dirichlet_convolution_multiplicative_exists_unique

Exact expanded first-order arithmetic statement

forall N F G. (((~((N)=0)) /\ (((exists dst_positive_code_exists_firsttable dst_positive_scale_exists_firsttable dst_negative_code_exists_firsttable dst_negative_scale_exists_firsttable. (((F) = (((((dst_positive_code_exists_firsttable) + (dst_positive_scale_exists_firsttable)) * S ((dst_positive_code_exists_firsttable) + (dst_positive_scale_exists_firsttable)) + ((dst_positive_scale_exists_firsttable) + (dst_positive_scale_exists_firsttable))) + (((dst_negative_code_exists_firsttable) + (dst_negative_scale_exists_firsttable)) * S ((dst_negative_code_exists_firsttable) + (dst_negative_scale_exists_firsttable)) + ((dst_negative_scale_exists_firsttable) + (dst_negative_scale_exists_firsttable)))) * S ((((dst_positive_code_exists_firsttable) + (dst_positive_scale_exists_firsttable)) * S ((dst_positive_code_exists_firsttable) + (dst_positive_scale_exists_firsttable)) + ((dst_positive_scale_exists_firsttable) + (dst_positive_scale_exists_firsttable))) + (((dst_negative_code_exists_firsttable) + (dst_negative_scale_exists_firsttable)) * S ((dst_negative_code_exists_firsttable) + (dst_negative_scale_exists_firsttable)) + ((dst_negative_scale_exists_firsttable) + (dst_negative_scale_exists_firsttable)))) + ((((dst_negative_code_exists_firsttable) + (dst_negative_scale_exists_firsttable)) * S ((dst_negative_code_exists_firsttable) + (dst_negative_scale_exists_firsttable)) + ((dst_negative_scale_exists_firsttable) + (dst_negative_scale_exists_firsttable))) + (((dst_negative_code_exists_firsttable) + (dst_negative_scale_exists_firsttable)) * S ((dst_negative_code_exists_firsttable) + (dst_negative_scale_exists_firsttable)) + ((dst_negative_scale_exists_firsttable) + (dst_negative_scale_exists_firsttable)))))) /\ (forall dst_index_exists_firsttable. (exists pvs_le_gap_exists_firsttabledomain. pvs_le_gap_exists_firsttabledomain + (dst_index_exists_firsttable) = (N)) -> exists dst_positive_exists_firsttable dst_negative_exists_firsttable dst_value_exists_firsttable. ((((exists ff_h_pvs_exists_firsttableentrypositive. ff_h_pvs_exists_firsttableentrypositive + S (dst_positive_exists_firsttable) = S ((S (dst_index_exists_firsttable)) * dst_positive_scale_exists_firsttable)) /\ exists ff_q_pvs_exists_firsttableentrypositive. dst_positive_code_exists_firsttable = ff_q_pvs_exists_firsttableentrypositive * S ((S (dst_index_exists_firsttable)) * dst_positive_scale_exists_firsttable) + (dst_positive_exists_firsttable))) /\ (((((exists ff_h_pvs_exists_firsttableentrynegative. ff_h_pvs_exists_firsttableentrynegative + S (dst_negative_exists_firsttable) = S ((S (dst_index_exists_firsttable)) * dst_negative_scale_exists_firsttable)) /\ exists ff_q_pvs_exists_firsttableentrynegative. dst_negative_code_exists_firsttable = ff_q_pvs_exists_firsttableentrynegative * S ((S (dst_index_exists_firsttable)) * dst_negative_scale_exists_firsttable) + (dst_negative_exists_firsttable))) /\ (exists ge_balance_positive_exists_firsttableentryvalue ge_balance_negative_exists_firsttableentryvalue. (((((dst_value_exists_firsttable) = 2 * (ge_balance_positive_exists_firsttableentryvalue) /\ (ge_balance_negative_exists_firsttableentryvalue) = 0) \/ exists ge_signed_half_exists_firsttableentryvaluedecode. (((dst_value_exists_firsttable) = 2 * ge_signed_half_exists_firsttableentryvaluedecode + 1 /\ (ge_balance_positive_exists_firsttableentryvalue) = 0) /\ (ge_balance_negative_exists_firsttableentryvalue) = S ge_signed_half_exists_firsttableentryvaluedecode))) /\ ((dst_positive_exists_firsttable) + ge_balance_negative_exists_firsttableentryvalue = (dst_negative_exists_firsttable) + ge_balance_positive_exists_firsttableentryvalue))))))))) /\ (((exists dst_positive_code_exists_firstone dst_positive_scale_exists_firstone dst_negative_code_exists_firstone dst_negative_scale_exists_firstone dst_positive_exists_firstone dst_negative_exists_firstone. (((F) = (((((dst_positive_code_exists_firstone) + (dst_positive_scale_exists_firstone)) * S ((dst_positive_code_exists_firstone) + (dst_positive_scale_exists_firstone)) + ((dst_positive_scale_exists_firstone) + (dst_positive_scale_exists_firstone))) + (((dst_negative_code_exists_firstone) + (dst_negative_scale_exists_firstone)) * S ((dst_negative_code_exists_firstone) + (dst_negative_scale_exists_firstone)) + ((dst_negative_scale_exists_firstone) + (dst_negative_scale_exists_firstone)))) * S ((((dst_positive_code_exists_firstone) + (dst_positive_scale_exists_firstone)) * S ((dst_positive_code_exists_firstone) + (dst_positive_scale_exists_firstone)) + ((dst_positive_scale_exists_firstone) + (dst_positive_scale_exists_firstone))) + (((dst_negative_code_exists_firstone) + (dst_negative_scale_exists_firstone)) * S ((dst_negative_code_exists_firstone) + (dst_negative_scale_exists_firstone)) + ((dst_negative_scale_exists_firstone) + (dst_negative_scale_exists_firstone)))) + ((((dst_negative_code_exists_firstone) + (dst_negative_scale_exists_firstone)) * S ((dst_negative_code_exists_firstone) + (dst_negative_scale_exists_firstone)) + ((dst_negative_scale_exists_firstone) + (dst_negative_scale_exists_firstone))) + (((dst_negative_code_exists_firstone) + (dst_negative_scale_exists_firstone)) * S ((dst_negative_code_exists_firstone) + (dst_negative_scale_exists_firstone)) + ((dst_negative_scale_exists_firstone) + (dst_negative_scale_exists_firstone)))))) /\ (((((exists ff_h_pvs_exists_firstonepositive. ff_h_pvs_exists_firstonepositive + S (dst_positive_exists_firstone) = S ((S (1)) * dst_positive_scale_exists_firstone)) /\ exists ff_q_pvs_exists_firstonepositive. dst_positive_code_exists_firstone = ff_q_pvs_exists_firstonepositive * S ((S (1)) * dst_positive_scale_exists_firstone) + (dst_positive_exists_firstone))) /\ (((((exists ff_h_pvs_exists_firstonenegative. ff_h_pvs_exists_firstonenegative + S (dst_negative_exists_firstone) = S ((S (1)) * dst_negative_scale_exists_firstone)) /\ exists ff_q_pvs_exists_firstonenegative. dst_negative_code_exists_firstone = ff_q_pvs_exists_firstonenegative * S ((S (1)) * dst_negative_scale_exists_firstone) + (dst_negative_exists_firstone))) /\ (exists ge_balance_positive_exists_firstonevalue ge_balance_negative_exists_firstonevalue. (((((2) = 2 * (ge_balance_positive_exists_firstonevalue) /\ (ge_balance_negative_exists_firstonevalue) = 0) \/ exists ge_signed_half_exists_firstonevaluedecode. (((2) = 2 * ge_signed_half_exists_firstonevaluedecode + 1 /\ (ge_balance_positive_exists_firstonevalue) = 0) /\ (ge_balance_negative_exists_firstonevalue) = S ge_signed_half_exists_firstonevaluedecode))) /\ ((dst_positive_exists_firstone) + ge_balance_negative_exists_firstonevalue = (dst_negative_exists_firstone) + ge_balance_positive_exists_firstonevalue))))))))) /\ (forall mp_a_exists_first mp_b_exists_first mp_x_exists_first mp_y_exists_first mp_z_exists_first. ~(mp_a_exists_first=0) -> ~(mp_b_exists_first=0) -> (exists pvs_le_gap_exists_firstbound. pvs_le_gap_exists_firstbound + (mp_a_exists_first*mp_b_exists_first) = (N)) -> (forall frp_divisor_exists_firstcoprime. (exists frp_left_factor_exists_firstcoprime. mp_a_exists_first = frp_divisor_exists_firstcoprime * frp_left_factor_exists_firstcoprime) -> (exists frp_right_factor_exists_firstcoprime. mp_b_exists_first = frp_divisor_exists_firstcoprime * frp_right_factor_exists_firstcoprime) -> frp_divisor_exists_firstcoprime = 1) -> (exists dst_positive_code_exists_firstfirst dst_positive_scale_exists_firstfirst dst_negative_code_exists_firstfirst dst_negative_scale_exists_firstfirst dst_positive_exists_firstfirst dst_negative_exists_firstfirst. (((F) = (((((dst_positive_code_exists_firstfirst) + (dst_positive_scale_exists_firstfirst)) * S ((dst_positive_code_exists_firstfirst) + (dst_positive_scale_exists_firstfirst)) + ((dst_positive_scale_exists_firstfirst) + (dst_positive_scale_exists_firstfirst))) + (((dst_negative_code_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)) * S ((dst_negative_code_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)) + ((dst_negative_scale_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)))) * S ((((dst_positive_code_exists_firstfirst) + (dst_positive_scale_exists_firstfirst)) * S ((dst_positive_code_exists_firstfirst) + (dst_positive_scale_exists_firstfirst)) + ((dst_positive_scale_exists_firstfirst) + (dst_positive_scale_exists_firstfirst))) + (((dst_negative_code_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)) * S ((dst_negative_code_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)) + ((dst_negative_scale_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)))) + ((((dst_negative_code_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)) * S ((dst_negative_code_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)) + ((dst_negative_scale_exists_firstfirst) + (dst_negative_scale_exists_firstfirst))) + (((dst_negative_code_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)) * S ((dst_negative_code_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)) + ((dst_negative_scale_exists_firstfirst) + (dst_negative_scale_exists_firstfirst)))))) /\ (((((exists ff_h_pvs_exists_firstfirstpositive. ff_h_pvs_exists_firstfirstpositive + S (dst_positive_exists_firstfirst) = S ((S (mp_a_exists_first)) * dst_positive_scale_exists_firstfirst)) /\ exists ff_q_pvs_exists_firstfirstpositive. dst_positive_code_exists_firstfirst = ff_q_pvs_exists_firstfirstpositive * S ((S (mp_a_exists_first)) * dst_positive_scale_exists_firstfirst) + (dst_positive_exists_firstfirst))) /\ (((((exists ff_h_pvs_exists_firstfirstnegative. ff_h_pvs_exists_firstfirstnegative + S (dst_negative_exists_firstfirst) = S ((S (mp_a_exists_first)) * dst_negative_scale_exists_firstfirst)) /\ exists ff_q_pvs_exists_firstfirstnegative. dst_negative_code_exists_firstfirst = ff_q_pvs_exists_firstfirstnegative * S ((S (mp_a_exists_first)) * dst_negative_scale_exists_firstfirst) + (dst_negative_exists_firstfirst))) /\ (exists ge_balance_positive_exists_firstfirstvalue ge_balance_negative_exists_firstfirstvalue. (((((mp_x_exists_first) = 2 * (ge_balance_positive_exists_firstfirstvalue) /\ (ge_balance_negative_exists_firstfirstvalue) = 0) \/ exists ge_signed_half_exists_firstfirstvaluedecode. (((mp_x_exists_first) = 2 * ge_signed_half_exists_firstfirstvaluedecode + 1 /\ (ge_balance_positive_exists_firstfirstvalue) = 0) /\ (ge_balance_negative_exists_firstfirstvalue) = S ge_signed_half_exists_firstfirstvaluedecode))) /\ ((dst_positive_exists_firstfirst) + ge_balance_negative_exists_firstfirstvalue = (dst_negative_exists_firstfirst) + ge_balance_positive_exists_firstfirstvalue))))))))) -> (exists dst_positive_code_exists_firstsecond dst_positive_scale_exists_firstsecond dst_negative_code_exists_firstsecond dst_negative_scale_exists_firstsecond dst_positive_exists_firstsecond dst_negative_exists_firstsecond. (((F) = (((((dst_positive_code_exists_firstsecond) + (dst_positive_scale_exists_firstsecond)) * S ((dst_positive_code_exists_firstsecond) + (dst_positive_scale_exists_firstsecond)) + ((dst_positive_scale_exists_firstsecond) + (dst_positive_scale_exists_firstsecond))) + (((dst_negative_code_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)) * S ((dst_negative_code_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)) + ((dst_negative_scale_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)))) * S ((((dst_positive_code_exists_firstsecond) + (dst_positive_scale_exists_firstsecond)) * S ((dst_positive_code_exists_firstsecond) + (dst_positive_scale_exists_firstsecond)) + ((dst_positive_scale_exists_firstsecond) + (dst_positive_scale_exists_firstsecond))) + (((dst_negative_code_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)) * S ((dst_negative_code_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)) + ((dst_negative_scale_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)))) + ((((dst_negative_code_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)) * S ((dst_negative_code_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)) + ((dst_negative_scale_exists_firstsecond) + (dst_negative_scale_exists_firstsecond))) + (((dst_negative_code_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)) * S ((dst_negative_code_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)) + ((dst_negative_scale_exists_firstsecond) + (dst_negative_scale_exists_firstsecond)))))) /\ (((((exists ff_h_pvs_exists_firstsecondpositive. ff_h_pvs_exists_firstsecondpositive + S (dst_positive_exists_firstsecond) = S ((S (mp_b_exists_first)) * dst_positive_scale_exists_firstsecond)) /\ exists ff_q_pvs_exists_firstsecondpositive. dst_positive_code_exists_firstsecond = ff_q_pvs_exists_firstsecondpositive * S ((S (mp_b_exists_first)) * dst_positive_scale_exists_firstsecond) + (dst_positive_exists_firstsecond))) /\ (((((exists ff_h_pvs_exists_firstsecondnegative. ff_h_pvs_exists_firstsecondnegative + S (dst_negative_exists_firstsecond) = S ((S (mp_b_exists_first)) * dst_negative_scale_exists_firstsecond)) /\ exists ff_q_pvs_exists_firstsecondnegative. dst_negative_code_exists_firstsecond = ff_q_pvs_exists_firstsecondnegative * S ((S (mp_b_exists_first)) * dst_negative_scale_exists_firstsecond) + (dst_negative_exists_firstsecond))) /\ (exists ge_balance_positive_exists_firstsecondvalue ge_balance_negative_exists_firstsecondvalue. (((((mp_y_exists_first) = 2 * (ge_balance_positive_exists_firstsecondvalue) /\ (ge_balance_negative_exists_firstsecondvalue) = 0) \/ exists ge_signed_half_exists_firstsecondvaluedecode. (((mp_y_exists_first) = 2 * ge_signed_half_exists_firstsecondvaluedecode + 1 /\ (ge_balance_positive_exists_firstsecondvalue) = 0) /\ (ge_balance_negative_exists_firstsecondvalue) = S ge_signed_half_exists_firstsecondvaluedecode))) /\ ((dst_positive_exists_firstsecond) + ge_balance_negative_exists_firstsecondvalue = (dst_negative_exists_firstsecond) + ge_balance_positive_exists_firstsecondvalue))))))))) -> (exists dst_positive_code_exists_firstproduct dst_positive_scale_exists_firstproduct dst_negative_code_exists_firstproduct dst_negative_scale_exists_firstproduct dst_positive_exists_firstproduct dst_negative_exists_firstproduct. (((F) = (((((dst_positive_code_exists_firstproduct) + (dst_positive_scale_exists_firstproduct)) * S ((dst_positive_code_exists_firstproduct) + (dst_positive_scale_exists_firstproduct)) + ((dst_positive_scale_exists_firstproduct) + (dst_positive_scale_exists_firstproduct))) + (((dst_negative_code_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)) * S ((dst_negative_code_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)) + ((dst_negative_scale_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)))) * S ((((dst_positive_code_exists_firstproduct) + (dst_positive_scale_exists_firstproduct)) * S ((dst_positive_code_exists_firstproduct) + (dst_positive_scale_exists_firstproduct)) + ((dst_positive_scale_exists_firstproduct) + (dst_positive_scale_exists_firstproduct))) + (((dst_negative_code_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)) * S ((dst_negative_code_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)) + ((dst_negative_scale_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)))) + ((((dst_negative_code_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)) * S ((dst_negative_code_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)) + ((dst_negative_scale_exists_firstproduct) + (dst_negative_scale_exists_firstproduct))) + (((dst_negative_code_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)) * S ((dst_negative_code_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)) + ((dst_negative_scale_exists_firstproduct) + (dst_negative_scale_exists_firstproduct)))))) /\ (((((exists ff_h_pvs_exists_firstproductpositive. ff_h_pvs_exists_firstproductpositive + S (dst_positive_exists_firstproduct) = S ((S (mp_a_exists_first*mp_b_exists_first)) * dst_positive_scale_exists_firstproduct)) /\ exists ff_q_pvs_exists_firstproductpositive. dst_positive_code_exists_firstproduct = ff_q_pvs_exists_firstproductpositive * S ((S (mp_a_exists_first*mp_b_exists_first)) * dst_positive_scale_exists_firstproduct) + (dst_positive_exists_firstproduct))) /\ (((((exists ff_h_pvs_exists_firstproductnegative. ff_h_pvs_exists_firstproductnegative + S (dst_negative_exists_firstproduct) = S ((S (mp_a_exists_first*mp_b_exists_first)) * dst_negative_scale_exists_firstproduct)) /\ exists ff_q_pvs_exists_firstproductnegative. dst_negative_code_exists_firstproduct = ff_q_pvs_exists_firstproductnegative * S ((S (mp_a_exists_first*mp_b_exists_first)) * dst_negative_scale_exists_firstproduct) + (dst_negative_exists_firstproduct))) /\ (exists ge_balance_positive_exists_firstproductvalue ge_balance_negative_exists_firstproductvalue. (((((mp_z_exists_first) = 2 * (ge_balance_positive_exists_firstproductvalue) /\ (ge_balance_negative_exists_firstproductvalue) = 0) \/ exists ge_signed_half_exists_firstproductvaluedecode. (((mp_z_exists_first) = 2 * ge_signed_half_exists_firstproductvaluedecode + 1 /\ (ge_balance_positive_exists_firstproductvalue) = 0) /\ (ge_balance_negative_exists_firstproductvalue) = S ge_signed_half_exists_firstproductvaluedecode))) /\ ((dst_positive_exists_firstproduct) + ge_balance_negative_exists_firstproductvalue = (dst_negative_exists_firstproduct) + ge_balance_positive_exists_firstproductvalue))))))))) -> (exists sto_ap_exists_firstlaw sto_an_exists_firstlaw sto_bp_exists_firstlaw sto_bn_exists_firstlaw sto_cp_exists_firstlaw sto_cn_exists_firstlaw. (((((mp_x_exists_first) = 2 * (sto_ap_exists_firstlaw) /\ (sto_an_exists_firstlaw) = 0) \/ exists ge_signed_half_exists_firstlawleft. (((mp_x_exists_first) = 2 * ge_signed_half_exists_firstlawleft + 1 /\ (sto_ap_exists_firstlaw) = 0) /\ (sto_an_exists_firstlaw) = S ge_signed_half_exists_firstlawleft))) /\ ((((((mp_y_exists_first) = 2 * (sto_bp_exists_firstlaw) /\ (sto_bn_exists_firstlaw) = 0) \/ exists ge_signed_half_exists_firstlawright. (((mp_y_exists_first) = 2 * ge_signed_half_exists_firstlawright + 1 /\ (sto_bp_exists_firstlaw) = 0) /\ (sto_bn_exists_firstlaw) = S ge_signed_half_exists_firstlawright))) /\ ((((((mp_z_exists_first) = 2 * (sto_cp_exists_firstlaw) /\ (sto_cn_exists_firstlaw) = 0) \/ exists ge_signed_half_exists_firstlawoutput. (((mp_z_exists_first) = 2 * ge_signed_half_exists_firstlawoutput + 1 /\ (sto_cp_exists_firstlaw) = 0) /\ (sto_cn_exists_firstlaw) = S ge_signed_half_exists_firstlawoutput))) /\ ((sto_ap_exists_firstlaw * sto_bp_exists_firstlaw + sto_an_exists_firstlaw * sto_bn_exists_firstlaw) + sto_cn_exists_firstlaw = (sto_ap_exists_firstlaw * sto_bn_exists_firstlaw + sto_an_exists_firstlaw * sto_bp_exists_firstlaw) + sto_cp_exists_firstlaw)))))))))))))) -> (((~((N)=0)) /\ (((exists dst_positive_code_exists_secondtable dst_positive_scale_exists_secondtable dst_negative_code_exists_secondtable dst_negative_scale_exists_secondtable. (((G) = (((((dst_positive_code_exists_secondtable) + (dst_positive_scale_exists_secondtable)) * S ((dst_positive_code_exists_secondtable) + (dst_positive_scale_exists_secondtable)) + ((dst_positive_scale_exists_secondtable) + (dst_positive_scale_exists_secondtable))) + (((dst_negative_code_exists_secondtable) + (dst_negative_scale_exists_secondtable)) * S ((dst_negative_code_exists_secondtable) + (dst_negative_scale_exists_secondtable)) + ((dst_negative_scale_exists_secondtable) + (dst_negative_scale_exists_secondtable)))) * S ((((dst_positive_code_exists_secondtable) + (dst_positive_scale_exists_secondtable)) * S ((dst_positive_code_exists_secondtable) + (dst_positive_scale_exists_secondtable)) + ((dst_positive_scale_exists_secondtable) + (dst_positive_scale_exists_secondtable))) + (((dst_negative_code_exists_secondtable) + (dst_negative_scale_exists_secondtable)) * S ((dst_negative_code_exists_secondtable) + (dst_negative_scale_exists_secondtable)) + ((dst_negative_scale_exists_secondtable) + (dst_negative_scale_exists_secondtable)))) + ((((dst_negative_code_exists_secondtable) + (dst_negative_scale_exists_secondtable)) * S ((dst_negative_code_exists_secondtable) + (dst_negative_scale_exists_secondtable)) + ((dst_negative_scale_exists_secondtable) + (dst_negative_scale_exists_secondtable))) + (((dst_negative_code_exists_secondtable) + (dst_negative_scale_exists_secondtable)) * S ((dst_negative_code_exists_secondtable) + (dst_negative_scale_exists_secondtable)) + ((dst_negative_scale_exists_secondtable) + (dst_negative_scale_exists_secondtable)))))) /\ (forall dst_index_exists_secondtable. (exists pvs_le_gap_exists_secondtabledomain. pvs_le_gap_exists_secondtabledomain + (dst_index_exists_secondtable) = (N)) -> exists dst_positive_exists_secondtable dst_negative_exists_secondtable dst_value_exists_secondtable. ((((exists ff_h_pvs_exists_secondtableentrypositive. ff_h_pvs_exists_secondtableentrypositive + S (dst_positive_exists_secondtable) = S ((S (dst_index_exists_secondtable)) * dst_positive_scale_exists_secondtable)) /\ exists ff_q_pvs_exists_secondtableentrypositive. dst_positive_code_exists_secondtable = ff_q_pvs_exists_secondtableentrypositive * S ((S (dst_index_exists_secondtable)) * dst_positive_scale_exists_secondtable) + (dst_positive_exists_secondtable))) /\ (((((exists ff_h_pvs_exists_secondtableentrynegative. ff_h_pvs_exists_secondtableentrynegative + S (dst_negative_exists_secondtable) = S ((S (dst_index_exists_secondtable)) * dst_negative_scale_exists_secondtable)) /\ exists ff_q_pvs_exists_secondtableentrynegative. dst_negative_code_exists_secondtable = ff_q_pvs_exists_secondtableentrynegative * S ((S (dst_index_exists_secondtable)) * dst_negative_scale_exists_secondtable) + (dst_negative_exists_secondtable))) /\ (exists ge_balance_positive_exists_secondtableentryvalue ge_balance_negative_exists_secondtableentryvalue. (((((dst_value_exists_secondtable) = 2 * (ge_balance_positive_exists_secondtableentryvalue) /\ (ge_balance_negative_exists_secondtableentryvalue) = 0) \/ exists ge_signed_half_exists_secondtableentryvaluedecode. (((dst_value_exists_secondtable) = 2 * ge_signed_half_exists_secondtableentryvaluedecode + 1 /\ (ge_balance_positive_exists_secondtableentryvalue) = 0) /\ (ge_balance_negative_exists_secondtableentryvalue) = S ge_signed_half_exists_secondtableentryvaluedecode))) /\ ((dst_positive_exists_secondtable) + ge_balance_negative_exists_secondtableentryvalue = (dst_negative_exists_secondtable) + ge_balance_positive_exists_secondtableentryvalue))))))))) /\ (((exists dst_positive_code_exists_secondone dst_positive_scale_exists_secondone dst_negative_code_exists_secondone dst_negative_scale_exists_secondone dst_positive_exists_secondone dst_negative_exists_secondone. (((G) = (((((dst_positive_code_exists_secondone) + (dst_positive_scale_exists_secondone)) * S ((dst_positive_code_exists_secondone) + (dst_positive_scale_exists_secondone)) + ((dst_positive_scale_exists_secondone) + (dst_positive_scale_exists_secondone))) + (((dst_negative_code_exists_secondone) + (dst_negative_scale_exists_secondone)) * S ((dst_negative_code_exists_secondone) + (dst_negative_scale_exists_secondone)) + ((dst_negative_scale_exists_secondone) + (dst_negative_scale_exists_secondone)))) * S ((((dst_positive_code_exists_secondone) + (dst_positive_scale_exists_secondone)) * S ((dst_positive_code_exists_secondone) + (dst_positive_scale_exists_secondone)) + ((dst_positive_scale_exists_secondone) + (dst_positive_scale_exists_secondone))) + (((dst_negative_code_exists_secondone) + (dst_negative_scale_exists_secondone)) * S ((dst_negative_code_exists_secondone) + (dst_negative_scale_exists_secondone)) + ((dst_negative_scale_exists_secondone) + (dst_negative_scale_exists_secondone)))) + ((((dst_negative_code_exists_secondone) + (dst_negative_scale_exists_secondone)) * S ((dst_negative_code_exists_secondone) + (dst_negative_scale_exists_secondone)) + ((dst_negative_scale_exists_secondone) + (dst_negative_scale_exists_secondone))) + (((dst_negative_code_exists_secondone) + (dst_negative_scale_exists_secondone)) * S ((dst_negative_code_exists_secondone) + (dst_negative_scale_exists_secondone)) + ((dst_negative_scale_exists_secondone) + (dst_negative_scale_exists_secondone)))))) /\ (((((exists ff_h_pvs_exists_secondonepositive. ff_h_pvs_exists_secondonepositive + S (dst_positive_exists_secondone) = S ((S (1)) * dst_positive_scale_exists_secondone)) /\ exists ff_q_pvs_exists_secondonepositive. dst_positive_code_exists_secondone = ff_q_pvs_exists_secondonepositive * S ((S (1)) * dst_positive_scale_exists_secondone) + (dst_positive_exists_secondone))) /\ (((((exists ff_h_pvs_exists_secondonenegative. ff_h_pvs_exists_secondonenegative + S (dst_negative_exists_secondone) = S ((S (1)) * dst_negative_scale_exists_secondone)) /\ exists ff_q_pvs_exists_secondonenegative. dst_negative_code_exists_secondone = ff_q_pvs_exists_secondonenegative * S ((S (1)) * dst_negative_scale_exists_secondone) + (dst_negative_exists_secondone))) /\ (exists ge_balance_positive_exists_secondonevalue ge_balance_negative_exists_secondonevalue. (((((2) = 2 * (ge_balance_positive_exists_secondonevalue) /\ (ge_balance_negative_exists_secondonevalue) = 0) \/ exists ge_signed_half_exists_secondonevaluedecode. (((2) = 2 * ge_signed_half_exists_secondonevaluedecode + 1 /\ (ge_balance_positive_exists_secondonevalue) = 0) /\ (ge_balance_negative_exists_secondonevalue) = S ge_signed_half_exists_secondonevaluedecode))) /\ ((dst_positive_exists_secondone) + ge_balance_negative_exists_secondonevalue = (dst_negative_exists_secondone) + ge_balance_positive_exists_secondonevalue))))))))) /\ (forall mp_a_exists_second mp_b_exists_second mp_x_exists_second mp_y_exists_second mp_z_exists_second. ~(mp_a_exists_second=0) -> ~(mp_b_exists_second=0) -> (exists pvs_le_gap_exists_secondbound. pvs_le_gap_exists_secondbound + (mp_a_exists_second*mp_b_exists_second) = (N)) -> (forall frp_divisor_exists_secondcoprime. (exists frp_left_factor_exists_secondcoprime. mp_a_exists_second = frp_divisor_exists_secondcoprime * frp_left_factor_exists_secondcoprime) -> (exists frp_right_factor_exists_secondcoprime. mp_b_exists_second = frp_divisor_exists_secondcoprime * frp_right_factor_exists_secondcoprime) -> frp_divisor_exists_secondcoprime = 1) -> (exists dst_positive_code_exists_secondfirst dst_positive_scale_exists_secondfirst dst_negative_code_exists_secondfirst dst_negative_scale_exists_secondfirst dst_positive_exists_secondfirst dst_negative_exists_secondfirst. (((G) = (((((dst_positive_code_exists_secondfirst) + (dst_positive_scale_exists_secondfirst)) * S ((dst_positive_code_exists_secondfirst) + (dst_positive_scale_exists_secondfirst)) + ((dst_positive_scale_exists_secondfirst) + (dst_positive_scale_exists_secondfirst))) + (((dst_negative_code_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)) * S ((dst_negative_code_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)) + ((dst_negative_scale_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)))) * S ((((dst_positive_code_exists_secondfirst) + (dst_positive_scale_exists_secondfirst)) * S ((dst_positive_code_exists_secondfirst) + (dst_positive_scale_exists_secondfirst)) + ((dst_positive_scale_exists_secondfirst) + (dst_positive_scale_exists_secondfirst))) + (((dst_negative_code_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)) * S ((dst_negative_code_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)) + ((dst_negative_scale_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)))) + ((((dst_negative_code_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)) * S ((dst_negative_code_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)) + ((dst_negative_scale_exists_secondfirst) + (dst_negative_scale_exists_secondfirst))) + (((dst_negative_code_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)) * S ((dst_negative_code_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)) + ((dst_negative_scale_exists_secondfirst) + (dst_negative_scale_exists_secondfirst)))))) /\ (((((exists ff_h_pvs_exists_secondfirstpositive. ff_h_pvs_exists_secondfirstpositive + S (dst_positive_exists_secondfirst) = S ((S (mp_a_exists_second)) * dst_positive_scale_exists_secondfirst)) /\ exists ff_q_pvs_exists_secondfirstpositive. dst_positive_code_exists_secondfirst = ff_q_pvs_exists_secondfirstpositive * S ((S (mp_a_exists_second)) * dst_positive_scale_exists_secondfirst) + (dst_positive_exists_secondfirst))) /\ (((((exists ff_h_pvs_exists_secondfirstnegative. ff_h_pvs_exists_secondfirstnegative + S (dst_negative_exists_secondfirst) = S ((S (mp_a_exists_second)) * dst_negative_scale_exists_secondfirst)) /\ exists ff_q_pvs_exists_secondfirstnegative. dst_negative_code_exists_secondfirst = ff_q_pvs_exists_secondfirstnegative * S ((S (mp_a_exists_second)) * dst_negative_scale_exists_secondfirst) + (dst_negative_exists_secondfirst))) /\ (exists ge_balance_positive_exists_secondfirstvalue ge_balance_negative_exists_secondfirstvalue. (((((mp_x_exists_second) = 2 * (ge_balance_positive_exists_secondfirstvalue) /\ (ge_balance_negative_exists_secondfirstvalue) = 0) \/ exists ge_signed_half_exists_secondfirstvaluedecode. (((mp_x_exists_second) = 2 * ge_signed_half_exists_secondfirstvaluedecode + 1 /\ (ge_balance_positive_exists_secondfirstvalue) = 0) /\ (ge_balance_negative_exists_secondfirstvalue) = S ge_signed_half_exists_secondfirstvaluedecode))) /\ ((dst_positive_exists_secondfirst) + ge_balance_negative_exists_secondfirstvalue = (dst_negative_exists_secondfirst) + ge_balance_positive_exists_secondfirstvalue))))))))) -> (exists dst_positive_code_exists_secondsecond dst_positive_scale_exists_secondsecond dst_negative_code_exists_secondsecond dst_negative_scale_exists_secondsecond dst_positive_exists_secondsecond dst_negative_exists_secondsecond. (((G) = (((((dst_positive_code_exists_secondsecond) + (dst_positive_scale_exists_secondsecond)) * S ((dst_positive_code_exists_secondsecond) + (dst_positive_scale_exists_secondsecond)) + ((dst_positive_scale_exists_secondsecond) + (dst_positive_scale_exists_secondsecond))) + (((dst_negative_code_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)) * S ((dst_negative_code_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)) + ((dst_negative_scale_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)))) * S ((((dst_positive_code_exists_secondsecond) + (dst_positive_scale_exists_secondsecond)) * S ((dst_positive_code_exists_secondsecond) + (dst_positive_scale_exists_secondsecond)) + ((dst_positive_scale_exists_secondsecond) + (dst_positive_scale_exists_secondsecond))) + (((dst_negative_code_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)) * S ((dst_negative_code_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)) + ((dst_negative_scale_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)))) + ((((dst_negative_code_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)) * S ((dst_negative_code_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)) + ((dst_negative_scale_exists_secondsecond) + (dst_negative_scale_exists_secondsecond))) + (((dst_negative_code_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)) * S ((dst_negative_code_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)) + ((dst_negative_scale_exists_secondsecond) + (dst_negative_scale_exists_secondsecond)))))) /\ (((((exists ff_h_pvs_exists_secondsecondpositive. ff_h_pvs_exists_secondsecondpositive + S (dst_positive_exists_secondsecond) = S ((S (mp_b_exists_second)) * dst_positive_scale_exists_secondsecond)) /\ exists ff_q_pvs_exists_secondsecondpositive. dst_positive_code_exists_secondsecond = ff_q_pvs_exists_secondsecondpositive * S ((S (mp_b_exists_second)) * dst_positive_scale_exists_secondsecond) + (dst_positive_exists_secondsecond))) /\ (((((exists ff_h_pvs_exists_secondsecondnegative. ff_h_pvs_exists_secondsecondnegative + S (dst_negative_exists_secondsecond) = S ((S (mp_b_exists_second)) * dst_negative_scale_exists_secondsecond)) /\ exists ff_q_pvs_exists_secondsecondnegative. dst_negative_code_exists_secondsecond = ff_q_pvs_exists_secondsecondnegative * S ((S (mp_b_exists_second)) * dst_negative_scale_exists_secondsecond) + (dst_negative_exists_secondsecond))) /\ (exists ge_balance_positive_exists_secondsecondvalue ge_balance_negative_exists_secondsecondvalue. (((((mp_y_exists_second) = 2 * (ge_balance_positive_exists_secondsecondvalue) /\ (ge_balance_negative_exists_secondsecondvalue) = 0) \/ exists ge_signed_half_exists_secondsecondvaluedecode. (((mp_y_exists_second) = 2 * ge_signed_half_exists_secondsecondvaluedecode + 1 /\ (ge_balance_positive_exists_secondsecondvalue) = 0) /\ (ge_balance_negative_exists_secondsecondvalue) = S ge_signed_half_exists_secondsecondvaluedecode))) /\ ((dst_positive_exists_secondsecond) + ge_balance_negative_exists_secondsecondvalue = (dst_negative_exists_secondsecond) + ge_balance_positive_exists_secondsecondvalue))))))))) -> (exists dst_positive_code_exists_secondproduct dst_positive_scale_exists_secondproduct dst_negative_code_exists_secondproduct dst_negative_scale_exists_secondproduct dst_positive_exists_secondproduct dst_negative_exists_secondproduct. (((G) = (((((dst_positive_code_exists_secondproduct) + (dst_positive_scale_exists_secondproduct)) * S ((dst_positive_code_exists_secondproduct) + (dst_positive_scale_exists_secondproduct)) + ((dst_positive_scale_exists_secondproduct) + (dst_positive_scale_exists_secondproduct))) + (((dst_negative_code_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)) * S ((dst_negative_code_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)) + ((dst_negative_scale_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)))) * S ((((dst_positive_code_exists_secondproduct) + (dst_positive_scale_exists_secondproduct)) * S ((dst_positive_code_exists_secondproduct) + (dst_positive_scale_exists_secondproduct)) + ((dst_positive_scale_exists_secondproduct) + (dst_positive_scale_exists_secondproduct))) + (((dst_negative_code_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)) * S ((dst_negative_code_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)) + ((dst_negative_scale_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)))) + ((((dst_negative_code_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)) * S ((dst_negative_code_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)) + ((dst_negative_scale_exists_secondproduct) + (dst_negative_scale_exists_secondproduct))) + (((dst_negative_code_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)) * S ((dst_negative_code_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)) + ((dst_negative_scale_exists_secondproduct) + (dst_negative_scale_exists_secondproduct)))))) /\ (((((exists ff_h_pvs_exists_secondproductpositive. ff_h_pvs_exists_secondproductpositive + S (dst_positive_exists_secondproduct) = S ((S (mp_a_exists_second*mp_b_exists_second)) * dst_positive_scale_exists_secondproduct)) /\ exists ff_q_pvs_exists_secondproductpositive. dst_positive_code_exists_secondproduct = ff_q_pvs_exists_secondproductpositive * S ((S (mp_a_exists_second*mp_b_exists_second)) * dst_positive_scale_exists_secondproduct) + (dst_positive_exists_secondproduct))) /\ (((((exists ff_h_pvs_exists_secondproductnegative. ff_h_pvs_exists_secondproductnegative + S (dst_negative_exists_secondproduct) = S ((S (mp_a_exists_second*mp_b_exists_second)) * dst_negative_scale_exists_secondproduct)) /\ exists ff_q_pvs_exists_secondproductnegative. dst_negative_code_exists_secondproduct = ff_q_pvs_exists_secondproductnegative * S ((S (mp_a_exists_second*mp_b_exists_second)) * dst_negative_scale_exists_secondproduct) + (dst_negative_exists_secondproduct))) /\ (exists ge_balance_positive_exists_secondproductvalue ge_balance_negative_exists_secondproductvalue. (((((mp_z_exists_second) = 2 * (ge_balance_positive_exists_secondproductvalue) /\ (ge_balance_negative_exists_secondproductvalue) = 0) \/ exists ge_signed_half_exists_secondproductvaluedecode. (((mp_z_exists_second) = 2 * ge_signed_half_exists_secondproductvaluedecode + 1 /\ (ge_balance_positive_exists_secondproductvalue) = 0) /\ (ge_balance_negative_exists_secondproductvalue) = S ge_signed_half_exists_secondproductvaluedecode))) /\ ((dst_positive_exists_secondproduct) + ge_balance_negative_exists_secondproductvalue = (dst_negative_exists_secondproduct) + ge_balance_positive_exists_secondproductvalue))))))))) -> (exists sto_ap_exists_secondlaw sto_an_exists_secondlaw sto_bp_exists_secondlaw sto_bn_exists_secondlaw sto_cp_exists_secondlaw sto_cn_exists_secondlaw. (((((mp_x_exists_second) = 2 * (sto_ap_exists_secondlaw) /\ (sto_an_exists_secondlaw) = 0) \/ exists ge_signed_half_exists_secondlawleft. (((mp_x_exists_second) = 2 * ge_signed_half_exists_secondlawleft + 1 /\ (sto_ap_exists_secondlaw) = 0) /\ (sto_an_exists_secondlaw) = S ge_signed_half_exists_secondlawleft))) /\ ((((((mp_y_exists_second) = 2 * (sto_bp_exists_secondlaw) /\ (sto_bn_exists_secondlaw) = 0) \/ exists ge_signed_half_exists_secondlawright. (((mp_y_exists_second) = 2 * ge_signed_half_exists_secondlawright + 1 /\ (sto_bp_exists_secondlaw) = 0) /\ (sto_bn_exists_secondlaw) = S ge_signed_half_exists_secondlawright))) /\ ((((((mp_z_exists_second) = 2 * (sto_cp_exists_secondlaw) /\ (sto_cn_exists_secondlaw) = 0) \/ exists ge_signed_half_exists_secondlawoutput. (((mp_z_exists_second) = 2 * ge_signed_half_exists_secondlawoutput + 1 /\ (sto_cp_exists_secondlaw) = 0) /\ (sto_cn_exists_secondlaw) = S ge_signed_half_exists_secondlawoutput))) /\ ((sto_ap_exists_secondlaw * sto_bp_exists_secondlaw + sto_an_exists_secondlaw * sto_bn_exists_secondlaw) + sto_cn_exists_secondlaw = (sto_ap_exists_secondlaw * sto_bn_exists_secondlaw + sto_an_exists_secondlaw * sto_bp_exists_secondlaw) + sto_cp_exists_secondlaw)))))))))))))) -> exists H. ((((exists dst_positive_code_exists_convolutionleft dst_positive_scale_exists_convolutionleft dst_negative_code_exists_convolutionleft dst_negative_scale_exists_convolutionleft. (((F) = (((((dst_positive_code_exists_convolutionleft) + (dst_positive_scale_exists_convolutionleft)) * S ((dst_positive_code_exists_convolutionleft) + (dst_positive_scale_exists_convolutionleft)) + ((dst_positive_scale_exists_convolutionleft) + (dst_positive_scale_exists_convolutionleft))) + (((dst_negative_code_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)) * S ((dst_negative_code_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)) + ((dst_negative_scale_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)))) * S ((((dst_positive_code_exists_convolutionleft) + (dst_positive_scale_exists_convolutionleft)) * S ((dst_positive_code_exists_convolutionleft) + (dst_positive_scale_exists_convolutionleft)) + ((dst_positive_scale_exists_convolutionleft) + (dst_positive_scale_exists_convolutionleft))) + (((dst_negative_code_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)) * S ((dst_negative_code_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)) + ((dst_negative_scale_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)))) + ((((dst_negative_code_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)) * S ((dst_negative_code_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)) + ((dst_negative_scale_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft))) + (((dst_negative_code_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)) * S ((dst_negative_code_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)) + ((dst_negative_scale_exists_convolutionleft) + (dst_negative_scale_exists_convolutionleft)))))) /\ (forall dst_index_exists_convolutionleft. (exists pvs_le_gap_exists_convolutionleftdomain. pvs_le_gap_exists_convolutionleftdomain + (dst_index_exists_convolutionleft) = (N)) -> exists dst_positive_exists_convolutionleft dst_negative_exists_convolutionleft dst_value_exists_convolutionleft. ((((exists ff_h_pvs_exists_convolutionleftentrypositive. ff_h_pvs_exists_convolutionleftentrypositive + S (dst_positive_exists_convolutionleft) = S ((S (dst_index_exists_convolutionleft)) * dst_positive_scale_exists_convolutionleft)) /\ exists ff_q_pvs_exists_convolutionleftentrypositive. dst_positive_code_exists_convolutionleft = ff_q_pvs_exists_convolutionleftentrypositive * S ((S (dst_index_exists_convolutionleft)) * dst_positive_scale_exists_convolutionleft) + (dst_positive_exists_convolutionleft))) /\ (((((exists ff_h_pvs_exists_convolutionleftentrynegative. ff_h_pvs_exists_convolutionleftentrynegative + S (dst_negative_exists_convolutionleft) = S ((S (dst_index_exists_convolutionleft)) * dst_negative_scale_exists_convolutionleft)) /\ exists ff_q_pvs_exists_convolutionleftentrynegative. dst_negative_code_exists_convolutionleft = ff_q_pvs_exists_convolutionleftentrynegative * S ((S (dst_index_exists_convolutionleft)) * dst_negative_scale_exists_convolutionleft) + (dst_negative_exists_convolutionleft))) /\ (exists ge_balance_positive_exists_convolutionleftentryvalue ge_balance_negative_exists_convolutionleftentryvalue. (((((dst_value_exists_convolutionleft) = 2 * (ge_balance_positive_exists_convolutionleftentryvalue) /\ (ge_balance_negative_exists_convolutionleftentryvalue) = 0) \/ exists ge_signed_half_exists_convolutionleftentryvaluedecode. (((dst_value_exists_convolutionleft) = 2 * ge_signed_half_exists_convolutionleftentryvaluedecode + 1 /\ (ge_balance_positive_exists_convolutionleftentryvalue) = 0) /\ (ge_balance_negative_exists_convolutionleftentryvalue) = S ge_signed_half_exists_convolutionleftentryvaluedecode))) /\ ((dst_positive_exists_convolutionleft) + ge_balance_negative_exists_convolutionleftentryvalue = (dst_negative_exists_convolutionleft) + ge_balance_positive_exists_convolutionleftentryvalue))))))))) /\ (((exists dst_positive_code_exists_convolutionright dst_positive_scale_exists_convolutionright dst_negative_code_exists_convolutionright dst_negative_scale_exists_convolutionright. (((G) = (((((dst_positive_code_exists_convolutionright) + (dst_positive_scale_exists_convolutionright)) * S ((dst_positive_code_exists_convolutionright) + (dst_positive_scale_exists_convolutionright)) + ((dst_positive_scale_exists_convolutionright) + (dst_positive_scale_exists_convolutionright))) + (((dst_negative_code_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)) * S ((dst_negative_code_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)) + ((dst_negative_scale_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)))) * S ((((dst_positive_code_exists_convolutionright) + (dst_positive_scale_exists_convolutionright)) * S ((dst_positive_code_exists_convolutionright) + (dst_positive_scale_exists_convolutionright)) + ((dst_positive_scale_exists_convolutionright) + (dst_positive_scale_exists_convolutionright))) + (((dst_negative_code_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)) * S ((dst_negative_code_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)) + ((dst_negative_scale_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)))) + ((((dst_negative_code_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)) * S ((dst_negative_code_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)) + ((dst_negative_scale_exists_convolutionright) + (dst_negative_scale_exists_convolutionright))) + (((dst_negative_code_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)) * S ((dst_negative_code_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)) + ((dst_negative_scale_exists_convolutionright) + (dst_negative_scale_exists_convolutionright)))))) /\ (forall dst_index_exists_convolutionright. (exists pvs_le_gap_exists_convolutionrightdomain. pvs_le_gap_exists_convolutionrightdomain + (dst_index_exists_convolutionright) = (N)) -> exists dst_positive_exists_convolutionright dst_negative_exists_convolutionright dst_value_exists_convolutionright. ((((exists ff_h_pvs_exists_convolutionrightentrypositive. ff_h_pvs_exists_convolutionrightentrypositive + S (dst_positive_exists_convolutionright) = S ((S (dst_index_exists_convolutionright)) * dst_positive_scale_exists_convolutionright)) /\ exists ff_q_pvs_exists_convolutionrightentrypositive. dst_positive_code_exists_convolutionright = ff_q_pvs_exists_convolutionrightentrypositive * S ((S (dst_index_exists_convolutionright)) * dst_positive_scale_exists_convolutionright) + (dst_positive_exists_convolutionright))) /\ (((((exists ff_h_pvs_exists_convolutionrightentrynegative. ff_h_pvs_exists_convolutionrightentrynegative + S (dst_negative_exists_convolutionright) = S ((S (dst_index_exists_convolutionright)) * dst_negative_scale_exists_convolutionright)) /\ exists ff_q_pvs_exists_convolutionrightentrynegative. dst_negative_code_exists_convolutionright = ff_q_pvs_exists_convolutionrightentrynegative * S ((S (dst_index_exists_convolutionright)) * dst_negative_scale_exists_convolutionright) + (dst_negative_exists_convolutionright))) /\ (exists ge_balance_positive_exists_convolutionrightentryvalue ge_balance_negative_exists_convolutionrightentryvalue. (((((dst_value_exists_convolutionright) = 2 * (ge_balance_positive_exists_convolutionrightentryvalue) /\ (ge_balance_negative_exists_convolutionrightentryvalue) = 0) \/ exists ge_signed_half_exists_convolutionrightentryvaluedecode. (((dst_value_exists_convolutionright) = 2 * ge_signed_half_exists_convolutionrightentryvaluedecode + 1 /\ (ge_balance_positive_exists_convolutionrightentryvalue) = 0) /\ (ge_balance_negative_exists_convolutionrightentryvalue) = S ge_signed_half_exists_convolutionrightentryvaluedecode))) /\ ((dst_positive_exists_convolutionright) + ge_balance_negative_exists_convolutionrightentryvalue = (dst_negative_exists_convolutionright) + ge_balance_positive_exists_convolutionrightentryvalue))))))))) /\ (((exists dst_positive_code_exists_convolutiontable dst_positive_scale_exists_convolutiontable dst_negative_code_exists_convolutiontable dst_negative_scale_exists_convolutiontable. (((H) = (((((dst_positive_code_exists_convolutiontable) + (dst_positive_scale_exists_convolutiontable)) * S ((dst_positive_code_exists_convolutiontable) + (dst_positive_scale_exists_convolutiontable)) + ((dst_positive_scale_exists_convolutiontable) + (dst_positive_scale_exists_convolutiontable))) + (((dst_negative_code_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)) * S ((dst_negative_code_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)) + ((dst_negative_scale_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)))) * S ((((dst_positive_code_exists_convolutiontable) + (dst_positive_scale_exists_convolutiontable)) * S ((dst_positive_code_exists_convolutiontable) + (dst_positive_scale_exists_convolutiontable)) + ((dst_positive_scale_exists_convolutiontable) + (dst_positive_scale_exists_convolutiontable))) + (((dst_negative_code_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)) * S ((dst_negative_code_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)) + ((dst_negative_scale_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)))) + ((((dst_negative_code_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)) * S ((dst_negative_code_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)) + ((dst_negative_scale_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable))) + (((dst_negative_code_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)) * S ((dst_negative_code_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)) + ((dst_negative_scale_exists_convolutiontable) + (dst_negative_scale_exists_convolutiontable)))))) /\ (forall dst_index_exists_convolutiontable. (exists pvs_le_gap_exists_convolutiontabledomain. pvs_le_gap_exists_convolutiontabledomain + (dst_index_exists_convolutiontable) = (N)) -> exists dst_positive_exists_convolutiontable dst_negative_exists_convolutiontable dst_value_exists_convolutiontable. ((((exists ff_h_pvs_exists_convolutiontableentrypositive. ff_h_pvs_exists_convolutiontableentrypositive + S (dst_positive_exists_convolutiontable) = S ((S (dst_index_exists_convolutiontable)) * dst_positive_scale_exists_convolutiontable)) /\ exists ff_q_pvs_exists_convolutiontableentrypositive. dst_positive_code_exists_convolutiontable = ff_q_pvs_exists_convolutiontableentrypositive * S ((S (dst_index_exists_convolutiontable)) * dst_positive_scale_exists_convolutiontable) + (dst_positive_exists_convolutiontable))) /\ (((((exists ff_h_pvs_exists_convolutiontableentrynegative. ff_h_pvs_exists_convolutiontableentrynegative + S (dst_negative_exists_convolutiontable) = S ((S (dst_index_exists_convolutiontable)) * dst_negative_scale_exists_convolutiontable)) /\ exists ff_q_pvs_exists_convolutiontableentrynegative. dst_negative_code_exists_convolutiontable = ff_q_pvs_exists_convolutiontableentrynegative * S ((S (dst_index_exists_convolutiontable)) * dst_negative_scale_exists_convolutiontable) + (dst_negative_exists_convolutiontable))) /\ (exists ge_balance_positive_exists_convolutiontableentryvalue ge_balance_negative_exists_convolutiontableentryvalue. (((((dst_value_exists_convolutiontable) = 2 * (ge_balance_positive_exists_convolutiontableentryvalue) /\ (ge_balance_negative_exists_convolutiontableentryvalue) = 0) \/ exists ge_signed_half_exists_convolutiontableentryvaluedecode. (((dst_value_exists_convolutiontable) = 2 * ge_signed_half_exists_convolutiontableentryvaluedecode + 1 /\ (ge_balance_positive_exists_convolutiontableentryvalue) = 0) /\ (ge_balance_negative_exists_convolutiontableentryvalue) = S ge_signed_half_exists_convolutiontableentryvaluedecode))) /\ ((dst_positive_exists_convolutiontable) + ge_balance_negative_exists_convolutiontableentryvalue = (dst_negative_exists_convolutiontable) + ge_balance_positive_exists_convolutiontableentryvalue))))))))) /\ (forall dc_input_exists_convolution dc_output_exists_convolution. ~(dc_input_exists_convolution=0) -> (exists pvs_le_gap_exists_convolutiondomain. pvs_le_gap_exists_convolutiondomain + (dc_input_exists_convolution) = (N)) -> (exists dst_positive_code_exists_convolutionlookup dst_positive_scale_exists_convolutionlookup dst_negative_code_exists_convolutionlookup dst_negative_scale_exists_convolutionlookup dst_positive_exists_convolutionlookup dst_negative_exists_convolutionlookup. (((H) = (((((dst_positive_code_exists_convolutionlookup) + (dst_positive_scale_exists_convolutionlookup)) * S ((dst_positive_code_exists_convolutionlookup) + (dst_positive_scale_exists_convolutionlookup)) + ((dst_positive_scale_exists_convolutionlookup) + (dst_positive_scale_exists_convolutionlookup))) + (((dst_negative_code_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)) * S ((dst_negative_code_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)) + ((dst_negative_scale_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)))) * S ((((dst_positive_code_exists_convolutionlookup) + (dst_positive_scale_exists_convolutionlookup)) * S ((dst_positive_code_exists_convolutionlookup) + (dst_positive_scale_exists_convolutionlookup)) + ((dst_positive_scale_exists_convolutionlookup) + (dst_positive_scale_exists_convolutionlookup))) + (((dst_negative_code_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)) * S ((dst_negative_code_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)) + ((dst_negative_scale_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)))) + ((((dst_negative_code_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)) * S ((dst_negative_code_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)) + ((dst_negative_scale_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup))) + (((dst_negative_code_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)) * S ((dst_negative_code_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)) + ((dst_negative_scale_exists_convolutionlookup) + (dst_negative_scale_exists_convolutionlookup)))))) /\ (((((exists ff_h_pvs_exists_convolutionlookuppositive. ff_h_pvs_exists_convolutionlookuppositive + S (dst_positive_exists_convolutionlookup) = S ((S (dc_input_exists_convolution)) * dst_positive_scale_exists_convolutionlookup)) /\ exists ff_q_pvs_exists_convolutionlookuppositive. dst_positive_code_exists_convolutionlookup = ff_q_pvs_exists_convolutionlookuppositive * S ((S (dc_input_exists_convolution)) * dst_positive_scale_exists_convolutionlookup) + (dst_positive_exists_convolutionlookup))) /\ (((((exists ff_h_pvs_exists_convolutionlookupnegative. ff_h_pvs_exists_convolutionlookupnegative + S (dst_negative_exists_convolutionlookup) = S ((S (dc_input_exists_convolution)) * dst_negative_scale_exists_convolutionlookup)) /\ exists ff_q_pvs_exists_convolutionlookupnegative. dst_negative_code_exists_convolutionlookup = ff_q_pvs_exists_convolutionlookupnegative * S ((S (dc_input_exists_convolution)) * dst_negative_scale_exists_convolutionlookup) + (dst_negative_exists_convolutionlookup))) /\ (exists ge_balance_positive_exists_convolutionlookupvalue ge_balance_negative_exists_convolutionlookupvalue. (((((dc_output_exists_convolution) = 2 * (ge_balance_positive_exists_convolutionlookupvalue) /\ (ge_balance_negative_exists_convolutionlookupvalue) = 0) \/ exists ge_signed_half_exists_convolutionlookupvaluedecode. (((dc_output_exists_convolution) = 2 * ge_signed_half_exists_convolutionlookupvaluedecode + 1 /\ (ge_balance_positive_exists_convolutionlookupvalue) = 0) /\ (ge_balance_negative_exists_convolutionlookupvalue) = S ge_signed_half_exists_convolutionlookupvaluedecode))) /\ ((dst_positive_exists_convolutionlookup) + ge_balance_negative_exists_convolutionlookupvalue = (dst_negative_exists_convolutionlookup) + ge_balance_positive_exists_convolutionlookupvalue))))))))) -> (((~((dc_input_exists_convolution)=0)) /\ (exists dc_mask_exists_convolutionvalue. ((((exists dst_positive_code_exists_convolutionvaluemasktable dst_positive_scale_exists_convolutionvaluemasktable dst_negative_code_exists_convolutionvaluemasktable dst_negative_scale_exists_convolutionvaluemasktable. (((dc_mask_exists_convolutionvalue) = (((((dst_positive_code_exists_convolutionvaluemasktable) + (dst_positive_scale_exists_convolutionvaluemasktable)) * S ((dst_positive_code_exists_convolutionvaluemasktable) + (dst_positive_scale_exists_convolutionvaluemasktable)) + ((dst_positive_scale_exists_convolutionvaluemasktable) + (dst_positive_scale_exists_convolutionvaluemasktable))) + (((dst_negative_code_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)) * S ((dst_negative_code_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)) + ((dst_negative_scale_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)))) * S ((((dst_positive_code_exists_convolutionvaluemasktable) + (dst_positive_scale_exists_convolutionvaluemasktable)) * S ((dst_positive_code_exists_convolutionvaluemasktable) + (dst_positive_scale_exists_convolutionvaluemasktable)) + ((dst_positive_scale_exists_convolutionvaluemasktable) + (dst_positive_scale_exists_convolutionvaluemasktable))) + (((dst_negative_code_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)) * S ((dst_negative_code_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)) + ((dst_negative_scale_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)))) + ((((dst_negative_code_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)) * S ((dst_negative_code_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)) + ((dst_negative_scale_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable))) + (((dst_negative_code_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)) * S ((dst_negative_code_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)) + ((dst_negative_scale_exists_convolutionvaluemasktable) + (dst_negative_scale_exists_convolutionvaluemasktable)))))) /\ (forall dst_index_exists_convolutionvaluemasktable. (exists pvs_le_gap_exists_convolutionvaluemasktabledomain. pvs_le_gap_exists_convolutionvaluemasktabledomain + (dst_index_exists_convolutionvaluemasktable) = (dc_input_exists_convolution)) -> exists dst_positive_exists_convolutionvaluemasktable dst_negative_exists_convolutionvaluemasktable dst_value_exists_convolutionvaluemasktable. ((((exists ff_h_pvs_exists_convolutionvaluemasktableentrypositive. ff_h_pvs_exists_convolutionvaluemasktableentrypositive + S (dst_positive_exists_convolutionvaluemasktable) = S ((S (dst_index_exists_convolutionvaluemasktable)) * dst_positive_scale_exists_convolutionvaluemasktable)) /\ exists ff_q_pvs_exists_convolutionvaluemasktableentrypositive. dst_positive_code_exists_convolutionvaluemasktable = ff_q_pvs_exists_convolutionvaluemasktableentrypositive * S ((S (dst_index_exists_convolutionvaluemasktable)) * dst_positive_scale_exists_convolutionvaluemasktable) + (dst_positive_exists_convolutionvaluemasktable))) /\ (((((exists ff_h_pvs_exists_convolutionvaluemasktableentrynegative. ff_h_pvs_exists_convolutionvaluemasktableentrynegative + S (dst_negative_exists_convolutionvaluemasktable) = S ((S (dst_index_exists_convolutionvaluemasktable)) * dst_negative_scale_exists_convolutionvaluemasktable)) /\ exists ff_q_pvs_exists_convolutionvaluemasktableentrynegative. dst_negative_code_exists_convolutionvaluemasktable = ff_q_pvs_exists_convolutionvaluemasktableentrynegative * S ((S (dst_index_exists_convolutionvaluemasktable)) * dst_negative_scale_exists_convolutionvaluemasktable) + (dst_negative_exists_convolutionvaluemasktable))) /\ (exists ge_balance_positive_exists_convolutionvaluemasktableentryvalue ge_balance_negative_exists_convolutionvaluemasktableentryvalue. (((((dst_value_exists_convolutionvaluemasktable) = 2 * (ge_balance_positive_exists_convolutionvaluemasktableentryvalue) /\ (ge_balance_negative_exists_convolutionvaluemasktableentryvalue) = 0) \/ exists ge_signed_half_exists_convolutionvaluemasktableentryvaluedecode. (((dst_value_exists_convolutionvaluemasktable) = 2 * ge_signed_half_exists_convolutionvaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_exists_convolutionvaluemasktableentryvalue) = 0) /\ (ge_balance_negative_exists_convolutionvaluemasktableentryvalue) = S ge_signed_half_exists_convolutionvaluemasktableentryvaluedecode))) /\ ((dst_positive_exists_convolutionvaluemasktable) + ge_balance_negative_exists_convolutionvaluemasktableentryvalue = (dst_negative_exists_convolutionvaluemasktable) + ge_balance_positive_exists_convolutionvaluemasktableentryvalue))))))))) /\ (forall dc_index_exists_convolutionvaluemask dc_value_exists_convolutionvaluemask. (exists pvs_le_gap_exists_convolutionvaluemaskdomain. pvs_le_gap_exists_convolutionvaluemaskdomain + (dc_index_exists_convolutionvaluemask) = (dc_input_exists_convolution)) -> (exists dst_positive_code_exists_convolutionvaluemasklookup dst_positive_scale_exists_convolutionvaluemasklookup dst_negative_code_exists_convolutionvaluemasklookup dst_negative_scale_exists_convolutionvaluemasklookup dst_positive_exists_convolutionvaluemasklookup dst_negative_exists_convolutionvaluemasklookup. (((dc_mask_exists_convolutionvalue) = (((((dst_positive_code_exists_convolutionvaluemasklookup) + (dst_positive_scale_exists_convolutionvaluemasklookup)) * S ((dst_positive_code_exists_convolutionvaluemasklookup) + (dst_positive_scale_exists_convolutionvaluemasklookup)) + ((dst_positive_scale_exists_convolutionvaluemasklookup) + (dst_positive_scale_exists_convolutionvaluemasklookup))) + (((dst_negative_code_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)) * S ((dst_negative_code_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)) + ((dst_negative_scale_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)))) * S ((((dst_positive_code_exists_convolutionvaluemasklookup) + (dst_positive_scale_exists_convolutionvaluemasklookup)) * S ((dst_positive_code_exists_convolutionvaluemasklookup) + (dst_positive_scale_exists_convolutionvaluemasklookup)) + ((dst_positive_scale_exists_convolutionvaluemasklookup) + (dst_positive_scale_exists_convolutionvaluemasklookup))) + (((dst_negative_code_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)) * S ((dst_negative_code_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)) + ((dst_negative_scale_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)))) + ((((dst_negative_code_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)) * S ((dst_negative_code_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)) + ((dst_negative_scale_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup))) + (((dst_negative_code_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)) * S ((dst_negative_code_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)) + ((dst_negative_scale_exists_convolutionvaluemasklookup) + (dst_negative_scale_exists_convolutionvaluemasklookup)))))) /\ (((((exists ff_h_pvs_exists_convolutionvaluemasklookuppositive. ff_h_pvs_exists_convolutionvaluemasklookuppositive + S (dst_positive_exists_convolutionvaluemasklookup) = S ((S (dc_index_exists_convolutionvaluemask)) * dst_positive_scale_exists_convolutionvaluemasklookup)) /\ exists ff_q_pvs_exists_convolutionvaluemasklookuppositive. dst_positive_code_exists_convolutionvaluemasklookup = ff_q_pvs_exists_convolutionvaluemasklookuppositive * S ((S (dc_index_exists_convolutionvaluemask)) * dst_positive_scale_exists_convolutionvaluemasklookup) + (dst_positive_exists_convolutionvaluemasklookup))) /\ (((((exists ff_h_pvs_exists_convolutionvaluemasklookupnegative. ff_h_pvs_exists_convolutionvaluemasklookupnegative + S (dst_negative_exists_convolutionvaluemasklookup) = S ((S (dc_index_exists_convolutionvaluemask)) * dst_negative_scale_exists_convolutionvaluemasklookup)) /\ exists ff_q_pvs_exists_convolutionvaluemasklookupnegative. dst_negative_code_exists_convolutionvaluemasklookup = ff_q_pvs_exists_convolutionvaluemasklookupnegative * S ((S (dc_index_exists_convolutionvaluemask)) * dst_negative_scale_exists_convolutionvaluemasklookup) + (dst_negative_exists_convolutionvaluemasklookup))) /\ (exists ge_balance_positive_exists_convolutionvaluemasklookupvalue ge_balance_negative_exists_convolutionvaluemasklookupvalue. (((((dc_value_exists_convolutionvaluemask) = 2 * (ge_balance_positive_exists_convolutionvaluemasklookupvalue) /\ (ge_balance_negative_exists_convolutionvaluemasklookupvalue) = 0) \/ exists ge_signed_half_exists_convolutionvaluemasklookupvaluedecode. (((dc_value_exists_convolutionvaluemask) = 2 * ge_signed_half_exists_convolutionvaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_exists_convolutionvaluemasklookupvalue) = 0) /\ (ge_balance_negative_exists_convolutionvaluemasklookupvalue) = S ge_signed_half_exists_convolutionvaluemasklookupvaluedecode))) /\ ((dst_positive_exists_convolutionvaluemasklookup) + ge_balance_negative_exists_convolutionvaluemasklookupvalue = (dst_negative_exists_convolutionvaluemasklookup) + ge_balance_positive_exists_convolutionvaluemasklookupvalue))))))))) -> ((((~((dc_index_exists_convolutionvaluemask)=0)) /\ (exists dc_quotient_exists_convolutionvaluemaskentry dc_left_exists_convolutionvaluemaskentry dc_right_exists_convolutionvaluemaskentry. (((dc_input_exists_convolution)=(dc_index_exists_convolutionvaluemask)*dc_quotient_exists_convolutionvaluemaskentry) /\ (((exists dst_positive_code_exists_convolutionvaluemaskentryleft dst_positive_scale_exists_convolutionvaluemaskentryleft dst_negative_code_exists_convolutionvaluemaskentryleft dst_negative_scale_exists_convolutionvaluemaskentryleft dst_positive_exists_convolutionvaluemaskentryleft dst_negative_exists_convolutionvaluemaskentryleft. (((F) = (((((dst_positive_code_exists_convolutionvaluemaskentryleft) + (dst_positive_scale_exists_convolutionvaluemaskentryleft)) * S ((dst_positive_code_exists_convolutionvaluemaskentryleft) + (dst_positive_scale_exists_convolutionvaluemaskentryleft)) + ((dst_positive_scale_exists_convolutionvaluemaskentryleft) + (dst_positive_scale_exists_convolutionvaluemaskentryleft))) + (((dst_negative_code_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)) * S ((dst_negative_code_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)) + ((dst_negative_scale_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)))) * S ((((dst_positive_code_exists_convolutionvaluemaskentryleft) + (dst_positive_scale_exists_convolutionvaluemaskentryleft)) * S ((dst_positive_code_exists_convolutionvaluemaskentryleft) + (dst_positive_scale_exists_convolutionvaluemaskentryleft)) + ((dst_positive_scale_exists_convolutionvaluemaskentryleft) + (dst_positive_scale_exists_convolutionvaluemaskentryleft))) + (((dst_negative_code_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)) * S ((dst_negative_code_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)) + ((dst_negative_scale_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)))) + ((((dst_negative_code_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)) * S ((dst_negative_code_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)) + ((dst_negative_scale_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft))) + (((dst_negative_code_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)) * S ((dst_negative_code_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)) + ((dst_negative_scale_exists_convolutionvaluemaskentryleft) + (dst_negative_scale_exists_convolutionvaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_exists_convolutionvaluemaskentryleftpositive. ff_h_pvs_exists_convolutionvaluemaskentryleftpositive + S (dst_positive_exists_convolutionvaluemaskentryleft) = S ((S (dc_index_exists_convolutionvaluemask)) * dst_positive_scale_exists_convolutionvaluemaskentryleft)) /\ exists ff_q_pvs_exists_convolutionvaluemaskentryleftpositive. dst_positive_code_exists_convolutionvaluemaskentryleft = ff_q_pvs_exists_convolutionvaluemaskentryleftpositive * S ((S (dc_index_exists_convolutionvaluemask)) * dst_positive_scale_exists_convolutionvaluemaskentryleft) + (dst_positive_exists_convolutionvaluemaskentryleft))) /\ (((((exists ff_h_pvs_exists_convolutionvaluemaskentryleftnegative. ff_h_pvs_exists_convolutionvaluemaskentryleftnegative + S (dst_negative_exists_convolutionvaluemaskentryleft) = S ((S (dc_index_exists_convolutionvaluemask)) * dst_negative_scale_exists_convolutionvaluemaskentryleft)) /\ exists ff_q_pvs_exists_convolutionvaluemaskentryleftnegative. dst_negative_code_exists_convolutionvaluemaskentryleft = ff_q_pvs_exists_convolutionvaluemaskentryleftnegative * S ((S (dc_index_exists_convolutionvaluemask)) * dst_negative_scale_exists_convolutionvaluemaskentryleft) + (dst_negative_exists_convolutionvaluemaskentryleft))) /\ (exists ge_balance_positive_exists_convolutionvaluemaskentryleftvalue ge_balance_negative_exists_convolutionvaluemaskentryleftvalue. (((((dc_left_exists_convolutionvaluemaskentry) = 2 * (ge_balance_positive_exists_convolutionvaluemaskentryleftvalue) /\ (ge_balance_negative_exists_convolutionvaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_exists_convolutionvaluemaskentryleftvaluedecode. (((dc_left_exists_convolutionvaluemaskentry) = 2 * ge_signed_half_exists_convolutionvaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_exists_convolutionvaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_exists_convolutionvaluemaskentryleftvalue) = S ge_signed_half_exists_convolutionvaluemaskentryleftvaluedecode))) /\ ((dst_positive_exists_convolutionvaluemaskentryleft) + ge_balance_negative_exists_convolutionvaluemaskentryleftvalue = (dst_negative_exists_convolutionvaluemaskentryleft) + ge_balance_positive_exists_convolutionvaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_exists_convolutionvaluemaskentryright dst_positive_scale_exists_convolutionvaluemaskentryright dst_negative_code_exists_convolutionvaluemaskentryright dst_negative_scale_exists_convolutionvaluemaskentryright dst_positive_exists_convolutionvaluemaskentryright dst_negative_exists_convolutionvaluemaskentryright. (((G) = (((((dst_positive_code_exists_convolutionvaluemaskentryright) + (dst_positive_scale_exists_convolutionvaluemaskentryright)) * S ((dst_positive_code_exists_convolutionvaluemaskentryright) + (dst_positive_scale_exists_convolutionvaluemaskentryright)) + ((dst_positive_scale_exists_convolutionvaluemaskentryright) + (dst_positive_scale_exists_convolutionvaluemaskentryright))) + (((dst_negative_code_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)) * S ((dst_negative_code_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)) + ((dst_negative_scale_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)))) * S ((((dst_positive_code_exists_convolutionvaluemaskentryright) + (dst_positive_scale_exists_convolutionvaluemaskentryright)) * S ((dst_positive_code_exists_convolutionvaluemaskentryright) + (dst_positive_scale_exists_convolutionvaluemaskentryright)) + ((dst_positive_scale_exists_convolutionvaluemaskentryright) + (dst_positive_scale_exists_convolutionvaluemaskentryright))) + (((dst_negative_code_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)) * S ((dst_negative_code_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)) + ((dst_negative_scale_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)))) + ((((dst_negative_code_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)) * S ((dst_negative_code_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)) + ((dst_negative_scale_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright))) + (((dst_negative_code_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)) * S ((dst_negative_code_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)) + ((dst_negative_scale_exists_convolutionvaluemaskentryright) + (dst_negative_scale_exists_convolutionvaluemaskentryright)))))) /\ (((((exists ff_h_pvs_exists_convolutionvaluemaskentryrightpositive. ff_h_pvs_exists_convolutionvaluemaskentryrightpositive + S (dst_positive_exists_convolutionvaluemaskentryright) = S ((S (dc_quotient_exists_convolutionvaluemaskentry)) * dst_positive_scale_exists_convolutionvaluemaskentryright)) /\ exists ff_q_pvs_exists_convolutionvaluemaskentryrightpositive. dst_positive_code_exists_convolutionvaluemaskentryright = ff_q_pvs_exists_convolutionvaluemaskentryrightpositive * S ((S (dc_quotient_exists_convolutionvaluemaskentry)) * dst_positive_scale_exists_convolutionvaluemaskentryright) + (dst_positive_exists_convolutionvaluemaskentryright))) /\ (((((exists ff_h_pvs_exists_convolutionvaluemaskentryrightnegative. ff_h_pvs_exists_convolutionvaluemaskentryrightnegative + S (dst_negative_exists_convolutionvaluemaskentryright) = S ((S (dc_quotient_exists_convolutionvaluemaskentry)) * dst_negative_scale_exists_convolutionvaluemaskentryright)) /\ exists ff_q_pvs_exists_convolutionvaluemaskentryrightnegative. dst_negative_code_exists_convolutionvaluemaskentryright = ff_q_pvs_exists_convolutionvaluemaskentryrightnegative * S ((S (dc_quotient_exists_convolutionvaluemaskentry)) * dst_negative_scale_exists_convolutionvaluemaskentryright) + (dst_negative_exists_convolutionvaluemaskentryright))) /\ (exists ge_balance_positive_exists_convolutionvaluemaskentryrightvalue ge_balance_negative_exists_convolutionvaluemaskentryrightvalue. (((((dc_right_exists_convolutionvaluemaskentry) = 2 * (ge_balance_positive_exists_convolutionvaluemaskentryrightvalue) /\ (ge_balance_negative_exists_convolutionvaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_exists_convolutionvaluemaskentryrightvaluedecode. (((dc_right_exists_convolutionvaluemaskentry) = 2 * ge_signed_half_exists_convolutionvaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_exists_convolutionvaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_exists_convolutionvaluemaskentryrightvalue) = S ge_signed_half_exists_convolutionvaluemaskentryrightvaluedecode))) /\ ((dst_positive_exists_convolutionvaluemaskentryright) + ge_balance_negative_exists_convolutionvaluemaskentryrightvalue = (dst_negative_exists_convolutionvaluemaskentryright) + ge_balance_positive_exists_convolutionvaluemaskentryrightvalue))))))))) /\ (exists sto_ap_exists_convolutionvaluemaskentryproduct sto_an_exists_convolutionvaluemaskentryproduct sto_bp_exists_convolutionvaluemaskentryproduct sto_bn_exists_convolutionvaluemaskentryproduct sto_cp_exists_convolutionvaluemaskentryproduct sto_cn_exists_convolutionvaluemaskentryproduct. (((((dc_left_exists_convolutionvaluemaskentry) = 2 * (sto_ap_exists_convolutionvaluemaskentryproduct) /\ (sto_an_exists_convolutionvaluemaskentryproduct) = 0) \/ exists ge_signed_half_exists_convolutionvaluemaskentryproductleft. (((dc_left_exists_convolutionvaluemaskentry) = 2 * ge_signed_half_exists_convolutionvaluemaskentryproductleft + 1 /\ (sto_ap_exists_convolutionvaluemaskentryproduct) = 0) /\ (sto_an_exists_convolutionvaluemaskentryproduct) = S ge_signed_half_exists_convolutionvaluemaskentryproductleft))) /\ ((((((dc_right_exists_convolutionvaluemaskentry) = 2 * (sto_bp_exists_convolutionvaluemaskentryproduct) /\ (sto_bn_exists_convolutionvaluemaskentryproduct) = 0) \/ exists ge_signed_half_exists_convolutionvaluemaskentryproductright. (((dc_right_exists_convolutionvaluemaskentry) = 2 * ge_signed_half_exists_convolutionvaluemaskentryproductright + 1 /\ (sto_bp_exists_convolutionvaluemaskentryproduct) = 0) /\ (sto_bn_exists_convolutionvaluemaskentryproduct) = S ge_signed_half_exists_convolutionvaluemaskentryproductright))) /\ ((((((dc_value_exists_convolutionvaluemask) = 2 * (sto_cp_exists_convolutionvaluemaskentryproduct) /\ (sto_cn_exists_convolutionvaluemaskentryproduct) = 0) \/ exists ge_signed_half_exists_convolutionvaluemaskentryproductoutput. (((dc_value_exists_convolutionvaluemask) = 2 * ge_signed_half_exists_convolutionvaluemaskentryproductoutput + 1 /\ (sto_cp_exists_convolutionvaluemaskentryproduct) = 0) /\ (sto_cn_exists_convolutionvaluemaskentryproduct) = S ge_signed_half_exists_convolutionvaluemaskentryproductoutput))) /\ ((sto_ap_exists_convolutionvaluemaskentryproduct * sto_bp_exists_convolutionvaluemaskentryproduct + sto_an_exists_convolutionvaluemaskentryproduct * sto_bn_exists_convolutionvaluemaskentryproduct) + sto_cn_exists_convolutionvaluemaskentryproduct = (sto_ap_exists_convolutionvaluemaskentryproduct * sto_bn_exists_convolutionvaluemaskentryproduct + sto_an_exists_convolutionvaluemaskentryproduct * sto_bp_exists_convolutionvaluemaskentryproduct) + sto_cp_exists_convolutionvaluemaskentryproduct))))))))))))))) \/ ((((dc_index_exists_convolutionvaluemask)=0 \/ ~(exists pvs_factor_exists_convolutionvaluemaskentrynondivisor. (dc_input_exists_convolution) = (dc_index_exists_convolutionvaluemask) * pvs_factor_exists_convolutionvaluemaskentrynondivisor)) /\ ((dc_value_exists_convolutionvaluemask)=0))))))) /\ (exists dst_positive_code_exists_convolutionvaluefold dst_positive_scale_exists_convolutionvaluefold dst_negative_code_exists_convolutionvaluefold dst_negative_scale_exists_convolutionvaluefold dst_positive_sum_exists_convolutionvaluefold dst_negative_sum_exists_convolutionvaluefold. (((dc_mask_exists_convolutionvalue) = (((((dst_positive_code_exists_convolutionvaluefold) + (dst_positive_scale_exists_convolutionvaluefold)) * S ((dst_positive_code_exists_convolutionvaluefold) + (dst_positive_scale_exists_convolutionvaluefold)) + ((dst_positive_scale_exists_convolutionvaluefold) + (dst_positive_scale_exists_convolutionvaluefold))) + (((dst_negative_code_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)) * S ((dst_negative_code_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)) + ((dst_negative_scale_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)))) * S ((((dst_positive_code_exists_convolutionvaluefold) + (dst_positive_scale_exists_convolutionvaluefold)) * S ((dst_positive_code_exists_convolutionvaluefold) + (dst_positive_scale_exists_convolutionvaluefold)) + ((dst_positive_scale_exists_convolutionvaluefold) + (dst_positive_scale_exists_convolutionvaluefold))) + (((dst_negative_code_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)) * S ((dst_negative_code_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)) + ((dst_negative_scale_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)))) + ((((dst_negative_code_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)) * S ((dst_negative_code_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)) + ((dst_negative_scale_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold))) + (((dst_negative_code_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)) * S ((dst_negative_code_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)) + ((dst_negative_scale_exists_convolutionvaluefold) + (dst_negative_scale_exists_convolutionvaluefold)))))) /\ (((exists fs_u_dst_exists_convolutionvaluefoldpositive fs_v_dst_exists_convolutionvaluefoldpositive. ((((exists fs_h_dst_exists_convolutionvaluefoldpositive_body_start. fs_h_dst_exists_convolutionvaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_exists_convolutionvaluefoldpositive)) /\ exists fs_q_dst_exists_convolutionvaluefoldpositive_body_start. fs_u_dst_exists_convolutionvaluefoldpositive = fs_q_dst_exists_convolutionvaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_exists_convolutionvaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_exists_convolutionvaluefoldpositive_body_terminal. fs_h_dst_exists_convolutionvaluefoldpositive_body_terminal + S (dst_positive_sum_exists_convolutionvaluefold) = S ((S (S (dc_input_exists_convolution))) * fs_v_dst_exists_convolutionvaluefoldpositive)) /\ exists fs_q_dst_exists_convolutionvaluefoldpositive_body_terminal. fs_u_dst_exists_convolutionvaluefoldpositive = fs_q_dst_exists_convolutionvaluefoldpositive_body_terminal * S ((S (S (dc_input_exists_convolution))) * fs_v_dst_exists_convolutionvaluefoldpositive) + (dst_positive_sum_exists_convolutionvaluefold))) /\ forall fs_i_dst_exists_convolutionvaluefoldpositive_body_steps. (exists fs_lt_dst_exists_convolutionvaluefoldpositive_body_steps_bound. fs_lt_dst_exists_convolutionvaluefoldpositive_body_steps_bound + S fs_i_dst_exists_convolutionvaluefoldpositive_body_steps = S (dc_input_exists_convolution)) -> exists fs_a_dst_exists_convolutionvaluefoldpositive_body_steps fs_r_dst_exists_convolutionvaluefoldpositive_body_steps fs_s_dst_exists_convolutionvaluefoldpositive_body_steps. ((((exists fs_h_dst_exists_convolutionvaluefoldpositive_body_steps_summand. fs_h_dst_exists_convolutionvaluefoldpositive_body_steps_summand + S (fs_a_dst_exists_convolutionvaluefoldpositive_body_steps) = S ((S (fs_i_dst_exists_convolutionvaluefoldpositive_body_steps)) * dst_positive_scale_exists_convolutionvaluefold)) /\ exists fs_q_dst_exists_convolutionvaluefoldpositive_body_steps_summand. dst_positive_code_exists_convolutionvaluefold = fs_q_dst_exists_convolutionvaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_exists_convolutionvaluefoldpositive_body_steps)) * dst_positive_scale_exists_convolutionvaluefold) + (fs_a_dst_exists_convolutionvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_exists_convolutionvaluefoldpositive_body_steps_partial. fs_h_dst_exists_convolutionvaluefoldpositive_body_steps_partial + S (fs_r_dst_exists_convolutionvaluefoldpositive_body_steps) = S ((S (fs_i_dst_exists_convolutionvaluefoldpositive_body_steps)) * fs_v_dst_exists_convolutionvaluefoldpositive)) /\ exists fs_q_dst_exists_convolutionvaluefoldpositive_body_steps_partial. fs_u_dst_exists_convolutionvaluefoldpositive = fs_q_dst_exists_convolutionvaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_exists_convolutionvaluefoldpositive_body_steps)) * fs_v_dst_exists_convolutionvaluefoldpositive) + (fs_r_dst_exists_convolutionvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_exists_convolutionvaluefoldpositive_body_steps_successor. fs_h_dst_exists_convolutionvaluefoldpositive_body_steps_successor + S (fs_s_dst_exists_convolutionvaluefoldpositive_body_steps) = S ((S (S fs_i_dst_exists_convolutionvaluefoldpositive_body_steps)) * fs_v_dst_exists_convolutionvaluefoldpositive)) /\ exists fs_q_dst_exists_convolutionvaluefoldpositive_body_steps_successor. fs_u_dst_exists_convolutionvaluefoldpositive = fs_q_dst_exists_convolutionvaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_exists_convolutionvaluefoldpositive_body_steps)) * fs_v_dst_exists_convolutionvaluefoldpositive) + (fs_s_dst_exists_convolutionvaluefoldpositive_body_steps))) /\ fs_s_dst_exists_convolutionvaluefoldpositive_body_steps = fs_r_dst_exists_convolutionvaluefoldpositive_body_steps + fs_a_dst_exists_convolutionvaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_exists_convolutionvaluefoldnegative fs_v_dst_exists_convolutionvaluefoldnegative. ((((exists fs_h_dst_exists_convolutionvaluefoldnegative_body_start. fs_h_dst_exists_convolutionvaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_exists_convolutionvaluefoldnegative)) /\ exists fs_q_dst_exists_convolutionvaluefoldnegative_body_start. fs_u_dst_exists_convolutionvaluefoldnegative = fs_q_dst_exists_convolutionvaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_exists_convolutionvaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_exists_convolutionvaluefoldnegative_body_terminal. fs_h_dst_exists_convolutionvaluefoldnegative_body_terminal + S (dst_negative_sum_exists_convolutionvaluefold) = S ((S (S (dc_input_exists_convolution))) * fs_v_dst_exists_convolutionvaluefoldnegative)) /\ exists fs_q_dst_exists_convolutionvaluefoldnegative_body_terminal. fs_u_dst_exists_convolutionvaluefoldnegative = fs_q_dst_exists_convolutionvaluefoldnegative_body_terminal * S ((S (S (dc_input_exists_convolution))) * fs_v_dst_exists_convolutionvaluefoldnegative) + (dst_negative_sum_exists_convolutionvaluefold))) /\ forall fs_i_dst_exists_convolutionvaluefoldnegative_body_steps. (exists fs_lt_dst_exists_convolutionvaluefoldnegative_body_steps_bound. fs_lt_dst_exists_convolutionvaluefoldnegative_body_steps_bound + S fs_i_dst_exists_convolutionvaluefoldnegative_body_steps = S (dc_input_exists_convolution)) -> exists fs_a_dst_exists_convolutionvaluefoldnegative_body_steps fs_r_dst_exists_convolutionvaluefoldnegative_body_steps fs_s_dst_exists_convolutionvaluefoldnegative_body_steps. ((((exists fs_h_dst_exists_convolutionvaluefoldnegative_body_steps_summand. fs_h_dst_exists_convolutionvaluefoldnegative_body_steps_summand + S (fs_a_dst_exists_convolutionvaluefoldnegative_body_steps) = S ((S (fs_i_dst_exists_convolutionvaluefoldnegative_body_steps)) * dst_negative_scale_exists_convolutionvaluefold)) /\ exists fs_q_dst_exists_convolutionvaluefoldnegative_body_steps_summand. dst_negative_code_exists_convolutionvaluefold = fs_q_dst_exists_convolutionvaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_exists_convolutionvaluefoldnegative_body_steps)) * dst_negative_scale_exists_convolutionvaluefold) + (fs_a_dst_exists_convolutionvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_exists_convolutionvaluefoldnegative_body_steps_partial. fs_h_dst_exists_convolutionvaluefoldnegative_body_steps_partial + S (fs_r_dst_exists_convolutionvaluefoldnegative_body_steps) = S ((S (fs_i_dst_exists_convolutionvaluefoldnegative_body_steps)) * fs_v_dst_exists_convolutionvaluefoldnegative)) /\ exists fs_q_dst_exists_convolutionvaluefoldnegative_body_steps_partial. fs_u_dst_exists_convolutionvaluefoldnegative = fs_q_dst_exists_convolutionvaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_exists_convolutionvaluefoldnegative_body_steps)) * fs_v_dst_exists_convolutionvaluefoldnegative) + (fs_r_dst_exists_convolutionvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_exists_convolutionvaluefoldnegative_body_steps_successor. fs_h_dst_exists_convolutionvaluefoldnegative_body_steps_successor + S (fs_s_dst_exists_convolutionvaluefoldnegative_body_steps) = S ((S (S fs_i_dst_exists_convolutionvaluefoldnegative_body_steps)) * fs_v_dst_exists_convolutionvaluefoldnegative)) /\ exists fs_q_dst_exists_convolutionvaluefoldnegative_body_steps_successor. fs_u_dst_exists_convolutionvaluefoldnegative = fs_q_dst_exists_convolutionvaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_exists_convolutionvaluefoldnegative_body_steps)) * fs_v_dst_exists_convolutionvaluefoldnegative) + (fs_s_dst_exists_convolutionvaluefoldnegative_body_steps))) /\ fs_s_dst_exists_convolutionvaluefoldnegative_body_steps = fs_r_dst_exists_convolutionvaluefoldnegative_body_steps + fs_a_dst_exists_convolutionvaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_exists_convolutionvaluefoldresult ge_balance_negative_exists_convolutionvaluefoldresult. (((((dc_output_exists_convolution) = 2 * (ge_balance_positive_exists_convolutionvaluefoldresult) /\ (ge_balance_negative_exists_convolutionvaluefoldresult) = 0) \/ exists ge_signed_half_exists_convolutionvaluefoldresultdecode. (((dc_output_exists_convolution) = 2 * ge_signed_half_exists_convolutionvaluefoldresultdecode + 1 /\ (ge_balance_positive_exists_convolutionvaluefoldresult) = 0) /\ (ge_balance_negative_exists_convolutionvaluefoldresult) = S ge_signed_half_exists_convolutionvaluefoldresultdecode))) /\ ((dst_positive_sum_exists_convolutionvaluefold) + ge_balance_negative_exists_convolutionvaluefoldresult = (dst_negative_sum_exists_convolutionvaluefold) + ge_balance_positive_exists_convolutionvaluefoldresult)))))))))))))))))))) /\ (((((~((N)=0)) /\ (((exists dst_positive_code_exists_multiplicativetable dst_positive_scale_exists_multiplicativetable dst_negative_code_exists_multiplicativetable dst_negative_scale_exists_multiplicativetable. (((H) = (((((dst_positive_code_exists_multiplicativetable) + (dst_positive_scale_exists_multiplicativetable)) * S ((dst_positive_code_exists_multiplicativetable) + (dst_positive_scale_exists_multiplicativetable)) + ((dst_positive_scale_exists_multiplicativetable) + (dst_positive_scale_exists_multiplicativetable))) + (((dst_negative_code_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)) * S ((dst_negative_code_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)) + ((dst_negative_scale_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)))) * S ((((dst_positive_code_exists_multiplicativetable) + (dst_positive_scale_exists_multiplicativetable)) * S ((dst_positive_code_exists_multiplicativetable) + (dst_positive_scale_exists_multiplicativetable)) + ((dst_positive_scale_exists_multiplicativetable) + (dst_positive_scale_exists_multiplicativetable))) + (((dst_negative_code_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)) * S ((dst_negative_code_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)) + ((dst_negative_scale_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)))) + ((((dst_negative_code_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)) * S ((dst_negative_code_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)) + ((dst_negative_scale_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable))) + (((dst_negative_code_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)) * S ((dst_negative_code_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)) + ((dst_negative_scale_exists_multiplicativetable) + (dst_negative_scale_exists_multiplicativetable)))))) /\ (forall dst_index_exists_multiplicativetable. (exists pvs_le_gap_exists_multiplicativetabledomain. pvs_le_gap_exists_multiplicativetabledomain + (dst_index_exists_multiplicativetable) = (N)) -> exists dst_positive_exists_multiplicativetable dst_negative_exists_multiplicativetable dst_value_exists_multiplicativetable. ((((exists ff_h_pvs_exists_multiplicativetableentrypositive. ff_h_pvs_exists_multiplicativetableentrypositive + S (dst_positive_exists_multiplicativetable) = S ((S (dst_index_exists_multiplicativetable)) * dst_positive_scale_exists_multiplicativetable)) /\ exists ff_q_pvs_exists_multiplicativetableentrypositive. dst_positive_code_exists_multiplicativetable = ff_q_pvs_exists_multiplicativetableentrypositive * S ((S (dst_index_exists_multiplicativetable)) * dst_positive_scale_exists_multiplicativetable) + (dst_positive_exists_multiplicativetable))) /\ (((((exists ff_h_pvs_exists_multiplicativetableentrynegative. ff_h_pvs_exists_multiplicativetableentrynegative + S (dst_negative_exists_multiplicativetable) = S ((S (dst_index_exists_multiplicativetable)) * dst_negative_scale_exists_multiplicativetable)) /\ exists ff_q_pvs_exists_multiplicativetableentrynegative. dst_negative_code_exists_multiplicativetable = ff_q_pvs_exists_multiplicativetableentrynegative * S ((S (dst_index_exists_multiplicativetable)) * dst_negative_scale_exists_multiplicativetable) + (dst_negative_exists_multiplicativetable))) /\ (exists ge_balance_positive_exists_multiplicativetableentryvalue ge_balance_negative_exists_multiplicativetableentryvalue. (((((dst_value_exists_multiplicativetable) = 2 * (ge_balance_positive_exists_multiplicativetableentryvalue) /\ (ge_balance_negative_exists_multiplicativetableentryvalue) = 0) \/ exists ge_signed_half_exists_multiplicativetableentryvaluedecode. (((dst_value_exists_multiplicativetable) = 2 * ge_signed_half_exists_multiplicativetableentryvaluedecode + 1 /\ (ge_balance_positive_exists_multiplicativetableentryvalue) = 0) /\ (ge_balance_negative_exists_multiplicativetableentryvalue) = S ge_signed_half_exists_multiplicativetableentryvaluedecode))) /\ ((dst_positive_exists_multiplicativetable) + ge_balance_negative_exists_multiplicativetableentryvalue = (dst_negative_exists_multiplicativetable) + ge_balance_positive_exists_multiplicativetableentryvalue))))))))) /\ (((exists dst_positive_code_exists_multiplicativeone dst_positive_scale_exists_multiplicativeone dst_negative_code_exists_multiplicativeone dst_negative_scale_exists_multiplicativeone dst_positive_exists_multiplicativeone dst_negative_exists_multiplicativeone. (((H) = (((((dst_positive_code_exists_multiplicativeone) + (dst_positive_scale_exists_multiplicativeone)) * S ((dst_positive_code_exists_multiplicativeone) + (dst_positive_scale_exists_multiplicativeone)) + ((dst_positive_scale_exists_multiplicativeone) + (dst_positive_scale_exists_multiplicativeone))) + (((dst_negative_code_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)) * S ((dst_negative_code_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)) + ((dst_negative_scale_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)))) * S ((((dst_positive_code_exists_multiplicativeone) + (dst_positive_scale_exists_multiplicativeone)) * S ((dst_positive_code_exists_multiplicativeone) + (dst_positive_scale_exists_multiplicativeone)) + ((dst_positive_scale_exists_multiplicativeone) + (dst_positive_scale_exists_multiplicativeone))) + (((dst_negative_code_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)) * S ((dst_negative_code_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)) + ((dst_negative_scale_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)))) + ((((dst_negative_code_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)) * S ((dst_negative_code_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)) + ((dst_negative_scale_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone))) + (((dst_negative_code_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)) * S ((dst_negative_code_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)) + ((dst_negative_scale_exists_multiplicativeone) + (dst_negative_scale_exists_multiplicativeone)))))) /\ (((((exists ff_h_pvs_exists_multiplicativeonepositive. ff_h_pvs_exists_multiplicativeonepositive + S (dst_positive_exists_multiplicativeone) = S ((S (1)) * dst_positive_scale_exists_multiplicativeone)) /\ exists ff_q_pvs_exists_multiplicativeonepositive. dst_positive_code_exists_multiplicativeone = ff_q_pvs_exists_multiplicativeonepositive * S ((S (1)) * dst_positive_scale_exists_multiplicativeone) + (dst_positive_exists_multiplicativeone))) /\ (((((exists ff_h_pvs_exists_multiplicativeonenegative. ff_h_pvs_exists_multiplicativeonenegative + S (dst_negative_exists_multiplicativeone) = S ((S (1)) * dst_negative_scale_exists_multiplicativeone)) /\ exists ff_q_pvs_exists_multiplicativeonenegative. dst_negative_code_exists_multiplicativeone = ff_q_pvs_exists_multiplicativeonenegative * S ((S (1)) * dst_negative_scale_exists_multiplicativeone) + (dst_negative_exists_multiplicativeone))) /\ (exists ge_balance_positive_exists_multiplicativeonevalue ge_balance_negative_exists_multiplicativeonevalue. (((((2) = 2 * (ge_balance_positive_exists_multiplicativeonevalue) /\ (ge_balance_negative_exists_multiplicativeonevalue) = 0) \/ exists ge_signed_half_exists_multiplicativeonevaluedecode. (((2) = 2 * ge_signed_half_exists_multiplicativeonevaluedecode + 1 /\ (ge_balance_positive_exists_multiplicativeonevalue) = 0) /\ (ge_balance_negative_exists_multiplicativeonevalue) = S ge_signed_half_exists_multiplicativeonevaluedecode))) /\ ((dst_positive_exists_multiplicativeone) + ge_balance_negative_exists_multiplicativeonevalue = (dst_negative_exists_multiplicativeone) + ge_balance_positive_exists_multiplicativeonevalue))))))))) /\ (forall mp_a_exists_multiplicative mp_b_exists_multiplicative mp_x_exists_multiplicative mp_y_exists_multiplicative mp_z_exists_multiplicative. ~(mp_a_exists_multiplicative=0) -> ~(mp_b_exists_multiplicative=0) -> (exists pvs_le_gap_exists_multiplicativebound. pvs_le_gap_exists_multiplicativebound + (mp_a_exists_multiplicative*mp_b_exists_multiplicative) = (N)) -> (forall frp_divisor_exists_multiplicativecoprime. (exists frp_left_factor_exists_multiplicativecoprime. mp_a_exists_multiplicative = frp_divisor_exists_multiplicativecoprime * frp_left_factor_exists_multiplicativecoprime) -> (exists frp_right_factor_exists_multiplicativecoprime. mp_b_exists_multiplicative = frp_divisor_exists_multiplicativecoprime * frp_right_factor_exists_multiplicativecoprime) -> frp_divisor_exists_multiplicativecoprime = 1) -> (exists dst_positive_code_exists_multiplicativefirst dst_positive_scale_exists_multiplicativefirst dst_negative_code_exists_multiplicativefirst dst_negative_scale_exists_multiplicativefirst dst_positive_exists_multiplicativefirst dst_negative_exists_multiplicativefirst. (((H) = (((((dst_positive_code_exists_multiplicativefirst) + (dst_positive_scale_exists_multiplicativefirst)) * S ((dst_positive_code_exists_multiplicativefirst) + (dst_positive_scale_exists_multiplicativefirst)) + ((dst_positive_scale_exists_multiplicativefirst) + (dst_positive_scale_exists_multiplicativefirst))) + (((dst_negative_code_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)) * S ((dst_negative_code_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)) + ((dst_negative_scale_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)))) * S ((((dst_positive_code_exists_multiplicativefirst) + (dst_positive_scale_exists_multiplicativefirst)) * S ((dst_positive_code_exists_multiplicativefirst) + (dst_positive_scale_exists_multiplicativefirst)) + ((dst_positive_scale_exists_multiplicativefirst) + (dst_positive_scale_exists_multiplicativefirst))) + (((dst_negative_code_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)) * S ((dst_negative_code_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)) + ((dst_negative_scale_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)))) + ((((dst_negative_code_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)) * S ((dst_negative_code_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)) + ((dst_negative_scale_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst))) + (((dst_negative_code_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)) * S ((dst_negative_code_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)) + ((dst_negative_scale_exists_multiplicativefirst) + (dst_negative_scale_exists_multiplicativefirst)))))) /\ (((((exists ff_h_pvs_exists_multiplicativefirstpositive. ff_h_pvs_exists_multiplicativefirstpositive + S (dst_positive_exists_multiplicativefirst) = S ((S (mp_a_exists_multiplicative)) * dst_positive_scale_exists_multiplicativefirst)) /\ exists ff_q_pvs_exists_multiplicativefirstpositive. dst_positive_code_exists_multiplicativefirst = ff_q_pvs_exists_multiplicativefirstpositive * S ((S (mp_a_exists_multiplicative)) * dst_positive_scale_exists_multiplicativefirst) + (dst_positive_exists_multiplicativefirst))) /\ (((((exists ff_h_pvs_exists_multiplicativefirstnegative. ff_h_pvs_exists_multiplicativefirstnegative + S (dst_negative_exists_multiplicativefirst) = S ((S (mp_a_exists_multiplicative)) * dst_negative_scale_exists_multiplicativefirst)) /\ exists ff_q_pvs_exists_multiplicativefirstnegative. dst_negative_code_exists_multiplicativefirst = ff_q_pvs_exists_multiplicativefirstnegative * S ((S (mp_a_exists_multiplicative)) * dst_negative_scale_exists_multiplicativefirst) + (dst_negative_exists_multiplicativefirst))) /\ (exists ge_balance_positive_exists_multiplicativefirstvalue ge_balance_negative_exists_multiplicativefirstvalue. (((((mp_x_exists_multiplicative) = 2 * (ge_balance_positive_exists_multiplicativefirstvalue) /\ (ge_balance_negative_exists_multiplicativefirstvalue) = 0) \/ exists ge_signed_half_exists_multiplicativefirstvaluedecode. (((mp_x_exists_multiplicative) = 2 * ge_signed_half_exists_multiplicativefirstvaluedecode + 1 /\ (ge_balance_positive_exists_multiplicativefirstvalue) = 0) /\ (ge_balance_negative_exists_multiplicativefirstvalue) = S ge_signed_half_exists_multiplicativefirstvaluedecode))) /\ ((dst_positive_exists_multiplicativefirst) + ge_balance_negative_exists_multiplicativefirstvalue = (dst_negative_exists_multiplicativefirst) + ge_balance_positive_exists_multiplicativefirstvalue))))))))) -> (exists dst_positive_code_exists_multiplicativesecond dst_positive_scale_exists_multiplicativesecond dst_negative_code_exists_multiplicativesecond dst_negative_scale_exists_multiplicativesecond dst_positive_exists_multiplicativesecond dst_negative_exists_multiplicativesecond. (((H) = (((((dst_positive_code_exists_multiplicativesecond) + (dst_positive_scale_exists_multiplicativesecond)) * S ((dst_positive_code_exists_multiplicativesecond) + (dst_positive_scale_exists_multiplicativesecond)) + ((dst_positive_scale_exists_multiplicativesecond) + (dst_positive_scale_exists_multiplicativesecond))) + (((dst_negative_code_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)) * S ((dst_negative_code_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)) + ((dst_negative_scale_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)))) * S ((((dst_positive_code_exists_multiplicativesecond) + (dst_positive_scale_exists_multiplicativesecond)) * S ((dst_positive_code_exists_multiplicativesecond) + (dst_positive_scale_exists_multiplicativesecond)) + ((dst_positive_scale_exists_multiplicativesecond) + (dst_positive_scale_exists_multiplicativesecond))) + (((dst_negative_code_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)) * S ((dst_negative_code_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)) + ((dst_negative_scale_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)))) + ((((dst_negative_code_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)) * S ((dst_negative_code_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)) + ((dst_negative_scale_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond))) + (((dst_negative_code_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)) * S ((dst_negative_code_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)) + ((dst_negative_scale_exists_multiplicativesecond) + (dst_negative_scale_exists_multiplicativesecond)))))) /\ (((((exists ff_h_pvs_exists_multiplicativesecondpositive. ff_h_pvs_exists_multiplicativesecondpositive + S (dst_positive_exists_multiplicativesecond) = S ((S (mp_b_exists_multiplicative)) * dst_positive_scale_exists_multiplicativesecond)) /\ exists ff_q_pvs_exists_multiplicativesecondpositive. dst_positive_code_exists_multiplicativesecond = ff_q_pvs_exists_multiplicativesecondpositive * S ((S (mp_b_exists_multiplicative)) * dst_positive_scale_exists_multiplicativesecond) + (dst_positive_exists_multiplicativesecond))) /\ (((((exists ff_h_pvs_exists_multiplicativesecondnegative. ff_h_pvs_exists_multiplicativesecondnegative + S (dst_negative_exists_multiplicativesecond) = S ((S (mp_b_exists_multiplicative)) * dst_negative_scale_exists_multiplicativesecond)) /\ exists ff_q_pvs_exists_multiplicativesecondnegative. dst_negative_code_exists_multiplicativesecond = ff_q_pvs_exists_multiplicativesecondnegative * S ((S (mp_b_exists_multiplicative)) * dst_negative_scale_exists_multiplicativesecond) + (dst_negative_exists_multiplicativesecond))) /\ (exists ge_balance_positive_exists_multiplicativesecondvalue ge_balance_negative_exists_multiplicativesecondvalue. (((((mp_y_exists_multiplicative) = 2 * (ge_balance_positive_exists_multiplicativesecondvalue) /\ (ge_balance_negative_exists_multiplicativesecondvalue) = 0) \/ exists ge_signed_half_exists_multiplicativesecondvaluedecode. (((mp_y_exists_multiplicative) = 2 * ge_signed_half_exists_multiplicativesecondvaluedecode + 1 /\ (ge_balance_positive_exists_multiplicativesecondvalue) = 0) /\ (ge_balance_negative_exists_multiplicativesecondvalue) = S ge_signed_half_exists_multiplicativesecondvaluedecode))) /\ ((dst_positive_exists_multiplicativesecond) + ge_balance_negative_exists_multiplicativesecondvalue = (dst_negative_exists_multiplicativesecond) + ge_balance_positive_exists_multiplicativesecondvalue))))))))) -> (exists dst_positive_code_exists_multiplicativeproduct dst_positive_scale_exists_multiplicativeproduct dst_negative_code_exists_multiplicativeproduct dst_negative_scale_exists_multiplicativeproduct dst_positive_exists_multiplicativeproduct dst_negative_exists_multiplicativeproduct. (((H) = (((((dst_positive_code_exists_multiplicativeproduct) + (dst_positive_scale_exists_multiplicativeproduct)) * S ((dst_positive_code_exists_multiplicativeproduct) + (dst_positive_scale_exists_multiplicativeproduct)) + ((dst_positive_scale_exists_multiplicativeproduct) + (dst_positive_scale_exists_multiplicativeproduct))) + (((dst_negative_code_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)) * S ((dst_negative_code_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)) + ((dst_negative_scale_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)))) * S ((((dst_positive_code_exists_multiplicativeproduct) + (dst_positive_scale_exists_multiplicativeproduct)) * S ((dst_positive_code_exists_multiplicativeproduct) + (dst_positive_scale_exists_multiplicativeproduct)) + ((dst_positive_scale_exists_multiplicativeproduct) + (dst_positive_scale_exists_multiplicativeproduct))) + (((dst_negative_code_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)) * S ((dst_negative_code_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)) + ((dst_negative_scale_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)))) + ((((dst_negative_code_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)) * S ((dst_negative_code_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)) + ((dst_negative_scale_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct))) + (((dst_negative_code_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)) * S ((dst_negative_code_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)) + ((dst_negative_scale_exists_multiplicativeproduct) + (dst_negative_scale_exists_multiplicativeproduct)))))) /\ (((((exists ff_h_pvs_exists_multiplicativeproductpositive. ff_h_pvs_exists_multiplicativeproductpositive + S (dst_positive_exists_multiplicativeproduct) = S ((S (mp_a_exists_multiplicative*mp_b_exists_multiplicative)) * dst_positive_scale_exists_multiplicativeproduct)) /\ exists ff_q_pvs_exists_multiplicativeproductpositive. dst_positive_code_exists_multiplicativeproduct = ff_q_pvs_exists_multiplicativeproductpositive * S ((S (mp_a_exists_multiplicative*mp_b_exists_multiplicative)) * dst_positive_scale_exists_multiplicativeproduct) + (dst_positive_exists_multiplicativeproduct))) /\ (((((exists ff_h_pvs_exists_multiplicativeproductnegative. ff_h_pvs_exists_multiplicativeproductnegative + S (dst_negative_exists_multiplicativeproduct) = S ((S (mp_a_exists_multiplicative*mp_b_exists_multiplicative)) * dst_negative_scale_exists_multiplicativeproduct)) /\ exists ff_q_pvs_exists_multiplicativeproductnegative. dst_negative_code_exists_multiplicativeproduct = ff_q_pvs_exists_multiplicativeproductnegative * S ((S (mp_a_exists_multiplicative*mp_b_exists_multiplicative)) * dst_negative_scale_exists_multiplicativeproduct) + (dst_negative_exists_multiplicativeproduct))) /\ (exists ge_balance_positive_exists_multiplicativeproductvalue ge_balance_negative_exists_multiplicativeproductvalue. (((((mp_z_exists_multiplicative) = 2 * (ge_balance_positive_exists_multiplicativeproductvalue) /\ (ge_balance_negative_exists_multiplicativeproductvalue) = 0) \/ exists ge_signed_half_exists_multiplicativeproductvaluedecode. (((mp_z_exists_multiplicative) = 2 * ge_signed_half_exists_multiplicativeproductvaluedecode + 1 /\ (ge_balance_positive_exists_multiplicativeproductvalue) = 0) /\ (ge_balance_negative_exists_multiplicativeproductvalue) = S ge_signed_half_exists_multiplicativeproductvaluedecode))) /\ ((dst_positive_exists_multiplicativeproduct) + ge_balance_negative_exists_multiplicativeproductvalue = (dst_negative_exists_multiplicativeproduct) + ge_balance_positive_exists_multiplicativeproductvalue))))))))) -> (exists sto_ap_exists_multiplicativelaw sto_an_exists_multiplicativelaw sto_bp_exists_multiplicativelaw sto_bn_exists_multiplicativelaw sto_cp_exists_multiplicativelaw sto_cn_exists_multiplicativelaw. (((((mp_x_exists_multiplicative) = 2 * (sto_ap_exists_multiplicativelaw) /\ (sto_an_exists_multiplicativelaw) = 0) \/ exists ge_signed_half_exists_multiplicativelawleft. (((mp_x_exists_multiplicative) = 2 * ge_signed_half_exists_multiplicativelawleft + 1 /\ (sto_ap_exists_multiplicativelaw) = 0) /\ (sto_an_exists_multiplicativelaw) = S ge_signed_half_exists_multiplicativelawleft))) /\ ((((((mp_y_exists_multiplicative) = 2 * (sto_bp_exists_multiplicativelaw) /\ (sto_bn_exists_multiplicativelaw) = 0) \/ exists ge_signed_half_exists_multiplicativelawright. (((mp_y_exists_multiplicative) = 2 * ge_signed_half_exists_multiplicativelawright + 1 /\ (sto_bp_exists_multiplicativelaw) = 0) /\ (sto_bn_exists_multiplicativelaw) = S ge_signed_half_exists_multiplicativelawright))) /\ ((((((mp_z_exists_multiplicative) = 2 * (sto_cp_exists_multiplicativelaw) /\ (sto_cn_exists_multiplicativelaw) = 0) \/ exists ge_signed_half_exists_multiplicativelawoutput. (((mp_z_exists_multiplicative) = 2 * ge_signed_half_exists_multiplicativelawoutput + 1 /\ (sto_cp_exists_multiplicativelaw) = 0) /\ (sto_cn_exists_multiplicativelaw) = S ge_signed_half_exists_multiplicativelawoutput))) /\ ((sto_ap_exists_multiplicativelaw * sto_bp_exists_multiplicativelaw + sto_an_exists_multiplicativelaw * sto_bn_exists_multiplicativelaw) + sto_cn_exists_multiplicativelaw = (sto_ap_exists_multiplicativelaw * sto_bn_exists_multiplicativelaw + sto_an_exists_multiplicativelaw * sto_bp_exists_multiplicativelaw) + sto_cp_exists_multiplicativelaw)))))))))))))) /\ (forall K. (((exists dst_positive_code_exists_otherleft dst_positive_scale_exists_otherleft dst_negative_code_exists_otherleft dst_negative_scale_exists_otherleft. (((F) = (((((dst_positive_code_exists_otherleft) + (dst_positive_scale_exists_otherleft)) * S ((dst_positive_code_exists_otherleft) + (dst_positive_scale_exists_otherleft)) + ((dst_positive_scale_exists_otherleft) + (dst_positive_scale_exists_otherleft))) + (((dst_negative_code_exists_otherleft) + (dst_negative_scale_exists_otherleft)) * S ((dst_negative_code_exists_otherleft) + (dst_negative_scale_exists_otherleft)) + ((dst_negative_scale_exists_otherleft) + (dst_negative_scale_exists_otherleft)))) * S ((((dst_positive_code_exists_otherleft) + (dst_positive_scale_exists_otherleft)) * S ((dst_positive_code_exists_otherleft) + (dst_positive_scale_exists_otherleft)) + ((dst_positive_scale_exists_otherleft) + (dst_positive_scale_exists_otherleft))) + (((dst_negative_code_exists_otherleft) + (dst_negative_scale_exists_otherleft)) * S ((dst_negative_code_exists_otherleft) + (dst_negative_scale_exists_otherleft)) + ((dst_negative_scale_exists_otherleft) + (dst_negative_scale_exists_otherleft)))) + ((((dst_negative_code_exists_otherleft) + (dst_negative_scale_exists_otherleft)) * S ((dst_negative_code_exists_otherleft) + (dst_negative_scale_exists_otherleft)) + ((dst_negative_scale_exists_otherleft) + (dst_negative_scale_exists_otherleft))) + (((dst_negative_code_exists_otherleft) + (dst_negative_scale_exists_otherleft)) * S ((dst_negative_code_exists_otherleft) + (dst_negative_scale_exists_otherleft)) + ((dst_negative_scale_exists_otherleft) + (dst_negative_scale_exists_otherleft)))))) /\ (forall dst_index_exists_otherleft. (exists pvs_le_gap_exists_otherleftdomain. pvs_le_gap_exists_otherleftdomain + (dst_index_exists_otherleft) = (N)) -> exists dst_positive_exists_otherleft dst_negative_exists_otherleft dst_value_exists_otherleft. ((((exists ff_h_pvs_exists_otherleftentrypositive. ff_h_pvs_exists_otherleftentrypositive + S (dst_positive_exists_otherleft) = S ((S (dst_index_exists_otherleft)) * dst_positive_scale_exists_otherleft)) /\ exists ff_q_pvs_exists_otherleftentrypositive. dst_positive_code_exists_otherleft = ff_q_pvs_exists_otherleftentrypositive * S ((S (dst_index_exists_otherleft)) * dst_positive_scale_exists_otherleft) + (dst_positive_exists_otherleft))) /\ (((((exists ff_h_pvs_exists_otherleftentrynegative. ff_h_pvs_exists_otherleftentrynegative + S (dst_negative_exists_otherleft) = S ((S (dst_index_exists_otherleft)) * dst_negative_scale_exists_otherleft)) /\ exists ff_q_pvs_exists_otherleftentrynegative. dst_negative_code_exists_otherleft = ff_q_pvs_exists_otherleftentrynegative * S ((S (dst_index_exists_otherleft)) * dst_negative_scale_exists_otherleft) + (dst_negative_exists_otherleft))) /\ (exists ge_balance_positive_exists_otherleftentryvalue ge_balance_negative_exists_otherleftentryvalue. (((((dst_value_exists_otherleft) = 2 * (ge_balance_positive_exists_otherleftentryvalue) /\ (ge_balance_negative_exists_otherleftentryvalue) = 0) \/ exists ge_signed_half_exists_otherleftentryvaluedecode. (((dst_value_exists_otherleft) = 2 * ge_signed_half_exists_otherleftentryvaluedecode + 1 /\ (ge_balance_positive_exists_otherleftentryvalue) = 0) /\ (ge_balance_negative_exists_otherleftentryvalue) = S ge_signed_half_exists_otherleftentryvaluedecode))) /\ ((dst_positive_exists_otherleft) + ge_balance_negative_exists_otherleftentryvalue = (dst_negative_exists_otherleft) + ge_balance_positive_exists_otherleftentryvalue))))))))) /\ (((exists dst_positive_code_exists_otherright dst_positive_scale_exists_otherright dst_negative_code_exists_otherright dst_negative_scale_exists_otherright. (((G) = (((((dst_positive_code_exists_otherright) + (dst_positive_scale_exists_otherright)) * S ((dst_positive_code_exists_otherright) + (dst_positive_scale_exists_otherright)) + ((dst_positive_scale_exists_otherright) + (dst_positive_scale_exists_otherright))) + (((dst_negative_code_exists_otherright) + (dst_negative_scale_exists_otherright)) * S ((dst_negative_code_exists_otherright) + (dst_negative_scale_exists_otherright)) + ((dst_negative_scale_exists_otherright) + (dst_negative_scale_exists_otherright)))) * S ((((dst_positive_code_exists_otherright) + (dst_positive_scale_exists_otherright)) * S ((dst_positive_code_exists_otherright) + (dst_positive_scale_exists_otherright)) + ((dst_positive_scale_exists_otherright) + (dst_positive_scale_exists_otherright))) + (((dst_negative_code_exists_otherright) + (dst_negative_scale_exists_otherright)) * S ((dst_negative_code_exists_otherright) + (dst_negative_scale_exists_otherright)) + ((dst_negative_scale_exists_otherright) + (dst_negative_scale_exists_otherright)))) + ((((dst_negative_code_exists_otherright) + (dst_negative_scale_exists_otherright)) * S ((dst_negative_code_exists_otherright) + (dst_negative_scale_exists_otherright)) + ((dst_negative_scale_exists_otherright) + (dst_negative_scale_exists_otherright))) + (((dst_negative_code_exists_otherright) + (dst_negative_scale_exists_otherright)) * S ((dst_negative_code_exists_otherright) + (dst_negative_scale_exists_otherright)) + ((dst_negative_scale_exists_otherright) + (dst_negative_scale_exists_otherright)))))) /\ (forall dst_index_exists_otherright. (exists pvs_le_gap_exists_otherrightdomain. pvs_le_gap_exists_otherrightdomain + (dst_index_exists_otherright) = (N)) -> exists dst_positive_exists_otherright dst_negative_exists_otherright dst_value_exists_otherright. ((((exists ff_h_pvs_exists_otherrightentrypositive. ff_h_pvs_exists_otherrightentrypositive + S (dst_positive_exists_otherright) = S ((S (dst_index_exists_otherright)) * dst_positive_scale_exists_otherright)) /\ exists ff_q_pvs_exists_otherrightentrypositive. dst_positive_code_exists_otherright = ff_q_pvs_exists_otherrightentrypositive * S ((S (dst_index_exists_otherright)) * dst_positive_scale_exists_otherright) + (dst_positive_exists_otherright))) /\ (((((exists ff_h_pvs_exists_otherrightentrynegative. ff_h_pvs_exists_otherrightentrynegative + S (dst_negative_exists_otherright) = S ((S (dst_index_exists_otherright)) * dst_negative_scale_exists_otherright)) /\ exists ff_q_pvs_exists_otherrightentrynegative. dst_negative_code_exists_otherright = ff_q_pvs_exists_otherrightentrynegative * S ((S (dst_index_exists_otherright)) * dst_negative_scale_exists_otherright) + (dst_negative_exists_otherright))) /\ (exists ge_balance_positive_exists_otherrightentryvalue ge_balance_negative_exists_otherrightentryvalue. (((((dst_value_exists_otherright) = 2 * (ge_balance_positive_exists_otherrightentryvalue) /\ (ge_balance_negative_exists_otherrightentryvalue) = 0) \/ exists ge_signed_half_exists_otherrightentryvaluedecode. (((dst_value_exists_otherright) = 2 * ge_signed_half_exists_otherrightentryvaluedecode + 1 /\ (ge_balance_positive_exists_otherrightentryvalue) = 0) /\ (ge_balance_negative_exists_otherrightentryvalue) = S ge_signed_half_exists_otherrightentryvaluedecode))) /\ ((dst_positive_exists_otherright) + ge_balance_negative_exists_otherrightentryvalue = (dst_negative_exists_otherright) + ge_balance_positive_exists_otherrightentryvalue))))))))) /\ (((exists dst_positive_code_exists_othertable dst_positive_scale_exists_othertable dst_negative_code_exists_othertable dst_negative_scale_exists_othertable. (((K) = (((((dst_positive_code_exists_othertable) + (dst_positive_scale_exists_othertable)) * S ((dst_positive_code_exists_othertable) + (dst_positive_scale_exists_othertable)) + ((dst_positive_scale_exists_othertable) + (dst_positive_scale_exists_othertable))) + (((dst_negative_code_exists_othertable) + (dst_negative_scale_exists_othertable)) * S ((dst_negative_code_exists_othertable) + (dst_negative_scale_exists_othertable)) + ((dst_negative_scale_exists_othertable) + (dst_negative_scale_exists_othertable)))) * S ((((dst_positive_code_exists_othertable) + (dst_positive_scale_exists_othertable)) * S ((dst_positive_code_exists_othertable) + (dst_positive_scale_exists_othertable)) + ((dst_positive_scale_exists_othertable) + (dst_positive_scale_exists_othertable))) + (((dst_negative_code_exists_othertable) + (dst_negative_scale_exists_othertable)) * S ((dst_negative_code_exists_othertable) + (dst_negative_scale_exists_othertable)) + ((dst_negative_scale_exists_othertable) + (dst_negative_scale_exists_othertable)))) + ((((dst_negative_code_exists_othertable) + (dst_negative_scale_exists_othertable)) * S ((dst_negative_code_exists_othertable) + (dst_negative_scale_exists_othertable)) + ((dst_negative_scale_exists_othertable) + (dst_negative_scale_exists_othertable))) + (((dst_negative_code_exists_othertable) + (dst_negative_scale_exists_othertable)) * S ((dst_negative_code_exists_othertable) + (dst_negative_scale_exists_othertable)) + ((dst_negative_scale_exists_othertable) + (dst_negative_scale_exists_othertable)))))) /\ (forall dst_index_exists_othertable. (exists pvs_le_gap_exists_othertabledomain. pvs_le_gap_exists_othertabledomain + (dst_index_exists_othertable) = (N)) -> exists dst_positive_exists_othertable dst_negative_exists_othertable dst_value_exists_othertable. ((((exists ff_h_pvs_exists_othertableentrypositive. ff_h_pvs_exists_othertableentrypositive + S (dst_positive_exists_othertable) = S ((S (dst_index_exists_othertable)) * dst_positive_scale_exists_othertable)) /\ exists ff_q_pvs_exists_othertableentrypositive. dst_positive_code_exists_othertable = ff_q_pvs_exists_othertableentrypositive * S ((S (dst_index_exists_othertable)) * dst_positive_scale_exists_othertable) + (dst_positive_exists_othertable))) /\ (((((exists ff_h_pvs_exists_othertableentrynegative. ff_h_pvs_exists_othertableentrynegative + S (dst_negative_exists_othertable) = S ((S (dst_index_exists_othertable)) * dst_negative_scale_exists_othertable)) /\ exists ff_q_pvs_exists_othertableentrynegative. dst_negative_code_exists_othertable = ff_q_pvs_exists_othertableentrynegative * S ((S (dst_index_exists_othertable)) * dst_negative_scale_exists_othertable) + (dst_negative_exists_othertable))) /\ (exists ge_balance_positive_exists_othertableentryvalue ge_balance_negative_exists_othertableentryvalue. (((((dst_value_exists_othertable) = 2 * (ge_balance_positive_exists_othertableentryvalue) /\ (ge_balance_negative_exists_othertableentryvalue) = 0) \/ exists ge_signed_half_exists_othertableentryvaluedecode. (((dst_value_exists_othertable) = 2 * ge_signed_half_exists_othertableentryvaluedecode + 1 /\ (ge_balance_positive_exists_othertableentryvalue) = 0) /\ (ge_balance_negative_exists_othertableentryvalue) = S ge_signed_half_exists_othertableentryvaluedecode))) /\ ((dst_positive_exists_othertable) + ge_balance_negative_exists_othertableentryvalue = (dst_negative_exists_othertable) + ge_balance_positive_exists_othertableentryvalue))))))))) /\ (forall dc_input_exists_other dc_output_exists_other. ~(dc_input_exists_other=0) -> (exists pvs_le_gap_exists_otherdomain. pvs_le_gap_exists_otherdomain + (dc_input_exists_other) = (N)) -> (exists dst_positive_code_exists_otherlookup dst_positive_scale_exists_otherlookup dst_negative_code_exists_otherlookup dst_negative_scale_exists_otherlookup dst_positive_exists_otherlookup dst_negative_exists_otherlookup. (((K) = (((((dst_positive_code_exists_otherlookup) + (dst_positive_scale_exists_otherlookup)) * S ((dst_positive_code_exists_otherlookup) + (dst_positive_scale_exists_otherlookup)) + ((dst_positive_scale_exists_otherlookup) + (dst_positive_scale_exists_otherlookup))) + (((dst_negative_code_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)) * S ((dst_negative_code_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)) + ((dst_negative_scale_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)))) * S ((((dst_positive_code_exists_otherlookup) + (dst_positive_scale_exists_otherlookup)) * S ((dst_positive_code_exists_otherlookup) + (dst_positive_scale_exists_otherlookup)) + ((dst_positive_scale_exists_otherlookup) + (dst_positive_scale_exists_otherlookup))) + (((dst_negative_code_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)) * S ((dst_negative_code_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)) + ((dst_negative_scale_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)))) + ((((dst_negative_code_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)) * S ((dst_negative_code_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)) + ((dst_negative_scale_exists_otherlookup) + (dst_negative_scale_exists_otherlookup))) + (((dst_negative_code_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)) * S ((dst_negative_code_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)) + ((dst_negative_scale_exists_otherlookup) + (dst_negative_scale_exists_otherlookup)))))) /\ (((((exists ff_h_pvs_exists_otherlookuppositive. ff_h_pvs_exists_otherlookuppositive + S (dst_positive_exists_otherlookup) = S ((S (dc_input_exists_other)) * dst_positive_scale_exists_otherlookup)) /\ exists ff_q_pvs_exists_otherlookuppositive. dst_positive_code_exists_otherlookup = ff_q_pvs_exists_otherlookuppositive * S ((S (dc_input_exists_other)) * dst_positive_scale_exists_otherlookup) + (dst_positive_exists_otherlookup))) /\ (((((exists ff_h_pvs_exists_otherlookupnegative. ff_h_pvs_exists_otherlookupnegative + S (dst_negative_exists_otherlookup) = S ((S (dc_input_exists_other)) * dst_negative_scale_exists_otherlookup)) /\ exists ff_q_pvs_exists_otherlookupnegative. dst_negative_code_exists_otherlookup = ff_q_pvs_exists_otherlookupnegative * S ((S (dc_input_exists_other)) * dst_negative_scale_exists_otherlookup) + (dst_negative_exists_otherlookup))) /\ (exists ge_balance_positive_exists_otherlookupvalue ge_balance_negative_exists_otherlookupvalue. (((((dc_output_exists_other) = 2 * (ge_balance_positive_exists_otherlookupvalue) /\ (ge_balance_negative_exists_otherlookupvalue) = 0) \/ exists ge_signed_half_exists_otherlookupvaluedecode. (((dc_output_exists_other) = 2 * ge_signed_half_exists_otherlookupvaluedecode + 1 /\ (ge_balance_positive_exists_otherlookupvalue) = 0) /\ (ge_balance_negative_exists_otherlookupvalue) = S ge_signed_half_exists_otherlookupvaluedecode))) /\ ((dst_positive_exists_otherlookup) + ge_balance_negative_exists_otherlookupvalue = (dst_negative_exists_otherlookup) + ge_balance_positive_exists_otherlookupvalue))))))))) -> (((~((dc_input_exists_other)=0)) /\ (exists dc_mask_exists_othervalue. ((((exists dst_positive_code_exists_othervaluemasktable dst_positive_scale_exists_othervaluemasktable dst_negative_code_exists_othervaluemasktable dst_negative_scale_exists_othervaluemasktable. (((dc_mask_exists_othervalue) = (((((dst_positive_code_exists_othervaluemasktable) + (dst_positive_scale_exists_othervaluemasktable)) * S ((dst_positive_code_exists_othervaluemasktable) + (dst_positive_scale_exists_othervaluemasktable)) + ((dst_positive_scale_exists_othervaluemasktable) + (dst_positive_scale_exists_othervaluemasktable))) + (((dst_negative_code_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)) * S ((dst_negative_code_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)) + ((dst_negative_scale_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)))) * S ((((dst_positive_code_exists_othervaluemasktable) + (dst_positive_scale_exists_othervaluemasktable)) * S ((dst_positive_code_exists_othervaluemasktable) + (dst_positive_scale_exists_othervaluemasktable)) + ((dst_positive_scale_exists_othervaluemasktable) + (dst_positive_scale_exists_othervaluemasktable))) + (((dst_negative_code_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)) * S ((dst_negative_code_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)) + ((dst_negative_scale_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)))) + ((((dst_negative_code_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)) * S ((dst_negative_code_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)) + ((dst_negative_scale_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable))) + (((dst_negative_code_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)) * S ((dst_negative_code_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)) + ((dst_negative_scale_exists_othervaluemasktable) + (dst_negative_scale_exists_othervaluemasktable)))))) /\ (forall dst_index_exists_othervaluemasktable. (exists pvs_le_gap_exists_othervaluemasktabledomain. pvs_le_gap_exists_othervaluemasktabledomain + (dst_index_exists_othervaluemasktable) = (dc_input_exists_other)) -> exists dst_positive_exists_othervaluemasktable dst_negative_exists_othervaluemasktable dst_value_exists_othervaluemasktable. ((((exists ff_h_pvs_exists_othervaluemasktableentrypositive. ff_h_pvs_exists_othervaluemasktableentrypositive + S (dst_positive_exists_othervaluemasktable) = S ((S (dst_index_exists_othervaluemasktable)) * dst_positive_scale_exists_othervaluemasktable)) /\ exists ff_q_pvs_exists_othervaluemasktableentrypositive. dst_positive_code_exists_othervaluemasktable = ff_q_pvs_exists_othervaluemasktableentrypositive * S ((S (dst_index_exists_othervaluemasktable)) * dst_positive_scale_exists_othervaluemasktable) + (dst_positive_exists_othervaluemasktable))) /\ (((((exists ff_h_pvs_exists_othervaluemasktableentrynegative. ff_h_pvs_exists_othervaluemasktableentrynegative + S (dst_negative_exists_othervaluemasktable) = S ((S (dst_index_exists_othervaluemasktable)) * dst_negative_scale_exists_othervaluemasktable)) /\ exists ff_q_pvs_exists_othervaluemasktableentrynegative. dst_negative_code_exists_othervaluemasktable = ff_q_pvs_exists_othervaluemasktableentrynegative * S ((S (dst_index_exists_othervaluemasktable)) * dst_negative_scale_exists_othervaluemasktable) + (dst_negative_exists_othervaluemasktable))) /\ (exists ge_balance_positive_exists_othervaluemasktableentryvalue ge_balance_negative_exists_othervaluemasktableentryvalue. (((((dst_value_exists_othervaluemasktable) = 2 * (ge_balance_positive_exists_othervaluemasktableentryvalue) /\ (ge_balance_negative_exists_othervaluemasktableentryvalue) = 0) \/ exists ge_signed_half_exists_othervaluemasktableentryvaluedecode. (((dst_value_exists_othervaluemasktable) = 2 * ge_signed_half_exists_othervaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_exists_othervaluemasktableentryvalue) = 0) /\ (ge_balance_negative_exists_othervaluemasktableentryvalue) = S ge_signed_half_exists_othervaluemasktableentryvaluedecode))) /\ ((dst_positive_exists_othervaluemasktable) + ge_balance_negative_exists_othervaluemasktableentryvalue = (dst_negative_exists_othervaluemasktable) + ge_balance_positive_exists_othervaluemasktableentryvalue))))))))) /\ (forall dc_index_exists_othervaluemask dc_value_exists_othervaluemask. (exists pvs_le_gap_exists_othervaluemaskdomain. pvs_le_gap_exists_othervaluemaskdomain + (dc_index_exists_othervaluemask) = (dc_input_exists_other)) -> (exists dst_positive_code_exists_othervaluemasklookup dst_positive_scale_exists_othervaluemasklookup dst_negative_code_exists_othervaluemasklookup dst_negative_scale_exists_othervaluemasklookup dst_positive_exists_othervaluemasklookup dst_negative_exists_othervaluemasklookup. (((dc_mask_exists_othervalue) = (((((dst_positive_code_exists_othervaluemasklookup) + (dst_positive_scale_exists_othervaluemasklookup)) * S ((dst_positive_code_exists_othervaluemasklookup) + (dst_positive_scale_exists_othervaluemasklookup)) + ((dst_positive_scale_exists_othervaluemasklookup) + (dst_positive_scale_exists_othervaluemasklookup))) + (((dst_negative_code_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)) * S ((dst_negative_code_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)) + ((dst_negative_scale_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)))) * S ((((dst_positive_code_exists_othervaluemasklookup) + (dst_positive_scale_exists_othervaluemasklookup)) * S ((dst_positive_code_exists_othervaluemasklookup) + (dst_positive_scale_exists_othervaluemasklookup)) + ((dst_positive_scale_exists_othervaluemasklookup) + (dst_positive_scale_exists_othervaluemasklookup))) + (((dst_negative_code_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)) * S ((dst_negative_code_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)) + ((dst_negative_scale_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)))) + ((((dst_negative_code_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)) * S ((dst_negative_code_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)) + ((dst_negative_scale_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup))) + (((dst_negative_code_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)) * S ((dst_negative_code_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)) + ((dst_negative_scale_exists_othervaluemasklookup) + (dst_negative_scale_exists_othervaluemasklookup)))))) /\ (((((exists ff_h_pvs_exists_othervaluemasklookuppositive. ff_h_pvs_exists_othervaluemasklookuppositive + S (dst_positive_exists_othervaluemasklookup) = S ((S (dc_index_exists_othervaluemask)) * dst_positive_scale_exists_othervaluemasklookup)) /\ exists ff_q_pvs_exists_othervaluemasklookuppositive. dst_positive_code_exists_othervaluemasklookup = ff_q_pvs_exists_othervaluemasklookuppositive * S ((S (dc_index_exists_othervaluemask)) * dst_positive_scale_exists_othervaluemasklookup) + (dst_positive_exists_othervaluemasklookup))) /\ (((((exists ff_h_pvs_exists_othervaluemasklookupnegative. ff_h_pvs_exists_othervaluemasklookupnegative + S (dst_negative_exists_othervaluemasklookup) = S ((S (dc_index_exists_othervaluemask)) * dst_negative_scale_exists_othervaluemasklookup)) /\ exists ff_q_pvs_exists_othervaluemasklookupnegative. dst_negative_code_exists_othervaluemasklookup = ff_q_pvs_exists_othervaluemasklookupnegative * S ((S (dc_index_exists_othervaluemask)) * dst_negative_scale_exists_othervaluemasklookup) + (dst_negative_exists_othervaluemasklookup))) /\ (exists ge_balance_positive_exists_othervaluemasklookupvalue ge_balance_negative_exists_othervaluemasklookupvalue. (((((dc_value_exists_othervaluemask) = 2 * (ge_balance_positive_exists_othervaluemasklookupvalue) /\ (ge_balance_negative_exists_othervaluemasklookupvalue) = 0) \/ exists ge_signed_half_exists_othervaluemasklookupvaluedecode. (((dc_value_exists_othervaluemask) = 2 * ge_signed_half_exists_othervaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_exists_othervaluemasklookupvalue) = 0) /\ (ge_balance_negative_exists_othervaluemasklookupvalue) = S ge_signed_half_exists_othervaluemasklookupvaluedecode))) /\ ((dst_positive_exists_othervaluemasklookup) + ge_balance_negative_exists_othervaluemasklookupvalue = (dst_negative_exists_othervaluemasklookup) + ge_balance_positive_exists_othervaluemasklookupvalue))))))))) -> ((((~((dc_index_exists_othervaluemask)=0)) /\ (exists dc_quotient_exists_othervaluemaskentry dc_left_exists_othervaluemaskentry dc_right_exists_othervaluemaskentry. (((dc_input_exists_other)=(dc_index_exists_othervaluemask)*dc_quotient_exists_othervaluemaskentry) /\ (((exists dst_positive_code_exists_othervaluemaskentryleft dst_positive_scale_exists_othervaluemaskentryleft dst_negative_code_exists_othervaluemaskentryleft dst_negative_scale_exists_othervaluemaskentryleft dst_positive_exists_othervaluemaskentryleft dst_negative_exists_othervaluemaskentryleft. (((F) = (((((dst_positive_code_exists_othervaluemaskentryleft) + (dst_positive_scale_exists_othervaluemaskentryleft)) * S ((dst_positive_code_exists_othervaluemaskentryleft) + (dst_positive_scale_exists_othervaluemaskentryleft)) + ((dst_positive_scale_exists_othervaluemaskentryleft) + (dst_positive_scale_exists_othervaluemaskentryleft))) + (((dst_negative_code_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)) * S ((dst_negative_code_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)) + ((dst_negative_scale_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)))) * S ((((dst_positive_code_exists_othervaluemaskentryleft) + (dst_positive_scale_exists_othervaluemaskentryleft)) * S ((dst_positive_code_exists_othervaluemaskentryleft) + (dst_positive_scale_exists_othervaluemaskentryleft)) + ((dst_positive_scale_exists_othervaluemaskentryleft) + (dst_positive_scale_exists_othervaluemaskentryleft))) + (((dst_negative_code_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)) * S ((dst_negative_code_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)) + ((dst_negative_scale_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)))) + ((((dst_negative_code_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)) * S ((dst_negative_code_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)) + ((dst_negative_scale_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft))) + (((dst_negative_code_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)) * S ((dst_negative_code_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)) + ((dst_negative_scale_exists_othervaluemaskentryleft) + (dst_negative_scale_exists_othervaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_exists_othervaluemaskentryleftpositive. ff_h_pvs_exists_othervaluemaskentryleftpositive + S (dst_positive_exists_othervaluemaskentryleft) = S ((S (dc_index_exists_othervaluemask)) * dst_positive_scale_exists_othervaluemaskentryleft)) /\ exists ff_q_pvs_exists_othervaluemaskentryleftpositive. dst_positive_code_exists_othervaluemaskentryleft = ff_q_pvs_exists_othervaluemaskentryleftpositive * S ((S (dc_index_exists_othervaluemask)) * dst_positive_scale_exists_othervaluemaskentryleft) + (dst_positive_exists_othervaluemaskentryleft))) /\ (((((exists ff_h_pvs_exists_othervaluemaskentryleftnegative. ff_h_pvs_exists_othervaluemaskentryleftnegative + S (dst_negative_exists_othervaluemaskentryleft) = S ((S (dc_index_exists_othervaluemask)) * dst_negative_scale_exists_othervaluemaskentryleft)) /\ exists ff_q_pvs_exists_othervaluemaskentryleftnegative. dst_negative_code_exists_othervaluemaskentryleft = ff_q_pvs_exists_othervaluemaskentryleftnegative * S ((S (dc_index_exists_othervaluemask)) * dst_negative_scale_exists_othervaluemaskentryleft) + (dst_negative_exists_othervaluemaskentryleft))) /\ (exists ge_balance_positive_exists_othervaluemaskentryleftvalue ge_balance_negative_exists_othervaluemaskentryleftvalue. (((((dc_left_exists_othervaluemaskentry) = 2 * (ge_balance_positive_exists_othervaluemaskentryleftvalue) /\ (ge_balance_negative_exists_othervaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_exists_othervaluemaskentryleftvaluedecode. (((dc_left_exists_othervaluemaskentry) = 2 * ge_signed_half_exists_othervaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_exists_othervaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_exists_othervaluemaskentryleftvalue) = S ge_signed_half_exists_othervaluemaskentryleftvaluedecode))) /\ ((dst_positive_exists_othervaluemaskentryleft) + ge_balance_negative_exists_othervaluemaskentryleftvalue = (dst_negative_exists_othervaluemaskentryleft) + ge_balance_positive_exists_othervaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_exists_othervaluemaskentryright dst_positive_scale_exists_othervaluemaskentryright dst_negative_code_exists_othervaluemaskentryright dst_negative_scale_exists_othervaluemaskentryright dst_positive_exists_othervaluemaskentryright dst_negative_exists_othervaluemaskentryright. (((G) = (((((dst_positive_code_exists_othervaluemaskentryright) + (dst_positive_scale_exists_othervaluemaskentryright)) * S ((dst_positive_code_exists_othervaluemaskentryright) + (dst_positive_scale_exists_othervaluemaskentryright)) + ((dst_positive_scale_exists_othervaluemaskentryright) + (dst_positive_scale_exists_othervaluemaskentryright))) + (((dst_negative_code_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)) * S ((dst_negative_code_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)) + ((dst_negative_scale_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)))) * S ((((dst_positive_code_exists_othervaluemaskentryright) + (dst_positive_scale_exists_othervaluemaskentryright)) * S ((dst_positive_code_exists_othervaluemaskentryright) + (dst_positive_scale_exists_othervaluemaskentryright)) + ((dst_positive_scale_exists_othervaluemaskentryright) + (dst_positive_scale_exists_othervaluemaskentryright))) + (((dst_negative_code_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)) * S ((dst_negative_code_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)) + ((dst_negative_scale_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)))) + ((((dst_negative_code_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)) * S ((dst_negative_code_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)) + ((dst_negative_scale_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright))) + (((dst_negative_code_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)) * S ((dst_negative_code_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)) + ((dst_negative_scale_exists_othervaluemaskentryright) + (dst_negative_scale_exists_othervaluemaskentryright)))))) /\ (((((exists ff_h_pvs_exists_othervaluemaskentryrightpositive. ff_h_pvs_exists_othervaluemaskentryrightpositive + S (dst_positive_exists_othervaluemaskentryright) = S ((S (dc_quotient_exists_othervaluemaskentry)) * dst_positive_scale_exists_othervaluemaskentryright)) /\ exists ff_q_pvs_exists_othervaluemaskentryrightpositive. dst_positive_code_exists_othervaluemaskentryright = ff_q_pvs_exists_othervaluemaskentryrightpositive * S ((S (dc_quotient_exists_othervaluemaskentry)) * dst_positive_scale_exists_othervaluemaskentryright) + (dst_positive_exists_othervaluemaskentryright))) /\ (((((exists ff_h_pvs_exists_othervaluemaskentryrightnegative. ff_h_pvs_exists_othervaluemaskentryrightnegative + S (dst_negative_exists_othervaluemaskentryright) = S ((S (dc_quotient_exists_othervaluemaskentry)) * dst_negative_scale_exists_othervaluemaskentryright)) /\ exists ff_q_pvs_exists_othervaluemaskentryrightnegative. dst_negative_code_exists_othervaluemaskentryright = ff_q_pvs_exists_othervaluemaskentryrightnegative * S ((S (dc_quotient_exists_othervaluemaskentry)) * dst_negative_scale_exists_othervaluemaskentryright) + (dst_negative_exists_othervaluemaskentryright))) /\ (exists ge_balance_positive_exists_othervaluemaskentryrightvalue ge_balance_negative_exists_othervaluemaskentryrightvalue. (((((dc_right_exists_othervaluemaskentry) = 2 * (ge_balance_positive_exists_othervaluemaskentryrightvalue) /\ (ge_balance_negative_exists_othervaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_exists_othervaluemaskentryrightvaluedecode. (((dc_right_exists_othervaluemaskentry) = 2 * ge_signed_half_exists_othervaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_exists_othervaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_exists_othervaluemaskentryrightvalue) = S ge_signed_half_exists_othervaluemaskentryrightvaluedecode))) /\ ((dst_positive_exists_othervaluemaskentryright) + ge_balance_negative_exists_othervaluemaskentryrightvalue = (dst_negative_exists_othervaluemaskentryright) + ge_balance_positive_exists_othervaluemaskentryrightvalue))))))))) /\ (exists sto_ap_exists_othervaluemaskentryproduct sto_an_exists_othervaluemaskentryproduct sto_bp_exists_othervaluemaskentryproduct sto_bn_exists_othervaluemaskentryproduct sto_cp_exists_othervaluemaskentryproduct sto_cn_exists_othervaluemaskentryproduct. (((((dc_left_exists_othervaluemaskentry) = 2 * (sto_ap_exists_othervaluemaskentryproduct) /\ (sto_an_exists_othervaluemaskentryproduct) = 0) \/ exists ge_signed_half_exists_othervaluemaskentryproductleft. (((dc_left_exists_othervaluemaskentry) = 2 * ge_signed_half_exists_othervaluemaskentryproductleft + 1 /\ (sto_ap_exists_othervaluemaskentryproduct) = 0) /\ (sto_an_exists_othervaluemaskentryproduct) = S ge_signed_half_exists_othervaluemaskentryproductleft))) /\ ((((((dc_right_exists_othervaluemaskentry) = 2 * (sto_bp_exists_othervaluemaskentryproduct) /\ (sto_bn_exists_othervaluemaskentryproduct) = 0) \/ exists ge_signed_half_exists_othervaluemaskentryproductright. (((dc_right_exists_othervaluemaskentry) = 2 * ge_signed_half_exists_othervaluemaskentryproductright + 1 /\ (sto_bp_exists_othervaluemaskentryproduct) = 0) /\ (sto_bn_exists_othervaluemaskentryproduct) = S ge_signed_half_exists_othervaluemaskentryproductright))) /\ ((((((dc_value_exists_othervaluemask) = 2 * (sto_cp_exists_othervaluemaskentryproduct) /\ (sto_cn_exists_othervaluemaskentryproduct) = 0) \/ exists ge_signed_half_exists_othervaluemaskentryproductoutput. (((dc_value_exists_othervaluemask) = 2 * ge_signed_half_exists_othervaluemaskentryproductoutput + 1 /\ (sto_cp_exists_othervaluemaskentryproduct) = 0) /\ (sto_cn_exists_othervaluemaskentryproduct) = S ge_signed_half_exists_othervaluemaskentryproductoutput))) /\ ((sto_ap_exists_othervaluemaskentryproduct * sto_bp_exists_othervaluemaskentryproduct + sto_an_exists_othervaluemaskentryproduct * sto_bn_exists_othervaluemaskentryproduct) + sto_cn_exists_othervaluemaskentryproduct = (sto_ap_exists_othervaluemaskentryproduct * sto_bn_exists_othervaluemaskentryproduct + sto_an_exists_othervaluemaskentryproduct * sto_bp_exists_othervaluemaskentryproduct) + sto_cp_exists_othervaluemaskentryproduct))))))))))))))) \/ ((((dc_index_exists_othervaluemask)=0 \/ ~(exists pvs_factor_exists_othervaluemaskentrynondivisor. (dc_input_exists_other) = (dc_index_exists_othervaluemask) * pvs_factor_exists_othervaluemaskentrynondivisor)) /\ ((dc_value_exists_othervaluemask)=0))))))) /\ (exists dst_positive_code_exists_othervaluefold dst_positive_scale_exists_othervaluefold dst_negative_code_exists_othervaluefold dst_negative_scale_exists_othervaluefold dst_positive_sum_exists_othervaluefold dst_negative_sum_exists_othervaluefold. (((dc_mask_exists_othervalue) = (((((dst_positive_code_exists_othervaluefold) + (dst_positive_scale_exists_othervaluefold)) * S ((dst_positive_code_exists_othervaluefold) + (dst_positive_scale_exists_othervaluefold)) + ((dst_positive_scale_exists_othervaluefold) + (dst_positive_scale_exists_othervaluefold))) + (((dst_negative_code_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)) * S ((dst_negative_code_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)) + ((dst_negative_scale_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)))) * S ((((dst_positive_code_exists_othervaluefold) + (dst_positive_scale_exists_othervaluefold)) * S ((dst_positive_code_exists_othervaluefold) + (dst_positive_scale_exists_othervaluefold)) + ((dst_positive_scale_exists_othervaluefold) + (dst_positive_scale_exists_othervaluefold))) + (((dst_negative_code_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)) * S ((dst_negative_code_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)) + ((dst_negative_scale_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)))) + ((((dst_negative_code_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)) * S ((dst_negative_code_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)) + ((dst_negative_scale_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold))) + (((dst_negative_code_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)) * S ((dst_negative_code_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)) + ((dst_negative_scale_exists_othervaluefold) + (dst_negative_scale_exists_othervaluefold)))))) /\ (((exists fs_u_dst_exists_othervaluefoldpositive fs_v_dst_exists_othervaluefoldpositive. ((((exists fs_h_dst_exists_othervaluefoldpositive_body_start. fs_h_dst_exists_othervaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_exists_othervaluefoldpositive)) /\ exists fs_q_dst_exists_othervaluefoldpositive_body_start. fs_u_dst_exists_othervaluefoldpositive = fs_q_dst_exists_othervaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_exists_othervaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_exists_othervaluefoldpositive_body_terminal. fs_h_dst_exists_othervaluefoldpositive_body_terminal + S (dst_positive_sum_exists_othervaluefold) = S ((S (S (dc_input_exists_other))) * fs_v_dst_exists_othervaluefoldpositive)) /\ exists fs_q_dst_exists_othervaluefoldpositive_body_terminal. fs_u_dst_exists_othervaluefoldpositive = fs_q_dst_exists_othervaluefoldpositive_body_terminal * S ((S (S (dc_input_exists_other))) * fs_v_dst_exists_othervaluefoldpositive) + (dst_positive_sum_exists_othervaluefold))) /\ forall fs_i_dst_exists_othervaluefoldpositive_body_steps. (exists fs_lt_dst_exists_othervaluefoldpositive_body_steps_bound. fs_lt_dst_exists_othervaluefoldpositive_body_steps_bound + S fs_i_dst_exists_othervaluefoldpositive_body_steps = S (dc_input_exists_other)) -> exists fs_a_dst_exists_othervaluefoldpositive_body_steps fs_r_dst_exists_othervaluefoldpositive_body_steps fs_s_dst_exists_othervaluefoldpositive_body_steps. ((((exists fs_h_dst_exists_othervaluefoldpositive_body_steps_summand. fs_h_dst_exists_othervaluefoldpositive_body_steps_summand + S (fs_a_dst_exists_othervaluefoldpositive_body_steps) = S ((S (fs_i_dst_exists_othervaluefoldpositive_body_steps)) * dst_positive_scale_exists_othervaluefold)) /\ exists fs_q_dst_exists_othervaluefoldpositive_body_steps_summand. dst_positive_code_exists_othervaluefold = fs_q_dst_exists_othervaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_exists_othervaluefoldpositive_body_steps)) * dst_positive_scale_exists_othervaluefold) + (fs_a_dst_exists_othervaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_exists_othervaluefoldpositive_body_steps_partial. fs_h_dst_exists_othervaluefoldpositive_body_steps_partial + S (fs_r_dst_exists_othervaluefoldpositive_body_steps) = S ((S (fs_i_dst_exists_othervaluefoldpositive_body_steps)) * fs_v_dst_exists_othervaluefoldpositive)) /\ exists fs_q_dst_exists_othervaluefoldpositive_body_steps_partial. fs_u_dst_exists_othervaluefoldpositive = fs_q_dst_exists_othervaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_exists_othervaluefoldpositive_body_steps)) * fs_v_dst_exists_othervaluefoldpositive) + (fs_r_dst_exists_othervaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_exists_othervaluefoldpositive_body_steps_successor. fs_h_dst_exists_othervaluefoldpositive_body_steps_successor + S (fs_s_dst_exists_othervaluefoldpositive_body_steps) = S ((S (S fs_i_dst_exists_othervaluefoldpositive_body_steps)) * fs_v_dst_exists_othervaluefoldpositive)) /\ exists fs_q_dst_exists_othervaluefoldpositive_body_steps_successor. fs_u_dst_exists_othervaluefoldpositive = fs_q_dst_exists_othervaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_exists_othervaluefoldpositive_body_steps)) * fs_v_dst_exists_othervaluefoldpositive) + (fs_s_dst_exists_othervaluefoldpositive_body_steps))) /\ fs_s_dst_exists_othervaluefoldpositive_body_steps = fs_r_dst_exists_othervaluefoldpositive_body_steps + fs_a_dst_exists_othervaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_exists_othervaluefoldnegative fs_v_dst_exists_othervaluefoldnegative. ((((exists fs_h_dst_exists_othervaluefoldnegative_body_start. fs_h_dst_exists_othervaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_exists_othervaluefoldnegative)) /\ exists fs_q_dst_exists_othervaluefoldnegative_body_start. fs_u_dst_exists_othervaluefoldnegative = fs_q_dst_exists_othervaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_exists_othervaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_exists_othervaluefoldnegative_body_terminal. fs_h_dst_exists_othervaluefoldnegative_body_terminal + S (dst_negative_sum_exists_othervaluefold) = S ((S (S (dc_input_exists_other))) * fs_v_dst_exists_othervaluefoldnegative)) /\ exists fs_q_dst_exists_othervaluefoldnegative_body_terminal. fs_u_dst_exists_othervaluefoldnegative = fs_q_dst_exists_othervaluefoldnegative_body_terminal * S ((S (S (dc_input_exists_other))) * fs_v_dst_exists_othervaluefoldnegative) + (dst_negative_sum_exists_othervaluefold))) /\ forall fs_i_dst_exists_othervaluefoldnegative_body_steps. (exists fs_lt_dst_exists_othervaluefoldnegative_body_steps_bound. fs_lt_dst_exists_othervaluefoldnegative_body_steps_bound + S fs_i_dst_exists_othervaluefoldnegative_body_steps = S (dc_input_exists_other)) -> exists fs_a_dst_exists_othervaluefoldnegative_body_steps fs_r_dst_exists_othervaluefoldnegative_body_steps fs_s_dst_exists_othervaluefoldnegative_body_steps. ((((exists fs_h_dst_exists_othervaluefoldnegative_body_steps_summand. fs_h_dst_exists_othervaluefoldnegative_body_steps_summand + S (fs_a_dst_exists_othervaluefoldnegative_body_steps) = S ((S (fs_i_dst_exists_othervaluefoldnegative_body_steps)) * dst_negative_scale_exists_othervaluefold)) /\ exists fs_q_dst_exists_othervaluefoldnegative_body_steps_summand. dst_negative_code_exists_othervaluefold = fs_q_dst_exists_othervaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_exists_othervaluefoldnegative_body_steps)) * dst_negative_scale_exists_othervaluefold) + (fs_a_dst_exists_othervaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_exists_othervaluefoldnegative_body_steps_partial. fs_h_dst_exists_othervaluefoldnegative_body_steps_partial + S (fs_r_dst_exists_othervaluefoldnegative_body_steps) = S ((S (fs_i_dst_exists_othervaluefoldnegative_body_steps)) * fs_v_dst_exists_othervaluefoldnegative)) /\ exists fs_q_dst_exists_othervaluefoldnegative_body_steps_partial. fs_u_dst_exists_othervaluefoldnegative = fs_q_dst_exists_othervaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_exists_othervaluefoldnegative_body_steps)) * fs_v_dst_exists_othervaluefoldnegative) + (fs_r_dst_exists_othervaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_exists_othervaluefoldnegative_body_steps_successor. fs_h_dst_exists_othervaluefoldnegative_body_steps_successor + S (fs_s_dst_exists_othervaluefoldnegative_body_steps) = S ((S (S fs_i_dst_exists_othervaluefoldnegative_body_steps)) * fs_v_dst_exists_othervaluefoldnegative)) /\ exists fs_q_dst_exists_othervaluefoldnegative_body_steps_successor. fs_u_dst_exists_othervaluefoldnegative = fs_q_dst_exists_othervaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_exists_othervaluefoldnegative_body_steps)) * fs_v_dst_exists_othervaluefoldnegative) + (fs_s_dst_exists_othervaluefoldnegative_body_steps))) /\ fs_s_dst_exists_othervaluefoldnegative_body_steps = fs_r_dst_exists_othervaluefoldnegative_body_steps + fs_a_dst_exists_othervaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_exists_othervaluefoldresult ge_balance_negative_exists_othervaluefoldresult. (((((dc_output_exists_other) = 2 * (ge_balance_positive_exists_othervaluefoldresult) /\ (ge_balance_negative_exists_othervaluefoldresult) = 0) \/ exists ge_signed_half_exists_othervaluefoldresultdecode. (((dc_output_exists_other) = 2 * ge_signed_half_exists_othervaluefoldresultdecode + 1 /\ (ge_balance_positive_exists_othervaluefoldresult) = 0) /\ (ge_balance_negative_exists_othervaluefoldresult) = S ge_signed_half_exists_othervaluefoldresultdecode))) /\ ((dst_positive_sum_exists_othervaluefold) + ge_balance_negative_exists_othervaluefoldresult = (dst_negative_sum_exists_othervaluefold) + ge_balance_positive_exists_othervaluefoldresult)))))))))))))))))))) -> (forall dm_index_exists_unique_positive dm_first_value_exists_unique_positive dm_second_value_exists_unique_positive. ~(dm_index_exists_unique_positive=0) -> (exists pvs_le_gap_exists_unique_positivedomain. pvs_le_gap_exists_unique_positivedomain + (dm_index_exists_unique_positive) = (N)) -> (exists dst_positive_code_exists_unique_positivefirst dst_positive_scale_exists_unique_positivefirst dst_negative_code_exists_unique_positivefirst dst_negative_scale_exists_unique_positivefirst dst_positive_exists_unique_positivefirst dst_negative_exists_unique_positivefirst. (((H) = (((((dst_positive_code_exists_unique_positivefirst) + (dst_positive_scale_exists_unique_positivefirst)) * S ((dst_positive_code_exists_unique_positivefirst) + (dst_positive_scale_exists_unique_positivefirst)) + ((dst_positive_scale_exists_unique_positivefirst) + (dst_positive_scale_exists_unique_positivefirst))) + (((dst_negative_code_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)) * S ((dst_negative_code_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)) + ((dst_negative_scale_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)))) * S ((((dst_positive_code_exists_unique_positivefirst) + (dst_positive_scale_exists_unique_positivefirst)) * S ((dst_positive_code_exists_unique_positivefirst) + (dst_positive_scale_exists_unique_positivefirst)) + ((dst_positive_scale_exists_unique_positivefirst) + (dst_positive_scale_exists_unique_positivefirst))) + (((dst_negative_code_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)) * S ((dst_negative_code_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)) + ((dst_negative_scale_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)))) + ((((dst_negative_code_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)) * S ((dst_negative_code_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)) + ((dst_negative_scale_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst))) + (((dst_negative_code_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)) * S ((dst_negative_code_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)) + ((dst_negative_scale_exists_unique_positivefirst) + (dst_negative_scale_exists_unique_positivefirst)))))) /\ (((((exists ff_h_pvs_exists_unique_positivefirstpositive. ff_h_pvs_exists_unique_positivefirstpositive + S (dst_positive_exists_unique_positivefirst) = S ((S (dm_index_exists_unique_positive)) * dst_positive_scale_exists_unique_positivefirst)) /\ exists ff_q_pvs_exists_unique_positivefirstpositive. dst_positive_code_exists_unique_positivefirst = ff_q_pvs_exists_unique_positivefirstpositive * S ((S (dm_index_exists_unique_positive)) * dst_positive_scale_exists_unique_positivefirst) + (dst_positive_exists_unique_positivefirst))) /\ (((((exists ff_h_pvs_exists_unique_positivefirstnegative. ff_h_pvs_exists_unique_positivefirstnegative + S (dst_negative_exists_unique_positivefirst) = S ((S (dm_index_exists_unique_positive)) * dst_negative_scale_exists_unique_positivefirst)) /\ exists ff_q_pvs_exists_unique_positivefirstnegative. dst_negative_code_exists_unique_positivefirst = ff_q_pvs_exists_unique_positivefirstnegative * S ((S (dm_index_exists_unique_positive)) * dst_negative_scale_exists_unique_positivefirst) + (dst_negative_exists_unique_positivefirst))) /\ (exists ge_balance_positive_exists_unique_positivefirstvalue ge_balance_negative_exists_unique_positivefirstvalue. (((((dm_first_value_exists_unique_positive) = 2 * (ge_balance_positive_exists_unique_positivefirstvalue) /\ (ge_balance_negative_exists_unique_positivefirstvalue) = 0) \/ exists ge_signed_half_exists_unique_positivefirstvaluedecode. (((dm_first_value_exists_unique_positive) = 2 * ge_signed_half_exists_unique_positivefirstvaluedecode + 1 /\ (ge_balance_positive_exists_unique_positivefirstvalue) = 0) /\ (ge_balance_negative_exists_unique_positivefirstvalue) = S ge_signed_half_exists_unique_positivefirstvaluedecode))) /\ ((dst_positive_exists_unique_positivefirst) + ge_balance_negative_exists_unique_positivefirstvalue = (dst_negative_exists_unique_positivefirst) + ge_balance_positive_exists_unique_positivefirstvalue))))))))) -> (exists dst_positive_code_exists_unique_positivesecond dst_positive_scale_exists_unique_positivesecond dst_negative_code_exists_unique_positivesecond dst_negative_scale_exists_unique_positivesecond dst_positive_exists_unique_positivesecond dst_negative_exists_unique_positivesecond. (((K) = (((((dst_positive_code_exists_unique_positivesecond) + (dst_positive_scale_exists_unique_positivesecond)) * S ((dst_positive_code_exists_unique_positivesecond) + (dst_positive_scale_exists_unique_positivesecond)) + ((dst_positive_scale_exists_unique_positivesecond) + (dst_positive_scale_exists_unique_positivesecond))) + (((dst_negative_code_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)) * S ((dst_negative_code_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)) + ((dst_negative_scale_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)))) * S ((((dst_positive_code_exists_unique_positivesecond) + (dst_positive_scale_exists_unique_positivesecond)) * S ((dst_positive_code_exists_unique_positivesecond) + (dst_positive_scale_exists_unique_positivesecond)) + ((dst_positive_scale_exists_unique_positivesecond) + (dst_positive_scale_exists_unique_positivesecond))) + (((dst_negative_code_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)) * S ((dst_negative_code_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)) + ((dst_negative_scale_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)))) + ((((dst_negative_code_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)) * S ((dst_negative_code_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)) + ((dst_negative_scale_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond))) + (((dst_negative_code_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)) * S ((dst_negative_code_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)) + ((dst_negative_scale_exists_unique_positivesecond) + (dst_negative_scale_exists_unique_positivesecond)))))) /\ (((((exists ff_h_pvs_exists_unique_positivesecondpositive. ff_h_pvs_exists_unique_positivesecondpositive + S (dst_positive_exists_unique_positivesecond) = S ((S (dm_index_exists_unique_positive)) * dst_positive_scale_exists_unique_positivesecond)) /\ exists ff_q_pvs_exists_unique_positivesecondpositive. dst_positive_code_exists_unique_positivesecond = ff_q_pvs_exists_unique_positivesecondpositive * S ((S (dm_index_exists_unique_positive)) * dst_positive_scale_exists_unique_positivesecond) + (dst_positive_exists_unique_positivesecond))) /\ (((((exists ff_h_pvs_exists_unique_positivesecondnegative. ff_h_pvs_exists_unique_positivesecondnegative + S (dst_negative_exists_unique_positivesecond) = S ((S (dm_index_exists_unique_positive)) * dst_negative_scale_exists_unique_positivesecond)) /\ exists ff_q_pvs_exists_unique_positivesecondnegative. dst_negative_code_exists_unique_positivesecond = ff_q_pvs_exists_unique_positivesecondnegative * S ((S (dm_index_exists_unique_positive)) * dst_negative_scale_exists_unique_positivesecond) + (dst_negative_exists_unique_positivesecond))) /\ (exists ge_balance_positive_exists_unique_positivesecondvalue ge_balance_negative_exists_unique_positivesecondvalue. (((((dm_second_value_exists_unique_positive) = 2 * (ge_balance_positive_exists_unique_positivesecondvalue) /\ (ge_balance_negative_exists_unique_positivesecondvalue) = 0) \/ exists ge_signed_half_exists_unique_positivesecondvaluedecode. (((dm_second_value_exists_unique_positive) = 2 * ge_signed_half_exists_unique_positivesecondvaluedecode + 1 /\ (ge_balance_positive_exists_unique_positivesecondvalue) = 0) /\ (ge_balance_negative_exists_unique_positivesecondvalue) = S ge_signed_half_exists_unique_positivesecondvaluedecode))) /\ ((dst_positive_exists_unique_positivesecond) + ge_balance_negative_exists_unique_positivesecondvalue = (dst_negative_exists_unique_positivesecond) + ge_balance_positive_exists_unique_positivesecondvalue))))))))) -> dm_first_value_exists_unique_positive=dm_second_value_exists_unique_positive)))))