive_code_scalar_actual_datarightentryleft dst_positive_scale_scalar_actual_datarightentryleft dst_negative_code_scalar_actual_datarightentryleft dst_negative_scale_scalar_actual_datarightentryleft dst_positive_scalar_actual_datarightentryleft dst_negative_scalar_actual_datarightentryleft. (((F) = (((((dst_positive_code_scalar_actual_datarightentryleft) + (dst_positive_scale_scalar_actual_datarightentryleft)) * S ((dst_positive_code_scalar_actual_datarightentryleft) + (dst_positive_scale_scalar_actual_datarightentryleft)) + ((dst_positive_scale_scalar_actual_datarightentryleft) + (dst_positive_scale_scalar_actual_datarightentryleft))) + (((dst_negative_code_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)) * S ((dst_negative_code_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)) + ((dst_negative_scale_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)))) * S ((((dst_positive_code_scalar_actual_datarightentryleft) + (dst_positive_scale_scalar_actual_datarightentryleft)) * S ((dst_positive_code_scalar_actual_datarightentryleft) + (dst_positive_scale_scalar_actual_datarightentryleft)) + ((dst_positive_scale_scalar_actual_datarightentryleft) + (dst_positive_scale_scalar_actual_datarightentryleft))) + (((dst_negative_code_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)) * S ((dst_negative_code_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)) + ((dst_negative_scale_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)))) + ((((dst_negative_code_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)) * S ((dst_negative_code_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)) + ((dst_negative_scale_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft))) + (((dst_negative_code_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)) * S ((dst_negative_code_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)) + ((dst_negative_scale_scalar_actual_datarightentryleft) + (dst_negative_scale_scalar_actual_datarightentryleft)))))) /\ (((((exists ff_h_pvs_scalar_actual_datarightentryleftpositive. ff_h_pvs_scalar_actual_datarightentryleftpositive + S (dst_positive_scalar_actual_datarightentryleft) = S ((S (dc_index_scalar_actual_dataright)) * dst_positive_scale_scalar_actual_datarightentryleft)) /\ exists ff_q_pvs_scalar_actual_datarightentryleftpositive. dst_positive_code_scalar_actual_datarightentryleft = ff_q_pvs_scalar_actual_datarightentryleftpositive * S ((S (dc_index_scalar_actual_dataright)) * dst_positive_scale_scalar_actual_datarightentryleft) + (dst_positive_scalar_actual_datarightentryleft))) /\ (((((exists ff_h_pvs_scalar_actual_datarightentryleftnegative. ff_h_pvs_scalar_actual_datarightentryleftnegative + S (dst_negative_scalar_actual_datarightentryleft) = S ((S (dc_index_scalar_actual_dataright)) * dst_negative_scale_scalar_actual_datarightentryleft)) /\ exists ff_q_pvs_scalar_actual_datarightentryleftnegative. dst_negative_code_scalar_actual_datarightentryleft = ff_q_pvs_scalar_actual_datarightentryleftnegative * S ((S (dc_index_scalar_actual_dataright)) * dst_negative_scale_scalar_actual_datarightentryleft) + (dst_negative_scalar_actual_datarightentryleft))) /\ (exists ge_balance_positive_scalar_actual_datarightentryleftvalue ge_balance_negative_scalar_actual_datarightentryleftvalue. (((((dc_left_scalar_actual_datarightentry) = 2 * (ge_balance_positive_scalar_actual_datarightentryleftvalue) /\ (ge_balance_negative_scalar_actual_datarightentryleftvalue) = 0) \/ exists ge_signed_half_scalar_actual_datarightentryleftvaluedecode. (((dc_left_scalar_actual_datarightentry) = 2 * ge_signed_half_scalar_actual_datarightentryleftvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datarightentryleftvalue) = 0) /\ (ge_balance_negative_scalar_actual_datarightentryleftvalue) = S ge_signed_half_scalar_actual_datarightentryleftvaluedecode))) /\ ((dst_positive_scalar_actual_datarightentryleft) + ge_balance_negative_scalar_actual_datarightentryleftvalue = (dst_negative_scalar_actual_datarightentryleft) + ge_balance_positive_scalar_actual_datarightentryleftvalue))))))))) /\ (((exists dst_positive_code_scalar_actual_datarightentryright dst_positive_scale_scalar_actual_datarightentryright dst_negative_code_scalar_actual_datarightentryright dst_negative_scale_scalar_actual_datarightentryright dst_positive_scalar_actual_datarightentryright dst_negative_scalar_actual_datarightentryright. (((G) = (((((dst_positive_code_scalar_actual_datarightentryright) + (dst_positive_scale_scalar_actual_datarightentryright)) * S ((dst_positive_code_scalar_actual_datarightentryright) + (dst_positive_scale_scalar_actual_datarightentryright)) + ((dst_positive_scale_scalar_actual_datarightentryright) + (dst_positive_scale_scalar_actual_datarightentryright))) + (((dst_negative_code_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)) * S ((dst_negative_code_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)) + ((dst_negative_scale_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)))) * S ((((dst_positive_code_scalar_actual_datarightentryright) + (dst_positive_scale_scalar_actual_datarightentryright)) * S ((dst_positive_code_scalar_actual_datarightentryright) + (dst_positive_scale_scalar_actual_datarightentryright)) + ((dst_positive_scale_scalar_actual_datarightentryright) + (dst_positive_scale_scalar_actual_datarightentryright))) + (((dst_negative_code_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)) * S ((dst_negative_code_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)) + ((dst_negative_scale_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)))) + ((((dst_negative_code_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)) * S ((dst_negative_code_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)) + ((dst_negative_scale_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright))) + (((dst_negative_code_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)) * S ((dst_negative_code_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)) + ((dst_negative_scale_scalar_actual_datarightentryright) + (dst_negative_scale_scalar_actual_datarightentryright)))))) /\ (((((exists ff_h_pvs_scalar_actual_datarightentryrightpositive. ff_h_pvs_scalar_actual_datarightentryrightpositive + S (dst_positive_scalar_actual_datarightentryright) = S ((S (dc_quotient_scalar_actual_datarightentry)) * dst_positive_scale_scalar_actual_datarightentryright)) /\ exists ff_q_pvs_scalar_actual_datarightentryrightpositive. dst_positive_code_scalar_actual_datarightentryright = ff_q_pvs_scalar_actual_datarightentryrightpositive * S ((S (dc_quotient_scalar_actual_datarightentry)) * dst_positive_scale_scalar_actual_datarightentryright) + (dst_positive_scalar_actual_datarightentryright))) /\ (((((exists ff_h_pvs_scalar_actual_datarightentryrightnegative. ff_h_pvs_scalar_actual_datarightentryrightnegative + S (dst_negative_scalar_actual_datarightentryright) = S ((S (dc_quotient_scalar_actual_datarightentry)) * dst_negative_scale_scalar_actual_datarightentryright)) /\ exists ff_q_pvs_scalar_actual_datarightentryrightnegative. dst_negative_code_scalar_actual_datarightentryright = ff_q_pvs_scalar_actual_datarightentryrightnegative * S ((S (dc_quotient_scalar_actual_datarightentry)) * dst_negative_scale_scalar_actual_datarightentryright) + (dst_negative_scalar_actual_datarightentryright))) /\ (exists ge_balance_positive_scalar_actual_datarightentryrightvalue ge_balance_negative_scalar_actual_datarightentryrightvalue. (((((dc_right_scalar_actual_datarightentry) = 2 * (ge_balance_positive_scalar_actual_datarightentryrightvalue) /\ (ge_balance_negative_scalar_actual_datarightentryrightvalue) = 0) \/ exists ge_signed_half_scalar_actual_datarightentryrightvaluedecode. (((dc_right_scalar_actual_datarightentry) = 2 * ge_signed_half_scalar_actual_datarightentryrightvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datarightentryrightvalue) = 0) /\ (ge_balance_negative_scalar_actual_datarightentryrightvalue) = S ge_signed_half_scalar_actual_datarightentryrightvaluedecode))) /\ ((dst_positive_scalar_actual_datarightentryright) + ge_balance_negative_scalar_actual_datarightentryrightvalue = (dst_negative_scalar_actual_datarightentryright) + ge_balance_positive_scalar_actual_datarightentryrightvalue))))))))) /\ (exists sto_ap_scalar_actual_datarightentryproduct sto_an_scalar_actual_datarightentryproduct sto_bp_scalar_actual_datarightentryproduct sto_bn_scalar_actual_datarightentryproduct sto_cp_scalar_actual_datarightentryproduct sto_cn_scalar_actual_datarightentryproduct. (((((dc_left_scalar_actual_datarightentry) = 2 * (sto_ap_scalar_actual_datarightentryproduct) /\ (sto_an_scalar_actual_datarightentryproduct) = 0) \/ exists ge_signed_half_scalar_actual_datarightentryproductleft. (((dc_left_scalar_actual_datarightentry) = 2 * ge_signed_half_scalar_actual_datarightentryproductleft + 1 /\ (sto_ap_scalar_actual_datarightentryproduct) = 0) /\ (sto_an_scalar_actual_datarightentryproduct) = S ge_signed_half_scalar_actual_datarightentryproductleft))) /\ ((((((dc_right_scalar_actual_datarightentry) = 2 * (sto_bp_scalar_actual_datarightentryproduct) /\ (sto_bn_scalar_actual_datarightentryproduct) = 0) \/ exists ge_signed_half_scalar_actual_datarightentryproductright. (((dc_right_scalar_actual_datarightentry) = 2 * ge_signed_half_scalar_actual_datarightentryproductright + 1 /\ (sto_bp_scalar_actual_datarightentryproduct) = 0) /\ (sto_bn_scalar_actual_datarightentryproduct) = S ge_signed_half_scalar_actual_datarightentryproductright))) /\ ((((((dc_value_scalar_actual_dataright) = 2 * (sto_cp_scalar_actual_datarightentryproduct) /\ (sto_cn_scalar_actual_datarightentryproduct) = 0) \/ exists ge_signed_half_scalar_actual_datarightentryproductoutput. (((dc_value_scalar_actual_dataright) = 2 * ge_signed_half_scalar_actual_datarightentryproductoutput + 1 /\ (sto_cp_scalar_actual_datarightentryproduct) = 0) /\ (sto_cn_scalar_actual_datarightentryproduct) = S ge_signed_half_scalar_actual_datarightentryproductoutput))) /\ ((sto_ap_scalar_actual_datarightentryproduct * sto_bp_scalar_actual_datarightentryproduct + sto_an_scalar_actual_datarightentryproduct * sto_bn_scalar_actual_datarightentryproduct) + sto_cn_scalar_actual_datarightentryproduct = (sto_ap_scalar_actual_datarightentryproduct * sto_bn_scalar_actual_datarightentryproduct + sto_an_scalar_actual_datarightentryproduct * sto_bp_scalar_actual_datarightentryproduct) + sto_cp_scalar_actual_datarightentryproduct))))))))))))))) \/ ((((dc_index_scalar_actual_dataright)=0 \/ ~(exists pvs_factor_scalar_actual_datarightentrynondivisor. (n) = (dc_index_scalar_actual_dataright) * pvs_factor_scalar_actual_datarightentrynondivisor)) /\ ((dc_value_scalar_actual_dataright)=0))))))) /\ (((((exists dst_positive_code_scalar_actual_datacartesianF dst_positive_scale_scalar_actual_datacartesianF dst_negative_code_scalar_actual_datacartesianF dst_negative_scale_scalar_actual_datacartesianF. (((x) = (((((dst_positive_code_scalar_actual_datacartesianF) + (dst_positive_scale_scalar_actual_datacartesianF)) * S ((dst_positive_code_scalar_actual_datacartesianF) + (dst_positive_scale_scalar_actual_datacartesianF)) + ((dst_positive_scale_scalar_actual_datacartesianF) + (dst_positive_scale_scalar_actual_datacartesianF))) + (((dst_negative_code_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)) * S ((dst_negative_code_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)) + ((dst_negative_scale_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)))) * S ((((dst_positive_code_scalar_actual_datacartesianF) + (dst_positive_scale_scalar_actual_datacartesianF)) * S ((dst_positive_code_scalar_actual_datacartesianF) + (dst_positive_scale_scalar_actual_datacartesianF)) + ((dst_positive_scale_scalar_actual_datacartesianF) + (dst_positive_scale_scalar_actual_datacartesianF))) + (((dst_negative_code_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)) * S ((dst_negative_code_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)) + ((dst_negative_scale_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)))) + ((((dst_negative_code_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)) * S ((dst_negative_code_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)) + ((dst_negative_scale_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF))) + (((dst_negative_code_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)) * S ((dst_negative_code_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)) + ((dst_negative_scale_scalar_actual_datacartesianF) + (dst_negative_scale_scalar_actual_datacartesianF)))))) /\ (forall dst_index_scalar_actual_datacartesianF. (exists pvs_le_gap_scalar_actual_datacartesianFdomain. pvs_le_gap_scalar_actual_datacartesianFdomain + (dst_index_scalar_actual_datacartesianF) = (0)) -> exists dst_positive_scalar_actual_datacartesianF dst_negative_scalar_actual_datacartesianF dst_value_scalar_actual_datacartesianF. ((((exists ff_h_pvs_scalar_actual_datacartesianFentrypositive. ff_h_pvs_scalar_actual_datacartesianFentrypositive + S (dst_positive_scalar_actual_datacartesianF) = S ((S (dst_index_scalar_actual_datacartesianF)) * dst_positive_scale_scalar_actual_datacartesianF)) /\ exists ff_q_pvs_scalar_actual_datacartesianFentrypositive. dst_positive_code_scalar_actual_datacartesianF = ff_q_pvs_scalar_actual_datacartesianFentrypositive * S ((S (dst_index_scalar_actual_datacartesianF)) * dst_positive_scale_scalar_actual_datacartesianF) + (dst_positive_scalar_actual_datacartesianF))) /\ (((((exists ff_h_pvs_scalar_actual_datacartesianFentrynegative. ff_h_pvs_scalar_actual_datacartesianFentrynegative + S (dst_negative_scalar_actual_datacartesianF) = S ((S (dst_index_scalar_actual_datacartesianF)) * dst_negative_scale_scalar_actual_datacartesianF)) /\ exists ff_q_pvs_scalar_actual_datacartesianFentrynegative. dst_negative_code_scalar_actual_datacartesianF = ff_q_pvs_scalar_actual_datacartesianFentrynegative * S ((S (dst_index_scalar_actual_datacartesianF)) * dst_negative_scale_scalar_actual_datacartesianF) + (dst_negative_scalar_actual_datacartesianF))) /\ (exists ge_balance_positive_scalar_actual_datacartesianFentryvalue ge_balance_negative_scalar_actual_datacartesianFentryvalue. (((((dst_value_scalar_actual_datacartesianF) = 2 * (ge_balance_positive_scalar_actual_datacartesianFentryvalue) /\ (ge_balance_negative_scalar_actual_datacartesianFentryvalue) = 0) \/ exists ge_signed_half_scalar_actual_datacartesianFentryvaluedecode. (((dst_value_scalar_actual_datacartesianF) = 2 * ge_signed_half_scalar_actual_datacartesianFentryvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datacartesianFentryvalue) = 0) /\ (ge_balance_negative_scalar_actual_datacartesianFentryvalue) = S ge_signed_half_scalar_actual_datacartesianFentryvaluedecode))) /\ ((dst_positive_scalar_actual_datacartesianF) + ge_balance_negative_scalar_actual_datacartesianFentryvalue = (dst_negative_scalar_actual_datacartesianF) + ge_balance_positive_scalar_actual_datacartesianFentryvalue))))))))) /\ (((exists dst_positive_code_scalar_actual_datacartesianG dst_positive_scale_scalar_actual_datacartesianG dst_negative_code_scalar_actual_datacartesianG dst_negative_scale_scalar_actual_datacartesianG. (((x1) = (((((dst_positive_code_scalar_actual_datacartesianG) + (dst_positive_scale_scalar_actual_datacartesianG)) * S ((dst_positive_code_scalar_actual_datacartesianG) + (dst_positive_scale_scalar_actual_datacartesianG)) + ((dst_positive_scale_scalar_actual_datacartesianG) + (dst_positive_scale_scalar_actual_datacartesianG))) + (((dst_negative_code_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)) * S ((dst_negative_code_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)) + ((dst_negative_scale_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)))) * S ((((dst_positive_code_scalar_actual_datacartesianG) + (dst_positive_scale_scalar_actual_datacartesianG)) * S ((dst_positive_code_scalar_actual_datacartesianG) + (dst_positive_scale_scalar_actual_datacartesianG)) + ((dst_positive_scale_scalar_actual_datacartesianG) + (dst_positive_scale_scalar_actual_datacartesianG))) + (((dst_negative_code_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)) * S ((dst_negative_code_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)) + ((dst_negative_scale_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)))) + ((((dst_negative_code_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)) * S ((dst_negative_code_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)) + ((dst_negative_scale_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG))) + (((dst_negative_code_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)) * S ((dst_negative_code_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)) + ((dst_negative_scale_scalar_actual_datacartesianG) + (dst_negative_scale_scalar_actual_datacartesianG)))))) /\ (forall dst_index_scalar_actual_datacartesianG. (exists pvs_le_gap_scalar_actual_datacartesianGdomain. pvs_le_gap_scalar_actual_datacartesianGdomain + (dst_index_scalar_actual_datacartesianG) = (0)) -> exists dst_positive_scalar_actual_datacartesianG dst_negative_scalar_actual_datacartesianG dst_value_scalar_actual_datacartesianG. ((((exists ff_h_pvs_scalar_actual_datacartesianGentrypositive. ff_h_pvs_scalar_actual_datacartesianGentrypositive + S (dst_positive_scalar_actual_datacartesianG) = S ((S (dst_index_scalar_actual_datacartesianG)) * dst_positive_scale_scalar_actual_datacartesianG)) /\ exists ff_q_pvs_scalar_actual_datacartesianGentrypositive. dst_positive_code_scalar_actual_datacartesianG = ff_q_pvs_scalar_actual_datacartesianGentrypositive * S ((S (dst_index_scalar_actual_datacartesianG)) * dst_positive_scale_scalar_actual_datacartesianG) + (dst_positive_scalar_actual_datacartesianG))) /\ (((((exists ff_h_pvs_scalar_actual_datacartesianGentrynegative. ff_h_pvs_scalar_actual_datacartesianGentrynegative + S (dst_negative_scalar_actual_datacartesianG) = S ((S (dst_index_scalar_actual_datacartesianG)) * dst_negative_scale_scalar_actual_datacartesianG)) /\ exists ff_q_pvs_scalar_actual_datacartesianGentrynegative. dst_negative_code_scalar_actual_datacartesianG = ff_q_pvs_scalar_actual_datacartesianGentrynegative * S ((S (dst_index_scalar_actual_datacartesianG)) * dst_negative_scale_scalar_actual_datacartesianG) + (dst_negative_scalar_actual_datacartesianG))) /\ (exists ge_balance_positive_scalar_actual_datacartesianGentryvalue ge_balance_negative_scalar_actual_datacartesianGentryvalue. (((((dst_value_scalar_actual_datacartesianG) = 2 * (ge_balance_positive_scalar_actual_datacartesianGentryvalue) /\ (ge_balance_negative_scalar_actual_datacartesianGentryvalue) = 0) \/ exists ge_signed_half_scalar_actual_datacartesianGentryvaluedecode. (((dst_value_scalar_actual_datacartesianG) = 2 * ge_signed_half_scalar_actual_datacartesianGentryvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datacartesianGentryvalue) = 0) /\ (ge_balance_negative_scalar_actual_datacartesianGentryvalue) = S ge_signed_half_scalar_actual_datacartesianGentryvaluedecode))) /\ ((dst_positive_scalar_actual_datacartesianG) + ge_balance_negative_scalar_actual_datacartesianGentryvalue = (dst_negative_scalar_actual_datacartesianG) + ge_balance_positive_scalar_actual_datacartesianGentryvalue))))))))) /\ (((exists dst_positive_code_scalar_actual_datacartesianT dst_positive_scale_scalar_actual_datacartesianT dst_negative_code_scalar_actual_datacartesianT dst_negative_scale_scalar_actual_datacartesianT. (((T) = (((((dst_positive_code_scalar_actual_datacartesianT) + (dst_positive_scale_scalar_actual_datacartesianT)) * S ((dst_positive_code_scalar_actual_datacartesianT) + (dst_positive_scale_scalar_actual_datacartesianT)) + ((dst_positive_scale_scalar_actual_datacartesianT) + (dst_positive_scale_scalar_actual_datacartesianT))) + (((dst_negative_code_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)) * S ((dst_negative_code_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)) + ((dst_negative_scale_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)))) * S ((((dst_positive_code_scalar_actual_datacartesianT) + (dst_positive_scale_scalar_actual_datacartesianT)) * S ((dst_positive_code_scalar_actual_datacartesianT) + (dst_positive_scale_scalar_actual_datacartesianT)) + ((dst_positive_scale_scalar_actual_datacartesianT) + (dst_positive_scale_scalar_actual_datacartesianT))) + (((dst_negative_code_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)) * S ((dst_negative_code_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)) + ((dst_negative_scale_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)))) + ((((dst_negative_code_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)) * S ((dst_negative_code_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)) + ((dst_negative_scale_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT))) + (((dst_negative_code_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)) * S ((dst_negative_code_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)) + ((dst_negative_scale_scalar_actual_datacartesianT) + (dst_negative_scale_scalar_actual_datacartesianT)))))) /\ (forall dst_index_scalar_actual_datacartesianT. (exists pvs_le_gap_scalar_actual_datacartesianTdomain. pvs_le_gap_scalar_actual_datacartesianTdomain + (dst_index_scalar_actual_datacartesianT) = ((S (m))*(S (n)))) -> exists dst_positive_scalar_actual_datacartesianT dst_negative_scalar_actual_datacartesianT dst_value_scalar_actual_datacartesianT. ((((exists ff_h_pvs_scalar_actual_datacartesianTentrypositive. ff_h_pvs_scalar_actual_datacartesianTentrypositive + S (dst_positive_scalar_actual_datacartesianT) = S ((S (dst_index_scalar_actual_datacartesianT)) * dst_positive_scale_scalar_actual_datacartesianT)) /\ exists ff_q_pvs_scalar_actual_datacartesianTentrypositive. dst_positive_code_scalar_actual_datacartesianT = ff_q_pvs_scalar_actual_datacartesianTentrypositive * S ((S (dst_index_scalar_actual_datacartesianT)) * dst_positive_scale_scalar_actual_datacartesianT) + (dst_positive_scalar_actual_datacartesianT))) /\ (((((exists ff_h_pvs_scalar_actual_datacartesianTentrynegative. ff_h_pvs_scalar_actual_datacartesianTentrynegative + S (dst_negative_scalar_actual_datacartesianT) = S ((S (dst_index_scalar_actual_datacartesianT)) * dst_negative_scale_scalar_actual_datacartesianT)) /\ exists ff_q_pvs_scalar_actual_datacartesianTentrynegative. dst_negative_code_scalar_actual_datacartesianT = ff_q_pvs_scalar_actual_datacartesianTentrynegative * S ((S (dst_index_scalar_actual_datacartesianT)) * dst_negative_scale_scalar_actual_datacartesianT) + (dst_negative_scalar_actual_datacartesianT))) /\ (exists ge_balance_positive_scalar_actual_datacartesianTentryvalue ge_balance_negative_scalar_actual_datacartesianTentryvalue. (((((dst_value_scalar_actual_datacartesianT) = 2 * (ge_balance_positive_scalar_actual_datacartesianTentryvalue) /\ (ge_balance_negative_scalar_actual_datacartesianTentryvalue) = 0) \/ exists ge_signed_half_scalar_actual_datacartesianTentryvaluedecode. (((dst_value_scalar_actual_datacartesianT) = 2 * ge_signed_half_scalar_actual_datacartesianTentryvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datacartesianTentryvalue) = 0) /\ (ge_balance_negative_scalar_actual_datacartesianTentryvalue) = S ge_signed_half_scalar_actual_datacartesianTentryvaluedecode))) /\ ((dst_positive_scalar_actual_datacartesianT) + ge_balance_negative_scalar_actual_datacartesianTentryvalue = (dst_negative_scalar_actual_datacartesianT) + ge_balance_positive_scalar_actual_datacartesianTentryvalue))))))))) /\ (forall scp_row_scalar_actual_datacartesian scp_column_scalar_actual_datacartesian scp_first_scalar_actual_datacartesian scp_second_scalar_actual_datacartesian scp_value_scalar_actual_datacartesian. (exists pvs_gap_scalar_actual_datacartesianrows. pvs_gap_scalar_actual_datacartesianrows + S (scp_row_scalar_actual_datacartesian) = (S (m))) -> (exists pvs_gap_scalar_actual_datacartesiancolumns. pvs_gap_scalar_actual_datacartesiancolumns + S (scp_column_scalar_actual_datacartesian) = (S (n))) -> (exists dst_positive_code_scalar_actual_datacartesianfirst dst_positive_scale_scalar_actual_datacartesianfirst dst_negative_code_scalar_actual_datacartesianfirst dst_negative_scale_scalar_actual_datacartesianfirst dst_positive_scalar_actual_datacartesianfirst dst_negative_scalar_actual_datacartesianfirst. (((x) = (((((dst_positive_code_scalar_actual_datacartesianfirst) + (dst_positive_scale_scalar_actual_datacartesianfirst)) * S ((dst_positive_code_scalar_actual_datacartesianfirst) + (dst_positive_scale_scalar_actual_datacartesianfirst)) + ((dst_positive_scale_scalar_actual_datacartesianfirst) + (dst_positive_scale_scalar_actual_datacartesianfirst))) + (((dst_negative_code_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)) * S ((dst_negative_code_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)) + ((dst_negative_scale_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)))) * S ((((dst_positive_code_scalar_actual_datacartesianfirst) + (dst_positive_scale_scalar_actual_datacartesianfirst)) * S ((dst_positive_code_scalar_actual_datacartesianfirst) + (dst_positive_scale_scalar_actual_datacartesianfirst)) + ((dst_positive_scale_scalar_actual_datacartesianfirst) + (dst_positive_scale_scalar_actual_datacartesianfirst))) + (((dst_negative_code_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)) * S ((dst_negative_code_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)) + ((dst_negative_scale_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)))) + ((((dst_negative_code_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)) * S ((dst_negative_code_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)) + ((dst_negative_scale_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst))) + (((dst_negative_code_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)) * S ((dst_negative_code_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)) + ((dst_negative_scale_scalar_actual_datacartesianfirst) + (dst_negative_scale_scalar_actual_datacartesianfirst)))))) /\ (((((exists ff_h_pvs_scalar_actual_datacartesianfirstpositive. ff_h_pvs_scalar_actual_datacartesianfirstpositive + S (dst_positive_scalar_actual_datacartesianfirst) = S ((S (scp_row_scalar_actual_datacartesian)) * dst_positive_scale_scalar_actual_datacartesianfirst)) /\ exists ff_q_pvs_scalar_actual_datacartesianfirstpositive. dst_positive_code_scalar_actual_datacartesianfirst = ff_q_pvs_scalar_actual_datacartesianfirstpositive * S ((S (scp_row_scalar_actual_datacartesian)) * dst_positive_scale_scalar_actual_datacartesianfirst) + (dst_positive_scalar_actual_datacartesianfirst))) /\ (((((exists ff_h_pvs_scalar_actual_datacartesianfirstnegative. ff_h_pvs_scalar_actual_datacartesianfirstnegative + S (dst_negative_scalar_actual_datacartesianfirst) = S ((S (scp_row_scalar_actual_datacartesian)) * dst_negative_scale_scalar_actual_datacartesianfirst)) /\ exists ff_q_pvs_scalar_actual_datacartesianfirstnegative. dst_negative_code_scalar_actual_datacartesianfirst = ff_q_pvs_scalar_actual_datacartesianfirstnegative * S ((S (scp_row_scalar_actual_datacartesian)) * dst_negative_scale_scalar_actual_datacartesianfirst) + (dst_negative_scalar_actual_datacartesianfirst))) /\ (exists ge_balance_positive_scalar_actual_datacartesianfirstvalue ge_balance_negative_scalar_actual_datacartesianfirstvalue. (((((scp_first_scalar_actual_datacartesian) = 2 * (ge_balance_positive_scalar_actual_datacartesianfirstvalue) /\ (ge_balance_negative_scalar_actual_datacartesianfirstvalue) = 0) \/ exists ge_signed_half_scalar_actual_datacartesianfirstvaluedecode. (((scp_first_scalar_actual_datacartesian) = 2 * ge_signed_half_scalar_actual_datacartesianfirstvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datacartesianfirstvalue) = 0) /\ (ge_balance_negative_scalar_actual_datacartesianfirstvalue) = S ge_signed_half_scalar_actual_datacartesianfirstvaluedecode))) /\ ((dst_positive_scalar_actual_datacartesianfirst) + ge_balance_negative_scalar_actual_datacartesianfirstvalue = (dst_negative_scalar_actual_datacartesianfirst) + ge_balance_positive_scalar_actual_datacartesianfirstvalue))))))))) -> (exists dst_positive_code_scalar_actual_datacartesiansecond dst_positive_scale_scalar_actual_datacartesiansecond dst_negative_code_scalar_actual_datacartesiansecond dst_negative_scale_scalar_actual_datacartesiansecond dst_positive_scalar_actual_datacartesiansecond dst_negative_scalar_actual_datacartesiansecond. (((x1) = (((((dst_positive_code_scalar_actual_datacartesiansecond) + (dst_positive_scale_scalar_actual_datacartesiansecond)) * S ((dst_positive_code_scalar_actual_datacartesiansecond) + (dst_positive_scale_scalar_actual_datacartesiansecond)) + ((dst_positive_scale_scalar_actual_datacartesiansecond) + (dst_positive_scale_scalar_actual_datacartesiansecond))) + (((dst_negative_code_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)) * S ((dst_negative_code_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)) + ((dst_negative_scale_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)))) * S ((((dst_positive_code_scalar_actual_datacartesiansecond) + (dst_positive_scale_scalar_actual_datacartesiansecond)) * S ((dst_positive_code_scalar_actual_datacartesiansecond) + (dst_positive_scale_scalar_actual_datacartesiansecond)) + ((dst_positive_scale_scalar_actual_datacartesiansecond) + (dst_positive_scale_scalar_actual_datacartesiansecond))) + (((dst_negative_code_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)) * S ((dst_negative_code_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)) + ((dst_negative_scale_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)))) + ((((dst_negative_code_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)) * S ((dst_negative_code_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)) + ((dst_negative_scale_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond))) + (((dst_negative_code_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)) * S ((dst_negative_code_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)) + ((dst_negative_scale_scalar_actual_datacartesiansecond) + (dst_negative_scale_scalar_actual_datacartesiansecond)))))) /\ (((((exists ff_h_pvs_scalar_actual_datacartesiansecondpositive. ff_h_pvs_scalar_actual_datacartesiansecondpositive + S (dst_positive_scalar_actual_datacartesiansecond) = S ((S (scp_column_scalar_actual_datacartesian)) * dst_positive_scale_scalar_actual_datacartesiansecond)) /\ exists ff_q_pvs_scalar_actual_datacartesiansecondpositive. dst_positive_code_scalar_actual_datacartesiansecond = ff_q_pvs_scalar_actual_datacartesiansecondpositive * S ((S (scp_column_scalar_actual_datacartesian)) * dst_positive_scale_scalar_actual_datacartesiansecond) + (dst_positive_scalar_actual_datacartesiansecond))) /\ (((((exists ff_h_pvs_scalar_actual_datacartesiansecondnegative. ff_h_pvs_scalar_actual_datacartesiansecondnegative + S (dst_negative_scalar_actual_datacartesiansecond) = S ((S (scp_column_scalar_actual_datacartesian)) * dst_negative_scale_scalar_actual_datacartesiansecond)) /\ exists ff_q_pvs_scalar_actual_datacartesiansecondnegative. dst_negative_code_scalar_actual_datacartesiansecond = ff_q_pvs_scalar_actual_datacartesiansecondnegative * S ((S (scp_column_scalar_actual_datacartesian)) * dst_negative_scale_scalar_actual_datacartesiansecond) + (dst_negative_scalar_actual_datacartesiansecond))) /\ (exists ge_balance_positive_scalar_actual_datacartesiansecondvalue ge_balance_negative_scalar_actual_datacartesiansecondvalue. (((((scp_second_scalar_actual_datacartesian) = 2 * (ge_balance_positive_scalar_actual_datacartesiansecondvalue) /\ (ge_balance_negative_scalar_actual_datacartesiansecondvalue) = 0) \/ exists ge_signed_half_scalar_actual_datacartesiansecondvaluedecode. (((scp_second_scalar_actual_datacartesian) = 2 * ge_signed_half_scalar_actual_datacartesiansecondvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datacartesiansecondvalue) = 0) /\ (ge_balance_negative_scalar_actual_datacartesiansecondvalue) = S ge_signed_half_scalar_actual_datacartesiansecondvaluedecode))) /\ ((dst_positive_scalar_actual_datacartesiansecond) + ge_balance_negative_scalar_actual_datacartesiansecondvalue = (dst_negative_scalar_actual_datacartesiansecond) + ge_balance_positive_scalar_actual_datacartesiansecondvalue))))))))) -> (exists dst_positive_code_scalar_actual_datacartesianentry dst_positive_scale_scalar_actual_datacartesianentry dst_negative_code_scalar_actual_datacartesianentry dst_negative_scale_scalar_actual_datacartesianentry dst_positive_scalar_actual_datacartesianentry dst_negative_scalar_actual_datacartesianentry. (((T) = (((((dst_positive_code_scalar_actual_datacartesianentry) + (dst_positive_scale_scalar_actual_datacartesianentry)) * S ((dst_positive_code_scalar_actual_datacartesianentry) + (dst_positive_scale_scalar_actual_datacartesianentry)) + ((dst_positive_scale_scalar_actual_datacartesianentry) + (dst_positive_scale_scalar_actual_datacartesianentry))) + (((dst_negative_code_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)) * S ((dst_negative_code_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)) + ((dst_negative_scale_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)))) * S ((((dst_positive_code_scalar_actual_datacartesianentry) + (dst_positive_scale_scalar_actual_datacartesianentry)) * S ((dst_positive_code_scalar_actual_datacartesianentry) + (dst_positive_scale_scalar_actual_datacartesianentry)) + ((dst_positive_scale_scalar_actual_datacartesianentry) + (dst_positive_scale_scalar_actual_datacartesianentry))) + (((dst_negative_code_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)) * S ((dst_negative_code_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)) + ((dst_negative_scale_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)))) + ((((dst_negative_code_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)) * S ((dst_negative_code_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)) + ((dst_negative_scale_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry))) + (((dst_negative_code_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)) * S ((dst_negative_code_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)) + ((dst_negative_scale_scalar_actual_datacartesianentry) + (dst_negative_scale_scalar_actual_datacartesianentry)))))) /\ (((((exists ff_h_pvs_scalar_actual_datacartesianentrypositive. ff_h_pvs_scalar_actual_datacartesianentrypositive + S (dst_positive_scalar_actual_datacartesianentry) = S ((S (((S (n))*(scp_row_scalar_actual_datacartesian)+(scp_column_scalar_actual_datacartesian)))) * dst_positive_scale_scalar_actual_datacartesianentry)) /\ exists ff_q_pvs_scalar_actual_datacartesianentrypositive. dst_positive_code_scalar_actual_datacartesianentry = ff_q_pvs_scalar_actual_datacartesianentrypositive * S ((S (((S (n))*(scp_row_scalar_actual_datacartesian)+(scp_column_scalar_actual_datacartesian)))) * dst_positive_scale_scalar_actual_datacartesianentry) + (dst_positive_scalar_actual_datacartesianentry))) /\ (((((exists ff_h_pvs_scalar_actual_datacartesianentrynegative. ff_h_pvs_scalar_actual_datacartesianentrynegative + S (dst_negative_scalar_actual_datacartesianentry) = S ((S (((S (n))*(scp_row_scalar_actual_datacartesian)+(scp_column_scalar_actual_datacartesian)))) * dst_negative_scale_scalar_actual_datacartesianentry)) /\ exists ff_q_pvs_scalar_actual_datacartesianentrynegative. dst_negative_code_scalar_actual_datacartesianentry = ff_q_pvs_scalar_actual_datacartesianentrynegative * S ((S (((S (n))*(scp_row_scalar_actual_datacartesian)+(scp_column_scalar_actual_datacartesian)))) * dst_negative_scale_scalar_actual_datacartesianentry) + (dst_negative_scalar_actual_datacartesianentry))) /\ (exists ge_balance_positive_scalar_actual_datacartesianentryvalue ge_balance_negative_scalar_actual_datacartesianentryvalue. (((((scp_value_scalar_actual_datacartesian) = 2 * (ge_balance_positive_scalar_actual_datacartesianentryvalue) /\ (ge_balance_negative_scalar_actual_datacartesianentryvalue) = 0) \/ exists ge_signed_half_scalar_actual_datacartesianentryvaluedecode. (((scp_value_scalar_actual_datacartesian) = 2 * ge_signed_half_scalar_actual_datacartesianentryvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datacartesianentryvalue) = 0) /\ (ge_balance_negative_scalar_actual_datacartesianentryvalue) = S ge_signed_half_scalar_actual_datacartesianentryvaluedecode))) /\ ((dst_positive_scalar_actual_datacartesianentry) + ge_balance_negative_scalar_actual_datacartesianentryvalue = (dst_negative_scalar_actual_datacartesianentry) + ge_balance_positive_scalar_actual_datacartesianentryvalue))))))))) -> (exists sto_ap_scalar_actual_datacartesianmultiply sto_an_scalar_actual_datacartesianmultiply sto_bp_scalar_actual_datacartesianmultiply sto_bn_scalar_actual_datacartesianmultiply sto_cp_scalar_actual_datacartesianmultiply sto_cn_scalar_actual_datacartesianmultiply. (((((scp_first_scalar_actual_datacartesian) = 2 * (sto_ap_scalar_actual_datacartesianmultiply) /\ (sto_an_scalar_actual_datacartesianmultiply) = 0) \/ exists ge_signed_half_scalar_actual_datacartesianmultiplyleft. (((scp_first_scalar_actual_datacartesian) = 2 * ge_signed_half_scalar_actual_datacartesianmultiplyleft + 1 /\ (sto_ap_scalar_actual_datacartesianmultiply) = 0) /\ (sto_an_scalar_actual_datacartesianmultiply) = S ge_signed_half_scalar_actual_datacartesianmultiplyleft))) /\ ((((((scp_second_scalar_actual_datacartesian) = 2 * (sto_bp_scalar_actual_datacartesianmultiply) /\ (sto_bn_scalar_actual_datacartesianmultiply) = 0) \/ exists ge_signed_half_scalar_actual_datacartesianmultiplyright. (((scp_second_scalar_actual_datacartesian) = 2 * ge_signed_half_scalar_actual_datacartesianmultiplyright + 1 /\ (sto_bp_scalar_actual_datacartesianmultiply) = 0) /\ (sto_bn_scalar_actual_datacartesianmultiply) = S ge_signed_half_scalar_actual_datacartesianmultiplyright))) /\ ((((((scp_value_scalar_actual_datacartesian) = 2 * (sto_cp_scalar_actual_datacartesianmultiply) /\ (sto_cn_scalar_actual_datacartesianmultiply) = 0) \/ exists ge_signed_half_scalar_actual_datacartesianmultiplyoutput. (((scp_value_scalar_actual_datacartesian) = 2 * ge_signed_half_scalar_actual_datacartesianmultiplyoutput + 1 /\ (sto_cp_scalar_actual_datacartesianmultiply) = 0) /\ (sto_cn_scalar_actual_datacartesianmultiply) = S ge_signed_half_scalar_actual_datacartesianmultiplyoutput))) /\ ((sto_ap_scalar_actual_datacartesianmultiply * sto_bp_scalar_actual_datacartesianmultiply + sto_an_scalar_actual_datacartesianmultiply * sto_bn_scalar_actual_datacartesianmultiply) + sto_cn_scalar_actual_datacartesianmultiply = (sto_ap_scalar_actual_datacartesianmultiply * sto_bn_scalar_actual_datacartesianmultiply + sto_an_scalar_actual_datacartesianmultiply * sto_bp_scalar_actual_datacartesianmultiply) + sto_cp_scalar_actual_datacartesianmultiply)))))))))))))) /\ (((((exists dst_positive_code_scalar_actual_datatargettable dst_positive_scale_scalar_actual_datatargettable dst_negative_code_scalar_actual_datatargettable dst_negative_scale_scalar_actual_datatargettable. (((x2) = (((((dst_positive_code_scalar_actual_datatargettable) + (dst_positive_scale_scalar_actual_datatargettable)) * S ((dst_positive_code_scalar_actual_datatargettable) + (dst_positive_scale_scalar_actual_datatargettable)) + ((dst_positive_scale_scalar_actual_datatargettable) + (dst_positive_scale_scalar_actual_datatargettable))) + (((dst_negative_code_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)) * S ((dst_negative_code_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)) + ((dst_negative_scale_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)))) * S ((((dst_positive_code_scalar_actual_datatargettable) + (dst_positive_scale_scalar_actual_datatargettable)) * S ((dst_positive_code_scalar_actual_datatargettable) + (dst_positive_scale_scalar_actual_datatargettable)) + ((dst_positive_scale_scalar_actual_datatargettable) + (dst_positive_scale_scalar_actual_datatargettable))) + (((dst_negative_code_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)) * S ((dst_negative_code_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)) + ((dst_negative_scale_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)))) + ((((dst_negative_code_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)) * S ((dst_negative_code_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)) + ((dst_negative_scale_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable))) + (((dst_negative_code_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)) * S ((dst_negative_code_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)) + ((dst_negative_scale_scalar_actual_datatargettable) + (dst_negative_scale_scalar_actual_datatargettable)))))) /\ (forall dst_index_scalar_actual_datatargettable. (exists pvs_le_gap_scalar_actual_datatargettabledomain. pvs_le_gap_scalar_actual_datatargettabledomain + (dst_index_scalar_actual_datatargettable) = ((m)*(n))) -> exists dst_positive_scalar_actual_datatargettable dst_negative_scalar_actual_datatargettable dst_value_scalar_actual_datatargettable. ((((exists ff_h_pvs_scalar_actual_datatargettableentrypositive. ff_h_pvs_scalar_actual_datatargettableentrypositive + S (dst_positive_scalar_actual_datatargettable) = S ((S (dst_index_scalar_actual_datatargettable)) * dst_positive_scale_scalar_actual_datatargettable)) /\ exists ff_q_pvs_scalar_actual_datatargettableentrypositive. dst_positive_code_scalar_actual_datatargettable = ff_q_pvs_scalar_actual_datatargettableentrypositive * S ((S (dst_index_scalar_actual_datatargettable)) * dst_positive_scale_scalar_actual_datatargettable) + (dst_positive_scalar_actual_datatargettable))) /\ (((((exists ff_h_pvs_scalar_actual_datatargettableentrynegative. ff_h_pvs_scalar_actual_datatargettableentrynegative + S (dst_negative_scalar_actual_datatargettable) = S ((S (dst_index_scalar_actual_datatargettable)) * dst_negative_scale_scalar_actual_datatargettable)) /\ exists ff_q_pvs_scalar_actual_datatargettableentrynegative. dst_negative_code_scalar_actual_datatargettable = ff_q_pvs_scalar_actual_datatargettableentrynegative * S ((S (dst_index_scalar_actual_datatargettable)) * dst_negative_scale_scalar_actual_datatargettable) + (dst_negative_scalar_actual_datatargettable))) /\ (exists ge_balance_positive_scalar_actual_datatargettableentryvalue ge_balance_negative_scalar_actual_datatargettableentryvalue. (((((dst_value_scalar_actual_datatargettable) = 2 * (ge_balance_positive_scalar_actual_datatargettableentryvalue) /\ (ge_balance_negative_scalar_actual_datatargettableentryvalue) = 0) \/ exists ge_signed_half_scalar_actual_datatargettableentryvaluedecode. (((dst_value_scalar_actual_datatargettable) = 2 * ge_signed_half_scalar_actual_datatargettableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datatargettableentryvalue) = 0) /\ (ge_balance_negative_scalar_actual_datatargettableentryvalue) = S ge_signed_half_scalar_actual_datatargettableentryvaluedecode))) /\ ((dst_positive_scalar_actual_datatargettable) + ge_balance_negative_scalar_actual_datatargettableentryvalue = (dst_negative_scalar_actual_datatargettable) + ge_balance_positive_scalar_actual_datatargettableentryvalue))))))))) /\ (forall dc_index_scalar_actual_datatarget dc_value_scalar_actual_datatarget. (exists pvs_le_gap_scalar_actual_datatargetdomain. pvs_le_gap_scalar_actual_datatargetdomain + (dc_index_scalar_actual_datatarget) = ((m)*(n))) -> (exists dst_positive_code_scalar_actual_datatargetlookup dst_positive_scale_scalar_actual_datatargetlookup dst_negative_code_scalar_actual_datatargetlookup dst_negative_scale_scalar_actual_datatargetlookup dst_positive_scalar_actual_datatargetlookup dst_negative_scalar_actual_datatargetlookup. (((x2) = (((((dst_positive_code_scalar_actual_datatargetlookup) + (dst_positive_scale_scalar_actual_datatargetlookup)) * S ((dst_positive_code_scalar_actual_datatargetlookup) + (dst_positive_scale_scalar_actual_datatargetlookup)) + ((dst_positive_scale_scalar_actual_datatargetlookup) + (dst_positive_scale_scalar_actual_datatargetlookup))) + (((dst_negative_code_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)) * S ((dst_negative_code_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)) + ((dst_negative_scale_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)))) * S ((((dst_positive_code_scalar_actual_datatargetlookup) + (dst_positive_scale_scalar_actual_datatargetlookup)) * S ((dst_positive_code_scalar_actual_datatargetlookup) + (dst_positive_scale_scalar_actual_datatargetlookup)) + ((dst_positive_scale_scalar_actual_datatargetlookup) + (dst_positive_scale_scalar_actual_datatargetlookup))) + (((dst_negative_code_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)) * S ((dst_negative_code_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)) + ((dst_negative_scale_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)))) + ((((dst_negative_code_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)) * S ((dst_negative_code_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)) + ((dst_negative_scale_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup))) + (((dst_negative_code_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)) * S ((dst_negative_code_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)) + ((dst_negative_scale_scalar_actual_datatargetlookup) + (dst_negative_scale_scalar_actual_datatargetlookup)))))) /\ (((((exists ff_h_pvs_scalar_actual_datatargetlookuppositive. ff_h_pvs_scalar_actual_datatargetlookuppositive + S (dst_positive_scalar_actual_datatargetlookup) = S ((S (dc_index_scalar_actual_datatarget)) * dst_positive_scale_scalar_actual_datatargetlookup)) /\ exists ff_q_pvs_scalar_actual_datatargetlookuppositive. dst_positive_code_scalar_actual_datatargetlookup = ff_q_pvs_scalar_actual_datatargetlookuppositive * S ((S (dc_index_scalar_actual_datatarget)) * dst_positive_scale_scalar_actual_datatargetlookup) + (dst_positive_scalar_actual_datatargetlookup))) /\ (((((exists ff_h_pvs_scalar_actual_datatargetlookupnegative. ff_h_pvs_scalar_actual_datatargetlookupnegative + S (dst_negative_scalar_actual_datatargetlookup) = S ((S (dc_index_scalar_actual_datatarget)) * dst_negative_scale_scalar_actual_datatargetlookup)) /\ exists ff_q_pvs_scalar_actual_datatargetlookupnegative. dst_negative_code_scalar_actual_datatargetlookup = ff_q_pvs_scalar_actual_datatargetlookupnegative * S ((S (dc_index_scalar_actual_datatarget)) * dst_negative_scale_scalar_actual_datatargetlookup) + (dst_negative_scalar_actual_datatargetlookup))) /\ (exists ge_balance_positive_scalar_actual_datatargetlookupvalue ge_balance_negative_scalar_actual_datatargetlookupvalue. (((((dc_value_scalar_actual_datatarget) = 2 * (ge_balance_positive_scalar_actual_datatargetlookupvalue) /\ (ge_balance_negative_scalar_actual_datatargetlookupvalue) = 0) \/ exists ge_signed_half_scalar_actual_datatargetlookupvaluedecode. (((dc_value_scalar_actual_datatarget) = 2 * ge_signed_half_scalar_actual_datatargetlookupvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datatargetlookupvalue) = 0) /\ (ge_balance_negative_scalar_actual_datatargetlookupvalue) = S ge_signed_half_scalar_actual_datatargetlookupvaluedecode))) /\ ((dst_positive_scalar_actual_datatargetlookup) + ge_balance_negative_scalar_actual_datatargetlookupvalue = (dst_negative_scalar_actual_datatargetlookup) + ge_balance_positive_scalar_actual_datatargetlookupvalue))))))))) -> ((((~((dc_index_scalar_actual_datatarget)=0)) /\ (exists dc_quotient_scalar_actual_datatargetentry dc_left_scalar_actual_datatargetentry dc_right_scalar_actual_datatargetentry. ((((m)*(n))=(dc_index_scalar_actual_datatarget)*dc_quotient_scalar_actual_datatargetentry) /\ (((exists dst_positive_code_scalar_actual_datatargetentryleft dst_positive_scale_scalar_actual_datatargetentryleft dst_negative_code_scalar_actual_datatargetentryleft dst_negative_scale_scalar_actual_datatargetentryleft dst_positive_scalar_actual_datatargetentryleft dst_negative_scalar_actual_datatargetentryleft. (((F) = (((((dst_positive_code_scalar_actual_datatargetentryleft) + (dst_positive_scale_scalar_actual_datatargetentryleft)) * S ((dst_positive_code_scalar_actual_datatargetentryleft) + (dst_positive_scale_scalar_actual_datatargetentryleft)) + ((dst_positive_scale_scalar_actual_datatargetentryleft) + (dst_positive_scale_scalar_actual_datatargetentryleft))) + (((dst_negative_code_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)) * S ((dst_negative_code_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)) + ((dst_negative_scale_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)))) * S ((((dst_positive_code_scalar_actual_datatargetentryleft) + (dst_positive_scale_scalar_actual_datatargetentryleft)) * S ((dst_positive_code_scalar_actual_datatargetentryleft) + (dst_positive_scale_scalar_actual_datatargetentryleft)) + ((dst_positive_scale_scalar_actual_datatargetentryleft) + (dst_positive_scale_scalar_actual_datatargetentryleft))) + (((dst_negative_code_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)) * S ((dst_negative_code_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)) + ((dst_negative_scale_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)))) + ((((dst_negative_code_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)) * S ((dst_negative_code_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)) + ((dst_negative_scale_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft))) + (((dst_negative_code_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)) * S ((dst_negative_code_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)) + ((dst_negative_scale_scalar_actual_datatargetentryleft) + (dst_negative_scale_scalar_actual_datatargetentryleft)))))) /\ (((((exists ff_h_pvs_scalar_actual_datatargetentryleftpositive. ff_h_pvs_scalar_actual_datatargetentryleftpositive + S (dst_positive_scalar_actual_datatargetentryleft) = S ((S (dc_index_scalar_actual_datatarget)) * dst_positive_scale_scalar_actual_datatargetentryleft)) /\ exists ff_q_pvs_scalar_actual_datatargetentryleftpositive. dst_positive_code_scalar_actual_datatargetentryleft = ff_q_pvs_scalar_actual_datatargetentryleftpositive * S ((S (dc_index_scalar_actual_datatarget)) * dst_positive_scale_scalar_actual_datatargetentryleft) + (dst_positive_scalar_actual_datatargetentryleft))) /\ (((((exists ff_h_pvs_scalar_actual_datatargetentryleftnegative. ff_h_pvs_scalar_actual_datatargetentryleftnegative + S (dst_negative_scalar_actual_datatargetentryleft) = S ((S (dc_index_scalar_actual_datatarget)) * dst_negative_scale_scalar_actual_datatargetentryleft)) /\ exists ff_q_pvs_scalar_actual_datatargetentryleftnegative. dst_negative_code_scalar_actual_datatargetentryleft = ff_q_pvs_scalar_actual_datatargetentryleftnegative * S ((S (dc_index_scalar_actual_datatarget)) * dst_negative_scale_scalar_actual_datatargetentryleft) + (dst_negative_scalar_actual_datatargetentryleft))) /\ (exists ge_balance_positive_scalar_actual_datatargetentryleftvalue ge_balance_negative_scalar_actual_datatargetentryleftvalue. (((((dc_left_scalar_actual_datatargetentry) = 2 * (ge_balance_positive_scalar_actual_datatargetentryleftvalue) /\ (ge_balance_negative_scalar_actual_datatargetentryleftvalue) = 0) \/ exists ge_signed_half_scalar_actual_datatargetentryleftvaluedecode. (((dc_left_scalar_actual_datatargetentry) = 2 * ge_signed_half_scalar_actual_datatargetentryleftvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datatargetentryleftvalue) = 0) /\ (ge_balance_negative_scalar_actual_datatargetentryleftvalue) = S ge_signed_half_scalar_actual_datatargetentryleftvaluedecode))) /\ ((dst_positive_scalar_actual_datatargetentryleft) + ge_balance_negative_scalar_actual_datatargetentryleftvalue = (dst_negative_scalar_actual_datatargetentryleft) + ge_balance_positive_scalar_actual_datatargetentryleftvalue))))))))) /\ (((exists dst_positive_code_scalar_actual_datatargetentryright dst_positive_scale_scalar_actual_datatargetentryright dst_negative_code_scalar_actual_datatargetentryright dst_negative_scale_scalar_actual_datatargetentryright dst_positive_scalar_actual_datatargetentryright dst_negative_scalar_actual_datatargetentryright. (((G) = (((((dst_positive_code_scalar_actual_datatargetentryright) + (dst_positive_scale_scalar_actual_datatargetentryright)) * S ((dst_positive_code_scalar_actual_datatargetentryright) + (dst_positive_scale_scalar_actual_datatargetentryright)) + ((dst_positive_scale_scalar_actual_datatargetentryright) + (dst_positive_scale_scalar_actual_datatargetentryright))) + (((dst_negative_code_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)) * S ((dst_negative_code_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)) + ((dst_negative_scale_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)))) * S ((((dst_positive_code_scalar_actual_datatargetentryright) + (dst_positive_scale_scalar_actual_datatargetentryright)) * S ((dst_positive_code_scalar_actual_datatargetentryright) + (dst_positive_scale_scalar_actual_datatargetentryright)) + ((dst_positive_scale_scalar_actual_datatargetentryright) + (dst_positive_scale_scalar_actual_datatargetentryright))) + (((dst_negative_code_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)) * S ((dst_negative_code_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)) + ((dst_negative_scale_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)))) + ((((dst_negative_code_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)) * S ((dst_negative_code_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)) + ((dst_negative_scale_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright))) + (((dst_negative_code_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)) * S ((dst_negative_code_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)) + ((dst_negative_scale_scalar_actual_datatargetentryright) + (dst_negative_scale_scalar_actual_datatargetentryright)))))) /\ (((((exists ff_h_pvs_scalar_actual_datatargetentryrightpositive. ff_h_pvs_scalar_actual_datatargetentryrightpositive + S (dst_positive_scalar_actual_datatargetentryright) = S ((S (dc_quotient_scalar_actual_datatargetentry)) * dst_positive_scale_scalar_actual_datatargetentryright)) /\ exists ff_q_pvs_scalar_actual_datatargetentryrightpositive. dst_positive_code_scalar_actual_datatargetentryright = ff_q_pvs_scalar_actual_datatargetentryrightpositive * S ((S (dc_quotient_scalar_actual_datatargetentry)) * dst_positive_scale_scalar_actual_datatargetentryright) + (dst_positive_scalar_actual_datatargetentryright))) /\ (((((exists ff_h_pvs_scalar_actual_datatargetentryrightnegative. ff_h_pvs_scalar_actual_datatargetentryrightnegative + S (dst_negative_scalar_actual_datatargetentryright) = S ((S (dc_quotient_scalar_actual_datatargetentry)) * dst_negative_scale_scalar_actual_datatargetentryright)) /\ exists ff_q_pvs_scalar_actual_datatargetentryrightnegative. dst_negative_code_scalar_actual_datatargetentryright = ff_q_pvs_scalar_actual_datatargetentryrightnegative * S ((S (dc_quotient_scalar_actual_datatargetentry)) * dst_negative_scale_scalar_actual_datatargetentryright) + (dst_negative_scalar_actual_datatargetentryright))) /\ (exists ge_balance_positive_scalar_actual_datatargetentryrightvalue ge_balance_negative_scalar_actual_datatargetentryrightvalue. (((((dc_right_scalar_actual_datatargetentry) = 2 * (ge_balance_positive_scalar_actual_datatargetentryrightvalue) /\ (ge_balance_negative_scalar_actual_datatargetentryrightvalue) = 0) \/ exists ge_signed_half_scalar_actual_datatargetentryrightvaluedecode. (((dc_right_scalar_actual_datatargetentry) = 2 * ge_signed_half_scalar_actual_datatargetentryrightvaluedecode + 1 /\ (ge_balance_positive_scalar_actual_datatargetentryrightvalue) = 0) /\ (ge_balance_negative_scalar_actual_datatargetentryrightvalue) = S ge_signed_half_scalar_actual_datatargetentryrightvaluedecode))) /\ ((dst_positive_scalar_actual_datatargetentryright) + ge_balance_negative_scalar_actual_datatargetentryrightvalue = (dst_negative_scalar_actual_datatargetentryright) + ge_balance_positive_scalar_actual_datatargetentryrightvalue))))))))) /\ (exists sto_ap_scalar_actual_datatargetentryproduct sto_an_scalar_actual_datatargetentryproduct sto_bp_scalar_actual_datatargetentryproduct sto_bn_scalar_actual_datatargetentryproduct sto_cp_scalar_actual_datatargetentryproduct sto_cn_scalar_actual_datatargetentryproduct. (((((dc_left_scalar_actual_datatargetentry) = 2 * (sto_ap_scalar_actual_datatargetentryproduct) /\ (sto_an_scalar_actual_datatargetentryproduct) = 0) \/ exists ge_signed_half_scalar_actual_datatargetentryproductleft. (((dc_left_scalar_actual_datatargetentry) = 2 * ge_signed_half_scalar_actual_datatargetentryproductleft + 1 /\ (sto_ap_scalar_actual_datatargetentryproduct) = 0) /\ (sto_an_scalar_actual_datatargetentryproduct) = S ge_signed_half_scalar_actual_datatargetentryproductleft))) /\ ((((((dc_right_scalar_actual_datatargetentry) = 2 * (sto_bp_scalar_actual_datatargetentryproduct) /\ (sto_bn_scalar_actual_datatargetentryproduct) = 0) \/ exists ge_signed_half_scalar_actual_datatargetentryproductright. (((dc_right_scalar_actual_datatargetentry) = 2 * ge_signed_half_scalar_actual_datatargetentryproductright + 1 /\ (sto_bp_scalar_actual_datatargetentryproduct) = 0) /\ (sto_bn_scalar_actual_datatargetentryproduct) = S ge_signed_half_scalar_actual_datatargetentryproductright))) /\ ((((((dc_value_scalar_actual_datatarget) = 2 * (sto_cp_scalar_actual_datatargetentryproduct) /\ (sto_cn_scalar_actual_datatargetentryproduct) = 0) \/ exists ge_signed_half_scalar_actual_datatargetentryproductoutput. (((dc_value_scalar_actual_datatarget) = 2 * ge_signed_half_scalar_actual_datatargetentryproductoutput + 1 /\ (sto_cp_scalar_actual_datatargetentryproduct) = 0) /\ (sto_cn_scalar_actual_datatargetentryproduct) = S ge_signed_half_scalar_actual_datatargetentryproductoutput))) /\ ((sto_ap_scalar_actual_datatargetentryproduct * sto_bp_scalar_actual_datatargetentryproduct + sto_an_scalar_actual_datatargetentryproduct * sto_bn_scalar_actual_datatargetentryproduct) + sto_cn_scalar_actual_datatargetentryproduct = (sto_ap_scalar_actual_datatargetentryproduct * sto_bn_scalar_actual_datatargetentryproduct + sto_an_scalar_actual_datatargetentryproduct * sto_bp_scalar_actual_datatargetentryproduct) + sto_cp_scalar_actual_datatargetentryproduct))))))))))))))) \/ ((((dc_index_scalar_actual_datatarget)=0 \/ ~(exists pvs_factor_scalar_actual_datatargetentrynondivisor. ((m)*(n)) = (dc_index_scalar_actual_datatarget) * pvs_factor_scalar_actual_datatargetentrynondivisor)) /\ ((dc_value_scalar_actual_datatarget)=0))))))) /\ (((~((S (n))=0)) /\ (forall dpi_index_scalar_actual_datamap dpi_row_scalar_actual_datamap dpi_column_scalar_actual_datamap. (exists pvs_gap_scalar_actual_datamapwindow. pvs_gap_scalar_actual_datamapwindow + S (dpi_index_scalar_actual_datamap) = ((S (m))*(S (n)))) -> (exists pvs_gap_scalar_actual_datamapremainder. pvs_gap_scalar_actual_datamapremainder + S (dpi_column_scalar_actual_datamap) = (S (n))) -> (dpi_index_scalar_actual_datamap)=(S (n))*(dpi_row_scalar_actual_datamap)+(dpi_column_scalar_actual_datamap) -> (((exists ff_h_pvs_scalar_actual_datamapvalue. ff_h_pvs_scalar_actual_datamapvalue + S ((dpi_row_scalar_actual_datamap)*(dpi_column_scalar_actual_datamap)) = S ((S (dpi_index_scalar_actual_datamap)) * s)) /\ exists ff_q_pvs_scalar_actual_datamapvalue. r = ff_q_pvs_scalar_actual_datamapvalue * S ((S (dpi_index_scalar_actual_datamap)) * s) + ((dpi_row_scalar_actual_datamap)*(dpi_column_scalar_actual_datamap))))))))))))))))))))))))))) - 0028
specialize dirichlet_coprime_product_data_construct (N) - 0029
specialize dirichlet_coprime_product_data_construct (F) - 0030
specialize dirichlet_coprime_product_data_construct (G) - 0031
specialize dirichlet_coprime_product_data_construct (m) - 0032
specialize dirichlet_coprime_product_data_construct (n) - 0033
specialize dirichlet_coprime_product_data_construct (x) - 0034
specialize dirichlet_coprime_product_data_construct (x1) - 0035
specialize dirichlet_coprime_product_data_construct (x2) - 0036
apply dirichlet_coprime_product_data_construct - 0037
exact hF - 0038
exact hG - 0039
exact hm - 0040
exact hn - 0041
exact hb - 0042
exact hc - 0043
exact hsm_right_witness_left - 0044
exact hsn_right_witness_left - 0045
exact hsc_right_witness_left - 0046
cases hd - 0047
cases hd_witness - 0048
cases hd_witness_witness - 0049
cases hd_witness_witness_witness - 0050
cases hd_witness_witness_witness_right - 0051
cases hd_witness_witness_witness_right_right - 0052
cases hd_witness_witness_witness_right_right_right - 0053
cases hd_witness_witness_witness_right_right_right_right - 0054
cases hd_witness_witness_witness_right_right_right_right_right - 0055
cases hd_witness_witness_witness_right_right_right_right_right_right - 0056
cases hd_witness_witness_witness_right_right_right_right_right_right_right - 0057
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right - 0058
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right_right - 0059
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right_left - 0060
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right_left_right - 0061
cases hd_witness_witness_witness_right_right_right_right_right_right_right_right_left_right_right - 0062
have hv : exists value. (exists dst_positive_code_scalar_product_sum dst_positive_scale_scalar_product_sum dst_negative_code_scalar_product_sum dst_negative_scale_scalar_product_sum dst_positive_sum_scalar_product_sum dst_negative_sum_scalar_product_sum. (((x3) = (((((dst_positive_code_scalar_product_sum) + (dst_positive_scale_scalar_product_sum)) * S ((dst_positive_code_scalar_product_sum) + (dst_positive_scale_scalar_product_sum)) + ((dst_positive_scale_scalar_product_sum) + (dst_positive_scale_scalar_product_sum))) + (((dst_negative_code_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)) * S ((dst_negative_code_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)) + ((dst_negative_scale_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)))) * S ((((dst_positive_code_scalar_product_sum) + (dst_positive_scale_scalar_product_sum)) * S ((dst_positive_code_scalar_product_sum) + (dst_positive_scale_scalar_product_sum)) + ((dst_positive_scale_scalar_product_sum) + (dst_positive_scale_scalar_product_sum))) + (((dst_negative_code_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)) * S ((dst_negative_code_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)) + ((dst_negative_scale_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)))) + ((((dst_negative_code_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)) * S ((dst_negative_code_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)) + ((dst_negative_scale_scalar_product_sum) + (dst_negative_scale_scalar_product_sum))) + (((dst_negative_code_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)) * S ((dst_negative_code_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)) + ((dst_negative_scale_scalar_product_sum) + (dst_negative_scale_scalar_product_sum)))))) /\ (((exists fs_u_dst_scalar_product_sumpositive fs_v_dst_scalar_product_sumpositive. ((((exists fs_h_dst_scalar_product_sumpositive_body_start. fs_h_dst_scalar_product_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_product_sumpositive)) /\ exists fs_q_dst_scalar_product_sumpositive_body_start. fs_u_dst_scalar_product_sumpositive = fs_q_dst_scalar_product_sumpositive_body_start * S ((S (0)) * fs_v_dst_scalar_product_sumpositive) + (0))) /\ ((((exists fs_h_dst_scalar_product_sumpositive_body_terminal. fs_h_dst_scalar_product_sumpositive_body_terminal + S (dst_positive_sum_scalar_product_sum) = S ((S ((S (m))*(S (n)))) * fs_v_dst_scalar_product_sumpositive)) /\ exists fs_q_dst_scalar_product_sumpositive_body_terminal. fs_u_dst_scalar_product_sumpositive = fs_q_dst_scalar_product_sumpositive_body_terminal * S ((S ((S (m))*(S (n)))) * fs_v_dst_scalar_product_sumpositive) + (dst_positive_sum_scalar_product_sum))) /\ forall fs_i_dst_scalar_product_sumpositive_body_steps. (exists fs_lt_dst_scalar_product_sumpositive_body_steps_bound. fs_lt_dst_scalar_product_sumpositive_body_steps_bound + S fs_i_dst_scalar_product_sumpositive_body_steps = (S (m))*(S (n))) -> exists fs_a_dst_scalar_product_sumpositive_body_steps fs_r_dst_scalar_product_sumpositive_body_steps fs_s_dst_scalar_product_sumpositive_body_steps. ((((exists fs_h_dst_scalar_product_sumpositive_body_steps_summand. fs_h_dst_scalar_product_sumpositive_body_steps_summand + S (fs_a_dst_scalar_product_sumpositive_body_steps) = S ((S (fs_i_dst_scalar_product_sumpositive_body_steps)) * dst_positive_scale_scalar_product_sum)) /\ exists fs_q_dst_scalar_product_sumpositive_body_steps_summand. dst_positive_code_scalar_product_sum = fs_q_dst_scalar_product_sumpositive_body_steps_summand * S ((S (fs_i_dst_scalar_product_sumpositive_body_steps)) * dst_positive_scale_scalar_product_sum) + (fs_a_dst_scalar_product_sumpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_product_sumpositive_body_steps_partial. fs_h_dst_scalar_product_sumpositive_body_steps_partial + S (fs_r_dst_scalar_product_sumpositive_body_steps) = S ((S (fs_i_dst_scalar_product_sumpositive_body_steps)) * fs_v_dst_scalar_product_sumpositive)) /\ exists fs_q_dst_scalar_product_sumpositive_body_steps_partial. fs_u_dst_scalar_product_sumpositive = fs_q_dst_scalar_product_sumpositive_body_steps_partial * S ((S (fs_i_dst_scalar_product_sumpositive_body_steps)) * fs_v_dst_scalar_product_sumpositive) + (fs_r_dst_scalar_product_sumpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_product_sumpositive_body_steps_successor. fs_h_dst_scalar_product_sumpositive_body_steps_successor + S (fs_s_dst_scalar_product_sumpositive_body_steps) = S ((S (S fs_i_dst_scalar_product_sumpositive_body_steps)) * fs_v_dst_scalar_product_sumpositive)) /\ exists fs_q_dst_scalar_product_sumpositive_body_steps_successor. fs_u_dst_scalar_product_sumpositive = fs_q_dst_scalar_product_sumpositive_body_steps_successor * S ((S (S fs_i_dst_scalar_product_sumpositive_body_steps)) * fs_v_dst_scalar_product_sumpositive) + (fs_s_dst_scalar_product_sumpositive_body_steps))) /\ fs_s_dst_scalar_product_sumpositive_body_steps = fs_r_dst_scalar_product_sumpositive_body_steps + fs_a_dst_scalar_product_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_scalar_product_sumnegative fs_v_dst_scalar_product_sumnegative. ((((exists fs_h_dst_scalar_product_sumnegative_body_start. fs_h_dst_scalar_product_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_product_sumnegative)) /\ exists fs_q_dst_scalar_product_sumnegative_body_start. fs_u_dst_scalar_product_sumnegative = fs_q_dst_scalar_product_sumnegative_body_start * S ((S (0)) * fs_v_dst_scalar_product_sumnegative) + (0))) /\ ((((exists fs_h_dst_scalar_product_sumnegative_body_terminal. fs_h_dst_scalar_product_sumnegative_body_terminal + S (dst_negative_sum_scalar_product_sum) = S ((S ((S (m))*(S (n)))) * fs_v_dst_scalar_product_sumnegative)) /\ exists fs_q_dst_scalar_product_sumnegative_body_terminal. fs_u_dst_scalar_product_sumnegative = fs_q_dst_scalar_product_sumnegative_body_terminal * S ((S ((S (m))*(S (n)))) * fs_v_dst_scalar_product_sumnegative) + (dst_negative_sum_scalar_product_sum))) /\ forall fs_i_dst_scalar_product_sumnegative_body_steps. (exists fs_lt_dst_scalar_product_sumnegative_body_steps_bound. fs_lt_dst_scalar_product_sumnegative_body_steps_bound + S fs_i_dst_scalar_product_sumnegative_body_steps = (S (m))*(S (n))) -> exists fs_a_dst_scalar_product_sumnegative_body_steps fs_r_dst_scalar_product_sumnegative_body_steps fs_s_dst_scalar_product_sumnegative_body_steps. ((((exists fs_h_dst_scalar_product_sumnegative_body_steps_summand. fs_h_dst_scalar_product_sumnegative_body_steps_summand + S (fs_a_dst_scalar_product_sumnegative_body_steps) = S ((S (fs_i_dst_scalar_product_sumnegative_body_steps)) * dst_negative_scale_scalar_product_sum)) /\ exists fs_q_dst_scalar_product_sumnegative_body_steps_summand. dst_negative_code_scalar_product_sum = fs_q_dst_scalar_product_sumnegative_body_steps_summand * S ((S (fs_i_dst_scalar_product_sumnegative_body_steps)) * dst_negative_scale_scalar_product_sum) + (fs_a_dst_scalar_product_sumnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_product_sumnegative_body_steps_partial. fs_h_dst_scalar_product_sumnegative_body_steps_partial + S (fs_r_dst_scalar_product_sumnegative_body_steps) = S ((S (fs_i_dst_scalar_product_sumnegative_body_steps)) * fs_v_dst_scalar_product_sumnegative)) /\ exists fs_q_dst_scalar_product_sumnegative_body_steps_partial. fs_u_dst_scalar_product_sumnegative = fs_q_dst_scalar_product_sumnegative_body_steps_partial * S ((S (fs_i_dst_scalar_product_sumnegative_body_steps)) * fs_v_dst_scalar_product_sumnegative) + (fs_r_dst_scalar_product_sumnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_product_sumnegative_body_steps_successor. fs_h_dst_scalar_product_sumnegative_body_steps_successor + S (fs_s_dst_scalar_product_sumnegative_body_steps) = S ((S (S fs_i_dst_scalar_product_sumnegative_body_steps)) * fs_v_dst_scalar_product_sumnegative)) /\ exists fs_q_dst_scalar_product_sumnegative_body_steps_successor. fs_u_dst_scalar_product_sumnegative = fs_q_dst_scalar_product_sumnegative_body_steps_successor * S ((S (S fs_i_dst_scalar_product_sumnegative_body_steps)) * fs_v_dst_scalar_product_sumnegative) + (fs_s_dst_scalar_product_sumnegative_body_steps))) /\ fs_s_dst_scalar_product_sumnegative_body_steps = fs_r_dst_scalar_product_sumnegative_body_steps + fs_a_dst_scalar_product_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_scalar_product_sumresult ge_balance_negative_scalar_product_sumresult. (((((value) = 2 * (ge_balance_positive_scalar_product_sumresult) /\ (ge_balance_negative_scalar_product_sumresult) = 0) \/ exists ge_signed_half_scalar_product_sumresultdecode. (((value) = 2 * ge_signed_half_scalar_product_sumresultdecode + 1 /\ (ge_balance_positive_scalar_product_sumresult) = 0) /\ (ge_balance_negative_scalar_product_sumresult) = S ge_signed_half_scalar_product_sumresultdecode))) /\ ((dst_positive_sum_scalar_product_sum) + ge_balance_negative_scalar_product_sumresult = (dst_negative_sum_scalar_product_sum) + ge_balance_positive_scalar_product_sumresult))))))))) - 0063
specialize arithmetic_signed_sum_exists ((S (m))*(S (n))) - 0064
specialize arithmetic_signed_sum_exists (x3) - 0065
specialize arithmetic_signed_sum_exists ((S (m))*(S (n))) - 0066
apply arithmetic_signed_sum_exists - 0067
exact hd_witness_witness_witness_right_right_right_right_right_right_right_right_left_right_right_left - 0068
cases hv - 0069
have heq : x6=c - 0070
specialize signed_support_reindex_sum_equal (x3) - 0071
specialize signed_support_reindex_sum_equal (x2) - 0072
specialize signed_support_reindex_sum_equal (x4) - 0073
specialize signed_support_reindex_sum_equal (x5) - 0074
specialize signed_support_reindex_sum_equal ((S (m))*(S (n))) - 0075
specialize signed_support_reindex_sum_equal (S (m*n)) - 0076
specialize signed_support_reindex_sum_equal (x6) - 0077
specialize signed_support_reindex_sum_equal (c) - 0078
apply signed_support_reindex_sum_equal - 0079
specialize dirichlet_coprime_grid_support_reindex (N) - 0080
specialize dirichlet_coprime_grid_support_reindex (F) - 0081
specialize dirichlet_coprime_grid_support_reindex (G) - 0082
specialize dirichlet_coprime_grid_support_reindex (m) - 0083
specialize dirichlet_coprime_grid_support_reindex (n) - 0084
specialize dirichlet_coprime_grid_support_reindex (x) - 0085
specialize dirichlet_coprime_grid_support_reindex (x1) - 0086
specialize dirichlet_coprime_grid_support_reindex (x3) - 0087
specialize dirichlet_coprime_grid_support_reindex (x2) - 0088
specialize dirichlet_coprime_grid_support_reindex (x4) - 0089
specialize dirichlet_coprime_grid_support_reindex (x5) - 0090
apply dirichlet_coprime_grid_support_reindex - 0091
exact hd_witness_witness_witness - 0092
exact hv_witness - 0093
exact hsc_right_witness_right - 0094
have hp : exists sto_ap_scalar_result_before_transport sto_an_scalar_result_before_transport sto_bp_scalar_result_before_transport sto_bn_scalar_result_before_transport sto_cp_scalar_result_before_transport sto_cn_scalar_result_before_transport. (((((a) = 2 * (sto_ap_scalar_result_before_transport) /\ (sto_an_scalar_result_before_transport) = 0) \/ exists ge_signed_half_scalar_result_before_transportleft. (((a) = 2 * ge_signed_half_scalar_result_before_transportleft + 1 /\ (sto_ap_scalar_result_before_transport) = 0) /\ (sto_an_scalar_result_before_transport) = S ge_signed_half_scalar_result_before_transportleft))) /\ ((((((b) = 2 * (sto_bp_scalar_result_before_transport) /\ (sto_bn_scalar_result_before_transport) = 0) \/ exists ge_signed_half_scalar_result_before_transportright. (((b) = 2 * ge_signed_half_scalar_result_before_transportright + 1 /\ (sto_bp_scalar_result_before_transport) = 0) /\ (sto_bn_scalar_result_before_transport) = S ge_signed_half_scalar_result_before_transportright))) /\ ((((((x6) = 2 * (sto_cp_scalar_result_before_transport) /\ (sto_cn_scalar_result_before_transport) = 0) \/ exists ge_signed_half_scalar_result_before_transportoutput. (((x6) = 2 * ge_signed_half_scalar_result_before_transportoutput + 1 /\ (sto_cp_scalar_result_before_transport) = 0) /\ (sto_cn_scalar_result_before_transport) = S ge_signed_half_scalar_result_before_transportoutput))) /\ ((sto_ap_scalar_result_before_transport * sto_bp_scalar_result_before_transport + sto_an_scalar_result_before_transport * sto_bn_scalar_result_before_transport) + sto_cn_scalar_result_before_transport = (sto_ap_scalar_result_before_transport * sto_bn_scalar_result_before_transport + sto_an_scalar_result_before_transport * sto_bp_scalar_result_before_transport) + sto_cp_scalar_result_before_transport)))))) - 0095
specialize signed_cartesian_product_prefix_sum (x) - 0096
specialize signed_cartesian_product_prefix_sum (x1) - 0097
specialize signed_cartesian_product_prefix_sum (x3) - 0098
specialize signed_cartesian_product_prefix_sum (S m) - 0099
specialize signed_cartesian_product_prefix_sum (S n) - 0100
specialize signed_cartesian_product_prefix_sum (a) - 0101
specialize signed_cartesian_product_prefix_sum (b) - 0102
specialize signed_cartesian_product_prefix_sum (x6) - 0103
apply signed_cartesian_product_prefix_sum - 0104
exact hd_witness_witness_witness_right_right_right_right_right_right_right_right_left - 0105
exact hsm_right_witness_right - 0106
exact hsn_right_witness_right - 0107
exact hv_witness - 0108
rewrite heq at hp - 0109
rewrite heq at hp - 0110
exact hp