Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Exact expanded first-order arithmetic statement
forall F G H K l. (((exists dst_positive_code_add_unique_firstleft_table dst_positive_scale_add_unique_firstleft_table dst_negative_code_add_unique_firstleft_table dst_negative_scale_add_unique_firstleft_table. (((F) = (((((dst_positive_code_add_unique_firstleft_table) + (dst_positive_scale_add_unique_firstleft_table)) * S ((dst_positive_code_add_unique_firstleft_table) + (dst_positive_scale_add_unique_firstleft_table)) + ((dst_positive_scale_add_unique_firstleft_table) + (dst_positive_scale_add_unique_firstleft_table))) + (((dst_negative_code_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)) * S ((dst_negative_code_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)) + ((dst_negative_scale_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)))) * S ((((dst_positive_code_add_unique_firstleft_table) + (dst_positive_scale_add_unique_firstleft_table)) * S ((dst_positive_code_add_unique_firstleft_table) + (dst_positive_scale_add_unique_firstleft_table)) + ((dst_positive_scale_add_unique_firstleft_table) + (dst_positive_scale_add_unique_firstleft_table))) + (((dst_negative_code_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)) * S ((dst_negative_code_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)) + ((dst_negative_scale_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)))) + ((((dst_negative_code_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)) * S ((dst_negative_code_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)) + ((dst_negative_scale_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table))) + (((dst_negative_code_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)) * S ((dst_negative_code_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)) + ((dst_negative_scale_add_unique_firstleft_table) + (dst_negative_scale_add_unique_firstleft_table)))))) /\ (forall dst_index_add_unique_firstleft_table. (exists pvs_le_gap_add_unique_firstleft_tabledomain. pvs_le_gap_add_unique_firstleft_tabledomain + (dst_index_add_unique_firstleft_table) = (l)) -> exists dst_positive_add_unique_firstleft_table dst_negative_add_unique_firstleft_table dst_value_add_unique_firstleft_table. ((((exists ff_h_pvs_add_unique_firstleft_tableentrypositive. ff_h_pvs_add_unique_firstleft_tableentrypositive + S (dst_positive_add_unique_firstleft_table) = S ((S (dst_index_add_unique_firstleft_table)) * dst_positive_scale_add_unique_firstleft_table)) /\ exists ff_q_pvs_add_unique_firstleft_tableentrypositive. dst_positive_code_add_unique_firstleft_table = ff_q_pvs_add_unique_firstleft_tableentrypositive * S ((S (dst_index_add_unique_firstleft_table)) * dst_positive_scale_add_unique_firstleft_table) + (dst_positive_add_unique_firstleft_table))) /\ (((((exists ff_h_pvs_add_unique_firstleft_tableentrynegative. ff_h_pvs_add_unique_firstleft_tableentrynegative + S (dst_negative_add_unique_firstleft_table) = S ((S (dst_index_add_unique_firstleft_table)) * dst_negative_scale_add_unique_firstleft_table)) /\ exists ff_q_pvs_add_unique_firstleft_tableentrynegative. dst_negative_code_add_unique_firstleft_table = ff_q_pvs_add_unique_firstleft_tableentrynegative * S ((S (dst_index_add_unique_firstleft_table)) * dst_negative_scale_add_unique_firstleft_table) + (dst_negative_add_unique_firstleft_table))) /\ (exists ge_balance_positive_add_unique_firstleft_tableentryvalue ge_balance_negative_add_unique_firstleft_tableentryvalue. (((((dst_value_add_unique_firstleft_table) = 2 * (ge_balance_positive_add_unique_firstleft_tableentryvalue) /\ (ge_balance_negative_add_unique_firstleft_tableentryvalue) = 0) \/ exists ge_signed_half_add_unique_firstleft_tableentryvaluedecode. (((dst_value_add_unique_firstleft_table) = 2 * ge_signed_half_add_unique_firstleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_unique_firstleft_tableentryvalue) = 0) /\ (ge_balance_negative_add_unique_firstleft_tableentryvalue) = S ge_signed_half_add_unique_firstleft_tableentryvaluedecode))) /\ ((dst_positive_add_unique_firstleft_table) + ge_balance_negative_add_unique_firstleft_tableentryvalue = (dst_negative_add_unique_firstleft_table) + ge_balance_positive_add_unique_firstleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_unique_firstright_table dst_positive_scale_add_unique_firstright_table dst_negative_code_add_unique_firstright_table dst_negative_scale_add_unique_firstright_table. (((G) = (((((dst_positive_code_add_unique_firstright_table) + (dst_positive_scale_add_unique_firstright_table)) * S ((dst_positive_code_add_unique_firstright_table) + (dst_positive_scale_add_unique_firstright_table)) + ((dst_positive_scale_add_unique_firstright_table) + (dst_positive_scale_add_unique_firstright_table))) + (((dst_negative_code_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)) * S ((dst_negative_code_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)) + ((dst_negative_scale_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)))) * S ((((dst_positive_code_add_unique_firstright_table) + (dst_positive_scale_add_unique_firstright_table)) * S ((dst_positive_code_add_unique_firstright_table) + (dst_positive_scale_add_unique_firstright_table)) + ((dst_positive_scale_add_unique_firstright_table) + (dst_positive_scale_add_unique_firstright_table))) + (((dst_negative_code_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)) * S ((dst_negative_code_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)) + ((dst_negative_scale_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)))) + ((((dst_negative_code_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)) * S ((dst_negative_code_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)) + ((dst_negative_scale_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table))) + (((dst_negative_code_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)) * S ((dst_negative_code_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)) + ((dst_negative_scale_add_unique_firstright_table) + (dst_negative_scale_add_unique_firstright_table)))))) /\ (forall dst_index_add_unique_firstright_table. (exists pvs_le_gap_add_unique_firstright_tabledomain. pvs_le_gap_add_unique_firstright_tabledomain + (dst_index_add_unique_firstright_table) = (l)) -> exists dst_positive_add_unique_firstright_table dst_negative_add_unique_firstright_table dst_value_add_unique_firstright_table. ((((exists ff_h_pvs_add_unique_firstright_tableentrypositive. ff_h_pvs_add_unique_firstright_tableentrypositive + S (dst_positive_add_unique_firstright_table) = S ((S (dst_index_add_unique_firstright_table)) * dst_positive_scale_add_unique_firstright_table)) /\ exists ff_q_pvs_add_unique_firstright_tableentrypositive. dst_positive_code_add_unique_firstright_table = ff_q_pvs_add_unique_firstright_tableentrypositive * S ((S (dst_index_add_unique_firstright_table)) * dst_positive_scale_add_unique_firstright_table) + (dst_positive_add_unique_firstright_table))) /\ (((((exists ff_h_pvs_add_unique_firstright_tableentrynegative. ff_h_pvs_add_unique_firstright_tableentrynegative + S (dst_negative_add_unique_firstright_table) = S ((S (dst_index_add_unique_firstright_table)) * dst_negative_scale_add_unique_firstright_table)) /\ exists ff_q_pvs_add_unique_firstright_tableentrynegative. dst_negative_code_add_unique_firstright_table = ff_q_pvs_add_unique_firstright_tableentrynegative * S ((S (dst_index_add_unique_firstright_table)) * dst_negative_scale_add_unique_firstright_table) + (dst_negative_add_unique_firstright_table))) /\ (exists ge_balance_positive_add_unique_firstright_tableentryvalue ge_balance_negative_add_unique_firstright_tableentryvalue. (((((dst_value_add_unique_firstright_table) = 2 * (ge_balance_positive_add_unique_firstright_tableentryvalue) /\ (ge_balance_negative_add_unique_firstright_tableentryvalue) = 0) \/ exists ge_signed_half_add_unique_firstright_tableentryvaluedecode. (((dst_value_add_unique_firstright_table) = 2 * ge_signed_half_add_unique_firstright_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_unique_firstright_tableentryvalue) = 0) /\ (ge_balance_negative_add_unique_firstright_tableentryvalue) = S ge_signed_half_add_unique_firstright_tableentryvaluedecode))) /\ ((dst_positive_add_unique_firstright_table) + ge_balance_negative_add_unique_firstright_tableentryvalue = (dst_negative_add_unique_firstright_table) + ge_balance_positive_add_unique_firstright_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_unique_firstoutput_table dst_positive_scale_add_unique_firstoutput_table dst_negative_code_add_unique_firstoutput_table dst_negative_scale_add_unique_firstoutput_table. (((H) = (((((dst_positive_code_add_unique_firstoutput_table) + (dst_positive_scale_add_unique_firstoutput_table)) * S ((dst_positive_code_add_unique_firstoutput_table) + (dst_positive_scale_add_unique_firstoutput_table)) + ((dst_positive_scale_add_unique_firstoutput_table) + (dst_positive_scale_add_unique_firstoutput_table))) + (((dst_negative_code_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)) * S ((dst_negative_code_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)) + ((dst_negative_scale_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)))) * S ((((dst_positive_code_add_unique_firstoutput_table) + (dst_positive_scale_add_unique_firstoutput_table)) * S ((dst_positive_code_add_unique_firstoutput_table) + (dst_positive_scale_add_unique_firstoutput_table)) + ((dst_positive_scale_add_unique_firstoutput_table) + (dst_positive_scale_add_unique_firstoutput_table))) + (((dst_negative_code_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)) * S ((dst_negative_code_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)) + ((dst_negative_scale_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)))) + ((((dst_negative_code_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)) * S ((dst_negative_code_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)) + ((dst_negative_scale_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table))) + (((dst_negative_code_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)) * S ((dst_negative_code_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)) + ((dst_negative_scale_add_unique_firstoutput_table) + (dst_negative_scale_add_unique_firstoutput_table)))))) /\ (forall dst_index_add_unique_firstoutput_table. (exists pvs_le_gap_add_unique_firstoutput_tabledomain. pvs_le_gap_add_unique_firstoutput_tabledomain + (dst_index_add_unique_firstoutput_table) = (l)) -> exists dst_positive_add_unique_firstoutput_table dst_negative_add_unique_firstoutput_table dst_value_add_unique_firstoutput_table. ((((exists ff_h_pvs_add_unique_firstoutput_tableentrypositive. ff_h_pvs_add_unique_firstoutput_tableentrypositive + S (dst_positive_add_unique_firstoutput_table) = S ((S (dst_index_add_unique_firstoutput_table)) * dst_positive_scale_add_unique_firstoutput_table)) /\ exists ff_q_pvs_add_unique_firstoutput_tableentrypositive. dst_positive_code_add_unique_firstoutput_table = ff_q_pvs_add_unique_firstoutput_tableentrypositive * S ((S (dst_index_add_unique_firstoutput_table)) * dst_positive_scale_add_unique_firstoutput_table) + (dst_positive_add_unique_firstoutput_table))) /\ (((((exists ff_h_pvs_add_unique_firstoutput_tableentrynegative. ff_h_pvs_add_unique_firstoutput_tableentrynegative + S (dst_negative_add_unique_firstoutput_table) = S ((S (dst_index_add_unique_firstoutput_table)) * dst_negative_scale_add_unique_firstoutput_table)) /\ exists ff_q_pvs_add_unique_firstoutput_tableentrynegative. dst_negative_code_add_unique_firstoutput_table = ff_q_pvs_add_unique_firstoutput_tableentrynegative * S ((S (dst_index_add_unique_firstoutput_table)) * dst_negative_scale_add_unique_firstoutput_table) + (dst_negative_add_unique_firstoutput_table))) /\ (exists ge_balance_positive_add_unique_firstoutput_tableentryvalue ge_balance_negative_add_unique_firstoutput_tableentryvalue. (((((dst_value_add_unique_firstoutput_table) = 2 * (ge_balance_positive_add_unique_firstoutput_tableentryvalue) /\ (ge_balance_negative_add_unique_firstoutput_tableentryvalue) = 0) \/ exists ge_signed_half_add_unique_firstoutput_tableentryvaluedecode. (((dst_value_add_unique_firstoutput_table) = 2 * ge_signed_half_add_unique_firstoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_unique_firstoutput_tableentryvalue) = 0) /\ (ge_balance_negative_add_unique_firstoutput_tableentryvalue) = S ge_signed_half_add_unique_firstoutput_tableentryvaluedecode))) /\ ((dst_positive_add_unique_firstoutput_table) + ge_balance_negative_add_unique_firstoutput_tableentryvalue = (dst_negative_add_unique_firstoutput_table) + ge_balance_positive_add_unique_firstoutput_tableentryvalue))))))))) /\ (forall sto_index_add_unique_firstentries. (exists pvs_gap_add_unique_firstentriesbound. pvs_gap_add_unique_firstentriesbound + S (sto_index_add_unique_firstentries) = (l)) -> exists sto_left_add_unique_firstentries sto_right_add_unique_firstentries sto_output_add_unique_firstentries. ((exists dst_positive_code_add_unique_firstentriesentryleft dst_positive_scale_add_unique_firstentriesentryleft dst_negative_code_add_unique_firstentriesentryleft dst_negative_scale_add_unique_firstentriesentryleft dst_positive_add_unique_firstentriesentryleft dst_negative_add_unique_firstentriesentryleft. (((F) = (((((dst_positive_code_add_unique_firstentriesentryleft) + (dst_positive_scale_add_unique_firstentriesentryleft)) * S ((dst_positive_code_add_unique_firstentriesentryleft) + (dst_positive_scale_add_unique_firstentriesentryleft)) + ((dst_positive_scale_add_unique_firstentriesentryleft) + (dst_positive_scale_add_unique_firstentriesentryleft))) + (((dst_negative_code_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)) * S ((dst_negative_code_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)) + ((dst_negative_scale_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)))) * S ((((dst_positive_code_add_unique_firstentriesentryleft) + (dst_positive_scale_add_unique_firstentriesentryleft)) * S ((dst_positive_code_add_unique_firstentriesentryleft) + (dst_positive_scale_add_unique_firstentriesentryleft)) + ((dst_positive_scale_add_unique_firstentriesentryleft) + (dst_positive_scale_add_unique_firstentriesentryleft))) + (((dst_negative_code_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)) * S ((dst_negative_code_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)) + ((dst_negative_scale_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)))) + ((((dst_negative_code_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)) * S ((dst_negative_code_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)) + ((dst_negative_scale_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft))) + (((dst_negative_code_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)) * S ((dst_negative_code_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)) + ((dst_negative_scale_add_unique_firstentriesentryleft) + (dst_negative_scale_add_unique_firstentriesentryleft)))))) /\ (((((exists ff_h_pvs_add_unique_firstentriesentryleftpositive. ff_h_pvs_add_unique_firstentriesentryleftpositive + S (dst_positive_add_unique_firstentriesentryleft) = S ((S (sto_index_add_unique_firstentries)) * dst_positive_scale_add_unique_firstentriesentryleft)) /\ exists ff_q_pvs_add_unique_firstentriesentryleftpositive. dst_positive_code_add_unique_firstentriesentryleft = ff_q_pvs_add_unique_firstentriesentryleftpositive * S ((S (sto_index_add_unique_firstentries)) * dst_positive_scale_add_unique_firstentriesentryleft) + (dst_positive_add_unique_firstentriesentryleft))) /\ (((((exists ff_h_pvs_add_unique_firstentriesentryleftnegative. ff_h_pvs_add_unique_firstentriesentryleftnegative + S (dst_negative_add_unique_firstentriesentryleft) = S ((S (sto_index_add_unique_firstentries)) * dst_negative_scale_add_unique_firstentriesentryleft)) /\ exists ff_q_pvs_add_unique_firstentriesentryleftnegative. dst_negative_code_add_unique_firstentriesentryleft = ff_q_pvs_add_unique_firstentriesentryleftnegative * S ((S (sto_index_add_unique_firstentries)) * dst_negative_scale_add_unique_firstentriesentryleft) + (dst_negative_add_unique_firstentriesentryleft))) /\ (exists ge_balance_positive_add_unique_firstentriesentryleftvalue ge_balance_negative_add_unique_firstentriesentryleftvalue. (((((sto_left_add_unique_firstentries) = 2 * (ge_balance_positive_add_unique_firstentriesentryleftvalue) /\ (ge_balance_negative_add_unique_firstentriesentryleftvalue) = 0) \/ exists ge_signed_half_add_unique_firstentriesentryleftvaluedecode. (((sto_left_add_unique_firstentries) = 2 * ge_signed_half_add_unique_firstentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_add_unique_firstentriesentryleftvalue) = 0) /\ (ge_balance_negative_add_unique_firstentriesentryleftvalue) = S ge_signed_half_add_unique_firstentriesentryleftvaluedecode))) /\ ((dst_positive_add_unique_firstentriesentryleft) + ge_balance_negative_add_unique_firstentriesentryleftvalue = (dst_negative_add_unique_firstentriesentryleft) + ge_balance_positive_add_unique_firstentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_add_unique_firstentriesentryright dst_positive_scale_add_unique_firstentriesentryright dst_negative_code_add_unique_firstentriesentryright dst_negative_scale_add_unique_firstentriesentryright dst_positive_add_unique_firstentriesentryright dst_negative_add_unique_firstentriesentryright. (((G) = (((((dst_positive_code_add_unique_firstentriesentryright) + (dst_positive_scale_add_unique_firstentriesentryright)) * S ((dst_positive_code_add_unique_firstentriesentryright) + (dst_positive_scale_add_unique_firstentriesentryright)) + ((dst_positive_scale_add_unique_firstentriesentryright) + (dst_positive_scale_add_unique_firstentriesentryright))) + (((dst_negative_code_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)) * S ((dst_negative_code_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)) + ((dst_negative_scale_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)))) * S ((((dst_positive_code_add_unique_firstentriesentryright) + (dst_positive_scale_add_unique_firstentriesentryright)) * S ((dst_positive_code_add_unique_firstentriesentryright) + (dst_positive_scale_add_unique_firstentriesentryright)) + ((dst_positive_scale_add_unique_firstentriesentryright) + (dst_positive_scale_add_unique_firstentriesentryright))) + (((dst_negative_code_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)) * S ((dst_negative_code_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)) + ((dst_negative_scale_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)))) + ((((dst_negative_code_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)) * S ((dst_negative_code_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)) + ((dst_negative_scale_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright))) + (((dst_negative_code_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)) * S ((dst_negative_code_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)) + ((dst_negative_scale_add_unique_firstentriesentryright) + (dst_negative_scale_add_unique_firstentriesentryright)))))) /\ (((((exists ff_h_pvs_add_unique_firstentriesentryrightpositive. ff_h_pvs_add_unique_firstentriesentryrightpositive + S (dst_positive_add_unique_firstentriesentryright) = S ((S (sto_index_add_unique_firstentries)) * dst_positive_scale_add_unique_firstentriesentryright)) /\ exists ff_q_pvs_add_unique_firstentriesentryrightpositive. dst_positive_code_add_unique_firstentriesentryright = ff_q_pvs_add_unique_firstentriesentryrightpositive * S ((S (sto_index_add_unique_firstentries)) * dst_positive_scale_add_unique_firstentriesentryright) + (dst_positive_add_unique_firstentriesentryright))) /\ (((((exists ff_h_pvs_add_unique_firstentriesentryrightnegative. ff_h_pvs_add_unique_firstentriesentryrightnegative + S (dst_negative_add_unique_firstentriesentryright) = S ((S (sto_index_add_unique_firstentries)) * dst_negative_scale_add_unique_firstentriesentryright)) /\ exists ff_q_pvs_add_unique_firstentriesentryrightnegative. dst_negative_code_add_unique_firstentriesentryright = ff_q_pvs_add_unique_firstentriesentryrightnegative * S ((S (sto_index_add_unique_firstentries)) * dst_negative_scale_add_unique_firstentriesentryright) + (dst_negative_add_unique_firstentriesentryright))) /\ (exists ge_balance_positive_add_unique_firstentriesentryrightvalue ge_balance_negative_add_unique_firstentriesentryrightvalue. (((((sto_right_add_unique_firstentries) = 2 * (ge_balance_positive_add_unique_firstentriesentryrightvalue) /\ (ge_balance_negative_add_unique_firstentriesentryrightvalue) = 0) \/ exists ge_signed_half_add_unique_firstentriesentryrightvaluedecode. (((sto_right_add_unique_firstentries) = 2 * ge_signed_half_add_unique_firstentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_add_unique_firstentriesentryrightvalue) = 0) /\ (ge_balance_negative_add_unique_firstentriesentryrightvalue) = S ge_signed_half_add_unique_firstentriesentryrightvaluedecode))) /\ ((dst_positive_add_unique_firstentriesentryright) + ge_balance_negative_add_unique_firstentriesentryrightvalue = (dst_negative_add_unique_firstentriesentryright) + ge_balance_positive_add_unique_firstentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_add_unique_firstentriesentryoutput dst_positive_scale_add_unique_firstentriesentryoutput dst_negative_code_add_unique_firstentriesentryoutput dst_negative_scale_add_unique_firstentriesentryoutput dst_positive_add_unique_firstentriesentryoutput dst_negative_add_unique_firstentriesentryoutput. (((H) = (((((dst_positive_code_add_unique_firstentriesentryoutput) + (dst_positive_scale_add_unique_firstentriesentryoutput)) * S ((dst_positive_code_add_unique_firstentriesentryoutput) + (dst_positive_scale_add_unique_firstentriesentryoutput)) + ((dst_positive_scale_add_unique_firstentriesentryoutput) + (dst_positive_scale_add_unique_firstentriesentryoutput))) + (((dst_negative_code_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)) * S ((dst_negative_code_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)) + ((dst_negative_scale_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)))) * S ((((dst_positive_code_add_unique_firstentriesentryoutput) + (dst_positive_scale_add_unique_firstentriesentryoutput)) * S ((dst_positive_code_add_unique_firstentriesentryoutput) + (dst_positive_scale_add_unique_firstentriesentryoutput)) + ((dst_positive_scale_add_unique_firstentriesentryoutput) + (dst_positive_scale_add_unique_firstentriesentryoutput))) + (((dst_negative_code_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)) * S ((dst_negative_code_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)) + ((dst_negative_scale_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)))) + ((((dst_negative_code_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)) * S ((dst_negative_code_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)) + ((dst_negative_scale_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput))) + (((dst_negative_code_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)) * S ((dst_negative_code_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)) + ((dst_negative_scale_add_unique_firstentriesentryoutput) + (dst_negative_scale_add_unique_firstentriesentryoutput)))))) /\ (((((exists ff_h_pvs_add_unique_firstentriesentryoutputpositive. ff_h_pvs_add_unique_firstentriesentryoutputpositive + S (dst_positive_add_unique_firstentriesentryoutput) = S ((S (sto_index_add_unique_firstentries)) * dst_positive_scale_add_unique_firstentriesentryoutput)) /\ exists ff_q_pvs_add_unique_firstentriesentryoutputpositive. dst_positive_code_add_unique_firstentriesentryoutput = ff_q_pvs_add_unique_firstentriesentryoutputpositive * S ((S (sto_index_add_unique_firstentries)) * dst_positive_scale_add_unique_firstentriesentryoutput) + (dst_positive_add_unique_firstentriesentryoutput))) /\ (((((exists ff_h_pvs_add_unique_firstentriesentryoutputnegative. ff_h_pvs_add_unique_firstentriesentryoutputnegative + S (dst_negative_add_unique_firstentriesentryoutput) = S ((S (sto_index_add_unique_firstentries)) * dst_negative_scale_add_unique_firstentriesentryoutput)) /\ exists ff_q_pvs_add_unique_firstentriesentryoutputnegative. dst_negative_code_add_unique_firstentriesentryoutput = ff_q_pvs_add_unique_firstentriesentryoutputnegative * S ((S (sto_index_add_unique_firstentries)) * dst_negative_scale_add_unique_firstentriesentryoutput) + (dst_negative_add_unique_firstentriesentryoutput))) /\ (exists ge_balance_positive_add_unique_firstentriesentryoutputvalue ge_balance_negative_add_unique_firstentriesentryoutputvalue. (((((sto_output_add_unique_firstentries) = 2 * (ge_balance_positive_add_unique_firstentriesentryoutputvalue) /\ (ge_balance_negative_add_unique_firstentriesentryoutputvalue) = 0) \/ exists ge_signed_half_add_unique_firstentriesentryoutputvaluedecode. (((sto_output_add_unique_firstentries) = 2 * ge_signed_half_add_unique_firstentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_add_unique_firstentriesentryoutputvalue) = 0) /\ (ge_balance_negative_add_unique_firstentriesentryoutputvalue) = S ge_signed_half_add_unique_firstentriesentryoutputvaluedecode))) /\ ((dst_positive_add_unique_firstentriesentryoutput) + ge_balance_negative_add_unique_firstentriesentryoutputvalue = (dst_negative_add_unique_firstentriesentryoutput) + ge_balance_positive_add_unique_firstentriesentryoutputvalue))))))))) /\ (exists dsa_ap_add_unique_firstentriesentryoperation dsa_an_add_unique_firstentriesentryoperation dsa_bp_add_unique_firstentriesentryoperation dsa_bn_add_unique_firstentriesentryoperation dsa_cp_add_unique_firstentriesentryoperation dsa_cn_add_unique_firstentriesentryoperation. (((((sto_left_add_unique_firstentries) = 2 * (dsa_ap_add_unique_firstentriesentryoperation) /\ (dsa_an_add_unique_firstentriesentryoperation) = 0) \/ exists ge_signed_half_add_unique_firstentriesentryoperationleft. (((sto_left_add_unique_firstentries) = 2 * ge_signed_half_add_unique_firstentriesentryoperationleft + 1 /\ (dsa_ap_add_unique_firstentriesentryoperation) = 0) /\ (dsa_an_add_unique_firstentriesentryoperation) = S ge_signed_half_add_unique_firstentriesentryoperationleft))) /\ ((((((sto_right_add_unique_firstentries) = 2 * (dsa_bp_add_unique_firstentriesentryoperation) /\ (dsa_bn_add_unique_firstentriesentryoperation) = 0) \/ exists ge_signed_half_add_unique_firstentriesentryoperationright. (((sto_right_add_unique_firstentries) = 2 * ge_signed_half_add_unique_firstentriesentryoperationright + 1 /\ (dsa_bp_add_unique_firstentriesentryoperation) = 0) /\ (dsa_bn_add_unique_firstentriesentryoperation) = S ge_signed_half_add_unique_firstentriesentryoperationright))) /\ ((((((sto_output_add_unique_firstentries) = 2 * (dsa_cp_add_unique_firstentriesentryoperation) /\ (dsa_cn_add_unique_firstentriesentryoperation) = 0) \/ exists ge_signed_half_add_unique_firstentriesentryoperationoutput. (((sto_output_add_unique_firstentries) = 2 * ge_signed_half_add_unique_firstentriesentryoperationoutput + 1 /\ (dsa_cp_add_unique_firstentriesentryoperation) = 0) /\ (dsa_cn_add_unique_firstentriesentryoperation) = S ge_signed_half_add_unique_firstentriesentryoperationoutput))) /\ ((dsa_ap_add_unique_firstentriesentryoperation + dsa_bp_add_unique_firstentriesentryoperation) + dsa_cn_add_unique_firstentriesentryoperation = (dsa_an_add_unique_firstentriesentryoperation + dsa_bn_add_unique_firstentriesentryoperation) + dsa_cp_add_unique_firstentriesentryoperation))))))))))))))))))) -> (((exists dst_positive_code_add_unique_secondleft_table dst_positive_scale_add_unique_secondleft_table dst_negative_code_add_unique_secondleft_table dst_negative_scale_add_unique_secondleft_table. (((F) = (((((dst_positive_code_add_unique_secondleft_table) + (dst_positive_scale_add_unique_secondleft_table)) * S ((dst_positive_code_add_unique_secondleft_table) + (dst_positive_scale_add_unique_secondleft_table)) + ((dst_positive_scale_add_unique_secondleft_table) + (dst_positive_scale_add_unique_secondleft_table))) + (((dst_negative_code_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)) * S ((dst_negative_code_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)) + ((dst_negative_scale_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)))) * S ((((dst_positive_code_add_unique_secondleft_table) + (dst_positive_scale_add_unique_secondleft_table)) * S ((dst_positive_code_add_unique_secondleft_table) + (dst_positive_scale_add_unique_secondleft_table)) + ((dst_positive_scale_add_unique_secondleft_table) + (dst_positive_scale_add_unique_secondleft_table))) + (((dst_negative_code_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)) * S ((dst_negative_code_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)) + ((dst_negative_scale_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)))) + ((((dst_negative_code_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)) * S ((dst_negative_code_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)) + ((dst_negative_scale_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table))) + (((dst_negative_code_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)) * S ((dst_negative_code_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)) + ((dst_negative_scale_add_unique_secondleft_table) + (dst_negative_scale_add_unique_secondleft_table)))))) /\ (forall dst_index_add_unique_secondleft_table. (exists pvs_le_gap_add_unique_secondleft_tabledomain. pvs_le_gap_add_unique_secondleft_tabledomain + (dst_index_add_unique_secondleft_table) = (l)) -> exists dst_positive_add_unique_secondleft_table dst_negative_add_unique_secondleft_table dst_value_add_unique_secondleft_table. ((((exists ff_h_pvs_add_unique_secondleft_tableentrypositive. ff_h_pvs_add_unique_secondleft_tableentrypositive + S (dst_positive_add_unique_secondleft_table) = S ((S (dst_index_add_unique_secondleft_table)) * dst_positive_scale_add_unique_secondleft_table)) /\ exists ff_q_pvs_add_unique_secondleft_tableentrypositive. dst_positive_code_add_unique_secondleft_table = ff_q_pvs_add_unique_secondleft_tableentrypositive * S ((S (dst_index_add_unique_secondleft_table)) * dst_positive_scale_add_unique_secondleft_table) + (dst_positive_add_unique_secondleft_table))) /\ (((((exists ff_h_pvs_add_unique_secondleft_tableentrynegative. ff_h_pvs_add_unique_secondleft_tableentrynegative + S (dst_negative_add_unique_secondleft_table) = S ((S (dst_index_add_unique_secondleft_table)) * dst_negative_scale_add_unique_secondleft_table)) /\ exists ff_q_pvs_add_unique_secondleft_tableentrynegative. dst_negative_code_add_unique_secondleft_table = ff_q_pvs_add_unique_secondleft_tableentrynegative * S ((S (dst_index_add_unique_secondleft_table)) * dst_negative_scale_add_unique_secondleft_table) + (dst_negative_add_unique_secondleft_table))) /\ (exists ge_balance_positive_add_unique_secondleft_tableentryvalue ge_balance_negative_add_unique_secondleft_tableentryvalue. (((((dst_value_add_unique_secondleft_table) = 2 * (ge_balance_positive_add_unique_secondleft_tableentryvalue) /\ (ge_balance_negative_add_unique_secondleft_tableentryvalue) = 0) \/ exists ge_signed_half_add_unique_secondleft_tableentryvaluedecode. (((dst_value_add_unique_secondleft_table) = 2 * ge_signed_half_add_unique_secondleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_unique_secondleft_tableentryvalue) = 0) /\ (ge_balance_negative_add_unique_secondleft_tableentryvalue) = S ge_signed_half_add_unique_secondleft_tableentryvaluedecode))) /\ ((dst_positive_add_unique_secondleft_table) + ge_balance_negative_add_unique_secondleft_tableentryvalue = (dst_negative_add_unique_secondleft_table) + ge_balance_positive_add_unique_secondleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_unique_secondright_table dst_positive_scale_add_unique_secondright_table dst_negative_code_add_unique_secondright_table dst_negative_scale_add_unique_secondright_table. (((G) = (((((dst_positive_code_add_unique_secondright_table) + (dst_positive_scale_add_unique_secondright_table)) * S ((dst_positive_code_add_unique_secondright_table) + (dst_positive_scale_add_unique_secondright_table)) + ((dst_positive_scale_add_unique_secondright_table) + (dst_positive_scale_add_unique_secondright_table))) + (((dst_negative_code_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)) * S ((dst_negative_code_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)) + ((dst_negative_scale_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)))) * S ((((dst_positive_code_add_unique_secondright_table) + (dst_positive_scale_add_unique_secondright_table)) * S ((dst_positive_code_add_unique_secondright_table) + (dst_positive_scale_add_unique_secondright_table)) + ((dst_positive_scale_add_unique_secondright_table) + (dst_positive_scale_add_unique_secondright_table))) + (((dst_negative_code_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)) * S ((dst_negative_code_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)) + ((dst_negative_scale_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)))) + ((((dst_negative_code_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)) * S ((dst_negative_code_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)) + ((dst_negative_scale_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table))) + (((dst_negative_code_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)) * S ((dst_negative_code_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)) + ((dst_negative_scale_add_unique_secondright_table) + (dst_negative_scale_add_unique_secondright_table)))))) /\ (forall dst_index_add_unique_secondright_table. (exists pvs_le_gap_add_unique_secondright_tabledomain. pvs_le_gap_add_unique_secondright_tabledomain + (dst_index_add_unique_secondright_table) = (l)) -> exists dst_positive_add_unique_secondright_table dst_negative_add_unique_secondright_table dst_value_add_unique_secondright_table. ((((exists ff_h_pvs_add_unique_secondright_tableentrypositive. ff_h_pvs_add_unique_secondright_tableentrypositive + S (dst_positive_add_unique_secondright_table) = S ((S (dst_index_add_unique_secondright_table)) * dst_positive_scale_add_unique_secondright_table)) /\ exists ff_q_pvs_add_unique_secondright_tableentrypositive. dst_positive_code_add_unique_secondright_table = ff_q_pvs_add_unique_secondright_tableentrypositive * S ((S (dst_index_add_unique_secondright_table)) * dst_positive_scale_add_unique_secondright_table) + (dst_positive_add_unique_secondright_table))) /\ (((((exists ff_h_pvs_add_unique_secondright_tableentrynegative. ff_h_pvs_add_unique_secondright_tableentrynegative + S (dst_negative_add_unique_secondright_table) = S ((S (dst_index_add_unique_secondright_table)) * dst_negative_scale_add_unique_secondright_table)) /\ exists ff_q_pvs_add_unique_secondright_tableentrynegative. dst_negative_code_add_unique_secondright_table = ff_q_pvs_add_unique_secondright_tableentrynegative * S ((S (dst_index_add_unique_secondright_table)) * dst_negative_scale_add_unique_secondright_table) + (dst_negative_add_unique_secondright_table))) /\ (exists ge_balance_positive_add_unique_secondright_tableentryvalue ge_balance_negative_add_unique_secondright_tableentryvalue. (((((dst_value_add_unique_secondright_table) = 2 * (ge_balance_positive_add_unique_secondright_tableentryvalue) /\ (ge_balance_negative_add_unique_secondright_tableentryvalue) = 0) \/ exists ge_signed_half_add_unique_secondright_tableentryvaluedecode. (((dst_value_add_unique_secondright_table) = 2 * ge_signed_half_add_unique_secondright_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_unique_secondright_tableentryvalue) = 0) /\ (ge_balance_negative_add_unique_secondright_tableentryvalue) = S ge_signed_half_add_unique_secondright_tableentryvaluedecode))) /\ ((dst_positive_add_unique_secondright_table) + ge_balance_negative_add_unique_secondright_tableentryvalue = (dst_negative_add_unique_secondright_table) + ge_balance_positive_add_unique_secondright_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_unique_secondoutput_table dst_positive_scale_add_unique_secondoutput_table dst_negative_code_add_unique_secondoutput_table dst_negative_scale_add_unique_secondoutput_table. (((K) = (((((dst_positive_code_add_unique_secondoutput_table) + (dst_positive_scale_add_unique_secondoutput_table)) * S ((dst_positive_code_add_unique_secondoutput_table) + (dst_positive_scale_add_unique_secondoutput_table)) + ((dst_positive_scale_add_unique_secondoutput_table) + (dst_positive_scale_add_unique_secondoutput_table))) + (((dst_negative_code_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)) * S ((dst_negative_code_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)) + ((dst_negative_scale_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)))) * S ((((dst_positive_code_add_unique_secondoutput_table) + (dst_positive_scale_add_unique_secondoutput_table)) * S ((dst_positive_code_add_unique_secondoutput_table) + (dst_positive_scale_add_unique_secondoutput_table)) + ((dst_positive_scale_add_unique_secondoutput_table) + (dst_positive_scale_add_unique_secondoutput_table))) + (((dst_negative_code_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)) * S ((dst_negative_code_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)) + ((dst_negative_scale_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)))) + ((((dst_negative_code_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)) * S ((dst_negative_code_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)) + ((dst_negative_scale_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table))) + (((dst_negative_code_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)) * S ((dst_negative_code_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)) + ((dst_negative_scale_add_unique_secondoutput_table) + (dst_negative_scale_add_unique_secondoutput_table)))))) /\ (forall dst_index_add_unique_secondoutput_table. (exists pvs_le_gap_add_unique_secondoutput_tabledomain. pvs_le_gap_add_unique_secondoutput_tabledomain + (dst_index_add_unique_secondoutput_table) = (l)) -> exists dst_positive_add_unique_secondoutput_table dst_negative_add_unique_secondoutput_table dst_value_add_unique_secondoutput_table. ((((exists ff_h_pvs_add_unique_secondoutput_tableentrypositive. ff_h_pvs_add_unique_secondoutput_tableentrypositive + S (dst_positive_add_unique_secondoutput_table) = S ((S (dst_index_add_unique_secondoutput_table)) * dst_positive_scale_add_unique_secondoutput_table)) /\ exists ff_q_pvs_add_unique_secondoutput_tableentrypositive. dst_positive_code_add_unique_secondoutput_table = ff_q_pvs_add_unique_secondoutput_tableentrypositive * S ((S (dst_index_add_unique_secondoutput_table)) * dst_positive_scale_add_unique_secondoutput_table) + (dst_positive_add_unique_secondoutput_table))) /\ (((((exists ff_h_pvs_add_unique_secondoutput_tableentrynegative. ff_h_pvs_add_unique_secondoutput_tableentrynegative + S (dst_negative_add_unique_secondoutput_table) = S ((S (dst_index_add_unique_secondoutput_table)) * dst_negative_scale_add_unique_secondoutput_table)) /\ exists ff_q_pvs_add_unique_secondoutput_tableentrynegative. dst_negative_code_add_unique_secondoutput_table = ff_q_pvs_add_unique_secondoutput_tableentrynegative * S ((S (dst_index_add_unique_secondoutput_table)) * dst_negative_scale_add_unique_secondoutput_table) + (dst_negative_add_unique_secondoutput_table))) /\ (exists ge_balance_positive_add_unique_secondoutput_tableentryvalue ge_balance_negative_add_unique_secondoutput_tableentryvalue. (((((dst_value_add_unique_secondoutput_table) = 2 * (ge_balance_positive_add_unique_secondoutput_tableentryvalue) /\ (ge_balance_negative_add_unique_secondoutput_tableentryvalue) = 0) \/ exists ge_signed_half_add_unique_secondoutput_tableentryvaluedecode. (((dst_value_add_unique_secondoutput_table) = 2 * ge_signed_half_add_unique_secondoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_unique_secondoutput_tableentryvalue) = 0) /\ (ge_balance_negative_add_unique_secondoutput_tableentryvalue) = S ge_signed_half_add_unique_secondoutput_tableentryvaluedecode))) /\ ((dst_positive_add_unique_secondoutput_table) + ge_balance_negative_add_unique_secondoutput_tableentryvalue = (dst_negative_add_unique_secondoutput_table) + ge_balance_positive_add_unique_secondoutput_tableentryvalue))))))))) /\ (forall sto_index_add_unique_secondentries. (exists pvs_gap_add_unique_secondentriesbound. pvs_gap_add_unique_secondentriesbound + S (sto_index_add_unique_secondentries) = (l)) -> exists sto_left_add_unique_secondentries sto_right_add_unique_secondentries sto_output_add_unique_secondentries. ((exists dst_positive_code_add_unique_secondentriesentryleft dst_positive_scale_add_unique_secondentriesentryleft dst_negative_code_add_unique_secondentriesentryleft dst_negative_scale_add_unique_secondentriesentryleft dst_positive_add_unique_secondentriesentryleft dst_negative_add_unique_secondentriesentryleft. (((F) = (((((dst_positive_code_add_unique_secondentriesentryleft) + (dst_positive_scale_add_unique_secondentriesentryleft)) * S ((dst_positive_code_add_unique_secondentriesentryleft) + (dst_positive_scale_add_unique_secondentriesentryleft)) + ((dst_positive_scale_add_unique_secondentriesentryleft) + (dst_positive_scale_add_unique_secondentriesentryleft))) + (((dst_negative_code_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)) * S ((dst_negative_code_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)) + ((dst_negative_scale_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)))) * S ((((dst_positive_code_add_unique_secondentriesentryleft) + (dst_positive_scale_add_unique_secondentriesentryleft)) * S ((dst_positive_code_add_unique_secondentriesentryleft) + (dst_positive_scale_add_unique_secondentriesentryleft)) + ((dst_positive_scale_add_unique_secondentriesentryleft) + (dst_positive_scale_add_unique_secondentriesentryleft))) + (((dst_negative_code_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)) * S ((dst_negative_code_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)) + ((dst_negative_scale_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)))) + ((((dst_negative_code_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)) * S ((dst_negative_code_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)) + ((dst_negative_scale_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft))) + (((dst_negative_code_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)) * S ((dst_negative_code_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)) + ((dst_negative_scale_add_unique_secondentriesentryleft) + (dst_negative_scale_add_unique_secondentriesentryleft)))))) /\ (((((exists ff_h_pvs_add_unique_secondentriesentryleftpositive. ff_h_pvs_add_unique_secondentriesentryleftpositive + S (dst_positive_add_unique_secondentriesentryleft) = S ((S (sto_index_add_unique_secondentries)) * dst_positive_scale_add_unique_secondentriesentryleft)) /\ exists ff_q_pvs_add_unique_secondentriesentryleftpositive. dst_positive_code_add_unique_secondentriesentryleft = ff_q_pvs_add_unique_secondentriesentryleftpositive * S ((S (sto_index_add_unique_secondentries)) * dst_positive_scale_add_unique_secondentriesentryleft) + (dst_positive_add_unique_secondentriesentryleft))) /\ (((((exists ff_h_pvs_add_unique_secondentriesentryleftnegative. ff_h_pvs_add_unique_secondentriesentryleftnegative + S (dst_negative_add_unique_secondentriesentryleft) = S ((S (sto_index_add_unique_secondentries)) * dst_negative_scale_add_unique_secondentriesentryleft)) /\ exists ff_q_pvs_add_unique_secondentriesentryleftnegative. dst_negative_code_add_unique_secondentriesentryleft = ff_q_pvs_add_unique_secondentriesentryleftnegative * S ((S (sto_index_add_unique_secondentries)) * dst_negative_scale_add_unique_secondentriesentryleft) + (dst_negative_add_unique_secondentriesentryleft))) /\ (exists ge_balance_positive_add_unique_secondentriesentryleftvalue ge_balance_negative_add_unique_secondentriesentryleftvalue. (((((sto_left_add_unique_secondentries) = 2 * (ge_balance_positive_add_unique_secondentriesentryleftvalue) /\ (ge_balance_negative_add_unique_secondentriesentryleftvalue) = 0) \/ exists ge_signed_half_add_unique_secondentriesentryleftvaluedecode. (((sto_left_add_unique_secondentries) = 2 * ge_signed_half_add_unique_secondentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_add_unique_secondentriesentryleftvalue) = 0) /\ (ge_balance_negative_add_unique_secondentriesentryleftvalue) = S ge_signed_half_add_unique_secondentriesentryleftvaluedecode))) /\ ((dst_positive_add_unique_secondentriesentryleft) + ge_balance_negative_add_unique_secondentriesentryleftvalue = (dst_negative_add_unique_secondentriesentryleft) + ge_balance_positive_add_unique_secondentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_add_unique_secondentriesentryright dst_positive_scale_add_unique_secondentriesentryright dst_negative_code_add_unique_secondentriesentryright dst_negative_scale_add_unique_secondentriesentryright dst_positive_add_unique_secondentriesentryright dst_negative_add_unique_secondentriesentryright. (((G) = (((((dst_positive_code_add_unique_secondentriesentryright) + (dst_positive_scale_add_unique_secondentriesentryright)) * S ((dst_positive_code_add_unique_secondentriesentryright) + (dst_positive_scale_add_unique_secondentriesentryright)) + ((dst_positive_scale_add_unique_secondentriesentryright) + (dst_positive_scale_add_unique_secondentriesentryright))) + (((dst_negative_code_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)) * S ((dst_negative_code_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)) + ((dst_negative_scale_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)))) * S ((((dst_positive_code_add_unique_secondentriesentryright) + (dst_positive_scale_add_unique_secondentriesentryright)) * S ((dst_positive_code_add_unique_secondentriesentryright) + (dst_positive_scale_add_unique_secondentriesentryright)) + ((dst_positive_scale_add_unique_secondentriesentryright) + (dst_positive_scale_add_unique_secondentriesentryright))) + (((dst_negative_code_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)) * S ((dst_negative_code_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)) + ((dst_negative_scale_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)))) + ((((dst_negative_code_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)) * S ((dst_negative_code_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)) + ((dst_negative_scale_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright))) + (((dst_negative_code_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)) * S ((dst_negative_code_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)) + ((dst_negative_scale_add_unique_secondentriesentryright) + (dst_negative_scale_add_unique_secondentriesentryright)))))) /\ (((((exists ff_h_pvs_add_unique_secondentriesentryrightpositive. ff_h_pvs_add_unique_secondentriesentryrightpositive + S (dst_positive_add_unique_secondentriesentryright) = S ((S (sto_index_add_unique_secondentries)) * dst_positive_scale_add_unique_secondentriesentryright)) /\ exists ff_q_pvs_add_unique_secondentriesentryrightpositive. dst_positive_code_add_unique_secondentriesentryright = ff_q_pvs_add_unique_secondentriesentryrightpositive * S ((S (sto_index_add_unique_secondentries)) * dst_positive_scale_add_unique_secondentriesentryright) + (dst_positive_add_unique_secondentriesentryright))) /\ (((((exists ff_h_pvs_add_unique_secondentriesentryrightnegative. ff_h_pvs_add_unique_secondentriesentryrightnegative + S (dst_negative_add_unique_secondentriesentryright) = S ((S (sto_index_add_unique_secondentries)) * dst_negative_scale_add_unique_secondentriesentryright)) /\ exists ff_q_pvs_add_unique_secondentriesentryrightnegative. dst_negative_code_add_unique_secondentriesentryright = ff_q_pvs_add_unique_secondentriesentryrightnegative * S ((S (sto_index_add_unique_secondentries)) * dst_negative_scale_add_unique_secondentriesentryright) + (dst_negative_add_unique_secondentriesentryright))) /\ (exists ge_balance_positive_add_unique_secondentriesentryrightvalue ge_balance_negative_add_unique_secondentriesentryrightvalue. (((((sto_right_add_unique_secondentries) = 2 * (ge_balance_positive_add_unique_secondentriesentryrightvalue) /\ (ge_balance_negative_add_unique_secondentriesentryrightvalue) = 0) \/ exists ge_signed_half_add_unique_secondentriesentryrightvaluedecode. (((sto_right_add_unique_secondentries) = 2 * ge_signed_half_add_unique_secondentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_add_unique_secondentriesentryrightvalue) = 0) /\ (ge_balance_negative_add_unique_secondentriesentryrightvalue) = S ge_signed_half_add_unique_secondentriesentryrightvaluedecode))) /\ ((dst_positive_add_unique_secondentriesentryright) + ge_balance_negative_add_unique_secondentriesentryrightvalue = (dst_negative_add_unique_secondentriesentryright) + ge_balance_positive_add_unique_secondentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_add_unique_secondentriesentryoutput dst_positive_scale_add_unique_secondentriesentryoutput dst_negative_code_add_unique_secondentriesentryoutput dst_negative_scale_add_unique_secondentriesentryoutput dst_positive_add_unique_secondentriesentryoutput dst_negative_add_unique_secondentriesentryoutput. (((K) = (((((dst_positive_code_add_unique_secondentriesentryoutput) + (dst_positive_scale_add_unique_secondentriesentryoutput)) * S ((dst_positive_code_add_unique_secondentriesentryoutput) + (dst_positive_scale_add_unique_secondentriesentryoutput)) + ((dst_positive_scale_add_unique_secondentriesentryoutput) + (dst_positive_scale_add_unique_secondentriesentryoutput))) + (((dst_negative_code_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)) * S ((dst_negative_code_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)) + ((dst_negative_scale_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)))) * S ((((dst_positive_code_add_unique_secondentriesentryoutput) + (dst_positive_scale_add_unique_secondentriesentryoutput)) * S ((dst_positive_code_add_unique_secondentriesentryoutput) + (dst_positive_scale_add_unique_secondentriesentryoutput)) + ((dst_positive_scale_add_unique_secondentriesentryoutput) + (dst_positive_scale_add_unique_secondentriesentryoutput))) + (((dst_negative_code_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)) * S ((dst_negative_code_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)) + ((dst_negative_scale_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)))) + ((((dst_negative_code_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)) * S ((dst_negative_code_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)) + ((dst_negative_scale_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput))) + (((dst_negative_code_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)) * S ((dst_negative_code_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)) + ((dst_negative_scale_add_unique_secondentriesentryoutput) + (dst_negative_scale_add_unique_secondentriesentryoutput)))))) /\ (((((exists ff_h_pvs_add_unique_secondentriesentryoutputpositive. ff_h_pvs_add_unique_secondentriesentryoutputpositive + S (dst_positive_add_unique_secondentriesentryoutput) = S ((S (sto_index_add_unique_secondentries)) * dst_positive_scale_add_unique_secondentriesentryoutput)) /\ exists ff_q_pvs_add_unique_secondentriesentryoutputpositive. dst_positive_code_add_unique_secondentriesentryoutput = ff_q_pvs_add_unique_secondentriesentryoutputpositive * S ((S (sto_index_add_unique_secondentries)) * dst_positive_scale_add_unique_secondentriesentryoutput) + (dst_positive_add_unique_secondentriesentryoutput))) /\ (((((exists ff_h_pvs_add_unique_secondentriesentryoutputnegative. ff_h_pvs_add_unique_secondentriesentryoutputnegative + S (dst_negative_add_unique_secondentriesentryoutput) = S ((S (sto_index_add_unique_secondentries)) * dst_negative_scale_add_unique_secondentriesentryoutput)) /\ exists ff_q_pvs_add_unique_secondentriesentryoutputnegative. dst_negative_code_add_unique_secondentriesentryoutput = ff_q_pvs_add_unique_secondentriesentryoutputnegative * S ((S (sto_index_add_unique_secondentries)) * dst_negative_scale_add_unique_secondentriesentryoutput) + (dst_negative_add_unique_secondentriesentryoutput))) /\ (exists ge_balance_positive_add_unique_secondentriesentryoutputvalue ge_balance_negative_add_unique_secondentriesentryoutputvalue. (((((sto_output_add_unique_secondentries) = 2 * (ge_balance_positive_add_unique_secondentriesentryoutputvalue) /\ (ge_balance_negative_add_unique_secondentriesentryoutputvalue) = 0) \/ exists ge_signed_half_add_unique_secondentriesentryoutputvaluedecode. (((sto_output_add_unique_secondentries) = 2 * ge_signed_half_add_unique_secondentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_add_unique_secondentriesentryoutputvalue) = 0) /\ (ge_balance_negative_add_unique_secondentriesentryoutputvalue) = S ge_signed_half_add_unique_secondentriesentryoutputvaluedecode))) /\ ((dst_positive_add_unique_secondentriesentryoutput) + ge_balance_negative_add_unique_secondentriesentryoutputvalue = (dst_negative_add_unique_secondentriesentryoutput) + ge_balance_positive_add_unique_secondentriesentryoutputvalue))))))))) /\ (exists dsa_ap_add_unique_secondentriesentryoperation dsa_an_add_unique_secondentriesentryoperation dsa_bp_add_unique_secondentriesentryoperation dsa_bn_add_unique_secondentriesentryoperation dsa_cp_add_unique_secondentriesentryoperation dsa_cn_add_unique_secondentriesentryoperation. (((((sto_left_add_unique_secondentries) = 2 * (dsa_ap_add_unique_secondentriesentryoperation) /\ (dsa_an_add_unique_secondentriesentryoperation) = 0) \/ exists ge_signed_half_add_unique_secondentriesentryoperationleft. (((sto_left_add_unique_secondentries) = 2 * ge_signed_half_add_unique_secondentriesentryoperationleft + 1 /\ (dsa_ap_add_unique_secondentriesentryoperation) = 0) /\ (dsa_an_add_unique_secondentriesentryoperation) = S ge_signed_half_add_unique_secondentriesentryoperationleft))) /\ ((((((sto_right_add_unique_secondentries) = 2 * (dsa_bp_add_unique_secondentriesentryoperation) /\ (dsa_bn_add_unique_secondentriesentryoperation) = 0) \/ exists ge_signed_half_add_unique_secondentriesentryoperationright. (((sto_right_add_unique_secondentries) = 2 * ge_signed_half_add_unique_secondentriesentryoperationright + 1 /\ (dsa_bp_add_unique_secondentriesentryoperation) = 0) /\ (dsa_bn_add_unique_secondentriesentryoperation) = S ge_signed_half_add_unique_secondentriesentryoperationright))) /\ ((((((sto_output_add_unique_secondentries) = 2 * (dsa_cp_add_unique_secondentriesentryoperation) /\ (dsa_cn_add_unique_secondentriesentryoperation) = 0) \/ exists ge_signed_half_add_unique_secondentriesentryoperationoutput. (((sto_output_add_unique_secondentries) = 2 * ge_signed_half_add_unique_secondentriesentryoperationoutput + 1 /\ (dsa_cp_add_unique_secondentriesentryoperation) = 0) /\ (dsa_cn_add_unique_secondentriesentryoperation) = S ge_signed_half_add_unique_secondentriesentryoperationoutput))) /\ ((dsa_ap_add_unique_secondentriesentryoperation + dsa_bp_add_unique_secondentriesentryoperation) + dsa_cn_add_unique_secondentriesentryoperation = (dsa_an_add_unique_secondentriesentryoperation + dsa_bn_add_unique_secondentriesentryoperation) + dsa_cp_add_unique_secondentriesentryoperation))))))))))))))))))) -> (forall dst_index_add_unique_result dst_first_add_unique_result dst_second_add_unique_result. (exists pvs_gap_add_unique_resultbound. pvs_gap_add_unique_resultbound + S (dst_index_add_unique_result) = (l)) -> (exists dst_positive_code_add_unique_resultfirst dst_positive_scale_add_unique_resultfirst dst_negative_code_add_unique_resultfirst dst_negative_scale_add_unique_resultfirst dst_positive_add_unique_resultfirst dst_negative_add_unique_resultfirst. (((H) = (((((dst_positive_code_add_unique_resultfirst) + (dst_positive_scale_add_unique_resultfirst)) * S ((dst_positive_code_add_unique_resultfirst) + (dst_positive_scale_add_unique_resultfirst)) + ((dst_positive_scale_add_unique_resultfirst) + (dst_positive_scale_add_unique_resultfirst))) + (((dst_negative_code_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)) * S ((dst_negative_code_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)) + ((dst_negative_scale_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)))) * S ((((dst_positive_code_add_unique_resultfirst) + (dst_positive_scale_add_unique_resultfirst)) * S ((dst_positive_code_add_unique_resultfirst) + (dst_positive_scale_add_unique_resultfirst)) + ((dst_positive_scale_add_unique_resultfirst) + (dst_positive_scale_add_unique_resultfirst))) + (((dst_negative_code_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)) * S ((dst_negative_code_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)) + ((dst_negative_scale_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)))) + ((((dst_negative_code_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)) * S ((dst_negative_code_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)) + ((dst_negative_scale_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst))) + (((dst_negative_code_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)) * S ((dst_negative_code_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)) + ((dst_negative_scale_add_unique_resultfirst) + (dst_negative_scale_add_unique_resultfirst)))))) /\ (((((exists ff_h_pvs_add_unique_resultfirstpositive. ff_h_pvs_add_unique_resultfirstpositive + S (dst_positive_add_unique_resultfirst) = S ((S (dst_index_add_unique_result)) * dst_positive_scale_add_unique_resultfirst)) /\ exists ff_q_pvs_add_unique_resultfirstpositive. dst_positive_code_add_unique_resultfirst = ff_q_pvs_add_unique_resultfirstpositive * S ((S (dst_index_add_unique_result)) * dst_positive_scale_add_unique_resultfirst) + (dst_positive_add_unique_resultfirst))) /\ (((((exists ff_h_pvs_add_unique_resultfirstnegative. ff_h_pvs_add_unique_resultfirstnegative + S (dst_negative_add_unique_resultfirst) = S ((S (dst_index_add_unique_result)) * dst_negative_scale_add_unique_resultfirst)) /\ exists ff_q_pvs_add_unique_resultfirstnegative. dst_negative_code_add_unique_resultfirst = ff_q_pvs_add_unique_resultfirstnegative * S ((S (dst_index_add_unique_result)) * dst_negative_scale_add_unique_resultfirst) + (dst_negative_add_unique_resultfirst))) /\ (exists ge_balance_positive_add_unique_resultfirstvalue ge_balance_negative_add_unique_resultfirstvalue. (((((dst_first_add_unique_result) = 2 * (ge_balance_positive_add_unique_resultfirstvalue) /\ (ge_balance_negative_add_unique_resultfirstvalue) = 0) \/ exists ge_signed_half_add_unique_resultfirstvaluedecode. (((dst_first_add_unique_result) = 2 * ge_signed_half_add_unique_resultfirstvaluedecode + 1 /\ (ge_balance_positive_add_unique_resultfirstvalue) = 0) /\ (ge_balance_negative_add_unique_resultfirstvalue) = S ge_signed_half_add_unique_resultfirstvaluedecode))) /\ ((dst_positive_add_unique_resultfirst) + ge_balance_negative_add_unique_resultfirstvalue = (dst_negative_add_unique_resultfirst) + ge_balance_positive_add_unique_resultfirstvalue))))))))) -> (exists dst_positive_code_add_unique_resultsecond dst_positive_scale_add_unique_resultsecond dst_negative_code_add_unique_resultsecond dst_negative_scale_add_unique_resultsecond dst_positive_add_unique_resultsecond dst_negative_add_unique_resultsecond. (((K) = (((((dst_positive_code_add_unique_resultsecond) + (dst_positive_scale_add_unique_resultsecond)) * S ((dst_positive_code_add_unique_resultsecond) + (dst_positive_scale_add_unique_resultsecond)) + ((dst_positive_scale_add_unique_resultsecond) + (dst_positive_scale_add_unique_resultsecond))) + (((dst_negative_code_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)) * S ((dst_negative_code_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)) + ((dst_negative_scale_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)))) * S ((((dst_positive_code_add_unique_resultsecond) + (dst_positive_scale_add_unique_resultsecond)) * S ((dst_positive_code_add_unique_resultsecond) + (dst_positive_scale_add_unique_resultsecond)) + ((dst_positive_scale_add_unique_resultsecond) + (dst_positive_scale_add_unique_resultsecond))) + (((dst_negative_code_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)) * S ((dst_negative_code_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)) + ((dst_negative_scale_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)))) + ((((dst_negative_code_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)) * S ((dst_negative_code_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)) + ((dst_negative_scale_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond))) + (((dst_negative_code_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)) * S ((dst_negative_code_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)) + ((dst_negative_scale_add_unique_resultsecond) + (dst_negative_scale_add_unique_resultsecond)))))) /\ (((((exists ff_h_pvs_add_unique_resultsecondpositive. ff_h_pvs_add_unique_resultsecondpositive + S (dst_positive_add_unique_resultsecond) = S ((S (dst_index_add_unique_result)) * dst_positive_scale_add_unique_resultsecond)) /\ exists ff_q_pvs_add_unique_resultsecondpositive. dst_positive_code_add_unique_resultsecond = ff_q_pvs_add_unique_resultsecondpositive * S ((S (dst_index_add_unique_result)) * dst_positive_scale_add_unique_resultsecond) + (dst_positive_add_unique_resultsecond))) /\ (((((exists ff_h_pvs_add_unique_resultsecondnegative. ff_h_pvs_add_unique_resultsecondnegative + S (dst_negative_add_unique_resultsecond) = S ((S (dst_index_add_unique_result)) * dst_negative_scale_add_unique_resultsecond)) /\ exists ff_q_pvs_add_unique_resultsecondnegative. dst_negative_code_add_unique_resultsecond = ff_q_pvs_add_unique_resultsecondnegative * S ((S (dst_index_add_unique_result)) * dst_negative_scale_add_unique_resultsecond) + (dst_negative_add_unique_resultsecond))) /\ (exists ge_balance_positive_add_unique_resultsecondvalue ge_balance_negative_add_unique_resultsecondvalue. (((((dst_second_add_unique_result) = 2 * (ge_balance_positive_add_unique_resultsecondvalue) /\ (ge_balance_negative_add_unique_resultsecondvalue) = 0) \/ exists ge_signed_half_add_unique_resultsecondvaluedecode. (((dst_second_add_unique_result) = 2 * ge_signed_half_add_unique_resultsecondvaluedecode + 1 /\ (ge_balance_positive_add_unique_resultsecondvalue) = 0) /\ (ge_balance_negative_add_unique_resultsecondvalue) = S ge_signed_half_add_unique_resultsecondvaluedecode))) /\ ((dst_positive_add_unique_resultsecond) + ge_balance_negative_add_unique_resultsecondvalue = (dst_negative_add_unique_resultsecond) + ge_balance_positive_add_unique_resultsecondvalue))))))))) -> dst_first_add_unique_result = dst_second_add_unique_result)Constructive proof overview
Generated structural guide
Outputs of the same pointwise add operation agree in every represented value, not necessarily in their table codes or raw components.
The unchanged tactic script uses 3 declared prerequisites and contains 70 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
WS0002 signed_table_lookup_any WS0003 signed_table_add_lookup signed_add_functional Alpha theorem; checked-use authorizedDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Named ingredients (2)
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–13
03Establish ht0L14–14
Establish this local claim before using it. It is not an additional assumption.
- L14
have ht0 : ArithTable(l,F)Definitions: ArithTable
04Separate the logical casesL15–17
05Use earlier factsL18–18
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L18
exact hop_left
06Establish he0L19–24
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed table lookup any.
07Separate the logical casesL25–25
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L25
cases he0
08Establish ht1L26–26
Establish this local claim before using it. It is not an additional assumption.
- L26
have ht1 : ArithTable(l,G)Definitions: ArithTable
09Separate the logical casesL27–29
10Use earlier factsL30–30
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L30
exact hop_right_left
11Establish he1L31–36
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed table lookup any.
12Separate the logical casesL37–37
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L37
cases he1
13Use earlier factsL38–47
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L38
specialize signed_add_functional (x) - L39
specialize signed_add_functional (x1) - L40
specialize signed_add_functional (u) - L41
specialize signed_add_functional (v) - L42
apply signed_add_functional - L43
specialize signed_table_add_lookup (F) - L44
specialize signed_table_add_lookup (G) - L45
specialize signed_table_add_lookup (H) - L46
specialize signed_table_add_lookup (l) - L47
specialize signed_table_add_lookup (i)
14Use earlier factsL48–57
Instantiate or apply named facts and discharge the corresponding proof obligations.
15Use earlier factsL58–67
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L58
specialize signed_table_add_lookup (G) - L59
specialize signed_table_add_lookup (K) - L60
specialize signed_table_add_lookup (l) - L61
specialize signed_table_add_lookup (i) - L62
specialize signed_table_add_lookup (x) - L63
specialize signed_table_add_lookup (x1) - L64
specialize signed_table_add_lookup (v) - L65
apply signed_table_add_lookup - L66
exact hother - L67
exact hi
Original exact command ledger · 70 lines
- 0001
intro F - 0002
intro G - 0003
intro H - 0004
intro K - 0005
intro l - 0006
intro hop - 0007
intro hother - 0008
intro i - 0009
intro u - 0010
intro v - 0011
intro hi - 0012
intro hu - 0013
intro hv - 0014
have ht0 : exists dst_positive_code_add_functional_table0 dst_positive_scale_add_functional_table0 dst_negative_code_add_functional_table0 dst_negative_scale_add_functional_table0. (((F) = (((((dst_positive_code_add_functional_table0) + (dst_positive_scale_add_functional_table0)) * S ((dst_positive_code_add_functional_table0) + (dst_positive_scale_add_functional_table0)) + ((dst_positive_scale_add_functional_table0) + (dst_positive_scale_add_functional_table0))) + (((dst_negative_code_add_functional_table0) + (dst_negative_scale_add_functional_table0)) * S ((dst_negative_code_add_functional_table0) + (dst_negative_scale_add_functional_table0)) + ((dst_negative_scale_add_functional_table0) + (dst_negative_scale_add_functional_table0)))) * S ((((dst_positive_code_add_functional_table0) + (dst_positive_scale_add_functional_table0)) * S ((dst_positive_code_add_functional_table0) + (dst_positive_scale_add_functional_table0)) + ((dst_positive_scale_add_functional_table0) + (dst_positive_scale_add_functional_table0))) + (((dst_negative_code_add_functional_table0) + (dst_negative_scale_add_functional_table0)) * S ((dst_negative_code_add_functional_table0) + (dst_negative_scale_add_functional_table0)) + ((dst_negative_scale_add_functional_table0) + (dst_negative_scale_add_functional_table0)))) + ((((dst_negative_code_add_functional_table0) + (dst_negative_scale_add_functional_table0)) * S ((dst_negative_code_add_functional_table0) + (dst_negative_scale_add_functional_table0)) + ((dst_negative_scale_add_functional_table0) + (dst_negative_scale_add_functional_table0))) + (((dst_negative_code_add_functional_table0) + (dst_negative_scale_add_functional_table0)) * S ((dst_negative_code_add_functional_table0) + (dst_negative_scale_add_functional_table0)) + ((dst_negative_scale_add_functional_table0) + (dst_negative_scale_add_functional_table0)))))) /\ (forall dst_index_add_functional_table0. (exists pvs_le_gap_add_functional_table0domain. pvs_le_gap_add_functional_table0domain + (dst_index_add_functional_table0) = (l)) -> exists dst_positive_add_functional_table0 dst_negative_add_functional_table0 dst_value_add_functional_table0. ((((exists ff_h_pvs_add_functional_table0entrypositive. ff_h_pvs_add_functional_table0entrypositive + S (dst_positive_add_functional_table0) = S ((S (dst_index_add_functional_table0)) * dst_positive_scale_add_functional_table0)) /\ exists ff_q_pvs_add_functional_table0entrypositive. dst_positive_code_add_functional_table0 = ff_q_pvs_add_functional_table0entrypositive * S ((S (dst_index_add_functional_table0)) * dst_positive_scale_add_functional_table0) + (dst_positive_add_functional_table0))) /\ (((((exists ff_h_pvs_add_functional_table0entrynegative. ff_h_pvs_add_functional_table0entrynegative + S (dst_negative_add_functional_table0) = S ((S (dst_index_add_functional_table0)) * dst_negative_scale_add_functional_table0)) /\ exists ff_q_pvs_add_functional_table0entrynegative. dst_negative_code_add_functional_table0 = ff_q_pvs_add_functional_table0entrynegative * S ((S (dst_index_add_functional_table0)) * dst_negative_scale_add_functional_table0) + (dst_negative_add_functional_table0))) /\ (exists ge_balance_positive_add_functional_table0entryvalue ge_balance_negative_add_functional_table0entryvalue. (((((dst_value_add_functional_table0) = 2 * (ge_balance_positive_add_functional_table0entryvalue) /\ (ge_balance_negative_add_functional_table0entryvalue) = 0) \/ exists ge_signed_half_add_functional_table0entryvaluedecode. (((dst_value_add_functional_table0) = 2 * ge_signed_half_add_functional_table0entryvaluedecode + 1 /\ (ge_balance_positive_add_functional_table0entryvalue) = 0) /\ (ge_balance_negative_add_functional_table0entryvalue) = S ge_signed_half_add_functional_table0entryvaluedecode))) /\ ((dst_positive_add_functional_table0) + ge_balance_negative_add_functional_table0entryvalue = (dst_negative_add_functional_table0) + ge_balance_positive_add_functional_table0entryvalue)))))))) - 0015
cases hop - 0016
cases hop_right - 0017
cases hop_right_right - 0018
exact hop_left - 0019
have he0 : exists z. (exists dst_positive_code_add_functional_value0 dst_positive_scale_add_functional_value0 dst_negative_code_add_functional_value0 dst_negative_scale_add_functional_value0 dst_positive_add_functional_value0 dst_negative_add_functional_value0. (((F) = (((((dst_positive_code_add_functional_value0) + (dst_positive_scale_add_functional_value0)) * S ((dst_positive_code_add_functional_value0) + (dst_positive_scale_add_functional_value0)) + ((dst_positive_scale_add_functional_value0) + (dst_positive_scale_add_functional_value0))) + (((dst_negative_code_add_functional_value0) + (dst_negative_scale_add_functional_value0)) * S ((dst_negative_code_add_functional_value0) + (dst_negative_scale_add_functional_value0)) + ((dst_negative_scale_add_functional_value0) + (dst_negative_scale_add_functional_value0)))) * S ((((dst_positive_code_add_functional_value0) + (dst_positive_scale_add_functional_value0)) * S ((dst_positive_code_add_functional_value0) + (dst_positive_scale_add_functional_value0)) + ((dst_positive_scale_add_functional_value0) + (dst_positive_scale_add_functional_value0))) + (((dst_negative_code_add_functional_value0) + (dst_negative_scale_add_functional_value0)) * S ((dst_negative_code_add_functional_value0) + (dst_negative_scale_add_functional_value0)) + ((dst_negative_scale_add_functional_value0) + (dst_negative_scale_add_functional_value0)))) + ((((dst_negative_code_add_functional_value0) + (dst_negative_scale_add_functional_value0)) * S ((dst_negative_code_add_functional_value0) + (dst_negative_scale_add_functional_value0)) + ((dst_negative_scale_add_functional_value0) + (dst_negative_scale_add_functional_value0))) + (((dst_negative_code_add_functional_value0) + (dst_negative_scale_add_functional_value0)) * S ((dst_negative_code_add_functional_value0) + (dst_negative_scale_add_functional_value0)) + ((dst_negative_scale_add_functional_value0) + (dst_negative_scale_add_functional_value0)))))) /\ (((((exists ff_h_pvs_add_functional_value0positive. ff_h_pvs_add_functional_value0positive + S (dst_positive_add_functional_value0) = S ((S (i)) * dst_positive_scale_add_functional_value0)) /\ exists ff_q_pvs_add_functional_value0positive. dst_positive_code_add_functional_value0 = ff_q_pvs_add_functional_value0positive * S ((S (i)) * dst_positive_scale_add_functional_value0) + (dst_positive_add_functional_value0))) /\ (((((exists ff_h_pvs_add_functional_value0negative. ff_h_pvs_add_functional_value0negative + S (dst_negative_add_functional_value0) = S ((S (i)) * dst_negative_scale_add_functional_value0)) /\ exists ff_q_pvs_add_functional_value0negative. dst_negative_code_add_functional_value0 = ff_q_pvs_add_functional_value0negative * S ((S (i)) * dst_negative_scale_add_functional_value0) + (dst_negative_add_functional_value0))) /\ (exists ge_balance_positive_add_functional_value0value ge_balance_negative_add_functional_value0value. (((((z) = 2 * (ge_balance_positive_add_functional_value0value) /\ (ge_balance_negative_add_functional_value0value) = 0) \/ exists ge_signed_half_add_functional_value0valuedecode. (((z) = 2 * ge_signed_half_add_functional_value0valuedecode + 1 /\ (ge_balance_positive_add_functional_value0value) = 0) /\ (ge_balance_negative_add_functional_value0value) = S ge_signed_half_add_functional_value0valuedecode))) /\ ((dst_positive_add_functional_value0) + ge_balance_negative_add_functional_value0value = (dst_negative_add_functional_value0) + ge_balance_positive_add_functional_value0value))))))))) - 0020
specialize signed_table_lookup_any (l) - 0021
specialize signed_table_lookup_any (F) - 0022
specialize signed_table_lookup_any (i) - 0023
apply signed_table_lookup_any - 0024
exact ht0 - 0025
cases he0 - 0026
have ht1 : exists dst_positive_code_add_functional_table1 dst_positive_scale_add_functional_table1 dst_negative_code_add_functional_table1 dst_negative_scale_add_functional_table1. (((G) = (((((dst_positive_code_add_functional_table1) + (dst_positive_scale_add_functional_table1)) * S ((dst_positive_code_add_functional_table1) + (dst_positive_scale_add_functional_table1)) + ((dst_positive_scale_add_functional_table1) + (dst_positive_scale_add_functional_table1))) + (((dst_negative_code_add_functional_table1) + (dst_negative_scale_add_functional_table1)) * S ((dst_negative_code_add_functional_table1) + (dst_negative_scale_add_functional_table1)) + ((dst_negative_scale_add_functional_table1) + (dst_negative_scale_add_functional_table1)))) * S ((((dst_positive_code_add_functional_table1) + (dst_positive_scale_add_functional_table1)) * S ((dst_positive_code_add_functional_table1) + (dst_positive_scale_add_functional_table1)) + ((dst_positive_scale_add_functional_table1) + (dst_positive_scale_add_functional_table1))) + (((dst_negative_code_add_functional_table1) + (dst_negative_scale_add_functional_table1)) * S ((dst_negative_code_add_functional_table1) + (dst_negative_scale_add_functional_table1)) + ((dst_negative_scale_add_functional_table1) + (dst_negative_scale_add_functional_table1)))) + ((((dst_negative_code_add_functional_table1) + (dst_negative_scale_add_functional_table1)) * S ((dst_negative_code_add_functional_table1) + (dst_negative_scale_add_functional_table1)) + ((dst_negative_scale_add_functional_table1) + (dst_negative_scale_add_functional_table1))) + (((dst_negative_code_add_functional_table1) + (dst_negative_scale_add_functional_table1)) * S ((dst_negative_code_add_functional_table1) + (dst_negative_scale_add_functional_table1)) + ((dst_negative_scale_add_functional_table1) + (dst_negative_scale_add_functional_table1)))))) /\ (forall dst_index_add_functional_table1. (exists pvs_le_gap_add_functional_table1domain. pvs_le_gap_add_functional_table1domain + (dst_index_add_functional_table1) = (l)) -> exists dst_positive_add_functional_table1 dst_negative_add_functional_table1 dst_value_add_functional_table1. ((((exists ff_h_pvs_add_functional_table1entrypositive. ff_h_pvs_add_functional_table1entrypositive + S (dst_positive_add_functional_table1) = S ((S (dst_index_add_functional_table1)) * dst_positive_scale_add_functional_table1)) /\ exists ff_q_pvs_add_functional_table1entrypositive. dst_positive_code_add_functional_table1 = ff_q_pvs_add_functional_table1entrypositive * S ((S (dst_index_add_functional_table1)) * dst_positive_scale_add_functional_table1) + (dst_positive_add_functional_table1))) /\ (((((exists ff_h_pvs_add_functional_table1entrynegative. ff_h_pvs_add_functional_table1entrynegative + S (dst_negative_add_functional_table1) = S ((S (dst_index_add_functional_table1)) * dst_negative_scale_add_functional_table1)) /\ exists ff_q_pvs_add_functional_table1entrynegative. dst_negative_code_add_functional_table1 = ff_q_pvs_add_functional_table1entrynegative * S ((S (dst_index_add_functional_table1)) * dst_negative_scale_add_functional_table1) + (dst_negative_add_functional_table1))) /\ (exists ge_balance_positive_add_functional_table1entryvalue ge_balance_negative_add_functional_table1entryvalue. (((((dst_value_add_functional_table1) = 2 * (ge_balance_positive_add_functional_table1entryvalue) /\ (ge_balance_negative_add_functional_table1entryvalue) = 0) \/ exists ge_signed_half_add_functional_table1entryvaluedecode. (((dst_value_add_functional_table1) = 2 * ge_signed_half_add_functional_table1entryvaluedecode + 1 /\ (ge_balance_positive_add_functional_table1entryvalue) = 0) /\ (ge_balance_negative_add_functional_table1entryvalue) = S ge_signed_half_add_functional_table1entryvaluedecode))) /\ ((dst_positive_add_functional_table1) + ge_balance_negative_add_functional_table1entryvalue = (dst_negative_add_functional_table1) + ge_balance_positive_add_functional_table1entryvalue)))))))) - 0027
cases hop - 0028
cases hop_right - 0029
cases hop_right_right - 0030
exact hop_right_left - 0031
have he1 : exists z. (exists dst_positive_code_add_functional_value1 dst_positive_scale_add_functional_value1 dst_negative_code_add_functional_value1 dst_negative_scale_add_functional_value1 dst_positive_add_functional_value1 dst_negative_add_functional_value1. (((G) = (((((dst_positive_code_add_functional_value1) + (dst_positive_scale_add_functional_value1)) * S ((dst_positive_code_add_functional_value1) + (dst_positive_scale_add_functional_value1)) + ((dst_positive_scale_add_functional_value1) + (dst_positive_scale_add_functional_value1))) + (((dst_negative_code_add_functional_value1) + (dst_negative_scale_add_functional_value1)) * S ((dst_negative_code_add_functional_value1) + (dst_negative_scale_add_functional_value1)) + ((dst_negative_scale_add_functional_value1) + (dst_negative_scale_add_functional_value1)))) * S ((((dst_positive_code_add_functional_value1) + (dst_positive_scale_add_functional_value1)) * S ((dst_positive_code_add_functional_value1) + (dst_positive_scale_add_functional_value1)) + ((dst_positive_scale_add_functional_value1) + (dst_positive_scale_add_functional_value1))) + (((dst_negative_code_add_functional_value1) + (dst_negative_scale_add_functional_value1)) * S ((dst_negative_code_add_functional_value1) + (dst_negative_scale_add_functional_value1)) + ((dst_negative_scale_add_functional_value1) + (dst_negative_scale_add_functional_value1)))) + ((((dst_negative_code_add_functional_value1) + (dst_negative_scale_add_functional_value1)) * S ((dst_negative_code_add_functional_value1) + (dst_negative_scale_add_functional_value1)) + ((dst_negative_scale_add_functional_value1) + (dst_negative_scale_add_functional_value1))) + (((dst_negative_code_add_functional_value1) + (dst_negative_scale_add_functional_value1)) * S ((dst_negative_code_add_functional_value1) + (dst_negative_scale_add_functional_value1)) + ((dst_negative_scale_add_functional_value1) + (dst_negative_scale_add_functional_value1)))))) /\ (((((exists ff_h_pvs_add_functional_value1positive. ff_h_pvs_add_functional_value1positive + S (dst_positive_add_functional_value1) = S ((S (i)) * dst_positive_scale_add_functional_value1)) /\ exists ff_q_pvs_add_functional_value1positive. dst_positive_code_add_functional_value1 = ff_q_pvs_add_functional_value1positive * S ((S (i)) * dst_positive_scale_add_functional_value1) + (dst_positive_add_functional_value1))) /\ (((((exists ff_h_pvs_add_functional_value1negative. ff_h_pvs_add_functional_value1negative + S (dst_negative_add_functional_value1) = S ((S (i)) * dst_negative_scale_add_functional_value1)) /\ exists ff_q_pvs_add_functional_value1negative. dst_negative_code_add_functional_value1 = ff_q_pvs_add_functional_value1negative * S ((S (i)) * dst_negative_scale_add_functional_value1) + (dst_negative_add_functional_value1))) /\ (exists ge_balance_positive_add_functional_value1value ge_balance_negative_add_functional_value1value. (((((z) = 2 * (ge_balance_positive_add_functional_value1value) /\ (ge_balance_negative_add_functional_value1value) = 0) \/ exists ge_signed_half_add_functional_value1valuedecode. (((z) = 2 * ge_signed_half_add_functional_value1valuedecode + 1 /\ (ge_balance_positive_add_functional_value1value) = 0) /\ (ge_balance_negative_add_functional_value1value) = S ge_signed_half_add_functional_value1valuedecode))) /\ ((dst_positive_add_functional_value1) + ge_balance_negative_add_functional_value1value = (dst_negative_add_functional_value1) + ge_balance_positive_add_functional_value1value))))))))) - 0032
specialize signed_table_lookup_any (l) - 0033
specialize signed_table_lookup_any (G) - 0034
specialize signed_table_lookup_any (i) - 0035
apply signed_table_lookup_any - 0036
exact ht1 - 0037
cases he1 - 0038
specialize signed_add_functional (x) - 0039
specialize signed_add_functional (x1) - 0040
specialize signed_add_functional (u) - 0041
specialize signed_add_functional (v) - 0042
apply signed_add_functional - 0043
specialize signed_table_add_lookup (F) - 0044
specialize signed_table_add_lookup (G) - 0045
specialize signed_table_add_lookup (H) - 0046
specialize signed_table_add_lookup (l) - 0047
specialize signed_table_add_lookup (i) - 0048
specialize signed_table_add_lookup (x) - 0049
specialize signed_table_add_lookup (x1) - 0050
specialize signed_table_add_lookup (u) - 0051
apply signed_table_add_lookup - 0052
exact hop - 0053
exact hi - 0054
exact he0_witness - 0055
exact he1_witness - 0056
exact hu - 0057
specialize signed_table_add_lookup (F) - 0058
specialize signed_table_add_lookup (G) - 0059
specialize signed_table_add_lookup (K) - 0060
specialize signed_table_add_lookup (l) - 0061
specialize signed_table_add_lookup (i) - 0062
specialize signed_table_add_lookup (x) - 0063
specialize signed_table_add_lookup (x1) - 0064
specialize signed_table_add_lookup (v) - 0065
apply signed_table_add_lookup - 0066
exact hother - 0067
exact hi - 0068
exact he0_witness - 0069
exact he1_witness - 0070
exact hv