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. ∀ F. ∀ G. ArithTable(l,F) → ArithTable(l,G) → ∃ x. ArithAdd(F,G,x,l) ∧ (∀ y. ArithAdd(F,G,y,l) → ArithTableEqual(x,y,l))
Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Original expanded first-order statement
forall l F G. (exists dst_positive_code_add_exists_unique_input0 dst_positive_scale_add_exists_unique_input0 dst_negative_code_add_exists_unique_input0 dst_negative_scale_add_exists_unique_input0. (((F) = (((((dst_positive_code_add_exists_unique_input0) + (dst_positive_scale_add_exists_unique_input0)) * S ((dst_positive_code_add_exists_unique_input0) + (dst_positive_scale_add_exists_unique_input0)) + ((dst_positive_scale_add_exists_unique_input0) + (dst_positive_scale_add_exists_unique_input0))) + (((dst_negative_code_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)) * S ((dst_negative_code_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)) + ((dst_negative_scale_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)))) * S ((((dst_positive_code_add_exists_unique_input0) + (dst_positive_scale_add_exists_unique_input0)) * S ((dst_positive_code_add_exists_unique_input0) + (dst_positive_scale_add_exists_unique_input0)) + ((dst_positive_scale_add_exists_unique_input0) + (dst_positive_scale_add_exists_unique_input0))) + (((dst_negative_code_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)) * S ((dst_negative_code_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)) + ((dst_negative_scale_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)))) + ((((dst_negative_code_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)) * S ((dst_negative_code_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)) + ((dst_negative_scale_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0))) + (((dst_negative_code_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)) * S ((dst_negative_code_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)) + ((dst_negative_scale_add_exists_unique_input0) + (dst_negative_scale_add_exists_unique_input0)))))) /\ (forall dst_index_add_exists_unique_input0. (exists pvs_le_gap_add_exists_unique_input0domain. pvs_le_gap_add_exists_unique_input0domain + (dst_index_add_exists_unique_input0) = (l)) -> exists dst_positive_add_exists_unique_input0 dst_negative_add_exists_unique_input0 dst_value_add_exists_unique_input0. ((((exists ff_h_pvs_add_exists_unique_input0entrypositive. ff_h_pvs_add_exists_unique_input0entrypositive + S (dst_positive_add_exists_unique_input0) = S ((S (dst_index_add_exists_unique_input0)) * dst_positive_scale_add_exists_unique_input0)) /\ exists ff_q_pvs_add_exists_unique_input0entrypositive. dst_positive_code_add_exists_unique_input0 = ff_q_pvs_add_exists_unique_input0entrypositive * S ((S (dst_index_add_exists_unique_input0)) * dst_positive_scale_add_exists_unique_input0) + (dst_positive_add_exists_unique_input0))) /\ (((((exists ff_h_pvs_add_exists_unique_input0entrynegative. ff_h_pvs_add_exists_unique_input0entrynegative + S (dst_negative_add_exists_unique_input0) = S ((S (dst_index_add_exists_unique_input0)) * dst_negative_scale_add_exists_unique_input0)) /\ exists ff_q_pvs_add_exists_unique_input0entrynegative. dst_negative_code_add_exists_unique_input0 = ff_q_pvs_add_exists_unique_input0entrynegative * S ((S (dst_index_add_exists_unique_input0)) * dst_negative_scale_add_exists_unique_input0) + (dst_negative_add_exists_unique_input0))) /\ (exists ge_balance_positive_add_exists_unique_input0entryvalue ge_balance_negative_add_exists_unique_input0entryvalue. (((((dst_value_add_exists_unique_input0) = 2 * (ge_balance_positive_add_exists_unique_input0entryvalue) /\ (ge_balance_negative_add_exists_unique_input0entryvalue) = 0) \/ exists ge_signed_half_add_exists_unique_input0entryvaluedecode. (((dst_value_add_exists_unique_input0) = 2 * ge_signed_half_add_exists_unique_input0entryvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_input0entryvalue) = 0) /\ (ge_balance_negative_add_exists_unique_input0entryvalue) = S ge_signed_half_add_exists_unique_input0entryvaluedecode))) /\ ((dst_positive_add_exists_unique_input0) + ge_balance_negative_add_exists_unique_input0entryvalue = (dst_negative_add_exists_unique_input0) + ge_balance_positive_add_exists_unique_input0entryvalue))))))))) -> (exists dst_positive_code_add_exists_unique_input1 dst_positive_scale_add_exists_unique_input1 dst_negative_code_add_exists_unique_input1 dst_negative_scale_add_exists_unique_input1. (((G) = (((((dst_positive_code_add_exists_unique_input1) + (dst_positive_scale_add_exists_unique_input1)) * S ((dst_positive_code_add_exists_unique_input1) + (dst_positive_scale_add_exists_unique_input1)) + ((dst_positive_scale_add_exists_unique_input1) + (dst_positive_scale_add_exists_unique_input1))) + (((dst_negative_code_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)) * S ((dst_negative_code_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)) + ((dst_negative_scale_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)))) * S ((((dst_positive_code_add_exists_unique_input1) + (dst_positive_scale_add_exists_unique_input1)) * S ((dst_positive_code_add_exists_unique_input1) + (dst_positive_scale_add_exists_unique_input1)) + ((dst_positive_scale_add_exists_unique_input1) + (dst_positive_scale_add_exists_unique_input1))) + (((dst_negative_code_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)) * S ((dst_negative_code_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)) + ((dst_negative_scale_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)))) + ((((dst_negative_code_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)) * S ((dst_negative_code_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)) + ((dst_negative_scale_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1))) + (((dst_negative_code_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)) * S ((dst_negative_code_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)) + ((dst_negative_scale_add_exists_unique_input1) + (dst_negative_scale_add_exists_unique_input1)))))) /\ (forall dst_index_add_exists_unique_input1. (exists pvs_le_gap_add_exists_unique_input1domain. pvs_le_gap_add_exists_unique_input1domain + (dst_index_add_exists_unique_input1) = (l)) -> exists dst_positive_add_exists_unique_input1 dst_negative_add_exists_unique_input1 dst_value_add_exists_unique_input1. ((((exists ff_h_pvs_add_exists_unique_input1entrypositive. ff_h_pvs_add_exists_unique_input1entrypositive + S (dst_positive_add_exists_unique_input1) = S ((S (dst_index_add_exists_unique_input1)) * dst_positive_scale_add_exists_unique_input1)) /\ exists ff_q_pvs_add_exists_unique_input1entrypositive. dst_positive_code_add_exists_unique_input1 = ff_q_pvs_add_exists_unique_input1entrypositive * S ((S (dst_index_add_exists_unique_input1)) * dst_positive_scale_add_exists_unique_input1) + (dst_positive_add_exists_unique_input1))) /\ (((((exists ff_h_pvs_add_exists_unique_input1entrynegative. ff_h_pvs_add_exists_unique_input1entrynegative + S (dst_negative_add_exists_unique_input1) = S ((S (dst_index_add_exists_unique_input1)) * dst_negative_scale_add_exists_unique_input1)) /\ exists ff_q_pvs_add_exists_unique_input1entrynegative. dst_negative_code_add_exists_unique_input1 = ff_q_pvs_add_exists_unique_input1entrynegative * S ((S (dst_index_add_exists_unique_input1)) * dst_negative_scale_add_exists_unique_input1) + (dst_negative_add_exists_unique_input1))) /\ (exists ge_balance_positive_add_exists_unique_input1entryvalue ge_balance_negative_add_exists_unique_input1entryvalue. (((((dst_value_add_exists_unique_input1) = 2 * (ge_balance_positive_add_exists_unique_input1entryvalue) /\ (ge_balance_negative_add_exists_unique_input1entryvalue) = 0) \/ exists ge_signed_half_add_exists_unique_input1entryvaluedecode. (((dst_value_add_exists_unique_input1) = 2 * ge_signed_half_add_exists_unique_input1entryvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_input1entryvalue) = 0) /\ (ge_balance_negative_add_exists_unique_input1entryvalue) = S ge_signed_half_add_exists_unique_input1entryvaluedecode))) /\ ((dst_positive_add_exists_unique_input1) + ge_balance_negative_add_exists_unique_input1entryvalue = (dst_negative_add_exists_unique_input1) + ge_balance_positive_add_exists_unique_input1entryvalue))))))))) -> exists H. ((((exists dst_positive_code_add_exists_unique_resultleft_table dst_positive_scale_add_exists_unique_resultleft_table dst_negative_code_add_exists_unique_resultleft_table dst_negative_scale_add_exists_unique_resultleft_table. (((F) = (((((dst_positive_code_add_exists_unique_resultleft_table) + (dst_positive_scale_add_exists_unique_resultleft_table)) * S ((dst_positive_code_add_exists_unique_resultleft_table) + (dst_positive_scale_add_exists_unique_resultleft_table)) + ((dst_positive_scale_add_exists_unique_resultleft_table) + (dst_positive_scale_add_exists_unique_resultleft_table))) + (((dst_negative_code_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)) * S ((dst_negative_code_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)) + ((dst_negative_scale_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)))) * S ((((dst_positive_code_add_exists_unique_resultleft_table) + (dst_positive_scale_add_exists_unique_resultleft_table)) * S ((dst_positive_code_add_exists_unique_resultleft_table) + (dst_positive_scale_add_exists_unique_resultleft_table)) + ((dst_positive_scale_add_exists_unique_resultleft_table) + (dst_positive_scale_add_exists_unique_resultleft_table))) + (((dst_negative_code_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)) * S ((dst_negative_code_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)) + ((dst_negative_scale_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)))) + ((((dst_negative_code_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)) * S ((dst_negative_code_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)) + ((dst_negative_scale_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table))) + (((dst_negative_code_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)) * S ((dst_negative_code_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)) + ((dst_negative_scale_add_exists_unique_resultleft_table) + (dst_negative_scale_add_exists_unique_resultleft_table)))))) /\ (forall dst_index_add_exists_unique_resultleft_table. (exists pvs_le_gap_add_exists_unique_resultleft_tabledomain. pvs_le_gap_add_exists_unique_resultleft_tabledomain + (dst_index_add_exists_unique_resultleft_table) = (l)) -> exists dst_positive_add_exists_unique_resultleft_table dst_negative_add_exists_unique_resultleft_table dst_value_add_exists_unique_resultleft_table. ((((exists ff_h_pvs_add_exists_unique_resultleft_tableentrypositive. ff_h_pvs_add_exists_unique_resultleft_tableentrypositive + S (dst_positive_add_exists_unique_resultleft_table) = S ((S (dst_index_add_exists_unique_resultleft_table)) * dst_positive_scale_add_exists_unique_resultleft_table)) /\ exists ff_q_pvs_add_exists_unique_resultleft_tableentrypositive. dst_positive_code_add_exists_unique_resultleft_table = ff_q_pvs_add_exists_unique_resultleft_tableentrypositive * S ((S (dst_index_add_exists_unique_resultleft_table)) * dst_positive_scale_add_exists_unique_resultleft_table) + (dst_positive_add_exists_unique_resultleft_table))) /\ (((((exists ff_h_pvs_add_exists_unique_resultleft_tableentrynegative. ff_h_pvs_add_exists_unique_resultleft_tableentrynegative + S (dst_negative_add_exists_unique_resultleft_table) = S ((S (dst_index_add_exists_unique_resultleft_table)) * dst_negative_scale_add_exists_unique_resultleft_table)) /\ exists ff_q_pvs_add_exists_unique_resultleft_tableentrynegative. dst_negative_code_add_exists_unique_resultleft_table = ff_q_pvs_add_exists_unique_resultleft_tableentrynegative * S ((S (dst_index_add_exists_unique_resultleft_table)) * dst_negative_scale_add_exists_unique_resultleft_table) + (dst_negative_add_exists_unique_resultleft_table))) /\ (exists ge_balance_positive_add_exists_unique_resultleft_tableentryvalue ge_balance_negative_add_exists_unique_resultleft_tableentryvalue. (((((dst_value_add_exists_unique_resultleft_table) = 2 * (ge_balance_positive_add_exists_unique_resultleft_tableentryvalue) /\ (ge_balance_negative_add_exists_unique_resultleft_tableentryvalue) = 0) \/ exists ge_signed_half_add_exists_unique_resultleft_tableentryvaluedecode. (((dst_value_add_exists_unique_resultleft_table) = 2 * ge_signed_half_add_exists_unique_resultleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_resultleft_tableentryvalue) = 0) /\ (ge_balance_negative_add_exists_unique_resultleft_tableentryvalue) = S ge_signed_half_add_exists_unique_resultleft_tableentryvaluedecode))) /\ ((dst_positive_add_exists_unique_resultleft_table) + ge_balance_negative_add_exists_unique_resultleft_tableentryvalue = (dst_negative_add_exists_unique_resultleft_table) + ge_balance_positive_add_exists_unique_resultleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_exists_unique_resultright_table dst_positive_scale_add_exists_unique_resultright_table dst_negative_code_add_exists_unique_resultright_table dst_negative_scale_add_exists_unique_resultright_table. (((G) = (((((dst_positive_code_add_exists_unique_resultright_table) + (dst_positive_scale_add_exists_unique_resultright_table)) * S ((dst_positive_code_add_exists_unique_resultright_table) + (dst_positive_scale_add_exists_unique_resultright_table)) + ((dst_positive_scale_add_exists_unique_resultright_table) + (dst_positive_scale_add_exists_unique_resultright_table))) + (((dst_negative_code_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)) * S ((dst_negative_code_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)) + ((dst_negative_scale_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)))) * S ((((dst_positive_code_add_exists_unique_resultright_table) + (dst_positive_scale_add_exists_unique_resultright_table)) * S ((dst_positive_code_add_exists_unique_resultright_table) + (dst_positive_scale_add_exists_unique_resultright_table)) + ((dst_positive_scale_add_exists_unique_resultright_table) + (dst_positive_scale_add_exists_unique_resultright_table))) + (((dst_negative_code_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)) * S ((dst_negative_code_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)) + ((dst_negative_scale_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)))) + ((((dst_negative_code_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)) * S ((dst_negative_code_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)) + ((dst_negative_scale_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table))) + (((dst_negative_code_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)) * S ((dst_negative_code_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)) + ((dst_negative_scale_add_exists_unique_resultright_table) + (dst_negative_scale_add_exists_unique_resultright_table)))))) /\ (forall dst_index_add_exists_unique_resultright_table. (exists pvs_le_gap_add_exists_unique_resultright_tabledomain. pvs_le_gap_add_exists_unique_resultright_tabledomain + (dst_index_add_exists_unique_resultright_table) = (l)) -> exists dst_positive_add_exists_unique_resultright_table dst_negative_add_exists_unique_resultright_table dst_value_add_exists_unique_resultright_table. ((((exists ff_h_pvs_add_exists_unique_resultright_tableentrypositive. ff_h_pvs_add_exists_unique_resultright_tableentrypositive + S (dst_positive_add_exists_unique_resultright_table) = S ((S (dst_index_add_exists_unique_resultright_table)) * dst_positive_scale_add_exists_unique_resultright_table)) /\ exists ff_q_pvs_add_exists_unique_resultright_tableentrypositive. dst_positive_code_add_exists_unique_resultright_table = ff_q_pvs_add_exists_unique_resultright_tableentrypositive * S ((S (dst_index_add_exists_unique_resultright_table)) * dst_positive_scale_add_exists_unique_resultright_table) + (dst_positive_add_exists_unique_resultright_table))) /\ (((((exists ff_h_pvs_add_exists_unique_resultright_tableentrynegative. ff_h_pvs_add_exists_unique_resultright_tableentrynegative + S (dst_negative_add_exists_unique_resultright_table) = S ((S (dst_index_add_exists_unique_resultright_table)) * dst_negative_scale_add_exists_unique_resultright_table)) /\ exists ff_q_pvs_add_exists_unique_resultright_tableentrynegative. dst_negative_code_add_exists_unique_resultright_table = ff_q_pvs_add_exists_unique_resultright_tableentrynegative * S ((S (dst_index_add_exists_unique_resultright_table)) * dst_negative_scale_add_exists_unique_resultright_table) + (dst_negative_add_exists_unique_resultright_table))) /\ (exists ge_balance_positive_add_exists_unique_resultright_tableentryvalue ge_balance_negative_add_exists_unique_resultright_tableentryvalue. (((((dst_value_add_exists_unique_resultright_table) = 2 * (ge_balance_positive_add_exists_unique_resultright_tableentryvalue) /\ (ge_balance_negative_add_exists_unique_resultright_tableentryvalue) = 0) \/ exists ge_signed_half_add_exists_unique_resultright_tableentryvaluedecode. (((dst_value_add_exists_unique_resultright_table) = 2 * ge_signed_half_add_exists_unique_resultright_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_resultright_tableentryvalue) = 0) /\ (ge_balance_negative_add_exists_unique_resultright_tableentryvalue) = S ge_signed_half_add_exists_unique_resultright_tableentryvaluedecode))) /\ ((dst_positive_add_exists_unique_resultright_table) + ge_balance_negative_add_exists_unique_resultright_tableentryvalue = (dst_negative_add_exists_unique_resultright_table) + ge_balance_positive_add_exists_unique_resultright_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_exists_unique_resultoutput_table dst_positive_scale_add_exists_unique_resultoutput_table dst_negative_code_add_exists_unique_resultoutput_table dst_negative_scale_add_exists_unique_resultoutput_table. (((H) = (((((dst_positive_code_add_exists_unique_resultoutput_table) + (dst_positive_scale_add_exists_unique_resultoutput_table)) * S ((dst_positive_code_add_exists_unique_resultoutput_table) + (dst_positive_scale_add_exists_unique_resultoutput_table)) + ((dst_positive_scale_add_exists_unique_resultoutput_table) + (dst_positive_scale_add_exists_unique_resultoutput_table))) + (((dst_negative_code_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)) * S ((dst_negative_code_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)) + ((dst_negative_scale_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)))) * S ((((dst_positive_code_add_exists_unique_resultoutput_table) + (dst_positive_scale_add_exists_unique_resultoutput_table)) * S ((dst_positive_code_add_exists_unique_resultoutput_table) + (dst_positive_scale_add_exists_unique_resultoutput_table)) + ((dst_positive_scale_add_exists_unique_resultoutput_table) + (dst_positive_scale_add_exists_unique_resultoutput_table))) + (((dst_negative_code_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)) * S ((dst_negative_code_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)) + ((dst_negative_scale_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)))) + ((((dst_negative_code_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)) * S ((dst_negative_code_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)) + ((dst_negative_scale_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table))) + (((dst_negative_code_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)) * S ((dst_negative_code_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)) + ((dst_negative_scale_add_exists_unique_resultoutput_table) + (dst_negative_scale_add_exists_unique_resultoutput_table)))))) /\ (forall dst_index_add_exists_unique_resultoutput_table. (exists pvs_le_gap_add_exists_unique_resultoutput_tabledomain. pvs_le_gap_add_exists_unique_resultoutput_tabledomain + (dst_index_add_exists_unique_resultoutput_table) = (l)) -> exists dst_positive_add_exists_unique_resultoutput_table dst_negative_add_exists_unique_resultoutput_table dst_value_add_exists_unique_resultoutput_table. ((((exists ff_h_pvs_add_exists_unique_resultoutput_tableentrypositive. ff_h_pvs_add_exists_unique_resultoutput_tableentrypositive + S (dst_positive_add_exists_unique_resultoutput_table) = S ((S (dst_index_add_exists_unique_resultoutput_table)) * dst_positive_scale_add_exists_unique_resultoutput_table)) /\ exists ff_q_pvs_add_exists_unique_resultoutput_tableentrypositive. dst_positive_code_add_exists_unique_resultoutput_table = ff_q_pvs_add_exists_unique_resultoutput_tableentrypositive * S ((S (dst_index_add_exists_unique_resultoutput_table)) * dst_positive_scale_add_exists_unique_resultoutput_table) + (dst_positive_add_exists_unique_resultoutput_table))) /\ (((((exists ff_h_pvs_add_exists_unique_resultoutput_tableentrynegative. ff_h_pvs_add_exists_unique_resultoutput_tableentrynegative + S (dst_negative_add_exists_unique_resultoutput_table) = S ((S (dst_index_add_exists_unique_resultoutput_table)) * dst_negative_scale_add_exists_unique_resultoutput_table)) /\ exists ff_q_pvs_add_exists_unique_resultoutput_tableentrynegative. dst_negative_code_add_exists_unique_resultoutput_table = ff_q_pvs_add_exists_unique_resultoutput_tableentrynegative * S ((S (dst_index_add_exists_unique_resultoutput_table)) * dst_negative_scale_add_exists_unique_resultoutput_table) + (dst_negative_add_exists_unique_resultoutput_table))) /\ (exists ge_balance_positive_add_exists_unique_resultoutput_tableentryvalue ge_balance_negative_add_exists_unique_resultoutput_tableentryvalue. (((((dst_value_add_exists_unique_resultoutput_table) = 2 * (ge_balance_positive_add_exists_unique_resultoutput_tableentryvalue) /\ (ge_balance_negative_add_exists_unique_resultoutput_tableentryvalue) = 0) \/ exists ge_signed_half_add_exists_unique_resultoutput_tableentryvaluedecode. (((dst_value_add_exists_unique_resultoutput_table) = 2 * ge_signed_half_add_exists_unique_resultoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_resultoutput_tableentryvalue) = 0) /\ (ge_balance_negative_add_exists_unique_resultoutput_tableentryvalue) = S ge_signed_half_add_exists_unique_resultoutput_tableentryvaluedecode))) /\ ((dst_positive_add_exists_unique_resultoutput_table) + ge_balance_negative_add_exists_unique_resultoutput_tableentryvalue = (dst_negative_add_exists_unique_resultoutput_table) + ge_balance_positive_add_exists_unique_resultoutput_tableentryvalue))))))))) /\ (forall sto_index_add_exists_unique_resultentries. (exists pvs_gap_add_exists_unique_resultentriesbound. pvs_gap_add_exists_unique_resultentriesbound + S (sto_index_add_exists_unique_resultentries) = (l)) -> exists sto_left_add_exists_unique_resultentries sto_right_add_exists_unique_resultentries sto_output_add_exists_unique_resultentries. ((exists dst_positive_code_add_exists_unique_resultentriesentryleft dst_positive_scale_add_exists_unique_resultentriesentryleft dst_negative_code_add_exists_unique_resultentriesentryleft dst_negative_scale_add_exists_unique_resultentriesentryleft dst_positive_add_exists_unique_resultentriesentryleft dst_negative_add_exists_unique_resultentriesentryleft. (((F) = (((((dst_positive_code_add_exists_unique_resultentriesentryleft) + (dst_positive_scale_add_exists_unique_resultentriesentryleft)) * S ((dst_positive_code_add_exists_unique_resultentriesentryleft) + (dst_positive_scale_add_exists_unique_resultentriesentryleft)) + ((dst_positive_scale_add_exists_unique_resultentriesentryleft) + (dst_positive_scale_add_exists_unique_resultentriesentryleft))) + (((dst_negative_code_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)) * S ((dst_negative_code_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)) + ((dst_negative_scale_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)))) * S ((((dst_positive_code_add_exists_unique_resultentriesentryleft) + (dst_positive_scale_add_exists_unique_resultentriesentryleft)) * S ((dst_positive_code_add_exists_unique_resultentriesentryleft) + (dst_positive_scale_add_exists_unique_resultentriesentryleft)) + ((dst_positive_scale_add_exists_unique_resultentriesentryleft) + (dst_positive_scale_add_exists_unique_resultentriesentryleft))) + (((dst_negative_code_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)) * S ((dst_negative_code_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)) + ((dst_negative_scale_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)))) + ((((dst_negative_code_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)) * S ((dst_negative_code_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)) + ((dst_negative_scale_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft))) + (((dst_negative_code_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)) * S ((dst_negative_code_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)) + ((dst_negative_scale_add_exists_unique_resultentriesentryleft) + (dst_negative_scale_add_exists_unique_resultentriesentryleft)))))) /\ (((((exists ff_h_pvs_add_exists_unique_resultentriesentryleftpositive. ff_h_pvs_add_exists_unique_resultentriesentryleftpositive + S (dst_positive_add_exists_unique_resultentriesentryleft) = S ((S (sto_index_add_exists_unique_resultentries)) * dst_positive_scale_add_exists_unique_resultentriesentryleft)) /\ exists ff_q_pvs_add_exists_unique_resultentriesentryleftpositive. dst_positive_code_add_exists_unique_resultentriesentryleft = ff_q_pvs_add_exists_unique_resultentriesentryleftpositive * S ((S (sto_index_add_exists_unique_resultentries)) * dst_positive_scale_add_exists_unique_resultentriesentryleft) + (dst_positive_add_exists_unique_resultentriesentryleft))) /\ (((((exists ff_h_pvs_add_exists_unique_resultentriesentryleftnegative. ff_h_pvs_add_exists_unique_resultentriesentryleftnegative + S (dst_negative_add_exists_unique_resultentriesentryleft) = S ((S (sto_index_add_exists_unique_resultentries)) * dst_negative_scale_add_exists_unique_resultentriesentryleft)) /\ exists ff_q_pvs_add_exists_unique_resultentriesentryleftnegative. dst_negative_code_add_exists_unique_resultentriesentryleft = ff_q_pvs_add_exists_unique_resultentriesentryleftnegative * S ((S (sto_index_add_exists_unique_resultentries)) * dst_negative_scale_add_exists_unique_resultentriesentryleft) + (dst_negative_add_exists_unique_resultentriesentryleft))) /\ (exists ge_balance_positive_add_exists_unique_resultentriesentryleftvalue ge_balance_negative_add_exists_unique_resultentriesentryleftvalue. (((((sto_left_add_exists_unique_resultentries) = 2 * (ge_balance_positive_add_exists_unique_resultentriesentryleftvalue) /\ (ge_balance_negative_add_exists_unique_resultentriesentryleftvalue) = 0) \/ exists ge_signed_half_add_exists_unique_resultentriesentryleftvaluedecode. (((sto_left_add_exists_unique_resultentries) = 2 * ge_signed_half_add_exists_unique_resultentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_resultentriesentryleftvalue) = 0) /\ (ge_balance_negative_add_exists_unique_resultentriesentryleftvalue) = S ge_signed_half_add_exists_unique_resultentriesentryleftvaluedecode))) /\ ((dst_positive_add_exists_unique_resultentriesentryleft) + ge_balance_negative_add_exists_unique_resultentriesentryleftvalue = (dst_negative_add_exists_unique_resultentriesentryleft) + ge_balance_positive_add_exists_unique_resultentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_add_exists_unique_resultentriesentryright dst_positive_scale_add_exists_unique_resultentriesentryright dst_negative_code_add_exists_unique_resultentriesentryright dst_negative_scale_add_exists_unique_resultentriesentryright dst_positive_add_exists_unique_resultentriesentryright dst_negative_add_exists_unique_resultentriesentryright. (((G) = (((((dst_positive_code_add_exists_unique_resultentriesentryright) + (dst_positive_scale_add_exists_unique_resultentriesentryright)) * S ((dst_positive_code_add_exists_unique_resultentriesentryright) + (dst_positive_scale_add_exists_unique_resultentriesentryright)) + ((dst_positive_scale_add_exists_unique_resultentriesentryright) + (dst_positive_scale_add_exists_unique_resultentriesentryright))) + (((dst_negative_code_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)) * S ((dst_negative_code_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)) + ((dst_negative_scale_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)))) * S ((((dst_positive_code_add_exists_unique_resultentriesentryright) + (dst_positive_scale_add_exists_unique_resultentriesentryright)) * S ((dst_positive_code_add_exists_unique_resultentriesentryright) + (dst_positive_scale_add_exists_unique_resultentriesentryright)) + ((dst_positive_scale_add_exists_unique_resultentriesentryright) + (dst_positive_scale_add_exists_unique_resultentriesentryright))) + (((dst_negative_code_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)) * S ((dst_negative_code_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)) + ((dst_negative_scale_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)))) + ((((dst_negative_code_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)) * S ((dst_negative_code_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)) + ((dst_negative_scale_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright))) + (((dst_negative_code_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)) * S ((dst_negative_code_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)) + ((dst_negative_scale_add_exists_unique_resultentriesentryright) + (dst_negative_scale_add_exists_unique_resultentriesentryright)))))) /\ (((((exists ff_h_pvs_add_exists_unique_resultentriesentryrightpositive. ff_h_pvs_add_exists_unique_resultentriesentryrightpositive + S (dst_positive_add_exists_unique_resultentriesentryright) = S ((S (sto_index_add_exists_unique_resultentries)) * dst_positive_scale_add_exists_unique_resultentriesentryright)) /\ exists ff_q_pvs_add_exists_unique_resultentriesentryrightpositive. dst_positive_code_add_exists_unique_resultentriesentryright = ff_q_pvs_add_exists_unique_resultentriesentryrightpositive * S ((S (sto_index_add_exists_unique_resultentries)) * dst_positive_scale_add_exists_unique_resultentriesentryright) + (dst_positive_add_exists_unique_resultentriesentryright))) /\ (((((exists ff_h_pvs_add_exists_unique_resultentriesentryrightnegative. ff_h_pvs_add_exists_unique_resultentriesentryrightnegative + S (dst_negative_add_exists_unique_resultentriesentryright) = S ((S (sto_index_add_exists_unique_resultentries)) * dst_negative_scale_add_exists_unique_resultentriesentryright)) /\ exists ff_q_pvs_add_exists_unique_resultentriesentryrightnegative. dst_negative_code_add_exists_unique_resultentriesentryright = ff_q_pvs_add_exists_unique_resultentriesentryrightnegative * S ((S (sto_index_add_exists_unique_resultentries)) * dst_negative_scale_add_exists_unique_resultentriesentryright) + (dst_negative_add_exists_unique_resultentriesentryright))) /\ (exists ge_balance_positive_add_exists_unique_resultentriesentryrightvalue ge_balance_negative_add_exists_unique_resultentriesentryrightvalue. (((((sto_right_add_exists_unique_resultentries) = 2 * (ge_balance_positive_add_exists_unique_resultentriesentryrightvalue) /\ (ge_balance_negative_add_exists_unique_resultentriesentryrightvalue) = 0) \/ exists ge_signed_half_add_exists_unique_resultentriesentryrightvaluedecode. (((sto_right_add_exists_unique_resultentries) = 2 * ge_signed_half_add_exists_unique_resultentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_resultentriesentryrightvalue) = 0) /\ (ge_balance_negative_add_exists_unique_resultentriesentryrightvalue) = S ge_signed_half_add_exists_unique_resultentriesentryrightvaluedecode))) /\ ((dst_positive_add_exists_unique_resultentriesentryright) + ge_balance_negative_add_exists_unique_resultentriesentryrightvalue = (dst_negative_add_exists_unique_resultentriesentryright) + ge_balance_positive_add_exists_unique_resultentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_add_exists_unique_resultentriesentryoutput dst_positive_scale_add_exists_unique_resultentriesentryoutput dst_negative_code_add_exists_unique_resultentriesentryoutput dst_negative_scale_add_exists_unique_resultentriesentryoutput dst_positive_add_exists_unique_resultentriesentryoutput dst_negative_add_exists_unique_resultentriesentryoutput. (((H) = (((((dst_positive_code_add_exists_unique_resultentriesentryoutput) + (dst_positive_scale_add_exists_unique_resultentriesentryoutput)) * S ((dst_positive_code_add_exists_unique_resultentriesentryoutput) + (dst_positive_scale_add_exists_unique_resultentriesentryoutput)) + ((dst_positive_scale_add_exists_unique_resultentriesentryoutput) + (dst_positive_scale_add_exists_unique_resultentriesentryoutput))) + (((dst_negative_code_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)) * S ((dst_negative_code_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)) + ((dst_negative_scale_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)))) * S ((((dst_positive_code_add_exists_unique_resultentriesentryoutput) + (dst_positive_scale_add_exists_unique_resultentriesentryoutput)) * S ((dst_positive_code_add_exists_unique_resultentriesentryoutput) + (dst_positive_scale_add_exists_unique_resultentriesentryoutput)) + ((dst_positive_scale_add_exists_unique_resultentriesentryoutput) + (dst_positive_scale_add_exists_unique_resultentriesentryoutput))) + (((dst_negative_code_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)) * S ((dst_negative_code_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)) + ((dst_negative_scale_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)))) + ((((dst_negative_code_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)) * S ((dst_negative_code_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)) + ((dst_negative_scale_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput))) + (((dst_negative_code_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)) * S ((dst_negative_code_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)) + ((dst_negative_scale_add_exists_unique_resultentriesentryoutput) + (dst_negative_scale_add_exists_unique_resultentriesentryoutput)))))) /\ (((((exists ff_h_pvs_add_exists_unique_resultentriesentryoutputpositive. ff_h_pvs_add_exists_unique_resultentriesentryoutputpositive + S (dst_positive_add_exists_unique_resultentriesentryoutput) = S ((S (sto_index_add_exists_unique_resultentries)) * dst_positive_scale_add_exists_unique_resultentriesentryoutput)) /\ exists ff_q_pvs_add_exists_unique_resultentriesentryoutputpositive. dst_positive_code_add_exists_unique_resultentriesentryoutput = ff_q_pvs_add_exists_unique_resultentriesentryoutputpositive * S ((S (sto_index_add_exists_unique_resultentries)) * dst_positive_scale_add_exists_unique_resultentriesentryoutput) + (dst_positive_add_exists_unique_resultentriesentryoutput))) /\ (((((exists ff_h_pvs_add_exists_unique_resultentriesentryoutputnegative. ff_h_pvs_add_exists_unique_resultentriesentryoutputnegative + S (dst_negative_add_exists_unique_resultentriesentryoutput) = S ((S (sto_index_add_exists_unique_resultentries)) * dst_negative_scale_add_exists_unique_resultentriesentryoutput)) /\ exists ff_q_pvs_add_exists_unique_resultentriesentryoutputnegative. dst_negative_code_add_exists_unique_resultentriesentryoutput = ff_q_pvs_add_exists_unique_resultentriesentryoutputnegative * S ((S (sto_index_add_exists_unique_resultentries)) * dst_negative_scale_add_exists_unique_resultentriesentryoutput) + (dst_negative_add_exists_unique_resultentriesentryoutput))) /\ (exists ge_balance_positive_add_exists_unique_resultentriesentryoutputvalue ge_balance_negative_add_exists_unique_resultentriesentryoutputvalue. (((((sto_output_add_exists_unique_resultentries) = 2 * (ge_balance_positive_add_exists_unique_resultentriesentryoutputvalue) /\ (ge_balance_negative_add_exists_unique_resultentriesentryoutputvalue) = 0) \/ exists ge_signed_half_add_exists_unique_resultentriesentryoutputvaluedecode. (((sto_output_add_exists_unique_resultentries) = 2 * ge_signed_half_add_exists_unique_resultentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_resultentriesentryoutputvalue) = 0) /\ (ge_balance_negative_add_exists_unique_resultentriesentryoutputvalue) = S ge_signed_half_add_exists_unique_resultentriesentryoutputvaluedecode))) /\ ((dst_positive_add_exists_unique_resultentriesentryoutput) + ge_balance_negative_add_exists_unique_resultentriesentryoutputvalue = (dst_negative_add_exists_unique_resultentriesentryoutput) + ge_balance_positive_add_exists_unique_resultentriesentryoutputvalue))))))))) /\ (exists dsa_ap_add_exists_unique_resultentriesentryoperation dsa_an_add_exists_unique_resultentriesentryoperation dsa_bp_add_exists_unique_resultentriesentryoperation dsa_bn_add_exists_unique_resultentriesentryoperation dsa_cp_add_exists_unique_resultentriesentryoperation dsa_cn_add_exists_unique_resultentriesentryoperation. (((((sto_left_add_exists_unique_resultentries) = 2 * (dsa_ap_add_exists_unique_resultentriesentryoperation) /\ (dsa_an_add_exists_unique_resultentriesentryoperation) = 0) \/ exists ge_signed_half_add_exists_unique_resultentriesentryoperationleft. (((sto_left_add_exists_unique_resultentries) = 2 * ge_signed_half_add_exists_unique_resultentriesentryoperationleft + 1 /\ (dsa_ap_add_exists_unique_resultentriesentryoperation) = 0) /\ (dsa_an_add_exists_unique_resultentriesentryoperation) = S ge_signed_half_add_exists_unique_resultentriesentryoperationleft))) /\ ((((((sto_right_add_exists_unique_resultentries) = 2 * (dsa_bp_add_exists_unique_resultentriesentryoperation) /\ (dsa_bn_add_exists_unique_resultentriesentryoperation) = 0) \/ exists ge_signed_half_add_exists_unique_resultentriesentryoperationright. (((sto_right_add_exists_unique_resultentries) = 2 * ge_signed_half_add_exists_unique_resultentriesentryoperationright + 1 /\ (dsa_bp_add_exists_unique_resultentriesentryoperation) = 0) /\ (dsa_bn_add_exists_unique_resultentriesentryoperation) = S ge_signed_half_add_exists_unique_resultentriesentryoperationright))) /\ ((((((sto_output_add_exists_unique_resultentries) = 2 * (dsa_cp_add_exists_unique_resultentriesentryoperation) /\ (dsa_cn_add_exists_unique_resultentriesentryoperation) = 0) \/ exists ge_signed_half_add_exists_unique_resultentriesentryoperationoutput. (((sto_output_add_exists_unique_resultentries) = 2 * ge_signed_half_add_exists_unique_resultentriesentryoperationoutput + 1 /\ (dsa_cp_add_exists_unique_resultentriesentryoperation) = 0) /\ (dsa_cn_add_exists_unique_resultentriesentryoperation) = S ge_signed_half_add_exists_unique_resultentriesentryoperationoutput))) /\ ((dsa_ap_add_exists_unique_resultentriesentryoperation + dsa_bp_add_exists_unique_resultentriesentryoperation) + dsa_cn_add_exists_unique_resultentriesentryoperation = (dsa_an_add_exists_unique_resultentriesentryoperation + dsa_bn_add_exists_unique_resultentriesentryoperation) + dsa_cp_add_exists_unique_resultentriesentryoperation))))))))))))))))))) /\ (forall K. (((exists dst_positive_code_add_exists_unique_otherleft_table dst_positive_scale_add_exists_unique_otherleft_table dst_negative_code_add_exists_unique_otherleft_table dst_negative_scale_add_exists_unique_otherleft_table. (((F) = (((((dst_positive_code_add_exists_unique_otherleft_table) + (dst_positive_scale_add_exists_unique_otherleft_table)) * S ((dst_positive_code_add_exists_unique_otherleft_table) + (dst_positive_scale_add_exists_unique_otherleft_table)) + ((dst_positive_scale_add_exists_unique_otherleft_table) + (dst_positive_scale_add_exists_unique_otherleft_table))) + (((dst_negative_code_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)) * S ((dst_negative_code_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)) + ((dst_negative_scale_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)))) * S ((((dst_positive_code_add_exists_unique_otherleft_table) + (dst_positive_scale_add_exists_unique_otherleft_table)) * S ((dst_positive_code_add_exists_unique_otherleft_table) + (dst_positive_scale_add_exists_unique_otherleft_table)) + ((dst_positive_scale_add_exists_unique_otherleft_table) + (dst_positive_scale_add_exists_unique_otherleft_table))) + (((dst_negative_code_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)) * S ((dst_negative_code_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)) + ((dst_negative_scale_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)))) + ((((dst_negative_code_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)) * S ((dst_negative_code_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)) + ((dst_negative_scale_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table))) + (((dst_negative_code_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)) * S ((dst_negative_code_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)) + ((dst_negative_scale_add_exists_unique_otherleft_table) + (dst_negative_scale_add_exists_unique_otherleft_table)))))) /\ (forall dst_index_add_exists_unique_otherleft_table. (exists pvs_le_gap_add_exists_unique_otherleft_tabledomain. pvs_le_gap_add_exists_unique_otherleft_tabledomain + (dst_index_add_exists_unique_otherleft_table) = (l)) -> exists dst_positive_add_exists_unique_otherleft_table dst_negative_add_exists_unique_otherleft_table dst_value_add_exists_unique_otherleft_table. ((((exists ff_h_pvs_add_exists_unique_otherleft_tableentrypositive. ff_h_pvs_add_exists_unique_otherleft_tableentrypositive + S (dst_positive_add_exists_unique_otherleft_table) = S ((S (dst_index_add_exists_unique_otherleft_table)) * dst_positive_scale_add_exists_unique_otherleft_table)) /\ exists ff_q_pvs_add_exists_unique_otherleft_tableentrypositive. dst_positive_code_add_exists_unique_otherleft_table = ff_q_pvs_add_exists_unique_otherleft_tableentrypositive * S ((S (dst_index_add_exists_unique_otherleft_table)) * dst_positive_scale_add_exists_unique_otherleft_table) + (dst_positive_add_exists_unique_otherleft_table))) /\ (((((exists ff_h_pvs_add_exists_unique_otherleft_tableentrynegative. ff_h_pvs_add_exists_unique_otherleft_tableentrynegative + S (dst_negative_add_exists_unique_otherleft_table) = S ((S (dst_index_add_exists_unique_otherleft_table)) * dst_negative_scale_add_exists_unique_otherleft_table)) /\ exists ff_q_pvs_add_exists_unique_otherleft_tableentrynegative. dst_negative_code_add_exists_unique_otherleft_table = ff_q_pvs_add_exists_unique_otherleft_tableentrynegative * S ((S (dst_index_add_exists_unique_otherleft_table)) * dst_negative_scale_add_exists_unique_otherleft_table) + (dst_negative_add_exists_unique_otherleft_table))) /\ (exists ge_balance_positive_add_exists_unique_otherleft_tableentryvalue ge_balance_negative_add_exists_unique_otherleft_tableentryvalue. (((((dst_value_add_exists_unique_otherleft_table) = 2 * (ge_balance_positive_add_exists_unique_otherleft_tableentryvalue) /\ (ge_balance_negative_add_exists_unique_otherleft_tableentryvalue) = 0) \/ exists ge_signed_half_add_exists_unique_otherleft_tableentryvaluedecode. (((dst_value_add_exists_unique_otherleft_table) = 2 * ge_signed_half_add_exists_unique_otherleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_otherleft_tableentryvalue) = 0) /\ (ge_balance_negative_add_exists_unique_otherleft_tableentryvalue) = S ge_signed_half_add_exists_unique_otherleft_tableentryvaluedecode))) /\ ((dst_positive_add_exists_unique_otherleft_table) + ge_balance_negative_add_exists_unique_otherleft_tableentryvalue = (dst_negative_add_exists_unique_otherleft_table) + ge_balance_positive_add_exists_unique_otherleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_exists_unique_otherright_table dst_positive_scale_add_exists_unique_otherright_table dst_negative_code_add_exists_unique_otherright_table dst_negative_scale_add_exists_unique_otherright_table. (((G) = (((((dst_positive_code_add_exists_unique_otherright_table) + (dst_positive_scale_add_exists_unique_otherright_table)) * S ((dst_positive_code_add_exists_unique_otherright_table) + (dst_positive_scale_add_exists_unique_otherright_table)) + ((dst_positive_scale_add_exists_unique_otherright_table) + (dst_positive_scale_add_exists_unique_otherright_table))) + (((dst_negative_code_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)) * S ((dst_negative_code_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)) + ((dst_negative_scale_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)))) * S ((((dst_positive_code_add_exists_unique_otherright_table) + (dst_positive_scale_add_exists_unique_otherright_table)) * S ((dst_positive_code_add_exists_unique_otherright_table) + (dst_positive_scale_add_exists_unique_otherright_table)) + ((dst_positive_scale_add_exists_unique_otherright_table) + (dst_positive_scale_add_exists_unique_otherright_table))) + (((dst_negative_code_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)) * S ((dst_negative_code_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)) + ((dst_negative_scale_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)))) + ((((dst_negative_code_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)) * S ((dst_negative_code_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)) + ((dst_negative_scale_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table))) + (((dst_negative_code_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)) * S ((dst_negative_code_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)) + ((dst_negative_scale_add_exists_unique_otherright_table) + (dst_negative_scale_add_exists_unique_otherright_table)))))) /\ (forall dst_index_add_exists_unique_otherright_table. (exists pvs_le_gap_add_exists_unique_otherright_tabledomain. pvs_le_gap_add_exists_unique_otherright_tabledomain + (dst_index_add_exists_unique_otherright_table) = (l)) -> exists dst_positive_add_exists_unique_otherright_table dst_negative_add_exists_unique_otherright_table dst_value_add_exists_unique_otherright_table. ((((exists ff_h_pvs_add_exists_unique_otherright_tableentrypositive. ff_h_pvs_add_exists_unique_otherright_tableentrypositive + S (dst_positive_add_exists_unique_otherright_table) = S ((S (dst_index_add_exists_unique_otherright_table)) * dst_positive_scale_add_exists_unique_otherright_table)) /\ exists ff_q_pvs_add_exists_unique_otherright_tableentrypositive. dst_positive_code_add_exists_unique_otherright_table = ff_q_pvs_add_exists_unique_otherright_tableentrypositive * S ((S (dst_index_add_exists_unique_otherright_table)) * dst_positive_scale_add_exists_unique_otherright_table) + (dst_positive_add_exists_unique_otherright_table))) /\ (((((exists ff_h_pvs_add_exists_unique_otherright_tableentrynegative. ff_h_pvs_add_exists_unique_otherright_tableentrynegative + S (dst_negative_add_exists_unique_otherright_table) = S ((S (dst_index_add_exists_unique_otherright_table)) * dst_negative_scale_add_exists_unique_otherright_table)) /\ exists ff_q_pvs_add_exists_unique_otherright_tableentrynegative. dst_negative_code_add_exists_unique_otherright_table = ff_q_pvs_add_exists_unique_otherright_tableentrynegative * S ((S (dst_index_add_exists_unique_otherright_table)) * dst_negative_scale_add_exists_unique_otherright_table) + (dst_negative_add_exists_unique_otherright_table))) /\ (exists ge_balance_positive_add_exists_unique_otherright_tableentryvalue ge_balance_negative_add_exists_unique_otherright_tableentryvalue. (((((dst_value_add_exists_unique_otherright_table) = 2 * (ge_balance_positive_add_exists_unique_otherright_tableentryvalue) /\ (ge_balance_negative_add_exists_unique_otherright_tableentryvalue) = 0) \/ exists ge_signed_half_add_exists_unique_otherright_tableentryvaluedecode. (((dst_value_add_exists_unique_otherright_table) = 2 * ge_signed_half_add_exists_unique_otherright_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_otherright_tableentryvalue) = 0) /\ (ge_balance_negative_add_exists_unique_otherright_tableentryvalue) = S ge_signed_half_add_exists_unique_otherright_tableentryvaluedecode))) /\ ((dst_positive_add_exists_unique_otherright_table) + ge_balance_negative_add_exists_unique_otherright_tableentryvalue = (dst_negative_add_exists_unique_otherright_table) + ge_balance_positive_add_exists_unique_otherright_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_exists_unique_otheroutput_table dst_positive_scale_add_exists_unique_otheroutput_table dst_negative_code_add_exists_unique_otheroutput_table dst_negative_scale_add_exists_unique_otheroutput_table. (((K) = (((((dst_positive_code_add_exists_unique_otheroutput_table) + (dst_positive_scale_add_exists_unique_otheroutput_table)) * S ((dst_positive_code_add_exists_unique_otheroutput_table) + (dst_positive_scale_add_exists_unique_otheroutput_table)) + ((dst_positive_scale_add_exists_unique_otheroutput_table) + (dst_positive_scale_add_exists_unique_otheroutput_table))) + (((dst_negative_code_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)) * S ((dst_negative_code_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)) + ((dst_negative_scale_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)))) * S ((((dst_positive_code_add_exists_unique_otheroutput_table) + (dst_positive_scale_add_exists_unique_otheroutput_table)) * S ((dst_positive_code_add_exists_unique_otheroutput_table) + (dst_positive_scale_add_exists_unique_otheroutput_table)) + ((dst_positive_scale_add_exists_unique_otheroutput_table) + (dst_positive_scale_add_exists_unique_otheroutput_table))) + (((dst_negative_code_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)) * S ((dst_negative_code_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)) + ((dst_negative_scale_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)))) + ((((dst_negative_code_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)) * S ((dst_negative_code_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)) + ((dst_negative_scale_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table))) + (((dst_negative_code_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)) * S ((dst_negative_code_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)) + ((dst_negative_scale_add_exists_unique_otheroutput_table) + (dst_negative_scale_add_exists_unique_otheroutput_table)))))) /\ (forall dst_index_add_exists_unique_otheroutput_table. (exists pvs_le_gap_add_exists_unique_otheroutput_tabledomain. pvs_le_gap_add_exists_unique_otheroutput_tabledomain + (dst_index_add_exists_unique_otheroutput_table) = (l)) -> exists dst_positive_add_exists_unique_otheroutput_table dst_negative_add_exists_unique_otheroutput_table dst_value_add_exists_unique_otheroutput_table. ((((exists ff_h_pvs_add_exists_unique_otheroutput_tableentrypositive. ff_h_pvs_add_exists_unique_otheroutput_tableentrypositive + S (dst_positive_add_exists_unique_otheroutput_table) = S ((S (dst_index_add_exists_unique_otheroutput_table)) * dst_positive_scale_add_exists_unique_otheroutput_table)) /\ exists ff_q_pvs_add_exists_unique_otheroutput_tableentrypositive. dst_positive_code_add_exists_unique_otheroutput_table = ff_q_pvs_add_exists_unique_otheroutput_tableentrypositive * S ((S (dst_index_add_exists_unique_otheroutput_table)) * dst_positive_scale_add_exists_unique_otheroutput_table) + (dst_positive_add_exists_unique_otheroutput_table))) /\ (((((exists ff_h_pvs_add_exists_unique_otheroutput_tableentrynegative. ff_h_pvs_add_exists_unique_otheroutput_tableentrynegative + S (dst_negative_add_exists_unique_otheroutput_table) = S ((S (dst_index_add_exists_unique_otheroutput_table)) * dst_negative_scale_add_exists_unique_otheroutput_table)) /\ exists ff_q_pvs_add_exists_unique_otheroutput_tableentrynegative. dst_negative_code_add_exists_unique_otheroutput_table = ff_q_pvs_add_exists_unique_otheroutput_tableentrynegative * S ((S (dst_index_add_exists_unique_otheroutput_table)) * dst_negative_scale_add_exists_unique_otheroutput_table) + (dst_negative_add_exists_unique_otheroutput_table))) /\ (exists ge_balance_positive_add_exists_unique_otheroutput_tableentryvalue ge_balance_negative_add_exists_unique_otheroutput_tableentryvalue. (((((dst_value_add_exists_unique_otheroutput_table) = 2 * (ge_balance_positive_add_exists_unique_otheroutput_tableentryvalue) /\ (ge_balance_negative_add_exists_unique_otheroutput_tableentryvalue) = 0) \/ exists ge_signed_half_add_exists_unique_otheroutput_tableentryvaluedecode. (((dst_value_add_exists_unique_otheroutput_table) = 2 * ge_signed_half_add_exists_unique_otheroutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_otheroutput_tableentryvalue) = 0) /\ (ge_balance_negative_add_exists_unique_otheroutput_tableentryvalue) = S ge_signed_half_add_exists_unique_otheroutput_tableentryvaluedecode))) /\ ((dst_positive_add_exists_unique_otheroutput_table) + ge_balance_negative_add_exists_unique_otheroutput_tableentryvalue = (dst_negative_add_exists_unique_otheroutput_table) + ge_balance_positive_add_exists_unique_otheroutput_tableentryvalue))))))))) /\ (forall sto_index_add_exists_unique_otherentries. (exists pvs_gap_add_exists_unique_otherentriesbound. pvs_gap_add_exists_unique_otherentriesbound + S (sto_index_add_exists_unique_otherentries) = (l)) -> exists sto_left_add_exists_unique_otherentries sto_right_add_exists_unique_otherentries sto_output_add_exists_unique_otherentries. ((exists dst_positive_code_add_exists_unique_otherentriesentryleft dst_positive_scale_add_exists_unique_otherentriesentryleft dst_negative_code_add_exists_unique_otherentriesentryleft dst_negative_scale_add_exists_unique_otherentriesentryleft dst_positive_add_exists_unique_otherentriesentryleft dst_negative_add_exists_unique_otherentriesentryleft. (((F) = (((((dst_positive_code_add_exists_unique_otherentriesentryleft) + (dst_positive_scale_add_exists_unique_otherentriesentryleft)) * S ((dst_positive_code_add_exists_unique_otherentriesentryleft) + (dst_positive_scale_add_exists_unique_otherentriesentryleft)) + ((dst_positive_scale_add_exists_unique_otherentriesentryleft) + (dst_positive_scale_add_exists_unique_otherentriesentryleft))) + (((dst_negative_code_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)) * S ((dst_negative_code_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)) + ((dst_negative_scale_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)))) * S ((((dst_positive_code_add_exists_unique_otherentriesentryleft) + (dst_positive_scale_add_exists_unique_otherentriesentryleft)) * S ((dst_positive_code_add_exists_unique_otherentriesentryleft) + (dst_positive_scale_add_exists_unique_otherentriesentryleft)) + ((dst_positive_scale_add_exists_unique_otherentriesentryleft) + (dst_positive_scale_add_exists_unique_otherentriesentryleft))) + (((dst_negative_code_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)) * S ((dst_negative_code_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)) + ((dst_negative_scale_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)))) + ((((dst_negative_code_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)) * S ((dst_negative_code_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)) + ((dst_negative_scale_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft))) + (((dst_negative_code_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)) * S ((dst_negative_code_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)) + ((dst_negative_scale_add_exists_unique_otherentriesentryleft) + (dst_negative_scale_add_exists_unique_otherentriesentryleft)))))) /\ (((((exists ff_h_pvs_add_exists_unique_otherentriesentryleftpositive. ff_h_pvs_add_exists_unique_otherentriesentryleftpositive + S (dst_positive_add_exists_unique_otherentriesentryleft) = S ((S (sto_index_add_exists_unique_otherentries)) * dst_positive_scale_add_exists_unique_otherentriesentryleft)) /\ exists ff_q_pvs_add_exists_unique_otherentriesentryleftpositive. dst_positive_code_add_exists_unique_otherentriesentryleft = ff_q_pvs_add_exists_unique_otherentriesentryleftpositive * S ((S (sto_index_add_exists_unique_otherentries)) * dst_positive_scale_add_exists_unique_otherentriesentryleft) + (dst_positive_add_exists_unique_otherentriesentryleft))) /\ (((((exists ff_h_pvs_add_exists_unique_otherentriesentryleftnegative. ff_h_pvs_add_exists_unique_otherentriesentryleftnegative + S (dst_negative_add_exists_unique_otherentriesentryleft) = S ((S (sto_index_add_exists_unique_otherentries)) * dst_negative_scale_add_exists_unique_otherentriesentryleft)) /\ exists ff_q_pvs_add_exists_unique_otherentriesentryleftnegative. dst_negative_code_add_exists_unique_otherentriesentryleft = ff_q_pvs_add_exists_unique_otherentriesentryleftnegative * S ((S (sto_index_add_exists_unique_otherentries)) * dst_negative_scale_add_exists_unique_otherentriesentryleft) + (dst_negative_add_exists_unique_otherentriesentryleft))) /\ (exists ge_balance_positive_add_exists_unique_otherentriesentryleftvalue ge_balance_negative_add_exists_unique_otherentriesentryleftvalue. (((((sto_left_add_exists_unique_otherentries) = 2 * (ge_balance_positive_add_exists_unique_otherentriesentryleftvalue) /\ (ge_balance_negative_add_exists_unique_otherentriesentryleftvalue) = 0) \/ exists ge_signed_half_add_exists_unique_otherentriesentryleftvaluedecode. (((sto_left_add_exists_unique_otherentries) = 2 * ge_signed_half_add_exists_unique_otherentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_otherentriesentryleftvalue) = 0) /\ (ge_balance_negative_add_exists_unique_otherentriesentryleftvalue) = S ge_signed_half_add_exists_unique_otherentriesentryleftvaluedecode))) /\ ((dst_positive_add_exists_unique_otherentriesentryleft) + ge_balance_negative_add_exists_unique_otherentriesentryleftvalue = (dst_negative_add_exists_unique_otherentriesentryleft) + ge_balance_positive_add_exists_unique_otherentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_add_exists_unique_otherentriesentryright dst_positive_scale_add_exists_unique_otherentriesentryright dst_negative_code_add_exists_unique_otherentriesentryright dst_negative_scale_add_exists_unique_otherentriesentryright dst_positive_add_exists_unique_otherentriesentryright dst_negative_add_exists_unique_otherentriesentryright. (((G) = (((((dst_positive_code_add_exists_unique_otherentriesentryright) + (dst_positive_scale_add_exists_unique_otherentriesentryright)) * S ((dst_positive_code_add_exists_unique_otherentriesentryright) + (dst_positive_scale_add_exists_unique_otherentriesentryright)) + ((dst_positive_scale_add_exists_unique_otherentriesentryright) + (dst_positive_scale_add_exists_unique_otherentriesentryright))) + (((dst_negative_code_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)) * S ((dst_negative_code_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)) + ((dst_negative_scale_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)))) * S ((((dst_positive_code_add_exists_unique_otherentriesentryright) + (dst_positive_scale_add_exists_unique_otherentriesentryright)) * S ((dst_positive_code_add_exists_unique_otherentriesentryright) + (dst_positive_scale_add_exists_unique_otherentriesentryright)) + ((dst_positive_scale_add_exists_unique_otherentriesentryright) + (dst_positive_scale_add_exists_unique_otherentriesentryright))) + (((dst_negative_code_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)) * S ((dst_negative_code_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)) + ((dst_negative_scale_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)))) + ((((dst_negative_code_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)) * S ((dst_negative_code_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)) + ((dst_negative_scale_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright))) + (((dst_negative_code_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)) * S ((dst_negative_code_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)) + ((dst_negative_scale_add_exists_unique_otherentriesentryright) + (dst_negative_scale_add_exists_unique_otherentriesentryright)))))) /\ (((((exists ff_h_pvs_add_exists_unique_otherentriesentryrightpositive. ff_h_pvs_add_exists_unique_otherentriesentryrightpositive + S (dst_positive_add_exists_unique_otherentriesentryright) = S ((S (sto_index_add_exists_unique_otherentries)) * dst_positive_scale_add_exists_unique_otherentriesentryright)) /\ exists ff_q_pvs_add_exists_unique_otherentriesentryrightpositive. dst_positive_code_add_exists_unique_otherentriesentryright = ff_q_pvs_add_exists_unique_otherentriesentryrightpositive * S ((S (sto_index_add_exists_unique_otherentries)) * dst_positive_scale_add_exists_unique_otherentriesentryright) + (dst_positive_add_exists_unique_otherentriesentryright))) /\ (((((exists ff_h_pvs_add_exists_unique_otherentriesentryrightnegative. ff_h_pvs_add_exists_unique_otherentriesentryrightnegative + S (dst_negative_add_exists_unique_otherentriesentryright) = S ((S (sto_index_add_exists_unique_otherentries)) * dst_negative_scale_add_exists_unique_otherentriesentryright)) /\ exists ff_q_pvs_add_exists_unique_otherentriesentryrightnegative. dst_negative_code_add_exists_unique_otherentriesentryright = ff_q_pvs_add_exists_unique_otherentriesentryrightnegative * S ((S (sto_index_add_exists_unique_otherentries)) * dst_negative_scale_add_exists_unique_otherentriesentryright) + (dst_negative_add_exists_unique_otherentriesentryright))) /\ (exists ge_balance_positive_add_exists_unique_otherentriesentryrightvalue ge_balance_negative_add_exists_unique_otherentriesentryrightvalue. (((((sto_right_add_exists_unique_otherentries) = 2 * (ge_balance_positive_add_exists_unique_otherentriesentryrightvalue) /\ (ge_balance_negative_add_exists_unique_otherentriesentryrightvalue) = 0) \/ exists ge_signed_half_add_exists_unique_otherentriesentryrightvaluedecode. (((sto_right_add_exists_unique_otherentries) = 2 * ge_signed_half_add_exists_unique_otherentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_otherentriesentryrightvalue) = 0) /\ (ge_balance_negative_add_exists_unique_otherentriesentryrightvalue) = S ge_signed_half_add_exists_unique_otherentriesentryrightvaluedecode))) /\ ((dst_positive_add_exists_unique_otherentriesentryright) + ge_balance_negative_add_exists_unique_otherentriesentryrightvalue = (dst_negative_add_exists_unique_otherentriesentryright) + ge_balance_positive_add_exists_unique_otherentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_add_exists_unique_otherentriesentryoutput dst_positive_scale_add_exists_unique_otherentriesentryoutput dst_negative_code_add_exists_unique_otherentriesentryoutput dst_negative_scale_add_exists_unique_otherentriesentryoutput dst_positive_add_exists_unique_otherentriesentryoutput dst_negative_add_exists_unique_otherentriesentryoutput. (((K) = (((((dst_positive_code_add_exists_unique_otherentriesentryoutput) + (dst_positive_scale_add_exists_unique_otherentriesentryoutput)) * S ((dst_positive_code_add_exists_unique_otherentriesentryoutput) + (dst_positive_scale_add_exists_unique_otherentriesentryoutput)) + ((dst_positive_scale_add_exists_unique_otherentriesentryoutput) + (dst_positive_scale_add_exists_unique_otherentriesentryoutput))) + (((dst_negative_code_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)) * S ((dst_negative_code_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)) + ((dst_negative_scale_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)))) * S ((((dst_positive_code_add_exists_unique_otherentriesentryoutput) + (dst_positive_scale_add_exists_unique_otherentriesentryoutput)) * S ((dst_positive_code_add_exists_unique_otherentriesentryoutput) + (dst_positive_scale_add_exists_unique_otherentriesentryoutput)) + ((dst_positive_scale_add_exists_unique_otherentriesentryoutput) + (dst_positive_scale_add_exists_unique_otherentriesentryoutput))) + (((dst_negative_code_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)) * S ((dst_negative_code_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)) + ((dst_negative_scale_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)))) + ((((dst_negative_code_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)) * S ((dst_negative_code_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)) + ((dst_negative_scale_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput))) + (((dst_negative_code_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)) * S ((dst_negative_code_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)) + ((dst_negative_scale_add_exists_unique_otherentriesentryoutput) + (dst_negative_scale_add_exists_unique_otherentriesentryoutput)))))) /\ (((((exists ff_h_pvs_add_exists_unique_otherentriesentryoutputpositive. ff_h_pvs_add_exists_unique_otherentriesentryoutputpositive + S (dst_positive_add_exists_unique_otherentriesentryoutput) = S ((S (sto_index_add_exists_unique_otherentries)) * dst_positive_scale_add_exists_unique_otherentriesentryoutput)) /\ exists ff_q_pvs_add_exists_unique_otherentriesentryoutputpositive. dst_positive_code_add_exists_unique_otherentriesentryoutput = ff_q_pvs_add_exists_unique_otherentriesentryoutputpositive * S ((S (sto_index_add_exists_unique_otherentries)) * dst_positive_scale_add_exists_unique_otherentriesentryoutput) + (dst_positive_add_exists_unique_otherentriesentryoutput))) /\ (((((exists ff_h_pvs_add_exists_unique_otherentriesentryoutputnegative. ff_h_pvs_add_exists_unique_otherentriesentryoutputnegative + S (dst_negative_add_exists_unique_otherentriesentryoutput) = S ((S (sto_index_add_exists_unique_otherentries)) * dst_negative_scale_add_exists_unique_otherentriesentryoutput)) /\ exists ff_q_pvs_add_exists_unique_otherentriesentryoutputnegative. dst_negative_code_add_exists_unique_otherentriesentryoutput = ff_q_pvs_add_exists_unique_otherentriesentryoutputnegative * S ((S (sto_index_add_exists_unique_otherentries)) * dst_negative_scale_add_exists_unique_otherentriesentryoutput) + (dst_negative_add_exists_unique_otherentriesentryoutput))) /\ (exists ge_balance_positive_add_exists_unique_otherentriesentryoutputvalue ge_balance_negative_add_exists_unique_otherentriesentryoutputvalue. (((((sto_output_add_exists_unique_otherentries) = 2 * (ge_balance_positive_add_exists_unique_otherentriesentryoutputvalue) /\ (ge_balance_negative_add_exists_unique_otherentriesentryoutputvalue) = 0) \/ exists ge_signed_half_add_exists_unique_otherentriesentryoutputvaluedecode. (((sto_output_add_exists_unique_otherentries) = 2 * ge_signed_half_add_exists_unique_otherentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_otherentriesentryoutputvalue) = 0) /\ (ge_balance_negative_add_exists_unique_otherentriesentryoutputvalue) = S ge_signed_half_add_exists_unique_otherentriesentryoutputvaluedecode))) /\ ((dst_positive_add_exists_unique_otherentriesentryoutput) + ge_balance_negative_add_exists_unique_otherentriesentryoutputvalue = (dst_negative_add_exists_unique_otherentriesentryoutput) + ge_balance_positive_add_exists_unique_otherentriesentryoutputvalue))))))))) /\ (exists dsa_ap_add_exists_unique_otherentriesentryoperation dsa_an_add_exists_unique_otherentriesentryoperation dsa_bp_add_exists_unique_otherentriesentryoperation dsa_bn_add_exists_unique_otherentriesentryoperation dsa_cp_add_exists_unique_otherentriesentryoperation dsa_cn_add_exists_unique_otherentriesentryoperation. (((((sto_left_add_exists_unique_otherentries) = 2 * (dsa_ap_add_exists_unique_otherentriesentryoperation) /\ (dsa_an_add_exists_unique_otherentriesentryoperation) = 0) \/ exists ge_signed_half_add_exists_unique_otherentriesentryoperationleft. (((sto_left_add_exists_unique_otherentries) = 2 * ge_signed_half_add_exists_unique_otherentriesentryoperationleft + 1 /\ (dsa_ap_add_exists_unique_otherentriesentryoperation) = 0) /\ (dsa_an_add_exists_unique_otherentriesentryoperation) = S ge_signed_half_add_exists_unique_otherentriesentryoperationleft))) /\ ((((((sto_right_add_exists_unique_otherentries) = 2 * (dsa_bp_add_exists_unique_otherentriesentryoperation) /\ (dsa_bn_add_exists_unique_otherentriesentryoperation) = 0) \/ exists ge_signed_half_add_exists_unique_otherentriesentryoperationright. (((sto_right_add_exists_unique_otherentries) = 2 * ge_signed_half_add_exists_unique_otherentriesentryoperationright + 1 /\ (dsa_bp_add_exists_unique_otherentriesentryoperation) = 0) /\ (dsa_bn_add_exists_unique_otherentriesentryoperation) = S ge_signed_half_add_exists_unique_otherentriesentryoperationright))) /\ ((((((sto_output_add_exists_unique_otherentries) = 2 * (dsa_cp_add_exists_unique_otherentriesentryoperation) /\ (dsa_cn_add_exists_unique_otherentriesentryoperation) = 0) \/ exists ge_signed_half_add_exists_unique_otherentriesentryoperationoutput. (((sto_output_add_exists_unique_otherentries) = 2 * ge_signed_half_add_exists_unique_otherentriesentryoperationoutput + 1 /\ (dsa_cp_add_exists_unique_otherentriesentryoperation) = 0) /\ (dsa_cn_add_exists_unique_otherentriesentryoperation) = S ge_signed_half_add_exists_unique_otherentriesentryoperationoutput))) /\ ((dsa_ap_add_exists_unique_otherentriesentryoperation + dsa_bp_add_exists_unique_otherentriesentryoperation) + dsa_cn_add_exists_unique_otherentriesentryoperation = (dsa_an_add_exists_unique_otherentriesentryoperation + dsa_bn_add_exists_unique_otherentriesentryoperation) + dsa_cp_add_exists_unique_otherentriesentryoperation))))))))))))))))))) -> (forall dst_index_add_exists_unique_equal dst_first_add_exists_unique_equal dst_second_add_exists_unique_equal. (exists pvs_gap_add_exists_unique_equalbound. pvs_gap_add_exists_unique_equalbound + S (dst_index_add_exists_unique_equal) = (l)) -> (exists dst_positive_code_add_exists_unique_equalfirst dst_positive_scale_add_exists_unique_equalfirst dst_negative_code_add_exists_unique_equalfirst dst_negative_scale_add_exists_unique_equalfirst dst_positive_add_exists_unique_equalfirst dst_negative_add_exists_unique_equalfirst. (((H) = (((((dst_positive_code_add_exists_unique_equalfirst) + (dst_positive_scale_add_exists_unique_equalfirst)) * S ((dst_positive_code_add_exists_unique_equalfirst) + (dst_positive_scale_add_exists_unique_equalfirst)) + ((dst_positive_scale_add_exists_unique_equalfirst) + (dst_positive_scale_add_exists_unique_equalfirst))) + (((dst_negative_code_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)) * S ((dst_negative_code_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)) + ((dst_negative_scale_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)))) * S ((((dst_positive_code_add_exists_unique_equalfirst) + (dst_positive_scale_add_exists_unique_equalfirst)) * S ((dst_positive_code_add_exists_unique_equalfirst) + (dst_positive_scale_add_exists_unique_equalfirst)) + ((dst_positive_scale_add_exists_unique_equalfirst) + (dst_positive_scale_add_exists_unique_equalfirst))) + (((dst_negative_code_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)) * S ((dst_negative_code_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)) + ((dst_negative_scale_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)))) + ((((dst_negative_code_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)) * S ((dst_negative_code_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)) + ((dst_negative_scale_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst))) + (((dst_negative_code_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)) * S ((dst_negative_code_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)) + ((dst_negative_scale_add_exists_unique_equalfirst) + (dst_negative_scale_add_exists_unique_equalfirst)))))) /\ (((((exists ff_h_pvs_add_exists_unique_equalfirstpositive. ff_h_pvs_add_exists_unique_equalfirstpositive + S (dst_positive_add_exists_unique_equalfirst) = S ((S (dst_index_add_exists_unique_equal)) * dst_positive_scale_add_exists_unique_equalfirst)) /\ exists ff_q_pvs_add_exists_unique_equalfirstpositive. dst_positive_code_add_exists_unique_equalfirst = ff_q_pvs_add_exists_unique_equalfirstpositive * S ((S (dst_index_add_exists_unique_equal)) * dst_positive_scale_add_exists_unique_equalfirst) + (dst_positive_add_exists_unique_equalfirst))) /\ (((((exists ff_h_pvs_add_exists_unique_equalfirstnegative. ff_h_pvs_add_exists_unique_equalfirstnegative + S (dst_negative_add_exists_unique_equalfirst) = S ((S (dst_index_add_exists_unique_equal)) * dst_negative_scale_add_exists_unique_equalfirst)) /\ exists ff_q_pvs_add_exists_unique_equalfirstnegative. dst_negative_code_add_exists_unique_equalfirst = ff_q_pvs_add_exists_unique_equalfirstnegative * S ((S (dst_index_add_exists_unique_equal)) * dst_negative_scale_add_exists_unique_equalfirst) + (dst_negative_add_exists_unique_equalfirst))) /\ (exists ge_balance_positive_add_exists_unique_equalfirstvalue ge_balance_negative_add_exists_unique_equalfirstvalue. (((((dst_first_add_exists_unique_equal) = 2 * (ge_balance_positive_add_exists_unique_equalfirstvalue) /\ (ge_balance_negative_add_exists_unique_equalfirstvalue) = 0) \/ exists ge_signed_half_add_exists_unique_equalfirstvaluedecode. (((dst_first_add_exists_unique_equal) = 2 * ge_signed_half_add_exists_unique_equalfirstvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_equalfirstvalue) = 0) /\ (ge_balance_negative_add_exists_unique_equalfirstvalue) = S ge_signed_half_add_exists_unique_equalfirstvaluedecode))) /\ ((dst_positive_add_exists_unique_equalfirst) + ge_balance_negative_add_exists_unique_equalfirstvalue = (dst_negative_add_exists_unique_equalfirst) + ge_balance_positive_add_exists_unique_equalfirstvalue))))))))) -> (exists dst_positive_code_add_exists_unique_equalsecond dst_positive_scale_add_exists_unique_equalsecond dst_negative_code_add_exists_unique_equalsecond dst_negative_scale_add_exists_unique_equalsecond dst_positive_add_exists_unique_equalsecond dst_negative_add_exists_unique_equalsecond. (((K) = (((((dst_positive_code_add_exists_unique_equalsecond) + (dst_positive_scale_add_exists_unique_equalsecond)) * S ((dst_positive_code_add_exists_unique_equalsecond) + (dst_positive_scale_add_exists_unique_equalsecond)) + ((dst_positive_scale_add_exists_unique_equalsecond) + (dst_positive_scale_add_exists_unique_equalsecond))) + (((dst_negative_code_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)) * S ((dst_negative_code_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)) + ((dst_negative_scale_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)))) * S ((((dst_positive_code_add_exists_unique_equalsecond) + (dst_positive_scale_add_exists_unique_equalsecond)) * S ((dst_positive_code_add_exists_unique_equalsecond) + (dst_positive_scale_add_exists_unique_equalsecond)) + ((dst_positive_scale_add_exists_unique_equalsecond) + (dst_positive_scale_add_exists_unique_equalsecond))) + (((dst_negative_code_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)) * S ((dst_negative_code_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)) + ((dst_negative_scale_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)))) + ((((dst_negative_code_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)) * S ((dst_negative_code_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)) + ((dst_negative_scale_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond))) + (((dst_negative_code_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)) * S ((dst_negative_code_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)) + ((dst_negative_scale_add_exists_unique_equalsecond) + (dst_negative_scale_add_exists_unique_equalsecond)))))) /\ (((((exists ff_h_pvs_add_exists_unique_equalsecondpositive. ff_h_pvs_add_exists_unique_equalsecondpositive + S (dst_positive_add_exists_unique_equalsecond) = S ((S (dst_index_add_exists_unique_equal)) * dst_positive_scale_add_exists_unique_equalsecond)) /\ exists ff_q_pvs_add_exists_unique_equalsecondpositive. dst_positive_code_add_exists_unique_equalsecond = ff_q_pvs_add_exists_unique_equalsecondpositive * S ((S (dst_index_add_exists_unique_equal)) * dst_positive_scale_add_exists_unique_equalsecond) + (dst_positive_add_exists_unique_equalsecond))) /\ (((((exists ff_h_pvs_add_exists_unique_equalsecondnegative. ff_h_pvs_add_exists_unique_equalsecondnegative + S (dst_negative_add_exists_unique_equalsecond) = S ((S (dst_index_add_exists_unique_equal)) * dst_negative_scale_add_exists_unique_equalsecond)) /\ exists ff_q_pvs_add_exists_unique_equalsecondnegative. dst_negative_code_add_exists_unique_equalsecond = ff_q_pvs_add_exists_unique_equalsecondnegative * S ((S (dst_index_add_exists_unique_equal)) * dst_negative_scale_add_exists_unique_equalsecond) + (dst_negative_add_exists_unique_equalsecond))) /\ (exists ge_balance_positive_add_exists_unique_equalsecondvalue ge_balance_negative_add_exists_unique_equalsecondvalue. (((((dst_second_add_exists_unique_equal) = 2 * (ge_balance_positive_add_exists_unique_equalsecondvalue) /\ (ge_balance_negative_add_exists_unique_equalsecondvalue) = 0) \/ exists ge_signed_half_add_exists_unique_equalsecondvaluedecode. (((dst_second_add_exists_unique_equal) = 2 * ge_signed_half_add_exists_unique_equalsecondvaluedecode + 1 /\ (ge_balance_positive_add_exists_unique_equalsecondvalue) = 0) /\ (ge_balance_negative_add_exists_unique_equalsecondvalue) = S ge_signed_half_add_exists_unique_equalsecondvaluedecode))) /\ ((dst_positive_add_exists_unique_equalsecond) + ge_balance_negative_add_exists_unique_equalsecondvalue = (dst_negative_add_exists_unique_equalsecond) + ge_balance_positive_add_exists_unique_equalsecondvalue))))))))) -> dst_first_add_exists_unique_equal = dst_second_add_exists_unique_equal)))Complete tactic proof in conservative notation
All 26 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
26 script commands · 8 reading checkpoints · 1 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 assumptionsL1–5
02Establish hwL6–12
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed table add exists.
- L6
have hw : ∃ H. ArithAdd(F,G,H,l)Definitions: ArithAdd(F,G,H,l)Original native command in the exact edition - L7
specialize signed_table_add_exists (l) - L8
specialize signed_table_add_exists (F) - L9
specialize signed_table_add_exists (G) - L10
apply signed_table_add_exists - L11
exact ht0 - L12
exact ht1
03Separate the logical casesL13–13
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L13
cases hw
04Construct an explicit witnessL14–14
Supply the displayed value, then prove that it has the required property.
- L14
exists x
05Separate the logical casesL15–15
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L15
split
06Use earlier factsL16–16
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L16
exact hw_witness
07Fix variables and assumptionsL17–18
08Use earlier factsL19–26
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L19
specialize signed_table_add_extensional_unique (F) - L20
specialize signed_table_add_extensional_unique (G) - L21
specialize signed_table_add_extensional_unique (x) - L22
specialize signed_table_add_extensional_unique (K) - L23
specialize signed_table_add_extensional_unique (l) - L24
apply signed_table_add_extensional_unique - L25
exact hw_witness - L26
exact hother
Original defined command ledger · 26 lines
- 0001
intro l - 0002
intro F - 0003
intro G - 0004
intro ht0 - 0005
intro ht1 - 0006
have hw : ∃ H. ArithAdd(F,G,H,l) - 0007
specialize signed_table_add_exists (l) - 0008
specialize signed_table_add_exists (F) - 0009
specialize signed_table_add_exists (G) - 0010
apply signed_table_add_exists - 0011
exact ht0 - 0012
exact ht1 - 0013
cases hw - 0014
exists x - 0015
split - 0016
exact hw_witness - 0017
intro K - 0018
intro hother - 0019
specialize signed_table_add_extensional_unique (F) - 0020
specialize signed_table_add_extensional_unique (G) - 0021
specialize signed_table_add_extensional_unique (x) - 0022
specialize signed_table_add_extensional_unique (K) - 0023
specialize signed_table_add_extensional_unique (l) - 0024
apply signed_table_add_extensional_unique - 0025
exact hw_witness - 0026
exact hother