Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Operation tables contain actual beta-coded entries and compare represented signed values, not encodings. The strict sum window is i<l and the separately certified endpoint i=l is unused. Rectangular Fubini and full finite signed Möbius inversion are separate, now-admitted families.
Exact theorem in conservative defined notation
∀ l. ∀ W. ∀ F. ∀ G. ∀ H. ∀ a. ∀ b. ∀ c. ArithAdd(F,G,H,l) → SignedWeightedSum(W,F,l,a) → SignedWeightedSum(W,G,l,b) → SignedWeightedSum(W,H,l,c) → SignedAdd(a,b,c)Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Original expanded first-order statement
forall l W F G H a b c. (((exists dst_positive_code_weighted_linearity_inputleft_table dst_positive_scale_weighted_linearity_inputleft_table dst_negative_code_weighted_linearity_inputleft_table dst_negative_scale_weighted_linearity_inputleft_table. (((F) = (((((dst_positive_code_weighted_linearity_inputleft_table) + (dst_positive_scale_weighted_linearity_inputleft_table)) * S ((dst_positive_code_weighted_linearity_inputleft_table) + (dst_positive_scale_weighted_linearity_inputleft_table)) + ((dst_positive_scale_weighted_linearity_inputleft_table) + (dst_positive_scale_weighted_linearity_inputleft_table))) + (((dst_negative_code_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)) * S ((dst_negative_code_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)) + ((dst_negative_scale_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)))) * S ((((dst_positive_code_weighted_linearity_inputleft_table) + (dst_positive_scale_weighted_linearity_inputleft_table)) * S ((dst_positive_code_weighted_linearity_inputleft_table) + (dst_positive_scale_weighted_linearity_inputleft_table)) + ((dst_positive_scale_weighted_linearity_inputleft_table) + (dst_positive_scale_weighted_linearity_inputleft_table))) + (((dst_negative_code_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)) * S ((dst_negative_code_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)) + ((dst_negative_scale_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)))) + ((((dst_negative_code_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)) * S ((dst_negative_code_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)) + ((dst_negative_scale_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table))) + (((dst_negative_code_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)) * S ((dst_negative_code_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)) + ((dst_negative_scale_weighted_linearity_inputleft_table) + (dst_negative_scale_weighted_linearity_inputleft_table)))))) /\ (forall dst_index_weighted_linearity_inputleft_table. (exists pvs_le_gap_weighted_linearity_inputleft_tabledomain. pvs_le_gap_weighted_linearity_inputleft_tabledomain + (dst_index_weighted_linearity_inputleft_table) = (l)) -> exists dst_positive_weighted_linearity_inputleft_table dst_negative_weighted_linearity_inputleft_table dst_value_weighted_linearity_inputleft_table. ((((exists ff_h_pvs_weighted_linearity_inputleft_tableentrypositive. ff_h_pvs_weighted_linearity_inputleft_tableentrypositive + S (dst_positive_weighted_linearity_inputleft_table) = S ((S (dst_index_weighted_linearity_inputleft_table)) * dst_positive_scale_weighted_linearity_inputleft_table)) /\ exists ff_q_pvs_weighted_linearity_inputleft_tableentrypositive. dst_positive_code_weighted_linearity_inputleft_table = ff_q_pvs_weighted_linearity_inputleft_tableentrypositive * S ((S (dst_index_weighted_linearity_inputleft_table)) * dst_positive_scale_weighted_linearity_inputleft_table) + (dst_positive_weighted_linearity_inputleft_table))) /\ (((((exists ff_h_pvs_weighted_linearity_inputleft_tableentrynegative. ff_h_pvs_weighted_linearity_inputleft_tableentrynegative + S (dst_negative_weighted_linearity_inputleft_table) = S ((S (dst_index_weighted_linearity_inputleft_table)) * dst_negative_scale_weighted_linearity_inputleft_table)) /\ exists ff_q_pvs_weighted_linearity_inputleft_tableentrynegative. dst_negative_code_weighted_linearity_inputleft_table = ff_q_pvs_weighted_linearity_inputleft_tableentrynegative * S ((S (dst_index_weighted_linearity_inputleft_table)) * dst_negative_scale_weighted_linearity_inputleft_table) + (dst_negative_weighted_linearity_inputleft_table))) /\ (exists ge_balance_positive_weighted_linearity_inputleft_tableentryvalue ge_balance_negative_weighted_linearity_inputleft_tableentryvalue. (((((dst_value_weighted_linearity_inputleft_table) = 2 * (ge_balance_positive_weighted_linearity_inputleft_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_inputleft_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_inputleft_tableentryvaluedecode. (((dst_value_weighted_linearity_inputleft_table) = 2 * ge_signed_half_weighted_linearity_inputleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_inputleft_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_inputleft_tableentryvalue) = S ge_signed_half_weighted_linearity_inputleft_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_inputleft_table) + ge_balance_negative_weighted_linearity_inputleft_tableentryvalue = (dst_negative_weighted_linearity_inputleft_table) + ge_balance_positive_weighted_linearity_inputleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_inputright_table dst_positive_scale_weighted_linearity_inputright_table dst_negative_code_weighted_linearity_inputright_table dst_negative_scale_weighted_linearity_inputright_table. (((G) = (((((dst_positive_code_weighted_linearity_inputright_table) + (dst_positive_scale_weighted_linearity_inputright_table)) * S ((dst_positive_code_weighted_linearity_inputright_table) + (dst_positive_scale_weighted_linearity_inputright_table)) + ((dst_positive_scale_weighted_linearity_inputright_table) + (dst_positive_scale_weighted_linearity_inputright_table))) + (((dst_negative_code_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)) * S ((dst_negative_code_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)) + ((dst_negative_scale_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)))) * S ((((dst_positive_code_weighted_linearity_inputright_table) + (dst_positive_scale_weighted_linearity_inputright_table)) * S ((dst_positive_code_weighted_linearity_inputright_table) + (dst_positive_scale_weighted_linearity_inputright_table)) + ((dst_positive_scale_weighted_linearity_inputright_table) + (dst_positive_scale_weighted_linearity_inputright_table))) + (((dst_negative_code_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)) * S ((dst_negative_code_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)) + ((dst_negative_scale_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)))) + ((((dst_negative_code_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)) * S ((dst_negative_code_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)) + ((dst_negative_scale_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table))) + (((dst_negative_code_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)) * S ((dst_negative_code_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)) + ((dst_negative_scale_weighted_linearity_inputright_table) + (dst_negative_scale_weighted_linearity_inputright_table)))))) /\ (forall dst_index_weighted_linearity_inputright_table. (exists pvs_le_gap_weighted_linearity_inputright_tabledomain. pvs_le_gap_weighted_linearity_inputright_tabledomain + (dst_index_weighted_linearity_inputright_table) = (l)) -> exists dst_positive_weighted_linearity_inputright_table dst_negative_weighted_linearity_inputright_table dst_value_weighted_linearity_inputright_table. ((((exists ff_h_pvs_weighted_linearity_inputright_tableentrypositive. ff_h_pvs_weighted_linearity_inputright_tableentrypositive + S (dst_positive_weighted_linearity_inputright_table) = S ((S (dst_index_weighted_linearity_inputright_table)) * dst_positive_scale_weighted_linearity_inputright_table)) /\ exists ff_q_pvs_weighted_linearity_inputright_tableentrypositive. dst_positive_code_weighted_linearity_inputright_table = ff_q_pvs_weighted_linearity_inputright_tableentrypositive * S ((S (dst_index_weighted_linearity_inputright_table)) * dst_positive_scale_weighted_linearity_inputright_table) + (dst_positive_weighted_linearity_inputright_table))) /\ (((((exists ff_h_pvs_weighted_linearity_inputright_tableentrynegative. ff_h_pvs_weighted_linearity_inputright_tableentrynegative + S (dst_negative_weighted_linearity_inputright_table) = S ((S (dst_index_weighted_linearity_inputright_table)) * dst_negative_scale_weighted_linearity_inputright_table)) /\ exists ff_q_pvs_weighted_linearity_inputright_tableentrynegative. dst_negative_code_weighted_linearity_inputright_table = ff_q_pvs_weighted_linearity_inputright_tableentrynegative * S ((S (dst_index_weighted_linearity_inputright_table)) * dst_negative_scale_weighted_linearity_inputright_table) + (dst_negative_weighted_linearity_inputright_table))) /\ (exists ge_balance_positive_weighted_linearity_inputright_tableentryvalue ge_balance_negative_weighted_linearity_inputright_tableentryvalue. (((((dst_value_weighted_linearity_inputright_table) = 2 * (ge_balance_positive_weighted_linearity_inputright_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_inputright_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_inputright_tableentryvaluedecode. (((dst_value_weighted_linearity_inputright_table) = 2 * ge_signed_half_weighted_linearity_inputright_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_inputright_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_inputright_tableentryvalue) = S ge_signed_half_weighted_linearity_inputright_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_inputright_table) + ge_balance_negative_weighted_linearity_inputright_tableentryvalue = (dst_negative_weighted_linearity_inputright_table) + ge_balance_positive_weighted_linearity_inputright_tableentryvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_inputoutput_table dst_positive_scale_weighted_linearity_inputoutput_table dst_negative_code_weighted_linearity_inputoutput_table dst_negative_scale_weighted_linearity_inputoutput_table. (((H) = (((((dst_positive_code_weighted_linearity_inputoutput_table) + (dst_positive_scale_weighted_linearity_inputoutput_table)) * S ((dst_positive_code_weighted_linearity_inputoutput_table) + (dst_positive_scale_weighted_linearity_inputoutput_table)) + ((dst_positive_scale_weighted_linearity_inputoutput_table) + (dst_positive_scale_weighted_linearity_inputoutput_table))) + (((dst_negative_code_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)) * S ((dst_negative_code_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)) + ((dst_negative_scale_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)))) * S ((((dst_positive_code_weighted_linearity_inputoutput_table) + (dst_positive_scale_weighted_linearity_inputoutput_table)) * S ((dst_positive_code_weighted_linearity_inputoutput_table) + (dst_positive_scale_weighted_linearity_inputoutput_table)) + ((dst_positive_scale_weighted_linearity_inputoutput_table) + (dst_positive_scale_weighted_linearity_inputoutput_table))) + (((dst_negative_code_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)) * S ((dst_negative_code_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)) + ((dst_negative_scale_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)))) + ((((dst_negative_code_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)) * S ((dst_negative_code_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)) + ((dst_negative_scale_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table))) + (((dst_negative_code_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)) * S ((dst_negative_code_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)) + ((dst_negative_scale_weighted_linearity_inputoutput_table) + (dst_negative_scale_weighted_linearity_inputoutput_table)))))) /\ (forall dst_index_weighted_linearity_inputoutput_table. (exists pvs_le_gap_weighted_linearity_inputoutput_tabledomain. pvs_le_gap_weighted_linearity_inputoutput_tabledomain + (dst_index_weighted_linearity_inputoutput_table) = (l)) -> exists dst_positive_weighted_linearity_inputoutput_table dst_negative_weighted_linearity_inputoutput_table dst_value_weighted_linearity_inputoutput_table. ((((exists ff_h_pvs_weighted_linearity_inputoutput_tableentrypositive. ff_h_pvs_weighted_linearity_inputoutput_tableentrypositive + S (dst_positive_weighted_linearity_inputoutput_table) = S ((S (dst_index_weighted_linearity_inputoutput_table)) * dst_positive_scale_weighted_linearity_inputoutput_table)) /\ exists ff_q_pvs_weighted_linearity_inputoutput_tableentrypositive. dst_positive_code_weighted_linearity_inputoutput_table = ff_q_pvs_weighted_linearity_inputoutput_tableentrypositive * S ((S (dst_index_weighted_linearity_inputoutput_table)) * dst_positive_scale_weighted_linearity_inputoutput_table) + (dst_positive_weighted_linearity_inputoutput_table))) /\ (((((exists ff_h_pvs_weighted_linearity_inputoutput_tableentrynegative. ff_h_pvs_weighted_linearity_inputoutput_tableentrynegative + S (dst_negative_weighted_linearity_inputoutput_table) = S ((S (dst_index_weighted_linearity_inputoutput_table)) * dst_negative_scale_weighted_linearity_inputoutput_table)) /\ exists ff_q_pvs_weighted_linearity_inputoutput_tableentrynegative. dst_negative_code_weighted_linearity_inputoutput_table = ff_q_pvs_weighted_linearity_inputoutput_tableentrynegative * S ((S (dst_index_weighted_linearity_inputoutput_table)) * dst_negative_scale_weighted_linearity_inputoutput_table) + (dst_negative_weighted_linearity_inputoutput_table))) /\ (exists ge_balance_positive_weighted_linearity_inputoutput_tableentryvalue ge_balance_negative_weighted_linearity_inputoutput_tableentryvalue. (((((dst_value_weighted_linearity_inputoutput_table) = 2 * (ge_balance_positive_weighted_linearity_inputoutput_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_inputoutput_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_inputoutput_tableentryvaluedecode. (((dst_value_weighted_linearity_inputoutput_table) = 2 * ge_signed_half_weighted_linearity_inputoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_inputoutput_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_inputoutput_tableentryvalue) = S ge_signed_half_weighted_linearity_inputoutput_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_inputoutput_table) + ge_balance_negative_weighted_linearity_inputoutput_tableentryvalue = (dst_negative_weighted_linearity_inputoutput_table) + ge_balance_positive_weighted_linearity_inputoutput_tableentryvalue))))))))) /\ (forall sto_index_weighted_linearity_inputentries. (exists pvs_gap_weighted_linearity_inputentriesbound. pvs_gap_weighted_linearity_inputentriesbound + S (sto_index_weighted_linearity_inputentries) = (l)) -> exists sto_left_weighted_linearity_inputentries sto_right_weighted_linearity_inputentries sto_output_weighted_linearity_inputentries. ((exists dst_positive_code_weighted_linearity_inputentriesentryleft dst_positive_scale_weighted_linearity_inputentriesentryleft dst_negative_code_weighted_linearity_inputentriesentryleft dst_negative_scale_weighted_linearity_inputentriesentryleft dst_positive_weighted_linearity_inputentriesentryleft dst_negative_weighted_linearity_inputentriesentryleft. (((F) = (((((dst_positive_code_weighted_linearity_inputentriesentryleft) + (dst_positive_scale_weighted_linearity_inputentriesentryleft)) * S ((dst_positive_code_weighted_linearity_inputentriesentryleft) + (dst_positive_scale_weighted_linearity_inputentriesentryleft)) + ((dst_positive_scale_weighted_linearity_inputentriesentryleft) + (dst_positive_scale_weighted_linearity_inputentriesentryleft))) + (((dst_negative_code_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)) * S ((dst_negative_code_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)) + ((dst_negative_scale_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)))) * S ((((dst_positive_code_weighted_linearity_inputentriesentryleft) + (dst_positive_scale_weighted_linearity_inputentriesentryleft)) * S ((dst_positive_code_weighted_linearity_inputentriesentryleft) + (dst_positive_scale_weighted_linearity_inputentriesentryleft)) + ((dst_positive_scale_weighted_linearity_inputentriesentryleft) + (dst_positive_scale_weighted_linearity_inputentriesentryleft))) + (((dst_negative_code_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)) * S ((dst_negative_code_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)) + ((dst_negative_scale_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)))) + ((((dst_negative_code_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)) * S ((dst_negative_code_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)) + ((dst_negative_scale_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft))) + (((dst_negative_code_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)) * S ((dst_negative_code_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)) + ((dst_negative_scale_weighted_linearity_inputentriesentryleft) + (dst_negative_scale_weighted_linearity_inputentriesentryleft)))))) /\ (((((exists ff_h_pvs_weighted_linearity_inputentriesentryleftpositive. ff_h_pvs_weighted_linearity_inputentriesentryleftpositive + S (dst_positive_weighted_linearity_inputentriesentryleft) = S ((S (sto_index_weighted_linearity_inputentries)) * dst_positive_scale_weighted_linearity_inputentriesentryleft)) /\ exists ff_q_pvs_weighted_linearity_inputentriesentryleftpositive. dst_positive_code_weighted_linearity_inputentriesentryleft = ff_q_pvs_weighted_linearity_inputentriesentryleftpositive * S ((S (sto_index_weighted_linearity_inputentries)) * dst_positive_scale_weighted_linearity_inputentriesentryleft) + (dst_positive_weighted_linearity_inputentriesentryleft))) /\ (((((exists ff_h_pvs_weighted_linearity_inputentriesentryleftnegative. ff_h_pvs_weighted_linearity_inputentriesentryleftnegative + S (dst_negative_weighted_linearity_inputentriesentryleft) = S ((S (sto_index_weighted_linearity_inputentries)) * dst_negative_scale_weighted_linearity_inputentriesentryleft)) /\ exists ff_q_pvs_weighted_linearity_inputentriesentryleftnegative. dst_negative_code_weighted_linearity_inputentriesentryleft = ff_q_pvs_weighted_linearity_inputentriesentryleftnegative * S ((S (sto_index_weighted_linearity_inputentries)) * dst_negative_scale_weighted_linearity_inputentriesentryleft) + (dst_negative_weighted_linearity_inputentriesentryleft))) /\ (exists ge_balance_positive_weighted_linearity_inputentriesentryleftvalue ge_balance_negative_weighted_linearity_inputentriesentryleftvalue. (((((sto_left_weighted_linearity_inputentries) = 2 * (ge_balance_positive_weighted_linearity_inputentriesentryleftvalue) /\ (ge_balance_negative_weighted_linearity_inputentriesentryleftvalue) = 0) \/ exists ge_signed_half_weighted_linearity_inputentriesentryleftvaluedecode. (((sto_left_weighted_linearity_inputentries) = 2 * ge_signed_half_weighted_linearity_inputentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_inputentriesentryleftvalue) = 0) /\ (ge_balance_negative_weighted_linearity_inputentriesentryleftvalue) = S ge_signed_half_weighted_linearity_inputentriesentryleftvaluedecode))) /\ ((dst_positive_weighted_linearity_inputentriesentryleft) + ge_balance_negative_weighted_linearity_inputentriesentryleftvalue = (dst_negative_weighted_linearity_inputentriesentryleft) + ge_balance_positive_weighted_linearity_inputentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_inputentriesentryright dst_positive_scale_weighted_linearity_inputentriesentryright dst_negative_code_weighted_linearity_inputentriesentryright dst_negative_scale_weighted_linearity_inputentriesentryright dst_positive_weighted_linearity_inputentriesentryright dst_negative_weighted_linearity_inputentriesentryright. (((G) = (((((dst_positive_code_weighted_linearity_inputentriesentryright) + (dst_positive_scale_weighted_linearity_inputentriesentryright)) * S ((dst_positive_code_weighted_linearity_inputentriesentryright) + (dst_positive_scale_weighted_linearity_inputentriesentryright)) + ((dst_positive_scale_weighted_linearity_inputentriesentryright) + (dst_positive_scale_weighted_linearity_inputentriesentryright))) + (((dst_negative_code_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)) * S ((dst_negative_code_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)) + ((dst_negative_scale_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)))) * S ((((dst_positive_code_weighted_linearity_inputentriesentryright) + (dst_positive_scale_weighted_linearity_inputentriesentryright)) * S ((dst_positive_code_weighted_linearity_inputentriesentryright) + (dst_positive_scale_weighted_linearity_inputentriesentryright)) + ((dst_positive_scale_weighted_linearity_inputentriesentryright) + (dst_positive_scale_weighted_linearity_inputentriesentryright))) + (((dst_negative_code_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)) * S ((dst_negative_code_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)) + ((dst_negative_scale_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)))) + ((((dst_negative_code_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)) * S ((dst_negative_code_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)) + ((dst_negative_scale_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright))) + (((dst_negative_code_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)) * S ((dst_negative_code_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)) + ((dst_negative_scale_weighted_linearity_inputentriesentryright) + (dst_negative_scale_weighted_linearity_inputentriesentryright)))))) /\ (((((exists ff_h_pvs_weighted_linearity_inputentriesentryrightpositive. ff_h_pvs_weighted_linearity_inputentriesentryrightpositive + S (dst_positive_weighted_linearity_inputentriesentryright) = S ((S (sto_index_weighted_linearity_inputentries)) * dst_positive_scale_weighted_linearity_inputentriesentryright)) /\ exists ff_q_pvs_weighted_linearity_inputentriesentryrightpositive. dst_positive_code_weighted_linearity_inputentriesentryright = ff_q_pvs_weighted_linearity_inputentriesentryrightpositive * S ((S (sto_index_weighted_linearity_inputentries)) * dst_positive_scale_weighted_linearity_inputentriesentryright) + (dst_positive_weighted_linearity_inputentriesentryright))) /\ (((((exists ff_h_pvs_weighted_linearity_inputentriesentryrightnegative. ff_h_pvs_weighted_linearity_inputentriesentryrightnegative + S (dst_negative_weighted_linearity_inputentriesentryright) = S ((S (sto_index_weighted_linearity_inputentries)) * dst_negative_scale_weighted_linearity_inputentriesentryright)) /\ exists ff_q_pvs_weighted_linearity_inputentriesentryrightnegative. dst_negative_code_weighted_linearity_inputentriesentryright = ff_q_pvs_weighted_linearity_inputentriesentryrightnegative * S ((S (sto_index_weighted_linearity_inputentries)) * dst_negative_scale_weighted_linearity_inputentriesentryright) + (dst_negative_weighted_linearity_inputentriesentryright))) /\ (exists ge_balance_positive_weighted_linearity_inputentriesentryrightvalue ge_balance_negative_weighted_linearity_inputentriesentryrightvalue. (((((sto_right_weighted_linearity_inputentries) = 2 * (ge_balance_positive_weighted_linearity_inputentriesentryrightvalue) /\ (ge_balance_negative_weighted_linearity_inputentriesentryrightvalue) = 0) \/ exists ge_signed_half_weighted_linearity_inputentriesentryrightvaluedecode. (((sto_right_weighted_linearity_inputentries) = 2 * ge_signed_half_weighted_linearity_inputentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_inputentriesentryrightvalue) = 0) /\ (ge_balance_negative_weighted_linearity_inputentriesentryrightvalue) = S ge_signed_half_weighted_linearity_inputentriesentryrightvaluedecode))) /\ ((dst_positive_weighted_linearity_inputentriesentryright) + ge_balance_negative_weighted_linearity_inputentriesentryrightvalue = (dst_negative_weighted_linearity_inputentriesentryright) + ge_balance_positive_weighted_linearity_inputentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_inputentriesentryoutput dst_positive_scale_weighted_linearity_inputentriesentryoutput dst_negative_code_weighted_linearity_inputentriesentryoutput dst_negative_scale_weighted_linearity_inputentriesentryoutput dst_positive_weighted_linearity_inputentriesentryoutput dst_negative_weighted_linearity_inputentriesentryoutput. (((H) = (((((dst_positive_code_weighted_linearity_inputentriesentryoutput) + (dst_positive_scale_weighted_linearity_inputentriesentryoutput)) * S ((dst_positive_code_weighted_linearity_inputentriesentryoutput) + (dst_positive_scale_weighted_linearity_inputentriesentryoutput)) + ((dst_positive_scale_weighted_linearity_inputentriesentryoutput) + (dst_positive_scale_weighted_linearity_inputentriesentryoutput))) + (((dst_negative_code_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)))) * S ((((dst_positive_code_weighted_linearity_inputentriesentryoutput) + (dst_positive_scale_weighted_linearity_inputentriesentryoutput)) * S ((dst_positive_code_weighted_linearity_inputentriesentryoutput) + (dst_positive_scale_weighted_linearity_inputentriesentryoutput)) + ((dst_positive_scale_weighted_linearity_inputentriesentryoutput) + (dst_positive_scale_weighted_linearity_inputentriesentryoutput))) + (((dst_negative_code_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)))) + ((((dst_negative_code_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput))) + (((dst_negative_code_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_inputentriesentryoutput) + (dst_negative_scale_weighted_linearity_inputentriesentryoutput)))))) /\ (((((exists ff_h_pvs_weighted_linearity_inputentriesentryoutputpositive. ff_h_pvs_weighted_linearity_inputentriesentryoutputpositive + S (dst_positive_weighted_linearity_inputentriesentryoutput) = S ((S (sto_index_weighted_linearity_inputentries)) * dst_positive_scale_weighted_linearity_inputentriesentryoutput)) /\ exists ff_q_pvs_weighted_linearity_inputentriesentryoutputpositive. dst_positive_code_weighted_linearity_inputentriesentryoutput = ff_q_pvs_weighted_linearity_inputentriesentryoutputpositive * S ((S (sto_index_weighted_linearity_inputentries)) * dst_positive_scale_weighted_linearity_inputentriesentryoutput) + (dst_positive_weighted_linearity_inputentriesentryoutput))) /\ (((((exists ff_h_pvs_weighted_linearity_inputentriesentryoutputnegative. ff_h_pvs_weighted_linearity_inputentriesentryoutputnegative + S (dst_negative_weighted_linearity_inputentriesentryoutput) = S ((S (sto_index_weighted_linearity_inputentries)) * dst_negative_scale_weighted_linearity_inputentriesentryoutput)) /\ exists ff_q_pvs_weighted_linearity_inputentriesentryoutputnegative. dst_negative_code_weighted_linearity_inputentriesentryoutput = ff_q_pvs_weighted_linearity_inputentriesentryoutputnegative * S ((S (sto_index_weighted_linearity_inputentries)) * dst_negative_scale_weighted_linearity_inputentriesentryoutput) + (dst_negative_weighted_linearity_inputentriesentryoutput))) /\ (exists ge_balance_positive_weighted_linearity_inputentriesentryoutputvalue ge_balance_negative_weighted_linearity_inputentriesentryoutputvalue. (((((sto_output_weighted_linearity_inputentries) = 2 * (ge_balance_positive_weighted_linearity_inputentriesentryoutputvalue) /\ (ge_balance_negative_weighted_linearity_inputentriesentryoutputvalue) = 0) \/ exists ge_signed_half_weighted_linearity_inputentriesentryoutputvaluedecode. (((sto_output_weighted_linearity_inputentries) = 2 * ge_signed_half_weighted_linearity_inputentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_inputentriesentryoutputvalue) = 0) /\ (ge_balance_negative_weighted_linearity_inputentriesentryoutputvalue) = S ge_signed_half_weighted_linearity_inputentriesentryoutputvaluedecode))) /\ ((dst_positive_weighted_linearity_inputentriesentryoutput) + ge_balance_negative_weighted_linearity_inputentriesentryoutputvalue = (dst_negative_weighted_linearity_inputentriesentryoutput) + ge_balance_positive_weighted_linearity_inputentriesentryoutputvalue))))))))) /\ (exists dsa_ap_weighted_linearity_inputentriesentryoperation dsa_an_weighted_linearity_inputentriesentryoperation dsa_bp_weighted_linearity_inputentriesentryoperation dsa_bn_weighted_linearity_inputentriesentryoperation dsa_cp_weighted_linearity_inputentriesentryoperation dsa_cn_weighted_linearity_inputentriesentryoperation. (((((sto_left_weighted_linearity_inputentries) = 2 * (dsa_ap_weighted_linearity_inputentriesentryoperation) /\ (dsa_an_weighted_linearity_inputentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_inputentriesentryoperationleft. (((sto_left_weighted_linearity_inputentries) = 2 * ge_signed_half_weighted_linearity_inputentriesentryoperationleft + 1 /\ (dsa_ap_weighted_linearity_inputentriesentryoperation) = 0) /\ (dsa_an_weighted_linearity_inputentriesentryoperation) = S ge_signed_half_weighted_linearity_inputentriesentryoperationleft))) /\ ((((((sto_right_weighted_linearity_inputentries) = 2 * (dsa_bp_weighted_linearity_inputentriesentryoperation) /\ (dsa_bn_weighted_linearity_inputentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_inputentriesentryoperationright. (((sto_right_weighted_linearity_inputentries) = 2 * ge_signed_half_weighted_linearity_inputentriesentryoperationright + 1 /\ (dsa_bp_weighted_linearity_inputentriesentryoperation) = 0) /\ (dsa_bn_weighted_linearity_inputentriesentryoperation) = S ge_signed_half_weighted_linearity_inputentriesentryoperationright))) /\ ((((((sto_output_weighted_linearity_inputentries) = 2 * (dsa_cp_weighted_linearity_inputentriesentryoperation) /\ (dsa_cn_weighted_linearity_inputentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_inputentriesentryoperationoutput. (((sto_output_weighted_linearity_inputentries) = 2 * ge_signed_half_weighted_linearity_inputentriesentryoperationoutput + 1 /\ (dsa_cp_weighted_linearity_inputentriesentryoperation) = 0) /\ (dsa_cn_weighted_linearity_inputentriesentryoperation) = S ge_signed_half_weighted_linearity_inputentriesentryoperationoutput))) /\ ((dsa_ap_weighted_linearity_inputentriesentryoperation + dsa_bp_weighted_linearity_inputentriesentryoperation) + dsa_cn_weighted_linearity_inputentriesentryoperation = (dsa_an_weighted_linearity_inputentriesentryoperation + dsa_bn_weighted_linearity_inputentriesentryoperation) + dsa_cp_weighted_linearity_inputentriesentryoperation))))))))))))))))))) -> (exists sws_product_table_weighted_linearity_first. ((((exists dst_positive_code_weighted_linearity_firstproductsleft_table dst_positive_scale_weighted_linearity_firstproductsleft_table dst_negative_code_weighted_linearity_firstproductsleft_table dst_negative_scale_weighted_linearity_firstproductsleft_table. (((W) = (((((dst_positive_code_weighted_linearity_firstproductsleft_table) + (dst_positive_scale_weighted_linearity_firstproductsleft_table)) * S ((dst_positive_code_weighted_linearity_firstproductsleft_table) + (dst_positive_scale_weighted_linearity_firstproductsleft_table)) + ((dst_positive_scale_weighted_linearity_firstproductsleft_table) + (dst_positive_scale_weighted_linearity_firstproductsleft_table))) + (((dst_negative_code_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)) * S ((dst_negative_code_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)) + ((dst_negative_scale_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)))) * S ((((dst_positive_code_weighted_linearity_firstproductsleft_table) + (dst_positive_scale_weighted_linearity_firstproductsleft_table)) * S ((dst_positive_code_weighted_linearity_firstproductsleft_table) + (dst_positive_scale_weighted_linearity_firstproductsleft_table)) + ((dst_positive_scale_weighted_linearity_firstproductsleft_table) + (dst_positive_scale_weighted_linearity_firstproductsleft_table))) + (((dst_negative_code_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)) * S ((dst_negative_code_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)) + ((dst_negative_scale_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)))) + ((((dst_negative_code_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)) * S ((dst_negative_code_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)) + ((dst_negative_scale_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table))) + (((dst_negative_code_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)) * S ((dst_negative_code_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)) + ((dst_negative_scale_weighted_linearity_firstproductsleft_table) + (dst_negative_scale_weighted_linearity_firstproductsleft_table)))))) /\ (forall dst_index_weighted_linearity_firstproductsleft_table. (exists pvs_le_gap_weighted_linearity_firstproductsleft_tabledomain. pvs_le_gap_weighted_linearity_firstproductsleft_tabledomain + (dst_index_weighted_linearity_firstproductsleft_table) = (l)) -> exists dst_positive_weighted_linearity_firstproductsleft_table dst_negative_weighted_linearity_firstproductsleft_table dst_value_weighted_linearity_firstproductsleft_table. ((((exists ff_h_pvs_weighted_linearity_firstproductsleft_tableentrypositive. ff_h_pvs_weighted_linearity_firstproductsleft_tableentrypositive + S (dst_positive_weighted_linearity_firstproductsleft_table) = S ((S (dst_index_weighted_linearity_firstproductsleft_table)) * dst_positive_scale_weighted_linearity_firstproductsleft_table)) /\ exists ff_q_pvs_weighted_linearity_firstproductsleft_tableentrypositive. dst_positive_code_weighted_linearity_firstproductsleft_table = ff_q_pvs_weighted_linearity_firstproductsleft_tableentrypositive * S ((S (dst_index_weighted_linearity_firstproductsleft_table)) * dst_positive_scale_weighted_linearity_firstproductsleft_table) + (dst_positive_weighted_linearity_firstproductsleft_table))) /\ (((((exists ff_h_pvs_weighted_linearity_firstproductsleft_tableentrynegative. ff_h_pvs_weighted_linearity_firstproductsleft_tableentrynegative + S (dst_negative_weighted_linearity_firstproductsleft_table) = S ((S (dst_index_weighted_linearity_firstproductsleft_table)) * dst_negative_scale_weighted_linearity_firstproductsleft_table)) /\ exists ff_q_pvs_weighted_linearity_firstproductsleft_tableentrynegative. dst_negative_code_weighted_linearity_firstproductsleft_table = ff_q_pvs_weighted_linearity_firstproductsleft_tableentrynegative * S ((S (dst_index_weighted_linearity_firstproductsleft_table)) * dst_negative_scale_weighted_linearity_firstproductsleft_table) + (dst_negative_weighted_linearity_firstproductsleft_table))) /\ (exists ge_balance_positive_weighted_linearity_firstproductsleft_tableentryvalue ge_balance_negative_weighted_linearity_firstproductsleft_tableentryvalue. (((((dst_value_weighted_linearity_firstproductsleft_table) = 2 * (ge_balance_positive_weighted_linearity_firstproductsleft_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_firstproductsleft_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_firstproductsleft_tableentryvaluedecode. (((dst_value_weighted_linearity_firstproductsleft_table) = 2 * ge_signed_half_weighted_linearity_firstproductsleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_firstproductsleft_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_firstproductsleft_tableentryvalue) = S ge_signed_half_weighted_linearity_firstproductsleft_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_firstproductsleft_table) + ge_balance_negative_weighted_linearity_firstproductsleft_tableentryvalue = (dst_negative_weighted_linearity_firstproductsleft_table) + ge_balance_positive_weighted_linearity_firstproductsleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_firstproductsright_table dst_positive_scale_weighted_linearity_firstproductsright_table dst_negative_code_weighted_linearity_firstproductsright_table dst_negative_scale_weighted_linearity_firstproductsright_table. (((F) = (((((dst_positive_code_weighted_linearity_firstproductsright_table) + (dst_positive_scale_weighted_linearity_firstproductsright_table)) * S ((dst_positive_code_weighted_linearity_firstproductsright_table) + (dst_positive_scale_weighted_linearity_firstproductsright_table)) + ((dst_positive_scale_weighted_linearity_firstproductsright_table) + (dst_positive_scale_weighted_linearity_firstproductsright_table))) + (((dst_negative_code_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)) * S ((dst_negative_code_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)) + ((dst_negative_scale_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)))) * S ((((dst_positive_code_weighted_linearity_firstproductsright_table) + (dst_positive_scale_weighted_linearity_firstproductsright_table)) * S ((dst_positive_code_weighted_linearity_firstproductsright_table) + (dst_positive_scale_weighted_linearity_firstproductsright_table)) + ((dst_positive_scale_weighted_linearity_firstproductsright_table) + (dst_positive_scale_weighted_linearity_firstproductsright_table))) + (((dst_negative_code_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)) * S ((dst_negative_code_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)) + ((dst_negative_scale_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)))) + ((((dst_negative_code_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)) * S ((dst_negative_code_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)) + ((dst_negative_scale_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table))) + (((dst_negative_code_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)) * S ((dst_negative_code_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)) + ((dst_negative_scale_weighted_linearity_firstproductsright_table) + (dst_negative_scale_weighted_linearity_firstproductsright_table)))))) /\ (forall dst_index_weighted_linearity_firstproductsright_table. (exists pvs_le_gap_weighted_linearity_firstproductsright_tabledomain. pvs_le_gap_weighted_linearity_firstproductsright_tabledomain + (dst_index_weighted_linearity_firstproductsright_table) = (l)) -> exists dst_positive_weighted_linearity_firstproductsright_table dst_negative_weighted_linearity_firstproductsright_table dst_value_weighted_linearity_firstproductsright_table. ((((exists ff_h_pvs_weighted_linearity_firstproductsright_tableentrypositive. ff_h_pvs_weighted_linearity_firstproductsright_tableentrypositive + S (dst_positive_weighted_linearity_firstproductsright_table) = S ((S (dst_index_weighted_linearity_firstproductsright_table)) * dst_positive_scale_weighted_linearity_firstproductsright_table)) /\ exists ff_q_pvs_weighted_linearity_firstproductsright_tableentrypositive. dst_positive_code_weighted_linearity_firstproductsright_table = ff_q_pvs_weighted_linearity_firstproductsright_tableentrypositive * S ((S (dst_index_weighted_linearity_firstproductsright_table)) * dst_positive_scale_weighted_linearity_firstproductsright_table) + (dst_positive_weighted_linearity_firstproductsright_table))) /\ (((((exists ff_h_pvs_weighted_linearity_firstproductsright_tableentrynegative. ff_h_pvs_weighted_linearity_firstproductsright_tableentrynegative + S (dst_negative_weighted_linearity_firstproductsright_table) = S ((S (dst_index_weighted_linearity_firstproductsright_table)) * dst_negative_scale_weighted_linearity_firstproductsright_table)) /\ exists ff_q_pvs_weighted_linearity_firstproductsright_tableentrynegative. dst_negative_code_weighted_linearity_firstproductsright_table = ff_q_pvs_weighted_linearity_firstproductsright_tableentrynegative * S ((S (dst_index_weighted_linearity_firstproductsright_table)) * dst_negative_scale_weighted_linearity_firstproductsright_table) + (dst_negative_weighted_linearity_firstproductsright_table))) /\ (exists ge_balance_positive_weighted_linearity_firstproductsright_tableentryvalue ge_balance_negative_weighted_linearity_firstproductsright_tableentryvalue. (((((dst_value_weighted_linearity_firstproductsright_table) = 2 * (ge_balance_positive_weighted_linearity_firstproductsright_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_firstproductsright_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_firstproductsright_tableentryvaluedecode. (((dst_value_weighted_linearity_firstproductsright_table) = 2 * ge_signed_half_weighted_linearity_firstproductsright_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_firstproductsright_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_firstproductsright_tableentryvalue) = S ge_signed_half_weighted_linearity_firstproductsright_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_firstproductsright_table) + ge_balance_negative_weighted_linearity_firstproductsright_tableentryvalue = (dst_negative_weighted_linearity_firstproductsright_table) + ge_balance_positive_weighted_linearity_firstproductsright_tableentryvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_firstproductsoutput_table dst_positive_scale_weighted_linearity_firstproductsoutput_table dst_negative_code_weighted_linearity_firstproductsoutput_table dst_negative_scale_weighted_linearity_firstproductsoutput_table. (((sws_product_table_weighted_linearity_first) = (((((dst_positive_code_weighted_linearity_firstproductsoutput_table) + (dst_positive_scale_weighted_linearity_firstproductsoutput_table)) * S ((dst_positive_code_weighted_linearity_firstproductsoutput_table) + (dst_positive_scale_weighted_linearity_firstproductsoutput_table)) + ((dst_positive_scale_weighted_linearity_firstproductsoutput_table) + (dst_positive_scale_weighted_linearity_firstproductsoutput_table))) + (((dst_negative_code_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)))) * S ((((dst_positive_code_weighted_linearity_firstproductsoutput_table) + (dst_positive_scale_weighted_linearity_firstproductsoutput_table)) * S ((dst_positive_code_weighted_linearity_firstproductsoutput_table) + (dst_positive_scale_weighted_linearity_firstproductsoutput_table)) + ((dst_positive_scale_weighted_linearity_firstproductsoutput_table) + (dst_positive_scale_weighted_linearity_firstproductsoutput_table))) + (((dst_negative_code_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)))) + ((((dst_negative_code_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table))) + (((dst_negative_code_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_firstproductsoutput_table) + (dst_negative_scale_weighted_linearity_firstproductsoutput_table)))))) /\ (forall dst_index_weighted_linearity_firstproductsoutput_table. (exists pvs_le_gap_weighted_linearity_firstproductsoutput_tabledomain. pvs_le_gap_weighted_linearity_firstproductsoutput_tabledomain + (dst_index_weighted_linearity_firstproductsoutput_table) = (l)) -> exists dst_positive_weighted_linearity_firstproductsoutput_table dst_negative_weighted_linearity_firstproductsoutput_table dst_value_weighted_linearity_firstproductsoutput_table. ((((exists ff_h_pvs_weighted_linearity_firstproductsoutput_tableentrypositive. ff_h_pvs_weighted_linearity_firstproductsoutput_tableentrypositive + S (dst_positive_weighted_linearity_firstproductsoutput_table) = S ((S (dst_index_weighted_linearity_firstproductsoutput_table)) * dst_positive_scale_weighted_linearity_firstproductsoutput_table)) /\ exists ff_q_pvs_weighted_linearity_firstproductsoutput_tableentrypositive. dst_positive_code_weighted_linearity_firstproductsoutput_table = ff_q_pvs_weighted_linearity_firstproductsoutput_tableentrypositive * S ((S (dst_index_weighted_linearity_firstproductsoutput_table)) * dst_positive_scale_weighted_linearity_firstproductsoutput_table) + (dst_positive_weighted_linearity_firstproductsoutput_table))) /\ (((((exists ff_h_pvs_weighted_linearity_firstproductsoutput_tableentrynegative. ff_h_pvs_weighted_linearity_firstproductsoutput_tableentrynegative + S (dst_negative_weighted_linearity_firstproductsoutput_table) = S ((S (dst_index_weighted_linearity_firstproductsoutput_table)) * dst_negative_scale_weighted_linearity_firstproductsoutput_table)) /\ exists ff_q_pvs_weighted_linearity_firstproductsoutput_tableentrynegative. dst_negative_code_weighted_linearity_firstproductsoutput_table = ff_q_pvs_weighted_linearity_firstproductsoutput_tableentrynegative * S ((S (dst_index_weighted_linearity_firstproductsoutput_table)) * dst_negative_scale_weighted_linearity_firstproductsoutput_table) + (dst_negative_weighted_linearity_firstproductsoutput_table))) /\ (exists ge_balance_positive_weighted_linearity_firstproductsoutput_tableentryvalue ge_balance_negative_weighted_linearity_firstproductsoutput_tableentryvalue. (((((dst_value_weighted_linearity_firstproductsoutput_table) = 2 * (ge_balance_positive_weighted_linearity_firstproductsoutput_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_firstproductsoutput_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_firstproductsoutput_tableentryvaluedecode. (((dst_value_weighted_linearity_firstproductsoutput_table) = 2 * ge_signed_half_weighted_linearity_firstproductsoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_firstproductsoutput_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_firstproductsoutput_tableentryvalue) = S ge_signed_half_weighted_linearity_firstproductsoutput_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_firstproductsoutput_table) + ge_balance_negative_weighted_linearity_firstproductsoutput_tableentryvalue = (dst_negative_weighted_linearity_firstproductsoutput_table) + ge_balance_positive_weighted_linearity_firstproductsoutput_tableentryvalue))))))))) /\ (forall sto_index_weighted_linearity_firstproductsentries. (exists pvs_gap_weighted_linearity_firstproductsentriesbound. pvs_gap_weighted_linearity_firstproductsentriesbound + S (sto_index_weighted_linearity_firstproductsentries) = (l)) -> exists sto_left_weighted_linearity_firstproductsentries sto_right_weighted_linearity_firstproductsentries sto_output_weighted_linearity_firstproductsentries. ((exists dst_positive_code_weighted_linearity_firstproductsentriesentryleft dst_positive_scale_weighted_linearity_firstproductsentriesentryleft dst_negative_code_weighted_linearity_firstproductsentriesentryleft dst_negative_scale_weighted_linearity_firstproductsentriesentryleft dst_positive_weighted_linearity_firstproductsentriesentryleft dst_negative_weighted_linearity_firstproductsentriesentryleft. (((W) = (((((dst_positive_code_weighted_linearity_firstproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryleft)) * S ((dst_positive_code_weighted_linearity_firstproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryleft)) + ((dst_positive_scale_weighted_linearity_firstproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryleft))) + (((dst_negative_code_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)))) * S ((((dst_positive_code_weighted_linearity_firstproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryleft)) * S ((dst_positive_code_weighted_linearity_firstproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryleft)) + ((dst_positive_scale_weighted_linearity_firstproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryleft))) + (((dst_negative_code_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)))) + ((((dst_negative_code_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft))) + (((dst_negative_code_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)))))) /\ (((((exists ff_h_pvs_weighted_linearity_firstproductsentriesentryleftpositive. ff_h_pvs_weighted_linearity_firstproductsentriesentryleftpositive + S (dst_positive_weighted_linearity_firstproductsentriesentryleft) = S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_positive_scale_weighted_linearity_firstproductsentriesentryleft)) /\ exists ff_q_pvs_weighted_linearity_firstproductsentriesentryleftpositive. dst_positive_code_weighted_linearity_firstproductsentriesentryleft = ff_q_pvs_weighted_linearity_firstproductsentriesentryleftpositive * S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_positive_scale_weighted_linearity_firstproductsentriesentryleft) + (dst_positive_weighted_linearity_firstproductsentriesentryleft))) /\ (((((exists ff_h_pvs_weighted_linearity_firstproductsentriesentryleftnegative. ff_h_pvs_weighted_linearity_firstproductsentriesentryleftnegative + S (dst_negative_weighted_linearity_firstproductsentriesentryleft) = S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_negative_scale_weighted_linearity_firstproductsentriesentryleft)) /\ exists ff_q_pvs_weighted_linearity_firstproductsentriesentryleftnegative. dst_negative_code_weighted_linearity_firstproductsentriesentryleft = ff_q_pvs_weighted_linearity_firstproductsentriesentryleftnegative * S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_negative_scale_weighted_linearity_firstproductsentriesentryleft) + (dst_negative_weighted_linearity_firstproductsentriesentryleft))) /\ (exists ge_balance_positive_weighted_linearity_firstproductsentriesentryleftvalue ge_balance_negative_weighted_linearity_firstproductsentriesentryleftvalue. (((((sto_left_weighted_linearity_firstproductsentries) = 2 * (ge_balance_positive_weighted_linearity_firstproductsentriesentryleftvalue) /\ (ge_balance_negative_weighted_linearity_firstproductsentriesentryleftvalue) = 0) \/ exists ge_signed_half_weighted_linearity_firstproductsentriesentryleftvaluedecode. (((sto_left_weighted_linearity_firstproductsentries) = 2 * ge_signed_half_weighted_linearity_firstproductsentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_firstproductsentriesentryleftvalue) = 0) /\ (ge_balance_negative_weighted_linearity_firstproductsentriesentryleftvalue) = S ge_signed_half_weighted_linearity_firstproductsentriesentryleftvaluedecode))) /\ ((dst_positive_weighted_linearity_firstproductsentriesentryleft) + ge_balance_negative_weighted_linearity_firstproductsentriesentryleftvalue = (dst_negative_weighted_linearity_firstproductsentriesentryleft) + ge_balance_positive_weighted_linearity_firstproductsentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_firstproductsentriesentryright dst_positive_scale_weighted_linearity_firstproductsentriesentryright dst_negative_code_weighted_linearity_firstproductsentriesentryright dst_negative_scale_weighted_linearity_firstproductsentriesentryright dst_positive_weighted_linearity_firstproductsentriesentryright dst_negative_weighted_linearity_firstproductsentriesentryright. (((F) = (((((dst_positive_code_weighted_linearity_firstproductsentriesentryright) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryright)) * S ((dst_positive_code_weighted_linearity_firstproductsentriesentryright) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryright)) + ((dst_positive_scale_weighted_linearity_firstproductsentriesentryright) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryright))) + (((dst_negative_code_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)))) * S ((((dst_positive_code_weighted_linearity_firstproductsentriesentryright) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryright)) * S ((dst_positive_code_weighted_linearity_firstproductsentriesentryright) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryright)) + ((dst_positive_scale_weighted_linearity_firstproductsentriesentryright) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryright))) + (((dst_negative_code_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)))) + ((((dst_negative_code_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright))) + (((dst_negative_code_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryright) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryright)))))) /\ (((((exists ff_h_pvs_weighted_linearity_firstproductsentriesentryrightpositive. ff_h_pvs_weighted_linearity_firstproductsentriesentryrightpositive + S (dst_positive_weighted_linearity_firstproductsentriesentryright) = S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_positive_scale_weighted_linearity_firstproductsentriesentryright)) /\ exists ff_q_pvs_weighted_linearity_firstproductsentriesentryrightpositive. dst_positive_code_weighted_linearity_firstproductsentriesentryright = ff_q_pvs_weighted_linearity_firstproductsentriesentryrightpositive * S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_positive_scale_weighted_linearity_firstproductsentriesentryright) + (dst_positive_weighted_linearity_firstproductsentriesentryright))) /\ (((((exists ff_h_pvs_weighted_linearity_firstproductsentriesentryrightnegative. ff_h_pvs_weighted_linearity_firstproductsentriesentryrightnegative + S (dst_negative_weighted_linearity_firstproductsentriesentryright) = S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_negative_scale_weighted_linearity_firstproductsentriesentryright)) /\ exists ff_q_pvs_weighted_linearity_firstproductsentriesentryrightnegative. dst_negative_code_weighted_linearity_firstproductsentriesentryright = ff_q_pvs_weighted_linearity_firstproductsentriesentryrightnegative * S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_negative_scale_weighted_linearity_firstproductsentriesentryright) + (dst_negative_weighted_linearity_firstproductsentriesentryright))) /\ (exists ge_balance_positive_weighted_linearity_firstproductsentriesentryrightvalue ge_balance_negative_weighted_linearity_firstproductsentriesentryrightvalue. (((((sto_right_weighted_linearity_firstproductsentries) = 2 * (ge_balance_positive_weighted_linearity_firstproductsentriesentryrightvalue) /\ (ge_balance_negative_weighted_linearity_firstproductsentriesentryrightvalue) = 0) \/ exists ge_signed_half_weighted_linearity_firstproductsentriesentryrightvaluedecode. (((sto_right_weighted_linearity_firstproductsentries) = 2 * ge_signed_half_weighted_linearity_firstproductsentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_firstproductsentriesentryrightvalue) = 0) /\ (ge_balance_negative_weighted_linearity_firstproductsentriesentryrightvalue) = S ge_signed_half_weighted_linearity_firstproductsentriesentryrightvaluedecode))) /\ ((dst_positive_weighted_linearity_firstproductsentriesentryright) + ge_balance_negative_weighted_linearity_firstproductsentriesentryrightvalue = (dst_negative_weighted_linearity_firstproductsentriesentryright) + ge_balance_positive_weighted_linearity_firstproductsentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_firstproductsentriesentryoutput dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput dst_negative_code_weighted_linearity_firstproductsentriesentryoutput dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput dst_positive_weighted_linearity_firstproductsentriesentryoutput dst_negative_weighted_linearity_firstproductsentriesentryoutput. (((sws_product_table_weighted_linearity_first) = (((((dst_positive_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput)) * S ((dst_positive_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput)) + ((dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput))) + (((dst_negative_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)))) * S ((((dst_positive_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput)) * S ((dst_positive_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput)) + ((dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput))) + (((dst_negative_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)))) + ((((dst_negative_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput))) + (((dst_negative_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)))))) /\ (((((exists ff_h_pvs_weighted_linearity_firstproductsentriesentryoutputpositive. ff_h_pvs_weighted_linearity_firstproductsentriesentryoutputpositive + S (dst_positive_weighted_linearity_firstproductsentriesentryoutput) = S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput)) /\ exists ff_q_pvs_weighted_linearity_firstproductsentriesentryoutputpositive. dst_positive_code_weighted_linearity_firstproductsentriesentryoutput = ff_q_pvs_weighted_linearity_firstproductsentriesentryoutputpositive * S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_positive_scale_weighted_linearity_firstproductsentriesentryoutput) + (dst_positive_weighted_linearity_firstproductsentriesentryoutput))) /\ (((((exists ff_h_pvs_weighted_linearity_firstproductsentriesentryoutputnegative. ff_h_pvs_weighted_linearity_firstproductsentriesentryoutputnegative + S (dst_negative_weighted_linearity_firstproductsentriesentryoutput) = S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput)) /\ exists ff_q_pvs_weighted_linearity_firstproductsentriesentryoutputnegative. dst_negative_code_weighted_linearity_firstproductsentriesentryoutput = ff_q_pvs_weighted_linearity_firstproductsentriesentryoutputnegative * S ((S (sto_index_weighted_linearity_firstproductsentries)) * dst_negative_scale_weighted_linearity_firstproductsentriesentryoutput) + (dst_negative_weighted_linearity_firstproductsentriesentryoutput))) /\ (exists ge_balance_positive_weighted_linearity_firstproductsentriesentryoutputvalue ge_balance_negative_weighted_linearity_firstproductsentriesentryoutputvalue. (((((sto_output_weighted_linearity_firstproductsentries) = 2 * (ge_balance_positive_weighted_linearity_firstproductsentriesentryoutputvalue) /\ (ge_balance_negative_weighted_linearity_firstproductsentriesentryoutputvalue) = 0) \/ exists ge_signed_half_weighted_linearity_firstproductsentriesentryoutputvaluedecode. (((sto_output_weighted_linearity_firstproductsentries) = 2 * ge_signed_half_weighted_linearity_firstproductsentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_firstproductsentriesentryoutputvalue) = 0) /\ (ge_balance_negative_weighted_linearity_firstproductsentriesentryoutputvalue) = S ge_signed_half_weighted_linearity_firstproductsentriesentryoutputvaluedecode))) /\ ((dst_positive_weighted_linearity_firstproductsentriesentryoutput) + ge_balance_negative_weighted_linearity_firstproductsentriesentryoutputvalue = (dst_negative_weighted_linearity_firstproductsentriesentryoutput) + ge_balance_positive_weighted_linearity_firstproductsentriesentryoutputvalue))))))))) /\ (exists sto_ap_weighted_linearity_firstproductsentriesentryoperation sto_an_weighted_linearity_firstproductsentriesentryoperation sto_bp_weighted_linearity_firstproductsentriesentryoperation sto_bn_weighted_linearity_firstproductsentriesentryoperation sto_cp_weighted_linearity_firstproductsentriesentryoperation sto_cn_weighted_linearity_firstproductsentriesentryoperation. (((((sto_left_weighted_linearity_firstproductsentries) = 2 * (sto_ap_weighted_linearity_firstproductsentriesentryoperation) /\ (sto_an_weighted_linearity_firstproductsentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_firstproductsentriesentryoperationleft. (((sto_left_weighted_linearity_firstproductsentries) = 2 * ge_signed_half_weighted_linearity_firstproductsentriesentryoperationleft + 1 /\ (sto_ap_weighted_linearity_firstproductsentriesentryoperation) = 0) /\ (sto_an_weighted_linearity_firstproductsentriesentryoperation) = S ge_signed_half_weighted_linearity_firstproductsentriesentryoperationleft))) /\ ((((((sto_right_weighted_linearity_firstproductsentries) = 2 * (sto_bp_weighted_linearity_firstproductsentriesentryoperation) /\ (sto_bn_weighted_linearity_firstproductsentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_firstproductsentriesentryoperationright. (((sto_right_weighted_linearity_firstproductsentries) = 2 * ge_signed_half_weighted_linearity_firstproductsentriesentryoperationright + 1 /\ (sto_bp_weighted_linearity_firstproductsentriesentryoperation) = 0) /\ (sto_bn_weighted_linearity_firstproductsentriesentryoperation) = S ge_signed_half_weighted_linearity_firstproductsentriesentryoperationright))) /\ ((((((sto_output_weighted_linearity_firstproductsentries) = 2 * (sto_cp_weighted_linearity_firstproductsentriesentryoperation) /\ (sto_cn_weighted_linearity_firstproductsentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_firstproductsentriesentryoperationoutput. (((sto_output_weighted_linearity_firstproductsentries) = 2 * ge_signed_half_weighted_linearity_firstproductsentriesentryoperationoutput + 1 /\ (sto_cp_weighted_linearity_firstproductsentriesentryoperation) = 0) /\ (sto_cn_weighted_linearity_firstproductsentriesentryoperation) = S ge_signed_half_weighted_linearity_firstproductsentriesentryoperationoutput))) /\ ((sto_ap_weighted_linearity_firstproductsentriesentryoperation * sto_bp_weighted_linearity_firstproductsentriesentryoperation + sto_an_weighted_linearity_firstproductsentriesentryoperation * sto_bn_weighted_linearity_firstproductsentriesentryoperation) + sto_cn_weighted_linearity_firstproductsentriesentryoperation = (sto_ap_weighted_linearity_firstproductsentriesentryoperation * sto_bn_weighted_linearity_firstproductsentriesentryoperation + sto_an_weighted_linearity_firstproductsentriesentryoperation * sto_bp_weighted_linearity_firstproductsentriesentryoperation) + sto_cp_weighted_linearity_firstproductsentriesentryoperation))))))))))))))))))) /\ (exists dst_positive_code_weighted_linearity_firstsum dst_positive_scale_weighted_linearity_firstsum dst_negative_code_weighted_linearity_firstsum dst_negative_scale_weighted_linearity_firstsum dst_positive_sum_weighted_linearity_firstsum dst_negative_sum_weighted_linearity_firstsum. (((sws_product_table_weighted_linearity_first) = (((((dst_positive_code_weighted_linearity_firstsum) + (dst_positive_scale_weighted_linearity_firstsum)) * S ((dst_positive_code_weighted_linearity_firstsum) + (dst_positive_scale_weighted_linearity_firstsum)) + ((dst_positive_scale_weighted_linearity_firstsum) + (dst_positive_scale_weighted_linearity_firstsum))) + (((dst_negative_code_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)) * S ((dst_negative_code_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)) + ((dst_negative_scale_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)))) * S ((((dst_positive_code_weighted_linearity_firstsum) + (dst_positive_scale_weighted_linearity_firstsum)) * S ((dst_positive_code_weighted_linearity_firstsum) + (dst_positive_scale_weighted_linearity_firstsum)) + ((dst_positive_scale_weighted_linearity_firstsum) + (dst_positive_scale_weighted_linearity_firstsum))) + (((dst_negative_code_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)) * S ((dst_negative_code_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)) + ((dst_negative_scale_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)))) + ((((dst_negative_code_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)) * S ((dst_negative_code_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)) + ((dst_negative_scale_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum))) + (((dst_negative_code_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)) * S ((dst_negative_code_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)) + ((dst_negative_scale_weighted_linearity_firstsum) + (dst_negative_scale_weighted_linearity_firstsum)))))) /\ (((exists fs_u_dst_weighted_linearity_firstsumpositive fs_v_dst_weighted_linearity_firstsumpositive. ((((exists fs_h_dst_weighted_linearity_firstsumpositive_body_start. fs_h_dst_weighted_linearity_firstsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_weighted_linearity_firstsumpositive)) /\ exists fs_q_dst_weighted_linearity_firstsumpositive_body_start. fs_u_dst_weighted_linearity_firstsumpositive = fs_q_dst_weighted_linearity_firstsumpositive_body_start * S ((S (0)) * fs_v_dst_weighted_linearity_firstsumpositive) + (0))) /\ ((((exists fs_h_dst_weighted_linearity_firstsumpositive_body_terminal. fs_h_dst_weighted_linearity_firstsumpositive_body_terminal + S (dst_positive_sum_weighted_linearity_firstsum) = S ((S (l)) * fs_v_dst_weighted_linearity_firstsumpositive)) /\ exists fs_q_dst_weighted_linearity_firstsumpositive_body_terminal. fs_u_dst_weighted_linearity_firstsumpositive = fs_q_dst_weighted_linearity_firstsumpositive_body_terminal * S ((S (l)) * fs_v_dst_weighted_linearity_firstsumpositive) + (dst_positive_sum_weighted_linearity_firstsum))) /\ forall fs_i_dst_weighted_linearity_firstsumpositive_body_steps. (exists fs_lt_dst_weighted_linearity_firstsumpositive_body_steps_bound. fs_lt_dst_weighted_linearity_firstsumpositive_body_steps_bound + S fs_i_dst_weighted_linearity_firstsumpositive_body_steps = l) -> exists fs_a_dst_weighted_linearity_firstsumpositive_body_steps fs_r_dst_weighted_linearity_firstsumpositive_body_steps fs_s_dst_weighted_linearity_firstsumpositive_body_steps. ((((exists fs_h_dst_weighted_linearity_firstsumpositive_body_steps_summand. fs_h_dst_weighted_linearity_firstsumpositive_body_steps_summand + S (fs_a_dst_weighted_linearity_firstsumpositive_body_steps) = S ((S (fs_i_dst_weighted_linearity_firstsumpositive_body_steps)) * dst_positive_scale_weighted_linearity_firstsum)) /\ exists fs_q_dst_weighted_linearity_firstsumpositive_body_steps_summand. dst_positive_code_weighted_linearity_firstsum = fs_q_dst_weighted_linearity_firstsumpositive_body_steps_summand * S ((S (fs_i_dst_weighted_linearity_firstsumpositive_body_steps)) * dst_positive_scale_weighted_linearity_firstsum) + (fs_a_dst_weighted_linearity_firstsumpositive_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_firstsumpositive_body_steps_partial. fs_h_dst_weighted_linearity_firstsumpositive_body_steps_partial + S (fs_r_dst_weighted_linearity_firstsumpositive_body_steps) = S ((S (fs_i_dst_weighted_linearity_firstsumpositive_body_steps)) * fs_v_dst_weighted_linearity_firstsumpositive)) /\ exists fs_q_dst_weighted_linearity_firstsumpositive_body_steps_partial. fs_u_dst_weighted_linearity_firstsumpositive = fs_q_dst_weighted_linearity_firstsumpositive_body_steps_partial * S ((S (fs_i_dst_weighted_linearity_firstsumpositive_body_steps)) * fs_v_dst_weighted_linearity_firstsumpositive) + (fs_r_dst_weighted_linearity_firstsumpositive_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_firstsumpositive_body_steps_successor. fs_h_dst_weighted_linearity_firstsumpositive_body_steps_successor + S (fs_s_dst_weighted_linearity_firstsumpositive_body_steps) = S ((S (S fs_i_dst_weighted_linearity_firstsumpositive_body_steps)) * fs_v_dst_weighted_linearity_firstsumpositive)) /\ exists fs_q_dst_weighted_linearity_firstsumpositive_body_steps_successor. fs_u_dst_weighted_linearity_firstsumpositive = fs_q_dst_weighted_linearity_firstsumpositive_body_steps_successor * S ((S (S fs_i_dst_weighted_linearity_firstsumpositive_body_steps)) * fs_v_dst_weighted_linearity_firstsumpositive) + (fs_s_dst_weighted_linearity_firstsumpositive_body_steps))) /\ fs_s_dst_weighted_linearity_firstsumpositive_body_steps = fs_r_dst_weighted_linearity_firstsumpositive_body_steps + fs_a_dst_weighted_linearity_firstsumpositive_body_steps)))))) /\ (((exists fs_u_dst_weighted_linearity_firstsumnegative fs_v_dst_weighted_linearity_firstsumnegative. ((((exists fs_h_dst_weighted_linearity_firstsumnegative_body_start. fs_h_dst_weighted_linearity_firstsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_weighted_linearity_firstsumnegative)) /\ exists fs_q_dst_weighted_linearity_firstsumnegative_body_start. fs_u_dst_weighted_linearity_firstsumnegative = fs_q_dst_weighted_linearity_firstsumnegative_body_start * S ((S (0)) * fs_v_dst_weighted_linearity_firstsumnegative) + (0))) /\ ((((exists fs_h_dst_weighted_linearity_firstsumnegative_body_terminal. fs_h_dst_weighted_linearity_firstsumnegative_body_terminal + S (dst_negative_sum_weighted_linearity_firstsum) = S ((S (l)) * fs_v_dst_weighted_linearity_firstsumnegative)) /\ exists fs_q_dst_weighted_linearity_firstsumnegative_body_terminal. fs_u_dst_weighted_linearity_firstsumnegative = fs_q_dst_weighted_linearity_firstsumnegative_body_terminal * S ((S (l)) * fs_v_dst_weighted_linearity_firstsumnegative) + (dst_negative_sum_weighted_linearity_firstsum))) /\ forall fs_i_dst_weighted_linearity_firstsumnegative_body_steps. (exists fs_lt_dst_weighted_linearity_firstsumnegative_body_steps_bound. fs_lt_dst_weighted_linearity_firstsumnegative_body_steps_bound + S fs_i_dst_weighted_linearity_firstsumnegative_body_steps = l) -> exists fs_a_dst_weighted_linearity_firstsumnegative_body_steps fs_r_dst_weighted_linearity_firstsumnegative_body_steps fs_s_dst_weighted_linearity_firstsumnegative_body_steps. ((((exists fs_h_dst_weighted_linearity_firstsumnegative_body_steps_summand. fs_h_dst_weighted_linearity_firstsumnegative_body_steps_summand + S (fs_a_dst_weighted_linearity_firstsumnegative_body_steps) = S ((S (fs_i_dst_weighted_linearity_firstsumnegative_body_steps)) * dst_negative_scale_weighted_linearity_firstsum)) /\ exists fs_q_dst_weighted_linearity_firstsumnegative_body_steps_summand. dst_negative_code_weighted_linearity_firstsum = fs_q_dst_weighted_linearity_firstsumnegative_body_steps_summand * S ((S (fs_i_dst_weighted_linearity_firstsumnegative_body_steps)) * dst_negative_scale_weighted_linearity_firstsum) + (fs_a_dst_weighted_linearity_firstsumnegative_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_firstsumnegative_body_steps_partial. fs_h_dst_weighted_linearity_firstsumnegative_body_steps_partial + S (fs_r_dst_weighted_linearity_firstsumnegative_body_steps) = S ((S (fs_i_dst_weighted_linearity_firstsumnegative_body_steps)) * fs_v_dst_weighted_linearity_firstsumnegative)) /\ exists fs_q_dst_weighted_linearity_firstsumnegative_body_steps_partial. fs_u_dst_weighted_linearity_firstsumnegative = fs_q_dst_weighted_linearity_firstsumnegative_body_steps_partial * S ((S (fs_i_dst_weighted_linearity_firstsumnegative_body_steps)) * fs_v_dst_weighted_linearity_firstsumnegative) + (fs_r_dst_weighted_linearity_firstsumnegative_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_firstsumnegative_body_steps_successor. fs_h_dst_weighted_linearity_firstsumnegative_body_steps_successor + S (fs_s_dst_weighted_linearity_firstsumnegative_body_steps) = S ((S (S fs_i_dst_weighted_linearity_firstsumnegative_body_steps)) * fs_v_dst_weighted_linearity_firstsumnegative)) /\ exists fs_q_dst_weighted_linearity_firstsumnegative_body_steps_successor. fs_u_dst_weighted_linearity_firstsumnegative = fs_q_dst_weighted_linearity_firstsumnegative_body_steps_successor * S ((S (S fs_i_dst_weighted_linearity_firstsumnegative_body_steps)) * fs_v_dst_weighted_linearity_firstsumnegative) + (fs_s_dst_weighted_linearity_firstsumnegative_body_steps))) /\ fs_s_dst_weighted_linearity_firstsumnegative_body_steps = fs_r_dst_weighted_linearity_firstsumnegative_body_steps + fs_a_dst_weighted_linearity_firstsumnegative_body_steps)))))) /\ (exists ge_balance_positive_weighted_linearity_firstsumresult ge_balance_negative_weighted_linearity_firstsumresult. (((((a) = 2 * (ge_balance_positive_weighted_linearity_firstsumresult) /\ (ge_balance_negative_weighted_linearity_firstsumresult) = 0) \/ exists ge_signed_half_weighted_linearity_firstsumresultdecode. (((a) = 2 * ge_signed_half_weighted_linearity_firstsumresultdecode + 1 /\ (ge_balance_positive_weighted_linearity_firstsumresult) = 0) /\ (ge_balance_negative_weighted_linearity_firstsumresult) = S ge_signed_half_weighted_linearity_firstsumresultdecode))) /\ ((dst_positive_sum_weighted_linearity_firstsum) + ge_balance_negative_weighted_linearity_firstsumresult = (dst_negative_sum_weighted_linearity_firstsum) + ge_balance_positive_weighted_linearity_firstsumresult))))))))))) -> (exists sws_product_table_weighted_linearity_second. ((((exists dst_positive_code_weighted_linearity_secondproductsleft_table dst_positive_scale_weighted_linearity_secondproductsleft_table dst_negative_code_weighted_linearity_secondproductsleft_table dst_negative_scale_weighted_linearity_secondproductsleft_table. (((W) = (((((dst_positive_code_weighted_linearity_secondproductsleft_table) + (dst_positive_scale_weighted_linearity_secondproductsleft_table)) * S ((dst_positive_code_weighted_linearity_secondproductsleft_table) + (dst_positive_scale_weighted_linearity_secondproductsleft_table)) + ((dst_positive_scale_weighted_linearity_secondproductsleft_table) + (dst_positive_scale_weighted_linearity_secondproductsleft_table))) + (((dst_negative_code_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)) * S ((dst_negative_code_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)) + ((dst_negative_scale_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)))) * S ((((dst_positive_code_weighted_linearity_secondproductsleft_table) + (dst_positive_scale_weighted_linearity_secondproductsleft_table)) * S ((dst_positive_code_weighted_linearity_secondproductsleft_table) + (dst_positive_scale_weighted_linearity_secondproductsleft_table)) + ((dst_positive_scale_weighted_linearity_secondproductsleft_table) + (dst_positive_scale_weighted_linearity_secondproductsleft_table))) + (((dst_negative_code_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)) * S ((dst_negative_code_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)) + ((dst_negative_scale_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)))) + ((((dst_negative_code_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)) * S ((dst_negative_code_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)) + ((dst_negative_scale_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table))) + (((dst_negative_code_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)) * S ((dst_negative_code_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)) + ((dst_negative_scale_weighted_linearity_secondproductsleft_table) + (dst_negative_scale_weighted_linearity_secondproductsleft_table)))))) /\ (forall dst_index_weighted_linearity_secondproductsleft_table. (exists pvs_le_gap_weighted_linearity_secondproductsleft_tabledomain. pvs_le_gap_weighted_linearity_secondproductsleft_tabledomain + (dst_index_weighted_linearity_secondproductsleft_table) = (l)) -> exists dst_positive_weighted_linearity_secondproductsleft_table dst_negative_weighted_linearity_secondproductsleft_table dst_value_weighted_linearity_secondproductsleft_table. ((((exists ff_h_pvs_weighted_linearity_secondproductsleft_tableentrypositive. ff_h_pvs_weighted_linearity_secondproductsleft_tableentrypositive + S (dst_positive_weighted_linearity_secondproductsleft_table) = S ((S (dst_index_weighted_linearity_secondproductsleft_table)) * dst_positive_scale_weighted_linearity_secondproductsleft_table)) /\ exists ff_q_pvs_weighted_linearity_secondproductsleft_tableentrypositive. dst_positive_code_weighted_linearity_secondproductsleft_table = ff_q_pvs_weighted_linearity_secondproductsleft_tableentrypositive * S ((S (dst_index_weighted_linearity_secondproductsleft_table)) * dst_positive_scale_weighted_linearity_secondproductsleft_table) + (dst_positive_weighted_linearity_secondproductsleft_table))) /\ (((((exists ff_h_pvs_weighted_linearity_secondproductsleft_tableentrynegative. ff_h_pvs_weighted_linearity_secondproductsleft_tableentrynegative + S (dst_negative_weighted_linearity_secondproductsleft_table) = S ((S (dst_index_weighted_linearity_secondproductsleft_table)) * dst_negative_scale_weighted_linearity_secondproductsleft_table)) /\ exists ff_q_pvs_weighted_linearity_secondproductsleft_tableentrynegative. dst_negative_code_weighted_linearity_secondproductsleft_table = ff_q_pvs_weighted_linearity_secondproductsleft_tableentrynegative * S ((S (dst_index_weighted_linearity_secondproductsleft_table)) * dst_negative_scale_weighted_linearity_secondproductsleft_table) + (dst_negative_weighted_linearity_secondproductsleft_table))) /\ (exists ge_balance_positive_weighted_linearity_secondproductsleft_tableentryvalue ge_balance_negative_weighted_linearity_secondproductsleft_tableentryvalue. (((((dst_value_weighted_linearity_secondproductsleft_table) = 2 * (ge_balance_positive_weighted_linearity_secondproductsleft_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_secondproductsleft_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_secondproductsleft_tableentryvaluedecode. (((dst_value_weighted_linearity_secondproductsleft_table) = 2 * ge_signed_half_weighted_linearity_secondproductsleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_secondproductsleft_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_secondproductsleft_tableentryvalue) = S ge_signed_half_weighted_linearity_secondproductsleft_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_secondproductsleft_table) + ge_balance_negative_weighted_linearity_secondproductsleft_tableentryvalue = (dst_negative_weighted_linearity_secondproductsleft_table) + ge_balance_positive_weighted_linearity_secondproductsleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_secondproductsright_table dst_positive_scale_weighted_linearity_secondproductsright_table dst_negative_code_weighted_linearity_secondproductsright_table dst_negative_scale_weighted_linearity_secondproductsright_table. (((G) = (((((dst_positive_code_weighted_linearity_secondproductsright_table) + (dst_positive_scale_weighted_linearity_secondproductsright_table)) * S ((dst_positive_code_weighted_linearity_secondproductsright_table) + (dst_positive_scale_weighted_linearity_secondproductsright_table)) + ((dst_positive_scale_weighted_linearity_secondproductsright_table) + (dst_positive_scale_weighted_linearity_secondproductsright_table))) + (((dst_negative_code_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)) * S ((dst_negative_code_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)) + ((dst_negative_scale_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)))) * S ((((dst_positive_code_weighted_linearity_secondproductsright_table) + (dst_positive_scale_weighted_linearity_secondproductsright_table)) * S ((dst_positive_code_weighted_linearity_secondproductsright_table) + (dst_positive_scale_weighted_linearity_secondproductsright_table)) + ((dst_positive_scale_weighted_linearity_secondproductsright_table) + (dst_positive_scale_weighted_linearity_secondproductsright_table))) + (((dst_negative_code_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)) * S ((dst_negative_code_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)) + ((dst_negative_scale_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)))) + ((((dst_negative_code_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)) * S ((dst_negative_code_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)) + ((dst_negative_scale_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table))) + (((dst_negative_code_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)) * S ((dst_negative_code_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)) + ((dst_negative_scale_weighted_linearity_secondproductsright_table) + (dst_negative_scale_weighted_linearity_secondproductsright_table)))))) /\ (forall dst_index_weighted_linearity_secondproductsright_table. (exists pvs_le_gap_weighted_linearity_secondproductsright_tabledomain. pvs_le_gap_weighted_linearity_secondproductsright_tabledomain + (dst_index_weighted_linearity_secondproductsright_table) = (l)) -> exists dst_positive_weighted_linearity_secondproductsright_table dst_negative_weighted_linearity_secondproductsright_table dst_value_weighted_linearity_secondproductsright_table. ((((exists ff_h_pvs_weighted_linearity_secondproductsright_tableentrypositive. ff_h_pvs_weighted_linearity_secondproductsright_tableentrypositive + S (dst_positive_weighted_linearity_secondproductsright_table) = S ((S (dst_index_weighted_linearity_secondproductsright_table)) * dst_positive_scale_weighted_linearity_secondproductsright_table)) /\ exists ff_q_pvs_weighted_linearity_secondproductsright_tableentrypositive. dst_positive_code_weighted_linearity_secondproductsright_table = ff_q_pvs_weighted_linearity_secondproductsright_tableentrypositive * S ((S (dst_index_weighted_linearity_secondproductsright_table)) * dst_positive_scale_weighted_linearity_secondproductsright_table) + (dst_positive_weighted_linearity_secondproductsright_table))) /\ (((((exists ff_h_pvs_weighted_linearity_secondproductsright_tableentrynegative. ff_h_pvs_weighted_linearity_secondproductsright_tableentrynegative + S (dst_negative_weighted_linearity_secondproductsright_table) = S ((S (dst_index_weighted_linearity_secondproductsright_table)) * dst_negative_scale_weighted_linearity_secondproductsright_table)) /\ exists ff_q_pvs_weighted_linearity_secondproductsright_tableentrynegative. dst_negative_code_weighted_linearity_secondproductsright_table = ff_q_pvs_weighted_linearity_secondproductsright_tableentrynegative * S ((S (dst_index_weighted_linearity_secondproductsright_table)) * dst_negative_scale_weighted_linearity_secondproductsright_table) + (dst_negative_weighted_linearity_secondproductsright_table))) /\ (exists ge_balance_positive_weighted_linearity_secondproductsright_tableentryvalue ge_balance_negative_weighted_linearity_secondproductsright_tableentryvalue. (((((dst_value_weighted_linearity_secondproductsright_table) = 2 * (ge_balance_positive_weighted_linearity_secondproductsright_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_secondproductsright_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_secondproductsright_tableentryvaluedecode. (((dst_value_weighted_linearity_secondproductsright_table) = 2 * ge_signed_half_weighted_linearity_secondproductsright_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_secondproductsright_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_secondproductsright_tableentryvalue) = S ge_signed_half_weighted_linearity_secondproductsright_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_secondproductsright_table) + ge_balance_negative_weighted_linearity_secondproductsright_tableentryvalue = (dst_negative_weighted_linearity_secondproductsright_table) + ge_balance_positive_weighted_linearity_secondproductsright_tableentryvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_secondproductsoutput_table dst_positive_scale_weighted_linearity_secondproductsoutput_table dst_negative_code_weighted_linearity_secondproductsoutput_table dst_negative_scale_weighted_linearity_secondproductsoutput_table. (((sws_product_table_weighted_linearity_second) = (((((dst_positive_code_weighted_linearity_secondproductsoutput_table) + (dst_positive_scale_weighted_linearity_secondproductsoutput_table)) * S ((dst_positive_code_weighted_linearity_secondproductsoutput_table) + (dst_positive_scale_weighted_linearity_secondproductsoutput_table)) + ((dst_positive_scale_weighted_linearity_secondproductsoutput_table) + (dst_positive_scale_weighted_linearity_secondproductsoutput_table))) + (((dst_negative_code_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)))) * S ((((dst_positive_code_weighted_linearity_secondproductsoutput_table) + (dst_positive_scale_weighted_linearity_secondproductsoutput_table)) * S ((dst_positive_code_weighted_linearity_secondproductsoutput_table) + (dst_positive_scale_weighted_linearity_secondproductsoutput_table)) + ((dst_positive_scale_weighted_linearity_secondproductsoutput_table) + (dst_positive_scale_weighted_linearity_secondproductsoutput_table))) + (((dst_negative_code_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)))) + ((((dst_negative_code_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table))) + (((dst_negative_code_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_secondproductsoutput_table) + (dst_negative_scale_weighted_linearity_secondproductsoutput_table)))))) /\ (forall dst_index_weighted_linearity_secondproductsoutput_table. (exists pvs_le_gap_weighted_linearity_secondproductsoutput_tabledomain. pvs_le_gap_weighted_linearity_secondproductsoutput_tabledomain + (dst_index_weighted_linearity_secondproductsoutput_table) = (l)) -> exists dst_positive_weighted_linearity_secondproductsoutput_table dst_negative_weighted_linearity_secondproductsoutput_table dst_value_weighted_linearity_secondproductsoutput_table. ((((exists ff_h_pvs_weighted_linearity_secondproductsoutput_tableentrypositive. ff_h_pvs_weighted_linearity_secondproductsoutput_tableentrypositive + S (dst_positive_weighted_linearity_secondproductsoutput_table) = S ((S (dst_index_weighted_linearity_secondproductsoutput_table)) * dst_positive_scale_weighted_linearity_secondproductsoutput_table)) /\ exists ff_q_pvs_weighted_linearity_secondproductsoutput_tableentrypositive. dst_positive_code_weighted_linearity_secondproductsoutput_table = ff_q_pvs_weighted_linearity_secondproductsoutput_tableentrypositive * S ((S (dst_index_weighted_linearity_secondproductsoutput_table)) * dst_positive_scale_weighted_linearity_secondproductsoutput_table) + (dst_positive_weighted_linearity_secondproductsoutput_table))) /\ (((((exists ff_h_pvs_weighted_linearity_secondproductsoutput_tableentrynegative. ff_h_pvs_weighted_linearity_secondproductsoutput_tableentrynegative + S (dst_negative_weighted_linearity_secondproductsoutput_table) = S ((S (dst_index_weighted_linearity_secondproductsoutput_table)) * dst_negative_scale_weighted_linearity_secondproductsoutput_table)) /\ exists ff_q_pvs_weighted_linearity_secondproductsoutput_tableentrynegative. dst_negative_code_weighted_linearity_secondproductsoutput_table = ff_q_pvs_weighted_linearity_secondproductsoutput_tableentrynegative * S ((S (dst_index_weighted_linearity_secondproductsoutput_table)) * dst_negative_scale_weighted_linearity_secondproductsoutput_table) + (dst_negative_weighted_linearity_secondproductsoutput_table))) /\ (exists ge_balance_positive_weighted_linearity_secondproductsoutput_tableentryvalue ge_balance_negative_weighted_linearity_secondproductsoutput_tableentryvalue. (((((dst_value_weighted_linearity_secondproductsoutput_table) = 2 * (ge_balance_positive_weighted_linearity_secondproductsoutput_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_secondproductsoutput_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_secondproductsoutput_tableentryvaluedecode. (((dst_value_weighted_linearity_secondproductsoutput_table) = 2 * ge_signed_half_weighted_linearity_secondproductsoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_secondproductsoutput_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_secondproductsoutput_tableentryvalue) = S ge_signed_half_weighted_linearity_secondproductsoutput_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_secondproductsoutput_table) + ge_balance_negative_weighted_linearity_secondproductsoutput_tableentryvalue = (dst_negative_weighted_linearity_secondproductsoutput_table) + ge_balance_positive_weighted_linearity_secondproductsoutput_tableentryvalue))))))))) /\ (forall sto_index_weighted_linearity_secondproductsentries. (exists pvs_gap_weighted_linearity_secondproductsentriesbound. pvs_gap_weighted_linearity_secondproductsentriesbound + S (sto_index_weighted_linearity_secondproductsentries) = (l)) -> exists sto_left_weighted_linearity_secondproductsentries sto_right_weighted_linearity_secondproductsentries sto_output_weighted_linearity_secondproductsentries. ((exists dst_positive_code_weighted_linearity_secondproductsentriesentryleft dst_positive_scale_weighted_linearity_secondproductsentriesentryleft dst_negative_code_weighted_linearity_secondproductsentriesentryleft dst_negative_scale_weighted_linearity_secondproductsentriesentryleft dst_positive_weighted_linearity_secondproductsentriesentryleft dst_negative_weighted_linearity_secondproductsentriesentryleft. (((W) = (((((dst_positive_code_weighted_linearity_secondproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryleft)) * S ((dst_positive_code_weighted_linearity_secondproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryleft)) + ((dst_positive_scale_weighted_linearity_secondproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryleft))) + (((dst_negative_code_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)))) * S ((((dst_positive_code_weighted_linearity_secondproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryleft)) * S ((dst_positive_code_weighted_linearity_secondproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryleft)) + ((dst_positive_scale_weighted_linearity_secondproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryleft))) + (((dst_negative_code_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)))) + ((((dst_negative_code_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft))) + (((dst_negative_code_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)))))) /\ (((((exists ff_h_pvs_weighted_linearity_secondproductsentriesentryleftpositive. ff_h_pvs_weighted_linearity_secondproductsentriesentryleftpositive + S (dst_positive_weighted_linearity_secondproductsentriesentryleft) = S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_positive_scale_weighted_linearity_secondproductsentriesentryleft)) /\ exists ff_q_pvs_weighted_linearity_secondproductsentriesentryleftpositive. dst_positive_code_weighted_linearity_secondproductsentriesentryleft = ff_q_pvs_weighted_linearity_secondproductsentriesentryleftpositive * S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_positive_scale_weighted_linearity_secondproductsentriesentryleft) + (dst_positive_weighted_linearity_secondproductsentriesentryleft))) /\ (((((exists ff_h_pvs_weighted_linearity_secondproductsentriesentryleftnegative. ff_h_pvs_weighted_linearity_secondproductsentriesentryleftnegative + S (dst_negative_weighted_linearity_secondproductsentriesentryleft) = S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_negative_scale_weighted_linearity_secondproductsentriesentryleft)) /\ exists ff_q_pvs_weighted_linearity_secondproductsentriesentryleftnegative. dst_negative_code_weighted_linearity_secondproductsentriesentryleft = ff_q_pvs_weighted_linearity_secondproductsentriesentryleftnegative * S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_negative_scale_weighted_linearity_secondproductsentriesentryleft) + (dst_negative_weighted_linearity_secondproductsentriesentryleft))) /\ (exists ge_balance_positive_weighted_linearity_secondproductsentriesentryleftvalue ge_balance_negative_weighted_linearity_secondproductsentriesentryleftvalue. (((((sto_left_weighted_linearity_secondproductsentries) = 2 * (ge_balance_positive_weighted_linearity_secondproductsentriesentryleftvalue) /\ (ge_balance_negative_weighted_linearity_secondproductsentriesentryleftvalue) = 0) \/ exists ge_signed_half_weighted_linearity_secondproductsentriesentryleftvaluedecode. (((sto_left_weighted_linearity_secondproductsentries) = 2 * ge_signed_half_weighted_linearity_secondproductsentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_secondproductsentriesentryleftvalue) = 0) /\ (ge_balance_negative_weighted_linearity_secondproductsentriesentryleftvalue) = S ge_signed_half_weighted_linearity_secondproductsentriesentryleftvaluedecode))) /\ ((dst_positive_weighted_linearity_secondproductsentriesentryleft) + ge_balance_negative_weighted_linearity_secondproductsentriesentryleftvalue = (dst_negative_weighted_linearity_secondproductsentriesentryleft) + ge_balance_positive_weighted_linearity_secondproductsentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_secondproductsentriesentryright dst_positive_scale_weighted_linearity_secondproductsentriesentryright dst_negative_code_weighted_linearity_secondproductsentriesentryright dst_negative_scale_weighted_linearity_secondproductsentriesentryright dst_positive_weighted_linearity_secondproductsentriesentryright dst_negative_weighted_linearity_secondproductsentriesentryright. (((G) = (((((dst_positive_code_weighted_linearity_secondproductsentriesentryright) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryright)) * S ((dst_positive_code_weighted_linearity_secondproductsentriesentryright) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryright)) + ((dst_positive_scale_weighted_linearity_secondproductsentriesentryright) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryright))) + (((dst_negative_code_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)))) * S ((((dst_positive_code_weighted_linearity_secondproductsentriesentryright) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryright)) * S ((dst_positive_code_weighted_linearity_secondproductsentriesentryright) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryright)) + ((dst_positive_scale_weighted_linearity_secondproductsentriesentryright) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryright))) + (((dst_negative_code_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)))) + ((((dst_negative_code_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright))) + (((dst_negative_code_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryright) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryright)))))) /\ (((((exists ff_h_pvs_weighted_linearity_secondproductsentriesentryrightpositive. ff_h_pvs_weighted_linearity_secondproductsentriesentryrightpositive + S (dst_positive_weighted_linearity_secondproductsentriesentryright) = S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_positive_scale_weighted_linearity_secondproductsentriesentryright)) /\ exists ff_q_pvs_weighted_linearity_secondproductsentriesentryrightpositive. dst_positive_code_weighted_linearity_secondproductsentriesentryright = ff_q_pvs_weighted_linearity_secondproductsentriesentryrightpositive * S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_positive_scale_weighted_linearity_secondproductsentriesentryright) + (dst_positive_weighted_linearity_secondproductsentriesentryright))) /\ (((((exists ff_h_pvs_weighted_linearity_secondproductsentriesentryrightnegative. ff_h_pvs_weighted_linearity_secondproductsentriesentryrightnegative + S (dst_negative_weighted_linearity_secondproductsentriesentryright) = S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_negative_scale_weighted_linearity_secondproductsentriesentryright)) /\ exists ff_q_pvs_weighted_linearity_secondproductsentriesentryrightnegative. dst_negative_code_weighted_linearity_secondproductsentriesentryright = ff_q_pvs_weighted_linearity_secondproductsentriesentryrightnegative * S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_negative_scale_weighted_linearity_secondproductsentriesentryright) + (dst_negative_weighted_linearity_secondproductsentriesentryright))) /\ (exists ge_balance_positive_weighted_linearity_secondproductsentriesentryrightvalue ge_balance_negative_weighted_linearity_secondproductsentriesentryrightvalue. (((((sto_right_weighted_linearity_secondproductsentries) = 2 * (ge_balance_positive_weighted_linearity_secondproductsentriesentryrightvalue) /\ (ge_balance_negative_weighted_linearity_secondproductsentriesentryrightvalue) = 0) \/ exists ge_signed_half_weighted_linearity_secondproductsentriesentryrightvaluedecode. (((sto_right_weighted_linearity_secondproductsentries) = 2 * ge_signed_half_weighted_linearity_secondproductsentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_secondproductsentriesentryrightvalue) = 0) /\ (ge_balance_negative_weighted_linearity_secondproductsentriesentryrightvalue) = S ge_signed_half_weighted_linearity_secondproductsentriesentryrightvaluedecode))) /\ ((dst_positive_weighted_linearity_secondproductsentriesentryright) + ge_balance_negative_weighted_linearity_secondproductsentriesentryrightvalue = (dst_negative_weighted_linearity_secondproductsentriesentryright) + ge_balance_positive_weighted_linearity_secondproductsentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_secondproductsentriesentryoutput dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput dst_negative_code_weighted_linearity_secondproductsentriesentryoutput dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput dst_positive_weighted_linearity_secondproductsentriesentryoutput dst_negative_weighted_linearity_secondproductsentriesentryoutput. (((sws_product_table_weighted_linearity_second) = (((((dst_positive_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput)) * S ((dst_positive_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput)) + ((dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput))) + (((dst_negative_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)))) * S ((((dst_positive_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput)) * S ((dst_positive_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput)) + ((dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput))) + (((dst_negative_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)))) + ((((dst_negative_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput))) + (((dst_negative_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)))))) /\ (((((exists ff_h_pvs_weighted_linearity_secondproductsentriesentryoutputpositive. ff_h_pvs_weighted_linearity_secondproductsentriesentryoutputpositive + S (dst_positive_weighted_linearity_secondproductsentriesentryoutput) = S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput)) /\ exists ff_q_pvs_weighted_linearity_secondproductsentriesentryoutputpositive. dst_positive_code_weighted_linearity_secondproductsentriesentryoutput = ff_q_pvs_weighted_linearity_secondproductsentriesentryoutputpositive * S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_positive_scale_weighted_linearity_secondproductsentriesentryoutput) + (dst_positive_weighted_linearity_secondproductsentriesentryoutput))) /\ (((((exists ff_h_pvs_weighted_linearity_secondproductsentriesentryoutputnegative. ff_h_pvs_weighted_linearity_secondproductsentriesentryoutputnegative + S (dst_negative_weighted_linearity_secondproductsentriesentryoutput) = S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput)) /\ exists ff_q_pvs_weighted_linearity_secondproductsentriesentryoutputnegative. dst_negative_code_weighted_linearity_secondproductsentriesentryoutput = ff_q_pvs_weighted_linearity_secondproductsentriesentryoutputnegative * S ((S (sto_index_weighted_linearity_secondproductsentries)) * dst_negative_scale_weighted_linearity_secondproductsentriesentryoutput) + (dst_negative_weighted_linearity_secondproductsentriesentryoutput))) /\ (exists ge_balance_positive_weighted_linearity_secondproductsentriesentryoutputvalue ge_balance_negative_weighted_linearity_secondproductsentriesentryoutputvalue. (((((sto_output_weighted_linearity_secondproductsentries) = 2 * (ge_balance_positive_weighted_linearity_secondproductsentriesentryoutputvalue) /\ (ge_balance_negative_weighted_linearity_secondproductsentriesentryoutputvalue) = 0) \/ exists ge_signed_half_weighted_linearity_secondproductsentriesentryoutputvaluedecode. (((sto_output_weighted_linearity_secondproductsentries) = 2 * ge_signed_half_weighted_linearity_secondproductsentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_secondproductsentriesentryoutputvalue) = 0) /\ (ge_balance_negative_weighted_linearity_secondproductsentriesentryoutputvalue) = S ge_signed_half_weighted_linearity_secondproductsentriesentryoutputvaluedecode))) /\ ((dst_positive_weighted_linearity_secondproductsentriesentryoutput) + ge_balance_negative_weighted_linearity_secondproductsentriesentryoutputvalue = (dst_negative_weighted_linearity_secondproductsentriesentryoutput) + ge_balance_positive_weighted_linearity_secondproductsentriesentryoutputvalue))))))))) /\ (exists sto_ap_weighted_linearity_secondproductsentriesentryoperation sto_an_weighted_linearity_secondproductsentriesentryoperation sto_bp_weighted_linearity_secondproductsentriesentryoperation sto_bn_weighted_linearity_secondproductsentriesentryoperation sto_cp_weighted_linearity_secondproductsentriesentryoperation sto_cn_weighted_linearity_secondproductsentriesentryoperation. (((((sto_left_weighted_linearity_secondproductsentries) = 2 * (sto_ap_weighted_linearity_secondproductsentriesentryoperation) /\ (sto_an_weighted_linearity_secondproductsentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_secondproductsentriesentryoperationleft. (((sto_left_weighted_linearity_secondproductsentries) = 2 * ge_signed_half_weighted_linearity_secondproductsentriesentryoperationleft + 1 /\ (sto_ap_weighted_linearity_secondproductsentriesentryoperation) = 0) /\ (sto_an_weighted_linearity_secondproductsentriesentryoperation) = S ge_signed_half_weighted_linearity_secondproductsentriesentryoperationleft))) /\ ((((((sto_right_weighted_linearity_secondproductsentries) = 2 * (sto_bp_weighted_linearity_secondproductsentriesentryoperation) /\ (sto_bn_weighted_linearity_secondproductsentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_secondproductsentriesentryoperationright. (((sto_right_weighted_linearity_secondproductsentries) = 2 * ge_signed_half_weighted_linearity_secondproductsentriesentryoperationright + 1 /\ (sto_bp_weighted_linearity_secondproductsentriesentryoperation) = 0) /\ (sto_bn_weighted_linearity_secondproductsentriesentryoperation) = S ge_signed_half_weighted_linearity_secondproductsentriesentryoperationright))) /\ ((((((sto_output_weighted_linearity_secondproductsentries) = 2 * (sto_cp_weighted_linearity_secondproductsentriesentryoperation) /\ (sto_cn_weighted_linearity_secondproductsentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_secondproductsentriesentryoperationoutput. (((sto_output_weighted_linearity_secondproductsentries) = 2 * ge_signed_half_weighted_linearity_secondproductsentriesentryoperationoutput + 1 /\ (sto_cp_weighted_linearity_secondproductsentriesentryoperation) = 0) /\ (sto_cn_weighted_linearity_secondproductsentriesentryoperation) = S ge_signed_half_weighted_linearity_secondproductsentriesentryoperationoutput))) /\ ((sto_ap_weighted_linearity_secondproductsentriesentryoperation * sto_bp_weighted_linearity_secondproductsentriesentryoperation + sto_an_weighted_linearity_secondproductsentriesentryoperation * sto_bn_weighted_linearity_secondproductsentriesentryoperation) + sto_cn_weighted_linearity_secondproductsentriesentryoperation = (sto_ap_weighted_linearity_secondproductsentriesentryoperation * sto_bn_weighted_linearity_secondproductsentriesentryoperation + sto_an_weighted_linearity_secondproductsentriesentryoperation * sto_bp_weighted_linearity_secondproductsentriesentryoperation) + sto_cp_weighted_linearity_secondproductsentriesentryoperation))))))))))))))))))) /\ (exists dst_positive_code_weighted_linearity_secondsum dst_positive_scale_weighted_linearity_secondsum dst_negative_code_weighted_linearity_secondsum dst_negative_scale_weighted_linearity_secondsum dst_positive_sum_weighted_linearity_secondsum dst_negative_sum_weighted_linearity_secondsum. (((sws_product_table_weighted_linearity_second) = (((((dst_positive_code_weighted_linearity_secondsum) + (dst_positive_scale_weighted_linearity_secondsum)) * S ((dst_positive_code_weighted_linearity_secondsum) + (dst_positive_scale_weighted_linearity_secondsum)) + ((dst_positive_scale_weighted_linearity_secondsum) + (dst_positive_scale_weighted_linearity_secondsum))) + (((dst_negative_code_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)) * S ((dst_negative_code_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)) + ((dst_negative_scale_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)))) * S ((((dst_positive_code_weighted_linearity_secondsum) + (dst_positive_scale_weighted_linearity_secondsum)) * S ((dst_positive_code_weighted_linearity_secondsum) + (dst_positive_scale_weighted_linearity_secondsum)) + ((dst_positive_scale_weighted_linearity_secondsum) + (dst_positive_scale_weighted_linearity_secondsum))) + (((dst_negative_code_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)) * S ((dst_negative_code_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)) + ((dst_negative_scale_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)))) + ((((dst_negative_code_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)) * S ((dst_negative_code_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)) + ((dst_negative_scale_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum))) + (((dst_negative_code_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)) * S ((dst_negative_code_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)) + ((dst_negative_scale_weighted_linearity_secondsum) + (dst_negative_scale_weighted_linearity_secondsum)))))) /\ (((exists fs_u_dst_weighted_linearity_secondsumpositive fs_v_dst_weighted_linearity_secondsumpositive. ((((exists fs_h_dst_weighted_linearity_secondsumpositive_body_start. fs_h_dst_weighted_linearity_secondsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_weighted_linearity_secondsumpositive)) /\ exists fs_q_dst_weighted_linearity_secondsumpositive_body_start. fs_u_dst_weighted_linearity_secondsumpositive = fs_q_dst_weighted_linearity_secondsumpositive_body_start * S ((S (0)) * fs_v_dst_weighted_linearity_secondsumpositive) + (0))) /\ ((((exists fs_h_dst_weighted_linearity_secondsumpositive_body_terminal. fs_h_dst_weighted_linearity_secondsumpositive_body_terminal + S (dst_positive_sum_weighted_linearity_secondsum) = S ((S (l)) * fs_v_dst_weighted_linearity_secondsumpositive)) /\ exists fs_q_dst_weighted_linearity_secondsumpositive_body_terminal. fs_u_dst_weighted_linearity_secondsumpositive = fs_q_dst_weighted_linearity_secondsumpositive_body_terminal * S ((S (l)) * fs_v_dst_weighted_linearity_secondsumpositive) + (dst_positive_sum_weighted_linearity_secondsum))) /\ forall fs_i_dst_weighted_linearity_secondsumpositive_body_steps. (exists fs_lt_dst_weighted_linearity_secondsumpositive_body_steps_bound. fs_lt_dst_weighted_linearity_secondsumpositive_body_steps_bound + S fs_i_dst_weighted_linearity_secondsumpositive_body_steps = l) -> exists fs_a_dst_weighted_linearity_secondsumpositive_body_steps fs_r_dst_weighted_linearity_secondsumpositive_body_steps fs_s_dst_weighted_linearity_secondsumpositive_body_steps. ((((exists fs_h_dst_weighted_linearity_secondsumpositive_body_steps_summand. fs_h_dst_weighted_linearity_secondsumpositive_body_steps_summand + S (fs_a_dst_weighted_linearity_secondsumpositive_body_steps) = S ((S (fs_i_dst_weighted_linearity_secondsumpositive_body_steps)) * dst_positive_scale_weighted_linearity_secondsum)) /\ exists fs_q_dst_weighted_linearity_secondsumpositive_body_steps_summand. dst_positive_code_weighted_linearity_secondsum = fs_q_dst_weighted_linearity_secondsumpositive_body_steps_summand * S ((S (fs_i_dst_weighted_linearity_secondsumpositive_body_steps)) * dst_positive_scale_weighted_linearity_secondsum) + (fs_a_dst_weighted_linearity_secondsumpositive_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_secondsumpositive_body_steps_partial. fs_h_dst_weighted_linearity_secondsumpositive_body_steps_partial + S (fs_r_dst_weighted_linearity_secondsumpositive_body_steps) = S ((S (fs_i_dst_weighted_linearity_secondsumpositive_body_steps)) * fs_v_dst_weighted_linearity_secondsumpositive)) /\ exists fs_q_dst_weighted_linearity_secondsumpositive_body_steps_partial. fs_u_dst_weighted_linearity_secondsumpositive = fs_q_dst_weighted_linearity_secondsumpositive_body_steps_partial * S ((S (fs_i_dst_weighted_linearity_secondsumpositive_body_steps)) * fs_v_dst_weighted_linearity_secondsumpositive) + (fs_r_dst_weighted_linearity_secondsumpositive_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_secondsumpositive_body_steps_successor. fs_h_dst_weighted_linearity_secondsumpositive_body_steps_successor + S (fs_s_dst_weighted_linearity_secondsumpositive_body_steps) = S ((S (S fs_i_dst_weighted_linearity_secondsumpositive_body_steps)) * fs_v_dst_weighted_linearity_secondsumpositive)) /\ exists fs_q_dst_weighted_linearity_secondsumpositive_body_steps_successor. fs_u_dst_weighted_linearity_secondsumpositive = fs_q_dst_weighted_linearity_secondsumpositive_body_steps_successor * S ((S (S fs_i_dst_weighted_linearity_secondsumpositive_body_steps)) * fs_v_dst_weighted_linearity_secondsumpositive) + (fs_s_dst_weighted_linearity_secondsumpositive_body_steps))) /\ fs_s_dst_weighted_linearity_secondsumpositive_body_steps = fs_r_dst_weighted_linearity_secondsumpositive_body_steps + fs_a_dst_weighted_linearity_secondsumpositive_body_steps)))))) /\ (((exists fs_u_dst_weighted_linearity_secondsumnegative fs_v_dst_weighted_linearity_secondsumnegative. ((((exists fs_h_dst_weighted_linearity_secondsumnegative_body_start. fs_h_dst_weighted_linearity_secondsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_weighted_linearity_secondsumnegative)) /\ exists fs_q_dst_weighted_linearity_secondsumnegative_body_start. fs_u_dst_weighted_linearity_secondsumnegative = fs_q_dst_weighted_linearity_secondsumnegative_body_start * S ((S (0)) * fs_v_dst_weighted_linearity_secondsumnegative) + (0))) /\ ((((exists fs_h_dst_weighted_linearity_secondsumnegative_body_terminal. fs_h_dst_weighted_linearity_secondsumnegative_body_terminal + S (dst_negative_sum_weighted_linearity_secondsum) = S ((S (l)) * fs_v_dst_weighted_linearity_secondsumnegative)) /\ exists fs_q_dst_weighted_linearity_secondsumnegative_body_terminal. fs_u_dst_weighted_linearity_secondsumnegative = fs_q_dst_weighted_linearity_secondsumnegative_body_terminal * S ((S (l)) * fs_v_dst_weighted_linearity_secondsumnegative) + (dst_negative_sum_weighted_linearity_secondsum))) /\ forall fs_i_dst_weighted_linearity_secondsumnegative_body_steps. (exists fs_lt_dst_weighted_linearity_secondsumnegative_body_steps_bound. fs_lt_dst_weighted_linearity_secondsumnegative_body_steps_bound + S fs_i_dst_weighted_linearity_secondsumnegative_body_steps = l) -> exists fs_a_dst_weighted_linearity_secondsumnegative_body_steps fs_r_dst_weighted_linearity_secondsumnegative_body_steps fs_s_dst_weighted_linearity_secondsumnegative_body_steps. ((((exists fs_h_dst_weighted_linearity_secondsumnegative_body_steps_summand. fs_h_dst_weighted_linearity_secondsumnegative_body_steps_summand + S (fs_a_dst_weighted_linearity_secondsumnegative_body_steps) = S ((S (fs_i_dst_weighted_linearity_secondsumnegative_body_steps)) * dst_negative_scale_weighted_linearity_secondsum)) /\ exists fs_q_dst_weighted_linearity_secondsumnegative_body_steps_summand. dst_negative_code_weighted_linearity_secondsum = fs_q_dst_weighted_linearity_secondsumnegative_body_steps_summand * S ((S (fs_i_dst_weighted_linearity_secondsumnegative_body_steps)) * dst_negative_scale_weighted_linearity_secondsum) + (fs_a_dst_weighted_linearity_secondsumnegative_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_secondsumnegative_body_steps_partial. fs_h_dst_weighted_linearity_secondsumnegative_body_steps_partial + S (fs_r_dst_weighted_linearity_secondsumnegative_body_steps) = S ((S (fs_i_dst_weighted_linearity_secondsumnegative_body_steps)) * fs_v_dst_weighted_linearity_secondsumnegative)) /\ exists fs_q_dst_weighted_linearity_secondsumnegative_body_steps_partial. fs_u_dst_weighted_linearity_secondsumnegative = fs_q_dst_weighted_linearity_secondsumnegative_body_steps_partial * S ((S (fs_i_dst_weighted_linearity_secondsumnegative_body_steps)) * fs_v_dst_weighted_linearity_secondsumnegative) + (fs_r_dst_weighted_linearity_secondsumnegative_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_secondsumnegative_body_steps_successor. fs_h_dst_weighted_linearity_secondsumnegative_body_steps_successor + S (fs_s_dst_weighted_linearity_secondsumnegative_body_steps) = S ((S (S fs_i_dst_weighted_linearity_secondsumnegative_body_steps)) * fs_v_dst_weighted_linearity_secondsumnegative)) /\ exists fs_q_dst_weighted_linearity_secondsumnegative_body_steps_successor. fs_u_dst_weighted_linearity_secondsumnegative = fs_q_dst_weighted_linearity_secondsumnegative_body_steps_successor * S ((S (S fs_i_dst_weighted_linearity_secondsumnegative_body_steps)) * fs_v_dst_weighted_linearity_secondsumnegative) + (fs_s_dst_weighted_linearity_secondsumnegative_body_steps))) /\ fs_s_dst_weighted_linearity_secondsumnegative_body_steps = fs_r_dst_weighted_linearity_secondsumnegative_body_steps + fs_a_dst_weighted_linearity_secondsumnegative_body_steps)))))) /\ (exists ge_balance_positive_weighted_linearity_secondsumresult ge_balance_negative_weighted_linearity_secondsumresult. (((((b) = 2 * (ge_balance_positive_weighted_linearity_secondsumresult) /\ (ge_balance_negative_weighted_linearity_secondsumresult) = 0) \/ exists ge_signed_half_weighted_linearity_secondsumresultdecode. (((b) = 2 * ge_signed_half_weighted_linearity_secondsumresultdecode + 1 /\ (ge_balance_positive_weighted_linearity_secondsumresult) = 0) /\ (ge_balance_negative_weighted_linearity_secondsumresult) = S ge_signed_half_weighted_linearity_secondsumresultdecode))) /\ ((dst_positive_sum_weighted_linearity_secondsum) + ge_balance_negative_weighted_linearity_secondsumresult = (dst_negative_sum_weighted_linearity_secondsum) + ge_balance_positive_weighted_linearity_secondsumresult))))))))))) -> (exists sws_product_table_weighted_linearity_output. ((((exists dst_positive_code_weighted_linearity_outputproductsleft_table dst_positive_scale_weighted_linearity_outputproductsleft_table dst_negative_code_weighted_linearity_outputproductsleft_table dst_negative_scale_weighted_linearity_outputproductsleft_table. (((W) = (((((dst_positive_code_weighted_linearity_outputproductsleft_table) + (dst_positive_scale_weighted_linearity_outputproductsleft_table)) * S ((dst_positive_code_weighted_linearity_outputproductsleft_table) + (dst_positive_scale_weighted_linearity_outputproductsleft_table)) + ((dst_positive_scale_weighted_linearity_outputproductsleft_table) + (dst_positive_scale_weighted_linearity_outputproductsleft_table))) + (((dst_negative_code_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)) * S ((dst_negative_code_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)) + ((dst_negative_scale_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)))) * S ((((dst_positive_code_weighted_linearity_outputproductsleft_table) + (dst_positive_scale_weighted_linearity_outputproductsleft_table)) * S ((dst_positive_code_weighted_linearity_outputproductsleft_table) + (dst_positive_scale_weighted_linearity_outputproductsleft_table)) + ((dst_positive_scale_weighted_linearity_outputproductsleft_table) + (dst_positive_scale_weighted_linearity_outputproductsleft_table))) + (((dst_negative_code_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)) * S ((dst_negative_code_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)) + ((dst_negative_scale_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)))) + ((((dst_negative_code_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)) * S ((dst_negative_code_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)) + ((dst_negative_scale_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table))) + (((dst_negative_code_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)) * S ((dst_negative_code_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)) + ((dst_negative_scale_weighted_linearity_outputproductsleft_table) + (dst_negative_scale_weighted_linearity_outputproductsleft_table)))))) /\ (forall dst_index_weighted_linearity_outputproductsleft_table. (exists pvs_le_gap_weighted_linearity_outputproductsleft_tabledomain. pvs_le_gap_weighted_linearity_outputproductsleft_tabledomain + (dst_index_weighted_linearity_outputproductsleft_table) = (l)) -> exists dst_positive_weighted_linearity_outputproductsleft_table dst_negative_weighted_linearity_outputproductsleft_table dst_value_weighted_linearity_outputproductsleft_table. ((((exists ff_h_pvs_weighted_linearity_outputproductsleft_tableentrypositive. ff_h_pvs_weighted_linearity_outputproductsleft_tableentrypositive + S (dst_positive_weighted_linearity_outputproductsleft_table) = S ((S (dst_index_weighted_linearity_outputproductsleft_table)) * dst_positive_scale_weighted_linearity_outputproductsleft_table)) /\ exists ff_q_pvs_weighted_linearity_outputproductsleft_tableentrypositive. dst_positive_code_weighted_linearity_outputproductsleft_table = ff_q_pvs_weighted_linearity_outputproductsleft_tableentrypositive * S ((S (dst_index_weighted_linearity_outputproductsleft_table)) * dst_positive_scale_weighted_linearity_outputproductsleft_table) + (dst_positive_weighted_linearity_outputproductsleft_table))) /\ (((((exists ff_h_pvs_weighted_linearity_outputproductsleft_tableentrynegative. ff_h_pvs_weighted_linearity_outputproductsleft_tableentrynegative + S (dst_negative_weighted_linearity_outputproductsleft_table) = S ((S (dst_index_weighted_linearity_outputproductsleft_table)) * dst_negative_scale_weighted_linearity_outputproductsleft_table)) /\ exists ff_q_pvs_weighted_linearity_outputproductsleft_tableentrynegative. dst_negative_code_weighted_linearity_outputproductsleft_table = ff_q_pvs_weighted_linearity_outputproductsleft_tableentrynegative * S ((S (dst_index_weighted_linearity_outputproductsleft_table)) * dst_negative_scale_weighted_linearity_outputproductsleft_table) + (dst_negative_weighted_linearity_outputproductsleft_table))) /\ (exists ge_balance_positive_weighted_linearity_outputproductsleft_tableentryvalue ge_balance_negative_weighted_linearity_outputproductsleft_tableentryvalue. (((((dst_value_weighted_linearity_outputproductsleft_table) = 2 * (ge_balance_positive_weighted_linearity_outputproductsleft_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_outputproductsleft_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_outputproductsleft_tableentryvaluedecode. (((dst_value_weighted_linearity_outputproductsleft_table) = 2 * ge_signed_half_weighted_linearity_outputproductsleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_outputproductsleft_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_outputproductsleft_tableentryvalue) = S ge_signed_half_weighted_linearity_outputproductsleft_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_outputproductsleft_table) + ge_balance_negative_weighted_linearity_outputproductsleft_tableentryvalue = (dst_negative_weighted_linearity_outputproductsleft_table) + ge_balance_positive_weighted_linearity_outputproductsleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_outputproductsright_table dst_positive_scale_weighted_linearity_outputproductsright_table dst_negative_code_weighted_linearity_outputproductsright_table dst_negative_scale_weighted_linearity_outputproductsright_table. (((H) = (((((dst_positive_code_weighted_linearity_outputproductsright_table) + (dst_positive_scale_weighted_linearity_outputproductsright_table)) * S ((dst_positive_code_weighted_linearity_outputproductsright_table) + (dst_positive_scale_weighted_linearity_outputproductsright_table)) + ((dst_positive_scale_weighted_linearity_outputproductsright_table) + (dst_positive_scale_weighted_linearity_outputproductsright_table))) + (((dst_negative_code_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)) * S ((dst_negative_code_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)) + ((dst_negative_scale_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)))) * S ((((dst_positive_code_weighted_linearity_outputproductsright_table) + (dst_positive_scale_weighted_linearity_outputproductsright_table)) * S ((dst_positive_code_weighted_linearity_outputproductsright_table) + (dst_positive_scale_weighted_linearity_outputproductsright_table)) + ((dst_positive_scale_weighted_linearity_outputproductsright_table) + (dst_positive_scale_weighted_linearity_outputproductsright_table))) + (((dst_negative_code_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)) * S ((dst_negative_code_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)) + ((dst_negative_scale_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)))) + ((((dst_negative_code_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)) * S ((dst_negative_code_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)) + ((dst_negative_scale_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table))) + (((dst_negative_code_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)) * S ((dst_negative_code_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)) + ((dst_negative_scale_weighted_linearity_outputproductsright_table) + (dst_negative_scale_weighted_linearity_outputproductsright_table)))))) /\ (forall dst_index_weighted_linearity_outputproductsright_table. (exists pvs_le_gap_weighted_linearity_outputproductsright_tabledomain. pvs_le_gap_weighted_linearity_outputproductsright_tabledomain + (dst_index_weighted_linearity_outputproductsright_table) = (l)) -> exists dst_positive_weighted_linearity_outputproductsright_table dst_negative_weighted_linearity_outputproductsright_table dst_value_weighted_linearity_outputproductsright_table. ((((exists ff_h_pvs_weighted_linearity_outputproductsright_tableentrypositive. ff_h_pvs_weighted_linearity_outputproductsright_tableentrypositive + S (dst_positive_weighted_linearity_outputproductsright_table) = S ((S (dst_index_weighted_linearity_outputproductsright_table)) * dst_positive_scale_weighted_linearity_outputproductsright_table)) /\ exists ff_q_pvs_weighted_linearity_outputproductsright_tableentrypositive. dst_positive_code_weighted_linearity_outputproductsright_table = ff_q_pvs_weighted_linearity_outputproductsright_tableentrypositive * S ((S (dst_index_weighted_linearity_outputproductsright_table)) * dst_positive_scale_weighted_linearity_outputproductsright_table) + (dst_positive_weighted_linearity_outputproductsright_table))) /\ (((((exists ff_h_pvs_weighted_linearity_outputproductsright_tableentrynegative. ff_h_pvs_weighted_linearity_outputproductsright_tableentrynegative + S (dst_negative_weighted_linearity_outputproductsright_table) = S ((S (dst_index_weighted_linearity_outputproductsright_table)) * dst_negative_scale_weighted_linearity_outputproductsright_table)) /\ exists ff_q_pvs_weighted_linearity_outputproductsright_tableentrynegative. dst_negative_code_weighted_linearity_outputproductsright_table = ff_q_pvs_weighted_linearity_outputproductsright_tableentrynegative * S ((S (dst_index_weighted_linearity_outputproductsright_table)) * dst_negative_scale_weighted_linearity_outputproductsright_table) + (dst_negative_weighted_linearity_outputproductsright_table))) /\ (exists ge_balance_positive_weighted_linearity_outputproductsright_tableentryvalue ge_balance_negative_weighted_linearity_outputproductsright_tableentryvalue. (((((dst_value_weighted_linearity_outputproductsright_table) = 2 * (ge_balance_positive_weighted_linearity_outputproductsright_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_outputproductsright_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_outputproductsright_tableentryvaluedecode. (((dst_value_weighted_linearity_outputproductsright_table) = 2 * ge_signed_half_weighted_linearity_outputproductsright_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_outputproductsright_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_outputproductsright_tableentryvalue) = S ge_signed_half_weighted_linearity_outputproductsright_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_outputproductsright_table) + ge_balance_negative_weighted_linearity_outputproductsright_tableentryvalue = (dst_negative_weighted_linearity_outputproductsright_table) + ge_balance_positive_weighted_linearity_outputproductsright_tableentryvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_outputproductsoutput_table dst_positive_scale_weighted_linearity_outputproductsoutput_table dst_negative_code_weighted_linearity_outputproductsoutput_table dst_negative_scale_weighted_linearity_outputproductsoutput_table. (((sws_product_table_weighted_linearity_output) = (((((dst_positive_code_weighted_linearity_outputproductsoutput_table) + (dst_positive_scale_weighted_linearity_outputproductsoutput_table)) * S ((dst_positive_code_weighted_linearity_outputproductsoutput_table) + (dst_positive_scale_weighted_linearity_outputproductsoutput_table)) + ((dst_positive_scale_weighted_linearity_outputproductsoutput_table) + (dst_positive_scale_weighted_linearity_outputproductsoutput_table))) + (((dst_negative_code_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)))) * S ((((dst_positive_code_weighted_linearity_outputproductsoutput_table) + (dst_positive_scale_weighted_linearity_outputproductsoutput_table)) * S ((dst_positive_code_weighted_linearity_outputproductsoutput_table) + (dst_positive_scale_weighted_linearity_outputproductsoutput_table)) + ((dst_positive_scale_weighted_linearity_outputproductsoutput_table) + (dst_positive_scale_weighted_linearity_outputproductsoutput_table))) + (((dst_negative_code_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)))) + ((((dst_negative_code_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table))) + (((dst_negative_code_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)) * S ((dst_negative_code_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)) + ((dst_negative_scale_weighted_linearity_outputproductsoutput_table) + (dst_negative_scale_weighted_linearity_outputproductsoutput_table)))))) /\ (forall dst_index_weighted_linearity_outputproductsoutput_table. (exists pvs_le_gap_weighted_linearity_outputproductsoutput_tabledomain. pvs_le_gap_weighted_linearity_outputproductsoutput_tabledomain + (dst_index_weighted_linearity_outputproductsoutput_table) = (l)) -> exists dst_positive_weighted_linearity_outputproductsoutput_table dst_negative_weighted_linearity_outputproductsoutput_table dst_value_weighted_linearity_outputproductsoutput_table. ((((exists ff_h_pvs_weighted_linearity_outputproductsoutput_tableentrypositive. ff_h_pvs_weighted_linearity_outputproductsoutput_tableentrypositive + S (dst_positive_weighted_linearity_outputproductsoutput_table) = S ((S (dst_index_weighted_linearity_outputproductsoutput_table)) * dst_positive_scale_weighted_linearity_outputproductsoutput_table)) /\ exists ff_q_pvs_weighted_linearity_outputproductsoutput_tableentrypositive. dst_positive_code_weighted_linearity_outputproductsoutput_table = ff_q_pvs_weighted_linearity_outputproductsoutput_tableentrypositive * S ((S (dst_index_weighted_linearity_outputproductsoutput_table)) * dst_positive_scale_weighted_linearity_outputproductsoutput_table) + (dst_positive_weighted_linearity_outputproductsoutput_table))) /\ (((((exists ff_h_pvs_weighted_linearity_outputproductsoutput_tableentrynegative. ff_h_pvs_weighted_linearity_outputproductsoutput_tableentrynegative + S (dst_negative_weighted_linearity_outputproductsoutput_table) = S ((S (dst_index_weighted_linearity_outputproductsoutput_table)) * dst_negative_scale_weighted_linearity_outputproductsoutput_table)) /\ exists ff_q_pvs_weighted_linearity_outputproductsoutput_tableentrynegative. dst_negative_code_weighted_linearity_outputproductsoutput_table = ff_q_pvs_weighted_linearity_outputproductsoutput_tableentrynegative * S ((S (dst_index_weighted_linearity_outputproductsoutput_table)) * dst_negative_scale_weighted_linearity_outputproductsoutput_table) + (dst_negative_weighted_linearity_outputproductsoutput_table))) /\ (exists ge_balance_positive_weighted_linearity_outputproductsoutput_tableentryvalue ge_balance_negative_weighted_linearity_outputproductsoutput_tableentryvalue. (((((dst_value_weighted_linearity_outputproductsoutput_table) = 2 * (ge_balance_positive_weighted_linearity_outputproductsoutput_tableentryvalue) /\ (ge_balance_negative_weighted_linearity_outputproductsoutput_tableentryvalue) = 0) \/ exists ge_signed_half_weighted_linearity_outputproductsoutput_tableentryvaluedecode. (((dst_value_weighted_linearity_outputproductsoutput_table) = 2 * ge_signed_half_weighted_linearity_outputproductsoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_outputproductsoutput_tableentryvalue) = 0) /\ (ge_balance_negative_weighted_linearity_outputproductsoutput_tableentryvalue) = S ge_signed_half_weighted_linearity_outputproductsoutput_tableentryvaluedecode))) /\ ((dst_positive_weighted_linearity_outputproductsoutput_table) + ge_balance_negative_weighted_linearity_outputproductsoutput_tableentryvalue = (dst_negative_weighted_linearity_outputproductsoutput_table) + ge_balance_positive_weighted_linearity_outputproductsoutput_tableentryvalue))))))))) /\ (forall sto_index_weighted_linearity_outputproductsentries. (exists pvs_gap_weighted_linearity_outputproductsentriesbound. pvs_gap_weighted_linearity_outputproductsentriesbound + S (sto_index_weighted_linearity_outputproductsentries) = (l)) -> exists sto_left_weighted_linearity_outputproductsentries sto_right_weighted_linearity_outputproductsentries sto_output_weighted_linearity_outputproductsentries. ((exists dst_positive_code_weighted_linearity_outputproductsentriesentryleft dst_positive_scale_weighted_linearity_outputproductsentriesentryleft dst_negative_code_weighted_linearity_outputproductsentriesentryleft dst_negative_scale_weighted_linearity_outputproductsentriesentryleft dst_positive_weighted_linearity_outputproductsentriesentryleft dst_negative_weighted_linearity_outputproductsentriesentryleft. (((W) = (((((dst_positive_code_weighted_linearity_outputproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryleft)) * S ((dst_positive_code_weighted_linearity_outputproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryleft)) + ((dst_positive_scale_weighted_linearity_outputproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryleft))) + (((dst_negative_code_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)))) * S ((((dst_positive_code_weighted_linearity_outputproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryleft)) * S ((dst_positive_code_weighted_linearity_outputproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryleft)) + ((dst_positive_scale_weighted_linearity_outputproductsentriesentryleft) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryleft))) + (((dst_negative_code_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)))) + ((((dst_negative_code_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft))) + (((dst_negative_code_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)))))) /\ (((((exists ff_h_pvs_weighted_linearity_outputproductsentriesentryleftpositive. ff_h_pvs_weighted_linearity_outputproductsentriesentryleftpositive + S (dst_positive_weighted_linearity_outputproductsentriesentryleft) = S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_positive_scale_weighted_linearity_outputproductsentriesentryleft)) /\ exists ff_q_pvs_weighted_linearity_outputproductsentriesentryleftpositive. dst_positive_code_weighted_linearity_outputproductsentriesentryleft = ff_q_pvs_weighted_linearity_outputproductsentriesentryleftpositive * S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_positive_scale_weighted_linearity_outputproductsentriesentryleft) + (dst_positive_weighted_linearity_outputproductsentriesentryleft))) /\ (((((exists ff_h_pvs_weighted_linearity_outputproductsentriesentryleftnegative. ff_h_pvs_weighted_linearity_outputproductsentriesentryleftnegative + S (dst_negative_weighted_linearity_outputproductsentriesentryleft) = S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_negative_scale_weighted_linearity_outputproductsentriesentryleft)) /\ exists ff_q_pvs_weighted_linearity_outputproductsentriesentryleftnegative. dst_negative_code_weighted_linearity_outputproductsentriesentryleft = ff_q_pvs_weighted_linearity_outputproductsentriesentryleftnegative * S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_negative_scale_weighted_linearity_outputproductsentriesentryleft) + (dst_negative_weighted_linearity_outputproductsentriesentryleft))) /\ (exists ge_balance_positive_weighted_linearity_outputproductsentriesentryleftvalue ge_balance_negative_weighted_linearity_outputproductsentriesentryleftvalue. (((((sto_left_weighted_linearity_outputproductsentries) = 2 * (ge_balance_positive_weighted_linearity_outputproductsentriesentryleftvalue) /\ (ge_balance_negative_weighted_linearity_outputproductsentriesentryleftvalue) = 0) \/ exists ge_signed_half_weighted_linearity_outputproductsentriesentryleftvaluedecode. (((sto_left_weighted_linearity_outputproductsentries) = 2 * ge_signed_half_weighted_linearity_outputproductsentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_outputproductsentriesentryleftvalue) = 0) /\ (ge_balance_negative_weighted_linearity_outputproductsentriesentryleftvalue) = S ge_signed_half_weighted_linearity_outputproductsentriesentryleftvaluedecode))) /\ ((dst_positive_weighted_linearity_outputproductsentriesentryleft) + ge_balance_negative_weighted_linearity_outputproductsentriesentryleftvalue = (dst_negative_weighted_linearity_outputproductsentriesentryleft) + ge_balance_positive_weighted_linearity_outputproductsentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_outputproductsentriesentryright dst_positive_scale_weighted_linearity_outputproductsentriesentryright dst_negative_code_weighted_linearity_outputproductsentriesentryright dst_negative_scale_weighted_linearity_outputproductsentriesentryright dst_positive_weighted_linearity_outputproductsentriesentryright dst_negative_weighted_linearity_outputproductsentriesentryright. (((H) = (((((dst_positive_code_weighted_linearity_outputproductsentriesentryright) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryright)) * S ((dst_positive_code_weighted_linearity_outputproductsentriesentryright) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryright)) + ((dst_positive_scale_weighted_linearity_outputproductsentriesentryright) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryright))) + (((dst_negative_code_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)))) * S ((((dst_positive_code_weighted_linearity_outputproductsentriesentryright) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryright)) * S ((dst_positive_code_weighted_linearity_outputproductsentriesentryright) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryright)) + ((dst_positive_scale_weighted_linearity_outputproductsentriesentryright) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryright))) + (((dst_negative_code_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)))) + ((((dst_negative_code_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright))) + (((dst_negative_code_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryright) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryright)))))) /\ (((((exists ff_h_pvs_weighted_linearity_outputproductsentriesentryrightpositive. ff_h_pvs_weighted_linearity_outputproductsentriesentryrightpositive + S (dst_positive_weighted_linearity_outputproductsentriesentryright) = S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_positive_scale_weighted_linearity_outputproductsentriesentryright)) /\ exists ff_q_pvs_weighted_linearity_outputproductsentriesentryrightpositive. dst_positive_code_weighted_linearity_outputproductsentriesentryright = ff_q_pvs_weighted_linearity_outputproductsentriesentryrightpositive * S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_positive_scale_weighted_linearity_outputproductsentriesentryright) + (dst_positive_weighted_linearity_outputproductsentriesentryright))) /\ (((((exists ff_h_pvs_weighted_linearity_outputproductsentriesentryrightnegative. ff_h_pvs_weighted_linearity_outputproductsentriesentryrightnegative + S (dst_negative_weighted_linearity_outputproductsentriesentryright) = S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_negative_scale_weighted_linearity_outputproductsentriesentryright)) /\ exists ff_q_pvs_weighted_linearity_outputproductsentriesentryrightnegative. dst_negative_code_weighted_linearity_outputproductsentriesentryright = ff_q_pvs_weighted_linearity_outputproductsentriesentryrightnegative * S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_negative_scale_weighted_linearity_outputproductsentriesentryright) + (dst_negative_weighted_linearity_outputproductsentriesentryright))) /\ (exists ge_balance_positive_weighted_linearity_outputproductsentriesentryrightvalue ge_balance_negative_weighted_linearity_outputproductsentriesentryrightvalue. (((((sto_right_weighted_linearity_outputproductsentries) = 2 * (ge_balance_positive_weighted_linearity_outputproductsentriesentryrightvalue) /\ (ge_balance_negative_weighted_linearity_outputproductsentriesentryrightvalue) = 0) \/ exists ge_signed_half_weighted_linearity_outputproductsentriesentryrightvaluedecode. (((sto_right_weighted_linearity_outputproductsentries) = 2 * ge_signed_half_weighted_linearity_outputproductsentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_outputproductsentriesentryrightvalue) = 0) /\ (ge_balance_negative_weighted_linearity_outputproductsentriesentryrightvalue) = S ge_signed_half_weighted_linearity_outputproductsentriesentryrightvaluedecode))) /\ ((dst_positive_weighted_linearity_outputproductsentriesentryright) + ge_balance_negative_weighted_linearity_outputproductsentriesentryrightvalue = (dst_negative_weighted_linearity_outputproductsentriesentryright) + ge_balance_positive_weighted_linearity_outputproductsentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_weighted_linearity_outputproductsentriesentryoutput dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput dst_negative_code_weighted_linearity_outputproductsentriesentryoutput dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput dst_positive_weighted_linearity_outputproductsentriesentryoutput dst_negative_weighted_linearity_outputproductsentriesentryoutput. (((sws_product_table_weighted_linearity_output) = (((((dst_positive_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput)) * S ((dst_positive_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput)) + ((dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput))) + (((dst_negative_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)))) * S ((((dst_positive_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput)) * S ((dst_positive_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput)) + ((dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput) + (dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput))) + (((dst_negative_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)))) + ((((dst_negative_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput))) + (((dst_negative_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)) * S ((dst_negative_code_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)) + ((dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)))))) /\ (((((exists ff_h_pvs_weighted_linearity_outputproductsentriesentryoutputpositive. ff_h_pvs_weighted_linearity_outputproductsentriesentryoutputpositive + S (dst_positive_weighted_linearity_outputproductsentriesentryoutput) = S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput)) /\ exists ff_q_pvs_weighted_linearity_outputproductsentriesentryoutputpositive. dst_positive_code_weighted_linearity_outputproductsentriesentryoutput = ff_q_pvs_weighted_linearity_outputproductsentriesentryoutputpositive * S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_positive_scale_weighted_linearity_outputproductsentriesentryoutput) + (dst_positive_weighted_linearity_outputproductsentriesentryoutput))) /\ (((((exists ff_h_pvs_weighted_linearity_outputproductsentriesentryoutputnegative. ff_h_pvs_weighted_linearity_outputproductsentriesentryoutputnegative + S (dst_negative_weighted_linearity_outputproductsentriesentryoutput) = S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput)) /\ exists ff_q_pvs_weighted_linearity_outputproductsentriesentryoutputnegative. dst_negative_code_weighted_linearity_outputproductsentriesentryoutput = ff_q_pvs_weighted_linearity_outputproductsentriesentryoutputnegative * S ((S (sto_index_weighted_linearity_outputproductsentries)) * dst_negative_scale_weighted_linearity_outputproductsentriesentryoutput) + (dst_negative_weighted_linearity_outputproductsentriesentryoutput))) /\ (exists ge_balance_positive_weighted_linearity_outputproductsentriesentryoutputvalue ge_balance_negative_weighted_linearity_outputproductsentriesentryoutputvalue. (((((sto_output_weighted_linearity_outputproductsentries) = 2 * (ge_balance_positive_weighted_linearity_outputproductsentriesentryoutputvalue) /\ (ge_balance_negative_weighted_linearity_outputproductsentriesentryoutputvalue) = 0) \/ exists ge_signed_half_weighted_linearity_outputproductsentriesentryoutputvaluedecode. (((sto_output_weighted_linearity_outputproductsentries) = 2 * ge_signed_half_weighted_linearity_outputproductsentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_weighted_linearity_outputproductsentriesentryoutputvalue) = 0) /\ (ge_balance_negative_weighted_linearity_outputproductsentriesentryoutputvalue) = S ge_signed_half_weighted_linearity_outputproductsentriesentryoutputvaluedecode))) /\ ((dst_positive_weighted_linearity_outputproductsentriesentryoutput) + ge_balance_negative_weighted_linearity_outputproductsentriesentryoutputvalue = (dst_negative_weighted_linearity_outputproductsentriesentryoutput) + ge_balance_positive_weighted_linearity_outputproductsentriesentryoutputvalue))))))))) /\ (exists sto_ap_weighted_linearity_outputproductsentriesentryoperation sto_an_weighted_linearity_outputproductsentriesentryoperation sto_bp_weighted_linearity_outputproductsentriesentryoperation sto_bn_weighted_linearity_outputproductsentriesentryoperation sto_cp_weighted_linearity_outputproductsentriesentryoperation sto_cn_weighted_linearity_outputproductsentriesentryoperation. (((((sto_left_weighted_linearity_outputproductsentries) = 2 * (sto_ap_weighted_linearity_outputproductsentriesentryoperation) /\ (sto_an_weighted_linearity_outputproductsentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_outputproductsentriesentryoperationleft. (((sto_left_weighted_linearity_outputproductsentries) = 2 * ge_signed_half_weighted_linearity_outputproductsentriesentryoperationleft + 1 /\ (sto_ap_weighted_linearity_outputproductsentriesentryoperation) = 0) /\ (sto_an_weighted_linearity_outputproductsentriesentryoperation) = S ge_signed_half_weighted_linearity_outputproductsentriesentryoperationleft))) /\ ((((((sto_right_weighted_linearity_outputproductsentries) = 2 * (sto_bp_weighted_linearity_outputproductsentriesentryoperation) /\ (sto_bn_weighted_linearity_outputproductsentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_outputproductsentriesentryoperationright. (((sto_right_weighted_linearity_outputproductsentries) = 2 * ge_signed_half_weighted_linearity_outputproductsentriesentryoperationright + 1 /\ (sto_bp_weighted_linearity_outputproductsentriesentryoperation) = 0) /\ (sto_bn_weighted_linearity_outputproductsentriesentryoperation) = S ge_signed_half_weighted_linearity_outputproductsentriesentryoperationright))) /\ ((((((sto_output_weighted_linearity_outputproductsentries) = 2 * (sto_cp_weighted_linearity_outputproductsentriesentryoperation) /\ (sto_cn_weighted_linearity_outputproductsentriesentryoperation) = 0) \/ exists ge_signed_half_weighted_linearity_outputproductsentriesentryoperationoutput. (((sto_output_weighted_linearity_outputproductsentries) = 2 * ge_signed_half_weighted_linearity_outputproductsentriesentryoperationoutput + 1 /\ (sto_cp_weighted_linearity_outputproductsentriesentryoperation) = 0) /\ (sto_cn_weighted_linearity_outputproductsentriesentryoperation) = S ge_signed_half_weighted_linearity_outputproductsentriesentryoperationoutput))) /\ ((sto_ap_weighted_linearity_outputproductsentriesentryoperation * sto_bp_weighted_linearity_outputproductsentriesentryoperation + sto_an_weighted_linearity_outputproductsentriesentryoperation * sto_bn_weighted_linearity_outputproductsentriesentryoperation) + sto_cn_weighted_linearity_outputproductsentriesentryoperation = (sto_ap_weighted_linearity_outputproductsentriesentryoperation * sto_bn_weighted_linearity_outputproductsentriesentryoperation + sto_an_weighted_linearity_outputproductsentriesentryoperation * sto_bp_weighted_linearity_outputproductsentriesentryoperation) + sto_cp_weighted_linearity_outputproductsentriesentryoperation))))))))))))))))))) /\ (exists dst_positive_code_weighted_linearity_outputsum dst_positive_scale_weighted_linearity_outputsum dst_negative_code_weighted_linearity_outputsum dst_negative_scale_weighted_linearity_outputsum dst_positive_sum_weighted_linearity_outputsum dst_negative_sum_weighted_linearity_outputsum. (((sws_product_table_weighted_linearity_output) = (((((dst_positive_code_weighted_linearity_outputsum) + (dst_positive_scale_weighted_linearity_outputsum)) * S ((dst_positive_code_weighted_linearity_outputsum) + (dst_positive_scale_weighted_linearity_outputsum)) + ((dst_positive_scale_weighted_linearity_outputsum) + (dst_positive_scale_weighted_linearity_outputsum))) + (((dst_negative_code_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)) * S ((dst_negative_code_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)) + ((dst_negative_scale_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)))) * S ((((dst_positive_code_weighted_linearity_outputsum) + (dst_positive_scale_weighted_linearity_outputsum)) * S ((dst_positive_code_weighted_linearity_outputsum) + (dst_positive_scale_weighted_linearity_outputsum)) + ((dst_positive_scale_weighted_linearity_outputsum) + (dst_positive_scale_weighted_linearity_outputsum))) + (((dst_negative_code_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)) * S ((dst_negative_code_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)) + ((dst_negative_scale_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)))) + ((((dst_negative_code_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)) * S ((dst_negative_code_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)) + ((dst_negative_scale_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum))) + (((dst_negative_code_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)) * S ((dst_negative_code_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)) + ((dst_negative_scale_weighted_linearity_outputsum) + (dst_negative_scale_weighted_linearity_outputsum)))))) /\ (((exists fs_u_dst_weighted_linearity_outputsumpositive fs_v_dst_weighted_linearity_outputsumpositive. ((((exists fs_h_dst_weighted_linearity_outputsumpositive_body_start. fs_h_dst_weighted_linearity_outputsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_weighted_linearity_outputsumpositive)) /\ exists fs_q_dst_weighted_linearity_outputsumpositive_body_start. fs_u_dst_weighted_linearity_outputsumpositive = fs_q_dst_weighted_linearity_outputsumpositive_body_start * S ((S (0)) * fs_v_dst_weighted_linearity_outputsumpositive) + (0))) /\ ((((exists fs_h_dst_weighted_linearity_outputsumpositive_body_terminal. fs_h_dst_weighted_linearity_outputsumpositive_body_terminal + S (dst_positive_sum_weighted_linearity_outputsum) = S ((S (l)) * fs_v_dst_weighted_linearity_outputsumpositive)) /\ exists fs_q_dst_weighted_linearity_outputsumpositive_body_terminal. fs_u_dst_weighted_linearity_outputsumpositive = fs_q_dst_weighted_linearity_outputsumpositive_body_terminal * S ((S (l)) * fs_v_dst_weighted_linearity_outputsumpositive) + (dst_positive_sum_weighted_linearity_outputsum))) /\ forall fs_i_dst_weighted_linearity_outputsumpositive_body_steps. (exists fs_lt_dst_weighted_linearity_outputsumpositive_body_steps_bound. fs_lt_dst_weighted_linearity_outputsumpositive_body_steps_bound + S fs_i_dst_weighted_linearity_outputsumpositive_body_steps = l) -> exists fs_a_dst_weighted_linearity_outputsumpositive_body_steps fs_r_dst_weighted_linearity_outputsumpositive_body_steps fs_s_dst_weighted_linearity_outputsumpositive_body_steps. ((((exists fs_h_dst_weighted_linearity_outputsumpositive_body_steps_summand. fs_h_dst_weighted_linearity_outputsumpositive_body_steps_summand + S (fs_a_dst_weighted_linearity_outputsumpositive_body_steps) = S ((S (fs_i_dst_weighted_linearity_outputsumpositive_body_steps)) * dst_positive_scale_weighted_linearity_outputsum)) /\ exists fs_q_dst_weighted_linearity_outputsumpositive_body_steps_summand. dst_positive_code_weighted_linearity_outputsum = fs_q_dst_weighted_linearity_outputsumpositive_body_steps_summand * S ((S (fs_i_dst_weighted_linearity_outputsumpositive_body_steps)) * dst_positive_scale_weighted_linearity_outputsum) + (fs_a_dst_weighted_linearity_outputsumpositive_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_outputsumpositive_body_steps_partial. fs_h_dst_weighted_linearity_outputsumpositive_body_steps_partial + S (fs_r_dst_weighted_linearity_outputsumpositive_body_steps) = S ((S (fs_i_dst_weighted_linearity_outputsumpositive_body_steps)) * fs_v_dst_weighted_linearity_outputsumpositive)) /\ exists fs_q_dst_weighted_linearity_outputsumpositive_body_steps_partial. fs_u_dst_weighted_linearity_outputsumpositive = fs_q_dst_weighted_linearity_outputsumpositive_body_steps_partial * S ((S (fs_i_dst_weighted_linearity_outputsumpositive_body_steps)) * fs_v_dst_weighted_linearity_outputsumpositive) + (fs_r_dst_weighted_linearity_outputsumpositive_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_outputsumpositive_body_steps_successor. fs_h_dst_weighted_linearity_outputsumpositive_body_steps_successor + S (fs_s_dst_weighted_linearity_outputsumpositive_body_steps) = S ((S (S fs_i_dst_weighted_linearity_outputsumpositive_body_steps)) * fs_v_dst_weighted_linearity_outputsumpositive)) /\ exists fs_q_dst_weighted_linearity_outputsumpositive_body_steps_successor. fs_u_dst_weighted_linearity_outputsumpositive = fs_q_dst_weighted_linearity_outputsumpositive_body_steps_successor * S ((S (S fs_i_dst_weighted_linearity_outputsumpositive_body_steps)) * fs_v_dst_weighted_linearity_outputsumpositive) + (fs_s_dst_weighted_linearity_outputsumpositive_body_steps))) /\ fs_s_dst_weighted_linearity_outputsumpositive_body_steps = fs_r_dst_weighted_linearity_outputsumpositive_body_steps + fs_a_dst_weighted_linearity_outputsumpositive_body_steps)))))) /\ (((exists fs_u_dst_weighted_linearity_outputsumnegative fs_v_dst_weighted_linearity_outputsumnegative. ((((exists fs_h_dst_weighted_linearity_outputsumnegative_body_start. fs_h_dst_weighted_linearity_outputsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_weighted_linearity_outputsumnegative)) /\ exists fs_q_dst_weighted_linearity_outputsumnegative_body_start. fs_u_dst_weighted_linearity_outputsumnegative = fs_q_dst_weighted_linearity_outputsumnegative_body_start * S ((S (0)) * fs_v_dst_weighted_linearity_outputsumnegative) + (0))) /\ ((((exists fs_h_dst_weighted_linearity_outputsumnegative_body_terminal. fs_h_dst_weighted_linearity_outputsumnegative_body_terminal + S (dst_negative_sum_weighted_linearity_outputsum) = S ((S (l)) * fs_v_dst_weighted_linearity_outputsumnegative)) /\ exists fs_q_dst_weighted_linearity_outputsumnegative_body_terminal. fs_u_dst_weighted_linearity_outputsumnegative = fs_q_dst_weighted_linearity_outputsumnegative_body_terminal * S ((S (l)) * fs_v_dst_weighted_linearity_outputsumnegative) + (dst_negative_sum_weighted_linearity_outputsum))) /\ forall fs_i_dst_weighted_linearity_outputsumnegative_body_steps. (exists fs_lt_dst_weighted_linearity_outputsumnegative_body_steps_bound. fs_lt_dst_weighted_linearity_outputsumnegative_body_steps_bound + S fs_i_dst_weighted_linearity_outputsumnegative_body_steps = l) -> exists fs_a_dst_weighted_linearity_outputsumnegative_body_steps fs_r_dst_weighted_linearity_outputsumnegative_body_steps fs_s_dst_weighted_linearity_outputsumnegative_body_steps. ((((exists fs_h_dst_weighted_linearity_outputsumnegative_body_steps_summand. fs_h_dst_weighted_linearity_outputsumnegative_body_steps_summand + S (fs_a_dst_weighted_linearity_outputsumnegative_body_steps) = S ((S (fs_i_dst_weighted_linearity_outputsumnegative_body_steps)) * dst_negative_scale_weighted_linearity_outputsum)) /\ exists fs_q_dst_weighted_linearity_outputsumnegative_body_steps_summand. dst_negative_code_weighted_linearity_outputsum = fs_q_dst_weighted_linearity_outputsumnegative_body_steps_summand * S ((S (fs_i_dst_weighted_linearity_outputsumnegative_body_steps)) * dst_negative_scale_weighted_linearity_outputsum) + (fs_a_dst_weighted_linearity_outputsumnegative_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_outputsumnegative_body_steps_partial. fs_h_dst_weighted_linearity_outputsumnegative_body_steps_partial + S (fs_r_dst_weighted_linearity_outputsumnegative_body_steps) = S ((S (fs_i_dst_weighted_linearity_outputsumnegative_body_steps)) * fs_v_dst_weighted_linearity_outputsumnegative)) /\ exists fs_q_dst_weighted_linearity_outputsumnegative_body_steps_partial. fs_u_dst_weighted_linearity_outputsumnegative = fs_q_dst_weighted_linearity_outputsumnegative_body_steps_partial * S ((S (fs_i_dst_weighted_linearity_outputsumnegative_body_steps)) * fs_v_dst_weighted_linearity_outputsumnegative) + (fs_r_dst_weighted_linearity_outputsumnegative_body_steps))) /\ ((((exists fs_h_dst_weighted_linearity_outputsumnegative_body_steps_successor. fs_h_dst_weighted_linearity_outputsumnegative_body_steps_successor + S (fs_s_dst_weighted_linearity_outputsumnegative_body_steps) = S ((S (S fs_i_dst_weighted_linearity_outputsumnegative_body_steps)) * fs_v_dst_weighted_linearity_outputsumnegative)) /\ exists fs_q_dst_weighted_linearity_outputsumnegative_body_steps_successor. fs_u_dst_weighted_linearity_outputsumnegative = fs_q_dst_weighted_linearity_outputsumnegative_body_steps_successor * S ((S (S fs_i_dst_weighted_linearity_outputsumnegative_body_steps)) * fs_v_dst_weighted_linearity_outputsumnegative) + (fs_s_dst_weighted_linearity_outputsumnegative_body_steps))) /\ fs_s_dst_weighted_linearity_outputsumnegative_body_steps = fs_r_dst_weighted_linearity_outputsumnegative_body_steps + fs_a_dst_weighted_linearity_outputsumnegative_body_steps)))))) /\ (exists ge_balance_positive_weighted_linearity_outputsumresult ge_balance_negative_weighted_linearity_outputsumresult. (((((c) = 2 * (ge_balance_positive_weighted_linearity_outputsumresult) /\ (ge_balance_negative_weighted_linearity_outputsumresult) = 0) \/ exists ge_signed_half_weighted_linearity_outputsumresultdecode. (((c) = 2 * ge_signed_half_weighted_linearity_outputsumresultdecode + 1 /\ (ge_balance_positive_weighted_linearity_outputsumresult) = 0) /\ (ge_balance_negative_weighted_linearity_outputsumresult) = S ge_signed_half_weighted_linearity_outputsumresultdecode))) /\ ((dst_positive_sum_weighted_linearity_outputsum) + ge_balance_negative_weighted_linearity_outputsumresult = (dst_negative_sum_weighted_linearity_outputsum) + ge_balance_positive_weighted_linearity_outputsumresult))))))))))) -> (exists dsa_ap_weighted_linearity_result dsa_an_weighted_linearity_result dsa_bp_weighted_linearity_result dsa_bn_weighted_linearity_result dsa_cp_weighted_linearity_result dsa_cn_weighted_linearity_result. (((((a) = 2 * (dsa_ap_weighted_linearity_result) /\ (dsa_an_weighted_linearity_result) = 0) \/ exists ge_signed_half_weighted_linearity_resultleft. (((a) = 2 * ge_signed_half_weighted_linearity_resultleft + 1 /\ (dsa_ap_weighted_linearity_result) = 0) /\ (dsa_an_weighted_linearity_result) = S ge_signed_half_weighted_linearity_resultleft))) /\ ((((((b) = 2 * (dsa_bp_weighted_linearity_result) /\ (dsa_bn_weighted_linearity_result) = 0) \/ exists ge_signed_half_weighted_linearity_resultright. (((b) = 2 * ge_signed_half_weighted_linearity_resultright + 1 /\ (dsa_bp_weighted_linearity_result) = 0) /\ (dsa_bn_weighted_linearity_result) = S ge_signed_half_weighted_linearity_resultright))) /\ ((((((c) = 2 * (dsa_cp_weighted_linearity_result) /\ (dsa_cn_weighted_linearity_result) = 0) \/ exists ge_signed_half_weighted_linearity_resultoutput. (((c) = 2 * ge_signed_half_weighted_linearity_resultoutput + 1 /\ (dsa_cp_weighted_linearity_result) = 0) /\ (dsa_cn_weighted_linearity_result) = S ge_signed_half_weighted_linearity_resultoutput))) /\ ((dsa_ap_weighted_linearity_result + dsa_bp_weighted_linearity_result) + dsa_cn_weighted_linearity_result = (dsa_an_weighted_linearity_result + dsa_bn_weighted_linearity_result) + dsa_cp_weighted_linearity_result)))))))Complete tactic proof in conservative notation
All 42 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay script.
Read the argument
Proof checkpoints
42 script commands · 6 reading checkpoints · 0 local claims
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.
Named ingredients (2)
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–12
03Separate the logical casesL13–18
04Use earlier factsL19–28
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L19
specialize signed_prefix_sum_pointwise_add (l) - L20
specialize signed_prefix_sum_pointwise_add (x) - L21
specialize signed_prefix_sum_pointwise_add (x1) - L22
specialize signed_prefix_sum_pointwise_add (x2) - L23
specialize signed_prefix_sum_pointwise_add (a) - L24
specialize signed_prefix_sum_pointwise_add (b) - L25
specialize signed_prefix_sum_pointwise_add (c) - L26
apply signed_prefix_sum_pointwise_add - L27
specialize signed_table_weighted_add_distributive (l) - L28
specialize signed_table_weighted_add_distributive (W)
05Use earlier factsL29–38
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L29
specialize signed_table_weighted_add_distributive (F) - L30
specialize signed_table_weighted_add_distributive (G) - L31
specialize signed_table_weighted_add_distributive (H) - L32
specialize signed_table_weighted_add_distributive (x) - L33
specialize signed_table_weighted_add_distributive (x1) - L34
specialize signed_table_weighted_add_distributive (x2) - L35
apply signed_table_weighted_add_distributive - L36
exact hpoint - L37
exact hF_witness_left - L38
exact hG_witness_left
Original defined command ledger · 42 lines
- 0001
intro l - 0002
intro W - 0003
intro F - 0004
intro G - 0005
intro H - 0006
intro a - 0007
intro b - 0008
intro c - 0009
intro hpoint - 0010
intro hF - 0011
intro hG - 0012
intro hH - 0013
cases hF - 0014
cases hF_witness - 0015
cases hG - 0016
cases hG_witness - 0017
cases hH - 0018
cases hH_witness - 0019
specialize signed_prefix_sum_pointwise_add (l) - 0020
specialize signed_prefix_sum_pointwise_add (x) - 0021
specialize signed_prefix_sum_pointwise_add (x1) - 0022
specialize signed_prefix_sum_pointwise_add (x2) - 0023
specialize signed_prefix_sum_pointwise_add (a) - 0024
specialize signed_prefix_sum_pointwise_add (b) - 0025
specialize signed_prefix_sum_pointwise_add (c) - 0026
apply signed_prefix_sum_pointwise_add - 0027
specialize signed_table_weighted_add_distributive (l) - 0028
specialize signed_table_weighted_add_distributive (W) - 0029
specialize signed_table_weighted_add_distributive (F) - 0030
specialize signed_table_weighted_add_distributive (G) - 0031
specialize signed_table_weighted_add_distributive (H) - 0032
specialize signed_table_weighted_add_distributive (x) - 0033
specialize signed_table_weighted_add_distributive (x1) - 0034
specialize signed_table_weighted_add_distributive (x2) - 0035
apply signed_table_weighted_add_distributive - 0036
exact hpoint - 0037
exact hF_witness_left - 0038
exact hG_witness_left - 0039
exact hH_witness_left - 0040
exact hF_witness_right - 0041
exact hG_witness_right - 0042
exact hH_witness_right