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
∀ F. ∀ G. ∀ H. ∀ l. ArithAdd(F,G,H,S l) → ArithAdd(F,G,H,l)
Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Original expanded first-order statement
forall F G H l. (((exists dst_positive_code_add_restrict_inputleft_table dst_positive_scale_add_restrict_inputleft_table dst_negative_code_add_restrict_inputleft_table dst_negative_scale_add_restrict_inputleft_table. (((F) = (((((dst_positive_code_add_restrict_inputleft_table) + (dst_positive_scale_add_restrict_inputleft_table)) * S ((dst_positive_code_add_restrict_inputleft_table) + (dst_positive_scale_add_restrict_inputleft_table)) + ((dst_positive_scale_add_restrict_inputleft_table) + (dst_positive_scale_add_restrict_inputleft_table))) + (((dst_negative_code_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)) * S ((dst_negative_code_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)) + ((dst_negative_scale_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)))) * S ((((dst_positive_code_add_restrict_inputleft_table) + (dst_positive_scale_add_restrict_inputleft_table)) * S ((dst_positive_code_add_restrict_inputleft_table) + (dst_positive_scale_add_restrict_inputleft_table)) + ((dst_positive_scale_add_restrict_inputleft_table) + (dst_positive_scale_add_restrict_inputleft_table))) + (((dst_negative_code_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)) * S ((dst_negative_code_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)) + ((dst_negative_scale_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)))) + ((((dst_negative_code_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)) * S ((dst_negative_code_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)) + ((dst_negative_scale_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table))) + (((dst_negative_code_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)) * S ((dst_negative_code_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)) + ((dst_negative_scale_add_restrict_inputleft_table) + (dst_negative_scale_add_restrict_inputleft_table)))))) /\ (forall dst_index_add_restrict_inputleft_table. (exists pvs_le_gap_add_restrict_inputleft_tabledomain. pvs_le_gap_add_restrict_inputleft_tabledomain + (dst_index_add_restrict_inputleft_table) = (S l)) -> exists dst_positive_add_restrict_inputleft_table dst_negative_add_restrict_inputleft_table dst_value_add_restrict_inputleft_table. ((((exists ff_h_pvs_add_restrict_inputleft_tableentrypositive. ff_h_pvs_add_restrict_inputleft_tableentrypositive + S (dst_positive_add_restrict_inputleft_table) = S ((S (dst_index_add_restrict_inputleft_table)) * dst_positive_scale_add_restrict_inputleft_table)) /\ exists ff_q_pvs_add_restrict_inputleft_tableentrypositive. dst_positive_code_add_restrict_inputleft_table = ff_q_pvs_add_restrict_inputleft_tableentrypositive * S ((S (dst_index_add_restrict_inputleft_table)) * dst_positive_scale_add_restrict_inputleft_table) + (dst_positive_add_restrict_inputleft_table))) /\ (((((exists ff_h_pvs_add_restrict_inputleft_tableentrynegative. ff_h_pvs_add_restrict_inputleft_tableentrynegative + S (dst_negative_add_restrict_inputleft_table) = S ((S (dst_index_add_restrict_inputleft_table)) * dst_negative_scale_add_restrict_inputleft_table)) /\ exists ff_q_pvs_add_restrict_inputleft_tableentrynegative. dst_negative_code_add_restrict_inputleft_table = ff_q_pvs_add_restrict_inputleft_tableentrynegative * S ((S (dst_index_add_restrict_inputleft_table)) * dst_negative_scale_add_restrict_inputleft_table) + (dst_negative_add_restrict_inputleft_table))) /\ (exists ge_balance_positive_add_restrict_inputleft_tableentryvalue ge_balance_negative_add_restrict_inputleft_tableentryvalue. (((((dst_value_add_restrict_inputleft_table) = 2 * (ge_balance_positive_add_restrict_inputleft_tableentryvalue) /\ (ge_balance_negative_add_restrict_inputleft_tableentryvalue) = 0) \/ exists ge_signed_half_add_restrict_inputleft_tableentryvaluedecode. (((dst_value_add_restrict_inputleft_table) = 2 * ge_signed_half_add_restrict_inputleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_restrict_inputleft_tableentryvalue) = 0) /\ (ge_balance_negative_add_restrict_inputleft_tableentryvalue) = S ge_signed_half_add_restrict_inputleft_tableentryvaluedecode))) /\ ((dst_positive_add_restrict_inputleft_table) + ge_balance_negative_add_restrict_inputleft_tableentryvalue = (dst_negative_add_restrict_inputleft_table) + ge_balance_positive_add_restrict_inputleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_restrict_inputright_table dst_positive_scale_add_restrict_inputright_table dst_negative_code_add_restrict_inputright_table dst_negative_scale_add_restrict_inputright_table. (((G) = (((((dst_positive_code_add_restrict_inputright_table) + (dst_positive_scale_add_restrict_inputright_table)) * S ((dst_positive_code_add_restrict_inputright_table) + (dst_positive_scale_add_restrict_inputright_table)) + ((dst_positive_scale_add_restrict_inputright_table) + (dst_positive_scale_add_restrict_inputright_table))) + (((dst_negative_code_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)) * S ((dst_negative_code_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)) + ((dst_negative_scale_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)))) * S ((((dst_positive_code_add_restrict_inputright_table) + (dst_positive_scale_add_restrict_inputright_table)) * S ((dst_positive_code_add_restrict_inputright_table) + (dst_positive_scale_add_restrict_inputright_table)) + ((dst_positive_scale_add_restrict_inputright_table) + (dst_positive_scale_add_restrict_inputright_table))) + (((dst_negative_code_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)) * S ((dst_negative_code_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)) + ((dst_negative_scale_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)))) + ((((dst_negative_code_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)) * S ((dst_negative_code_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)) + ((dst_negative_scale_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table))) + (((dst_negative_code_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)) * S ((dst_negative_code_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)) + ((dst_negative_scale_add_restrict_inputright_table) + (dst_negative_scale_add_restrict_inputright_table)))))) /\ (forall dst_index_add_restrict_inputright_table. (exists pvs_le_gap_add_restrict_inputright_tabledomain. pvs_le_gap_add_restrict_inputright_tabledomain + (dst_index_add_restrict_inputright_table) = (S l)) -> exists dst_positive_add_restrict_inputright_table dst_negative_add_restrict_inputright_table dst_value_add_restrict_inputright_table. ((((exists ff_h_pvs_add_restrict_inputright_tableentrypositive. ff_h_pvs_add_restrict_inputright_tableentrypositive + S (dst_positive_add_restrict_inputright_table) = S ((S (dst_index_add_restrict_inputright_table)) * dst_positive_scale_add_restrict_inputright_table)) /\ exists ff_q_pvs_add_restrict_inputright_tableentrypositive. dst_positive_code_add_restrict_inputright_table = ff_q_pvs_add_restrict_inputright_tableentrypositive * S ((S (dst_index_add_restrict_inputright_table)) * dst_positive_scale_add_restrict_inputright_table) + (dst_positive_add_restrict_inputright_table))) /\ (((((exists ff_h_pvs_add_restrict_inputright_tableentrynegative. ff_h_pvs_add_restrict_inputright_tableentrynegative + S (dst_negative_add_restrict_inputright_table) = S ((S (dst_index_add_restrict_inputright_table)) * dst_negative_scale_add_restrict_inputright_table)) /\ exists ff_q_pvs_add_restrict_inputright_tableentrynegative. dst_negative_code_add_restrict_inputright_table = ff_q_pvs_add_restrict_inputright_tableentrynegative * S ((S (dst_index_add_restrict_inputright_table)) * dst_negative_scale_add_restrict_inputright_table) + (dst_negative_add_restrict_inputright_table))) /\ (exists ge_balance_positive_add_restrict_inputright_tableentryvalue ge_balance_negative_add_restrict_inputright_tableentryvalue. (((((dst_value_add_restrict_inputright_table) = 2 * (ge_balance_positive_add_restrict_inputright_tableentryvalue) /\ (ge_balance_negative_add_restrict_inputright_tableentryvalue) = 0) \/ exists ge_signed_half_add_restrict_inputright_tableentryvaluedecode. (((dst_value_add_restrict_inputright_table) = 2 * ge_signed_half_add_restrict_inputright_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_restrict_inputright_tableentryvalue) = 0) /\ (ge_balance_negative_add_restrict_inputright_tableentryvalue) = S ge_signed_half_add_restrict_inputright_tableentryvaluedecode))) /\ ((dst_positive_add_restrict_inputright_table) + ge_balance_negative_add_restrict_inputright_tableentryvalue = (dst_negative_add_restrict_inputright_table) + ge_balance_positive_add_restrict_inputright_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_restrict_inputoutput_table dst_positive_scale_add_restrict_inputoutput_table dst_negative_code_add_restrict_inputoutput_table dst_negative_scale_add_restrict_inputoutput_table. (((H) = (((((dst_positive_code_add_restrict_inputoutput_table) + (dst_positive_scale_add_restrict_inputoutput_table)) * S ((dst_positive_code_add_restrict_inputoutput_table) + (dst_positive_scale_add_restrict_inputoutput_table)) + ((dst_positive_scale_add_restrict_inputoutput_table) + (dst_positive_scale_add_restrict_inputoutput_table))) + (((dst_negative_code_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)) * S ((dst_negative_code_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)) + ((dst_negative_scale_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)))) * S ((((dst_positive_code_add_restrict_inputoutput_table) + (dst_positive_scale_add_restrict_inputoutput_table)) * S ((dst_positive_code_add_restrict_inputoutput_table) + (dst_positive_scale_add_restrict_inputoutput_table)) + ((dst_positive_scale_add_restrict_inputoutput_table) + (dst_positive_scale_add_restrict_inputoutput_table))) + (((dst_negative_code_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)) * S ((dst_negative_code_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)) + ((dst_negative_scale_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)))) + ((((dst_negative_code_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)) * S ((dst_negative_code_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)) + ((dst_negative_scale_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table))) + (((dst_negative_code_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)) * S ((dst_negative_code_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)) + ((dst_negative_scale_add_restrict_inputoutput_table) + (dst_negative_scale_add_restrict_inputoutput_table)))))) /\ (forall dst_index_add_restrict_inputoutput_table. (exists pvs_le_gap_add_restrict_inputoutput_tabledomain. pvs_le_gap_add_restrict_inputoutput_tabledomain + (dst_index_add_restrict_inputoutput_table) = (S l)) -> exists dst_positive_add_restrict_inputoutput_table dst_negative_add_restrict_inputoutput_table dst_value_add_restrict_inputoutput_table. ((((exists ff_h_pvs_add_restrict_inputoutput_tableentrypositive. ff_h_pvs_add_restrict_inputoutput_tableentrypositive + S (dst_positive_add_restrict_inputoutput_table) = S ((S (dst_index_add_restrict_inputoutput_table)) * dst_positive_scale_add_restrict_inputoutput_table)) /\ exists ff_q_pvs_add_restrict_inputoutput_tableentrypositive. dst_positive_code_add_restrict_inputoutput_table = ff_q_pvs_add_restrict_inputoutput_tableentrypositive * S ((S (dst_index_add_restrict_inputoutput_table)) * dst_positive_scale_add_restrict_inputoutput_table) + (dst_positive_add_restrict_inputoutput_table))) /\ (((((exists ff_h_pvs_add_restrict_inputoutput_tableentrynegative. ff_h_pvs_add_restrict_inputoutput_tableentrynegative + S (dst_negative_add_restrict_inputoutput_table) = S ((S (dst_index_add_restrict_inputoutput_table)) * dst_negative_scale_add_restrict_inputoutput_table)) /\ exists ff_q_pvs_add_restrict_inputoutput_tableentrynegative. dst_negative_code_add_restrict_inputoutput_table = ff_q_pvs_add_restrict_inputoutput_tableentrynegative * S ((S (dst_index_add_restrict_inputoutput_table)) * dst_negative_scale_add_restrict_inputoutput_table) + (dst_negative_add_restrict_inputoutput_table))) /\ (exists ge_balance_positive_add_restrict_inputoutput_tableentryvalue ge_balance_negative_add_restrict_inputoutput_tableentryvalue. (((((dst_value_add_restrict_inputoutput_table) = 2 * (ge_balance_positive_add_restrict_inputoutput_tableentryvalue) /\ (ge_balance_negative_add_restrict_inputoutput_tableentryvalue) = 0) \/ exists ge_signed_half_add_restrict_inputoutput_tableentryvaluedecode. (((dst_value_add_restrict_inputoutput_table) = 2 * ge_signed_half_add_restrict_inputoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_restrict_inputoutput_tableentryvalue) = 0) /\ (ge_balance_negative_add_restrict_inputoutput_tableentryvalue) = S ge_signed_half_add_restrict_inputoutput_tableentryvaluedecode))) /\ ((dst_positive_add_restrict_inputoutput_table) + ge_balance_negative_add_restrict_inputoutput_tableentryvalue = (dst_negative_add_restrict_inputoutput_table) + ge_balance_positive_add_restrict_inputoutput_tableentryvalue))))))))) /\ (forall sto_index_add_restrict_inputentries. (exists pvs_gap_add_restrict_inputentriesbound. pvs_gap_add_restrict_inputentriesbound + S (sto_index_add_restrict_inputentries) = (S l)) -> exists sto_left_add_restrict_inputentries sto_right_add_restrict_inputentries sto_output_add_restrict_inputentries. ((exists dst_positive_code_add_restrict_inputentriesentryleft dst_positive_scale_add_restrict_inputentriesentryleft dst_negative_code_add_restrict_inputentriesentryleft dst_negative_scale_add_restrict_inputentriesentryleft dst_positive_add_restrict_inputentriesentryleft dst_negative_add_restrict_inputentriesentryleft. (((F) = (((((dst_positive_code_add_restrict_inputentriesentryleft) + (dst_positive_scale_add_restrict_inputentriesentryleft)) * S ((dst_positive_code_add_restrict_inputentriesentryleft) + (dst_positive_scale_add_restrict_inputentriesentryleft)) + ((dst_positive_scale_add_restrict_inputentriesentryleft) + (dst_positive_scale_add_restrict_inputentriesentryleft))) + (((dst_negative_code_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)) * S ((dst_negative_code_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)) + ((dst_negative_scale_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)))) * S ((((dst_positive_code_add_restrict_inputentriesentryleft) + (dst_positive_scale_add_restrict_inputentriesentryleft)) * S ((dst_positive_code_add_restrict_inputentriesentryleft) + (dst_positive_scale_add_restrict_inputentriesentryleft)) + ((dst_positive_scale_add_restrict_inputentriesentryleft) + (dst_positive_scale_add_restrict_inputentriesentryleft))) + (((dst_negative_code_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)) * S ((dst_negative_code_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)) + ((dst_negative_scale_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)))) + ((((dst_negative_code_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)) * S ((dst_negative_code_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)) + ((dst_negative_scale_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft))) + (((dst_negative_code_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)) * S ((dst_negative_code_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)) + ((dst_negative_scale_add_restrict_inputentriesentryleft) + (dst_negative_scale_add_restrict_inputentriesentryleft)))))) /\ (((((exists ff_h_pvs_add_restrict_inputentriesentryleftpositive. ff_h_pvs_add_restrict_inputentriesentryleftpositive + S (dst_positive_add_restrict_inputentriesentryleft) = S ((S (sto_index_add_restrict_inputentries)) * dst_positive_scale_add_restrict_inputentriesentryleft)) /\ exists ff_q_pvs_add_restrict_inputentriesentryleftpositive. dst_positive_code_add_restrict_inputentriesentryleft = ff_q_pvs_add_restrict_inputentriesentryleftpositive * S ((S (sto_index_add_restrict_inputentries)) * dst_positive_scale_add_restrict_inputentriesentryleft) + (dst_positive_add_restrict_inputentriesentryleft))) /\ (((((exists ff_h_pvs_add_restrict_inputentriesentryleftnegative. ff_h_pvs_add_restrict_inputentriesentryleftnegative + S (dst_negative_add_restrict_inputentriesentryleft) = S ((S (sto_index_add_restrict_inputentries)) * dst_negative_scale_add_restrict_inputentriesentryleft)) /\ exists ff_q_pvs_add_restrict_inputentriesentryleftnegative. dst_negative_code_add_restrict_inputentriesentryleft = ff_q_pvs_add_restrict_inputentriesentryleftnegative * S ((S (sto_index_add_restrict_inputentries)) * dst_negative_scale_add_restrict_inputentriesentryleft) + (dst_negative_add_restrict_inputentriesentryleft))) /\ (exists ge_balance_positive_add_restrict_inputentriesentryleftvalue ge_balance_negative_add_restrict_inputentriesentryleftvalue. (((((sto_left_add_restrict_inputentries) = 2 * (ge_balance_positive_add_restrict_inputentriesentryleftvalue) /\ (ge_balance_negative_add_restrict_inputentriesentryleftvalue) = 0) \/ exists ge_signed_half_add_restrict_inputentriesentryleftvaluedecode. (((sto_left_add_restrict_inputentries) = 2 * ge_signed_half_add_restrict_inputentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_add_restrict_inputentriesentryleftvalue) = 0) /\ (ge_balance_negative_add_restrict_inputentriesentryleftvalue) = S ge_signed_half_add_restrict_inputentriesentryleftvaluedecode))) /\ ((dst_positive_add_restrict_inputentriesentryleft) + ge_balance_negative_add_restrict_inputentriesentryleftvalue = (dst_negative_add_restrict_inputentriesentryleft) + ge_balance_positive_add_restrict_inputentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_add_restrict_inputentriesentryright dst_positive_scale_add_restrict_inputentriesentryright dst_negative_code_add_restrict_inputentriesentryright dst_negative_scale_add_restrict_inputentriesentryright dst_positive_add_restrict_inputentriesentryright dst_negative_add_restrict_inputentriesentryright. (((G) = (((((dst_positive_code_add_restrict_inputentriesentryright) + (dst_positive_scale_add_restrict_inputentriesentryright)) * S ((dst_positive_code_add_restrict_inputentriesentryright) + (dst_positive_scale_add_restrict_inputentriesentryright)) + ((dst_positive_scale_add_restrict_inputentriesentryright) + (dst_positive_scale_add_restrict_inputentriesentryright))) + (((dst_negative_code_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)) * S ((dst_negative_code_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)) + ((dst_negative_scale_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)))) * S ((((dst_positive_code_add_restrict_inputentriesentryright) + (dst_positive_scale_add_restrict_inputentriesentryright)) * S ((dst_positive_code_add_restrict_inputentriesentryright) + (dst_positive_scale_add_restrict_inputentriesentryright)) + ((dst_positive_scale_add_restrict_inputentriesentryright) + (dst_positive_scale_add_restrict_inputentriesentryright))) + (((dst_negative_code_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)) * S ((dst_negative_code_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)) + ((dst_negative_scale_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)))) + ((((dst_negative_code_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)) * S ((dst_negative_code_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)) + ((dst_negative_scale_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright))) + (((dst_negative_code_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)) * S ((dst_negative_code_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)) + ((dst_negative_scale_add_restrict_inputentriesentryright) + (dst_negative_scale_add_restrict_inputentriesentryright)))))) /\ (((((exists ff_h_pvs_add_restrict_inputentriesentryrightpositive. ff_h_pvs_add_restrict_inputentriesentryrightpositive + S (dst_positive_add_restrict_inputentriesentryright) = S ((S (sto_index_add_restrict_inputentries)) * dst_positive_scale_add_restrict_inputentriesentryright)) /\ exists ff_q_pvs_add_restrict_inputentriesentryrightpositive. dst_positive_code_add_restrict_inputentriesentryright = ff_q_pvs_add_restrict_inputentriesentryrightpositive * S ((S (sto_index_add_restrict_inputentries)) * dst_positive_scale_add_restrict_inputentriesentryright) + (dst_positive_add_restrict_inputentriesentryright))) /\ (((((exists ff_h_pvs_add_restrict_inputentriesentryrightnegative. ff_h_pvs_add_restrict_inputentriesentryrightnegative + S (dst_negative_add_restrict_inputentriesentryright) = S ((S (sto_index_add_restrict_inputentries)) * dst_negative_scale_add_restrict_inputentriesentryright)) /\ exists ff_q_pvs_add_restrict_inputentriesentryrightnegative. dst_negative_code_add_restrict_inputentriesentryright = ff_q_pvs_add_restrict_inputentriesentryrightnegative * S ((S (sto_index_add_restrict_inputentries)) * dst_negative_scale_add_restrict_inputentriesentryright) + (dst_negative_add_restrict_inputentriesentryright))) /\ (exists ge_balance_positive_add_restrict_inputentriesentryrightvalue ge_balance_negative_add_restrict_inputentriesentryrightvalue. (((((sto_right_add_restrict_inputentries) = 2 * (ge_balance_positive_add_restrict_inputentriesentryrightvalue) /\ (ge_balance_negative_add_restrict_inputentriesentryrightvalue) = 0) \/ exists ge_signed_half_add_restrict_inputentriesentryrightvaluedecode. (((sto_right_add_restrict_inputentries) = 2 * ge_signed_half_add_restrict_inputentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_add_restrict_inputentriesentryrightvalue) = 0) /\ (ge_balance_negative_add_restrict_inputentriesentryrightvalue) = S ge_signed_half_add_restrict_inputentriesentryrightvaluedecode))) /\ ((dst_positive_add_restrict_inputentriesentryright) + ge_balance_negative_add_restrict_inputentriesentryrightvalue = (dst_negative_add_restrict_inputentriesentryright) + ge_balance_positive_add_restrict_inputentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_add_restrict_inputentriesentryoutput dst_positive_scale_add_restrict_inputentriesentryoutput dst_negative_code_add_restrict_inputentriesentryoutput dst_negative_scale_add_restrict_inputentriesentryoutput dst_positive_add_restrict_inputentriesentryoutput dst_negative_add_restrict_inputentriesentryoutput. (((H) = (((((dst_positive_code_add_restrict_inputentriesentryoutput) + (dst_positive_scale_add_restrict_inputentriesentryoutput)) * S ((dst_positive_code_add_restrict_inputentriesentryoutput) + (dst_positive_scale_add_restrict_inputentriesentryoutput)) + ((dst_positive_scale_add_restrict_inputentriesentryoutput) + (dst_positive_scale_add_restrict_inputentriesentryoutput))) + (((dst_negative_code_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)) * S ((dst_negative_code_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)) + ((dst_negative_scale_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)))) * S ((((dst_positive_code_add_restrict_inputentriesentryoutput) + (dst_positive_scale_add_restrict_inputentriesentryoutput)) * S ((dst_positive_code_add_restrict_inputentriesentryoutput) + (dst_positive_scale_add_restrict_inputentriesentryoutput)) + ((dst_positive_scale_add_restrict_inputentriesentryoutput) + (dst_positive_scale_add_restrict_inputentriesentryoutput))) + (((dst_negative_code_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)) * S ((dst_negative_code_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)) + ((dst_negative_scale_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)))) + ((((dst_negative_code_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)) * S ((dst_negative_code_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)) + ((dst_negative_scale_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput))) + (((dst_negative_code_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)) * S ((dst_negative_code_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)) + ((dst_negative_scale_add_restrict_inputentriesentryoutput) + (dst_negative_scale_add_restrict_inputentriesentryoutput)))))) /\ (((((exists ff_h_pvs_add_restrict_inputentriesentryoutputpositive. ff_h_pvs_add_restrict_inputentriesentryoutputpositive + S (dst_positive_add_restrict_inputentriesentryoutput) = S ((S (sto_index_add_restrict_inputentries)) * dst_positive_scale_add_restrict_inputentriesentryoutput)) /\ exists ff_q_pvs_add_restrict_inputentriesentryoutputpositive. dst_positive_code_add_restrict_inputentriesentryoutput = ff_q_pvs_add_restrict_inputentriesentryoutputpositive * S ((S (sto_index_add_restrict_inputentries)) * dst_positive_scale_add_restrict_inputentriesentryoutput) + (dst_positive_add_restrict_inputentriesentryoutput))) /\ (((((exists ff_h_pvs_add_restrict_inputentriesentryoutputnegative. ff_h_pvs_add_restrict_inputentriesentryoutputnegative + S (dst_negative_add_restrict_inputentriesentryoutput) = S ((S (sto_index_add_restrict_inputentries)) * dst_negative_scale_add_restrict_inputentriesentryoutput)) /\ exists ff_q_pvs_add_restrict_inputentriesentryoutputnegative. dst_negative_code_add_restrict_inputentriesentryoutput = ff_q_pvs_add_restrict_inputentriesentryoutputnegative * S ((S (sto_index_add_restrict_inputentries)) * dst_negative_scale_add_restrict_inputentriesentryoutput) + (dst_negative_add_restrict_inputentriesentryoutput))) /\ (exists ge_balance_positive_add_restrict_inputentriesentryoutputvalue ge_balance_negative_add_restrict_inputentriesentryoutputvalue. (((((sto_output_add_restrict_inputentries) = 2 * (ge_balance_positive_add_restrict_inputentriesentryoutputvalue) /\ (ge_balance_negative_add_restrict_inputentriesentryoutputvalue) = 0) \/ exists ge_signed_half_add_restrict_inputentriesentryoutputvaluedecode. (((sto_output_add_restrict_inputentries) = 2 * ge_signed_half_add_restrict_inputentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_add_restrict_inputentriesentryoutputvalue) = 0) /\ (ge_balance_negative_add_restrict_inputentriesentryoutputvalue) = S ge_signed_half_add_restrict_inputentriesentryoutputvaluedecode))) /\ ((dst_positive_add_restrict_inputentriesentryoutput) + ge_balance_negative_add_restrict_inputentriesentryoutputvalue = (dst_negative_add_restrict_inputentriesentryoutput) + ge_balance_positive_add_restrict_inputentriesentryoutputvalue))))))))) /\ (exists dsa_ap_add_restrict_inputentriesentryoperation dsa_an_add_restrict_inputentriesentryoperation dsa_bp_add_restrict_inputentriesentryoperation dsa_bn_add_restrict_inputentriesentryoperation dsa_cp_add_restrict_inputentriesentryoperation dsa_cn_add_restrict_inputentriesentryoperation. (((((sto_left_add_restrict_inputentries) = 2 * (dsa_ap_add_restrict_inputentriesentryoperation) /\ (dsa_an_add_restrict_inputentriesentryoperation) = 0) \/ exists ge_signed_half_add_restrict_inputentriesentryoperationleft. (((sto_left_add_restrict_inputentries) = 2 * ge_signed_half_add_restrict_inputentriesentryoperationleft + 1 /\ (dsa_ap_add_restrict_inputentriesentryoperation) = 0) /\ (dsa_an_add_restrict_inputentriesentryoperation) = S ge_signed_half_add_restrict_inputentriesentryoperationleft))) /\ ((((((sto_right_add_restrict_inputentries) = 2 * (dsa_bp_add_restrict_inputentriesentryoperation) /\ (dsa_bn_add_restrict_inputentriesentryoperation) = 0) \/ exists ge_signed_half_add_restrict_inputentriesentryoperationright. (((sto_right_add_restrict_inputentries) = 2 * ge_signed_half_add_restrict_inputentriesentryoperationright + 1 /\ (dsa_bp_add_restrict_inputentriesentryoperation) = 0) /\ (dsa_bn_add_restrict_inputentriesentryoperation) = S ge_signed_half_add_restrict_inputentriesentryoperationright))) /\ ((((((sto_output_add_restrict_inputentries) = 2 * (dsa_cp_add_restrict_inputentriesentryoperation) /\ (dsa_cn_add_restrict_inputentriesentryoperation) = 0) \/ exists ge_signed_half_add_restrict_inputentriesentryoperationoutput. (((sto_output_add_restrict_inputentries) = 2 * ge_signed_half_add_restrict_inputentriesentryoperationoutput + 1 /\ (dsa_cp_add_restrict_inputentriesentryoperation) = 0) /\ (dsa_cn_add_restrict_inputentriesentryoperation) = S ge_signed_half_add_restrict_inputentriesentryoperationoutput))) /\ ((dsa_ap_add_restrict_inputentriesentryoperation + dsa_bp_add_restrict_inputentriesentryoperation) + dsa_cn_add_restrict_inputentriesentryoperation = (dsa_an_add_restrict_inputentriesentryoperation + dsa_bn_add_restrict_inputentriesentryoperation) + dsa_cp_add_restrict_inputentriesentryoperation))))))))))))))))))) -> (((exists dst_positive_code_add_restrict_outputleft_table dst_positive_scale_add_restrict_outputleft_table dst_negative_code_add_restrict_outputleft_table dst_negative_scale_add_restrict_outputleft_table. (((F) = (((((dst_positive_code_add_restrict_outputleft_table) + (dst_positive_scale_add_restrict_outputleft_table)) * S ((dst_positive_code_add_restrict_outputleft_table) + (dst_positive_scale_add_restrict_outputleft_table)) + ((dst_positive_scale_add_restrict_outputleft_table) + (dst_positive_scale_add_restrict_outputleft_table))) + (((dst_negative_code_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)) * S ((dst_negative_code_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)) + ((dst_negative_scale_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)))) * S ((((dst_positive_code_add_restrict_outputleft_table) + (dst_positive_scale_add_restrict_outputleft_table)) * S ((dst_positive_code_add_restrict_outputleft_table) + (dst_positive_scale_add_restrict_outputleft_table)) + ((dst_positive_scale_add_restrict_outputleft_table) + (dst_positive_scale_add_restrict_outputleft_table))) + (((dst_negative_code_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)) * S ((dst_negative_code_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)) + ((dst_negative_scale_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)))) + ((((dst_negative_code_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)) * S ((dst_negative_code_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)) + ((dst_negative_scale_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table))) + (((dst_negative_code_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)) * S ((dst_negative_code_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)) + ((dst_negative_scale_add_restrict_outputleft_table) + (dst_negative_scale_add_restrict_outputleft_table)))))) /\ (forall dst_index_add_restrict_outputleft_table. (exists pvs_le_gap_add_restrict_outputleft_tabledomain. pvs_le_gap_add_restrict_outputleft_tabledomain + (dst_index_add_restrict_outputleft_table) = (l)) -> exists dst_positive_add_restrict_outputleft_table dst_negative_add_restrict_outputleft_table dst_value_add_restrict_outputleft_table. ((((exists ff_h_pvs_add_restrict_outputleft_tableentrypositive. ff_h_pvs_add_restrict_outputleft_tableentrypositive + S (dst_positive_add_restrict_outputleft_table) = S ((S (dst_index_add_restrict_outputleft_table)) * dst_positive_scale_add_restrict_outputleft_table)) /\ exists ff_q_pvs_add_restrict_outputleft_tableentrypositive. dst_positive_code_add_restrict_outputleft_table = ff_q_pvs_add_restrict_outputleft_tableentrypositive * S ((S (dst_index_add_restrict_outputleft_table)) * dst_positive_scale_add_restrict_outputleft_table) + (dst_positive_add_restrict_outputleft_table))) /\ (((((exists ff_h_pvs_add_restrict_outputleft_tableentrynegative. ff_h_pvs_add_restrict_outputleft_tableentrynegative + S (dst_negative_add_restrict_outputleft_table) = S ((S (dst_index_add_restrict_outputleft_table)) * dst_negative_scale_add_restrict_outputleft_table)) /\ exists ff_q_pvs_add_restrict_outputleft_tableentrynegative. dst_negative_code_add_restrict_outputleft_table = ff_q_pvs_add_restrict_outputleft_tableentrynegative * S ((S (dst_index_add_restrict_outputleft_table)) * dst_negative_scale_add_restrict_outputleft_table) + (dst_negative_add_restrict_outputleft_table))) /\ (exists ge_balance_positive_add_restrict_outputleft_tableentryvalue ge_balance_negative_add_restrict_outputleft_tableentryvalue. (((((dst_value_add_restrict_outputleft_table) = 2 * (ge_balance_positive_add_restrict_outputleft_tableentryvalue) /\ (ge_balance_negative_add_restrict_outputleft_tableentryvalue) = 0) \/ exists ge_signed_half_add_restrict_outputleft_tableentryvaluedecode. (((dst_value_add_restrict_outputleft_table) = 2 * ge_signed_half_add_restrict_outputleft_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_restrict_outputleft_tableentryvalue) = 0) /\ (ge_balance_negative_add_restrict_outputleft_tableentryvalue) = S ge_signed_half_add_restrict_outputleft_tableentryvaluedecode))) /\ ((dst_positive_add_restrict_outputleft_table) + ge_balance_negative_add_restrict_outputleft_tableentryvalue = (dst_negative_add_restrict_outputleft_table) + ge_balance_positive_add_restrict_outputleft_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_restrict_outputright_table dst_positive_scale_add_restrict_outputright_table dst_negative_code_add_restrict_outputright_table dst_negative_scale_add_restrict_outputright_table. (((G) = (((((dst_positive_code_add_restrict_outputright_table) + (dst_positive_scale_add_restrict_outputright_table)) * S ((dst_positive_code_add_restrict_outputright_table) + (dst_positive_scale_add_restrict_outputright_table)) + ((dst_positive_scale_add_restrict_outputright_table) + (dst_positive_scale_add_restrict_outputright_table))) + (((dst_negative_code_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)) * S ((dst_negative_code_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)) + ((dst_negative_scale_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)))) * S ((((dst_positive_code_add_restrict_outputright_table) + (dst_positive_scale_add_restrict_outputright_table)) * S ((dst_positive_code_add_restrict_outputright_table) + (dst_positive_scale_add_restrict_outputright_table)) + ((dst_positive_scale_add_restrict_outputright_table) + (dst_positive_scale_add_restrict_outputright_table))) + (((dst_negative_code_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)) * S ((dst_negative_code_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)) + ((dst_negative_scale_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)))) + ((((dst_negative_code_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)) * S ((dst_negative_code_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)) + ((dst_negative_scale_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table))) + (((dst_negative_code_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)) * S ((dst_negative_code_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)) + ((dst_negative_scale_add_restrict_outputright_table) + (dst_negative_scale_add_restrict_outputright_table)))))) /\ (forall dst_index_add_restrict_outputright_table. (exists pvs_le_gap_add_restrict_outputright_tabledomain. pvs_le_gap_add_restrict_outputright_tabledomain + (dst_index_add_restrict_outputright_table) = (l)) -> exists dst_positive_add_restrict_outputright_table dst_negative_add_restrict_outputright_table dst_value_add_restrict_outputright_table. ((((exists ff_h_pvs_add_restrict_outputright_tableentrypositive. ff_h_pvs_add_restrict_outputright_tableentrypositive + S (dst_positive_add_restrict_outputright_table) = S ((S (dst_index_add_restrict_outputright_table)) * dst_positive_scale_add_restrict_outputright_table)) /\ exists ff_q_pvs_add_restrict_outputright_tableentrypositive. dst_positive_code_add_restrict_outputright_table = ff_q_pvs_add_restrict_outputright_tableentrypositive * S ((S (dst_index_add_restrict_outputright_table)) * dst_positive_scale_add_restrict_outputright_table) + (dst_positive_add_restrict_outputright_table))) /\ (((((exists ff_h_pvs_add_restrict_outputright_tableentrynegative. ff_h_pvs_add_restrict_outputright_tableentrynegative + S (dst_negative_add_restrict_outputright_table) = S ((S (dst_index_add_restrict_outputright_table)) * dst_negative_scale_add_restrict_outputright_table)) /\ exists ff_q_pvs_add_restrict_outputright_tableentrynegative. dst_negative_code_add_restrict_outputright_table = ff_q_pvs_add_restrict_outputright_tableentrynegative * S ((S (dst_index_add_restrict_outputright_table)) * dst_negative_scale_add_restrict_outputright_table) + (dst_negative_add_restrict_outputright_table))) /\ (exists ge_balance_positive_add_restrict_outputright_tableentryvalue ge_balance_negative_add_restrict_outputright_tableentryvalue. (((((dst_value_add_restrict_outputright_table) = 2 * (ge_balance_positive_add_restrict_outputright_tableentryvalue) /\ (ge_balance_negative_add_restrict_outputright_tableentryvalue) = 0) \/ exists ge_signed_half_add_restrict_outputright_tableentryvaluedecode. (((dst_value_add_restrict_outputright_table) = 2 * ge_signed_half_add_restrict_outputright_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_restrict_outputright_tableentryvalue) = 0) /\ (ge_balance_negative_add_restrict_outputright_tableentryvalue) = S ge_signed_half_add_restrict_outputright_tableentryvaluedecode))) /\ ((dst_positive_add_restrict_outputright_table) + ge_balance_negative_add_restrict_outputright_tableentryvalue = (dst_negative_add_restrict_outputright_table) + ge_balance_positive_add_restrict_outputright_tableentryvalue))))))))) /\ (((exists dst_positive_code_add_restrict_outputoutput_table dst_positive_scale_add_restrict_outputoutput_table dst_negative_code_add_restrict_outputoutput_table dst_negative_scale_add_restrict_outputoutput_table. (((H) = (((((dst_positive_code_add_restrict_outputoutput_table) + (dst_positive_scale_add_restrict_outputoutput_table)) * S ((dst_positive_code_add_restrict_outputoutput_table) + (dst_positive_scale_add_restrict_outputoutput_table)) + ((dst_positive_scale_add_restrict_outputoutput_table) + (dst_positive_scale_add_restrict_outputoutput_table))) + (((dst_negative_code_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)) * S ((dst_negative_code_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)) + ((dst_negative_scale_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)))) * S ((((dst_positive_code_add_restrict_outputoutput_table) + (dst_positive_scale_add_restrict_outputoutput_table)) * S ((dst_positive_code_add_restrict_outputoutput_table) + (dst_positive_scale_add_restrict_outputoutput_table)) + ((dst_positive_scale_add_restrict_outputoutput_table) + (dst_positive_scale_add_restrict_outputoutput_table))) + (((dst_negative_code_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)) * S ((dst_negative_code_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)) + ((dst_negative_scale_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)))) + ((((dst_negative_code_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)) * S ((dst_negative_code_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)) + ((dst_negative_scale_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table))) + (((dst_negative_code_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)) * S ((dst_negative_code_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)) + ((dst_negative_scale_add_restrict_outputoutput_table) + (dst_negative_scale_add_restrict_outputoutput_table)))))) /\ (forall dst_index_add_restrict_outputoutput_table. (exists pvs_le_gap_add_restrict_outputoutput_tabledomain. pvs_le_gap_add_restrict_outputoutput_tabledomain + (dst_index_add_restrict_outputoutput_table) = (l)) -> exists dst_positive_add_restrict_outputoutput_table dst_negative_add_restrict_outputoutput_table dst_value_add_restrict_outputoutput_table. ((((exists ff_h_pvs_add_restrict_outputoutput_tableentrypositive. ff_h_pvs_add_restrict_outputoutput_tableentrypositive + S (dst_positive_add_restrict_outputoutput_table) = S ((S (dst_index_add_restrict_outputoutput_table)) * dst_positive_scale_add_restrict_outputoutput_table)) /\ exists ff_q_pvs_add_restrict_outputoutput_tableentrypositive. dst_positive_code_add_restrict_outputoutput_table = ff_q_pvs_add_restrict_outputoutput_tableentrypositive * S ((S (dst_index_add_restrict_outputoutput_table)) * dst_positive_scale_add_restrict_outputoutput_table) + (dst_positive_add_restrict_outputoutput_table))) /\ (((((exists ff_h_pvs_add_restrict_outputoutput_tableentrynegative. ff_h_pvs_add_restrict_outputoutput_tableentrynegative + S (dst_negative_add_restrict_outputoutput_table) = S ((S (dst_index_add_restrict_outputoutput_table)) * dst_negative_scale_add_restrict_outputoutput_table)) /\ exists ff_q_pvs_add_restrict_outputoutput_tableentrynegative. dst_negative_code_add_restrict_outputoutput_table = ff_q_pvs_add_restrict_outputoutput_tableentrynegative * S ((S (dst_index_add_restrict_outputoutput_table)) * dst_negative_scale_add_restrict_outputoutput_table) + (dst_negative_add_restrict_outputoutput_table))) /\ (exists ge_balance_positive_add_restrict_outputoutput_tableentryvalue ge_balance_negative_add_restrict_outputoutput_tableentryvalue. (((((dst_value_add_restrict_outputoutput_table) = 2 * (ge_balance_positive_add_restrict_outputoutput_tableentryvalue) /\ (ge_balance_negative_add_restrict_outputoutput_tableentryvalue) = 0) \/ exists ge_signed_half_add_restrict_outputoutput_tableentryvaluedecode. (((dst_value_add_restrict_outputoutput_table) = 2 * ge_signed_half_add_restrict_outputoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_add_restrict_outputoutput_tableentryvalue) = 0) /\ (ge_balance_negative_add_restrict_outputoutput_tableentryvalue) = S ge_signed_half_add_restrict_outputoutput_tableentryvaluedecode))) /\ ((dst_positive_add_restrict_outputoutput_table) + ge_balance_negative_add_restrict_outputoutput_tableentryvalue = (dst_negative_add_restrict_outputoutput_table) + ge_balance_positive_add_restrict_outputoutput_tableentryvalue))))))))) /\ (forall sto_index_add_restrict_outputentries. (exists pvs_gap_add_restrict_outputentriesbound. pvs_gap_add_restrict_outputentriesbound + S (sto_index_add_restrict_outputentries) = (l)) -> exists sto_left_add_restrict_outputentries sto_right_add_restrict_outputentries sto_output_add_restrict_outputentries. ((exists dst_positive_code_add_restrict_outputentriesentryleft dst_positive_scale_add_restrict_outputentriesentryleft dst_negative_code_add_restrict_outputentriesentryleft dst_negative_scale_add_restrict_outputentriesentryleft dst_positive_add_restrict_outputentriesentryleft dst_negative_add_restrict_outputentriesentryleft. (((F) = (((((dst_positive_code_add_restrict_outputentriesentryleft) + (dst_positive_scale_add_restrict_outputentriesentryleft)) * S ((dst_positive_code_add_restrict_outputentriesentryleft) + (dst_positive_scale_add_restrict_outputentriesentryleft)) + ((dst_positive_scale_add_restrict_outputentriesentryleft) + (dst_positive_scale_add_restrict_outputentriesentryleft))) + (((dst_negative_code_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)) * S ((dst_negative_code_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)) + ((dst_negative_scale_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)))) * S ((((dst_positive_code_add_restrict_outputentriesentryleft) + (dst_positive_scale_add_restrict_outputentriesentryleft)) * S ((dst_positive_code_add_restrict_outputentriesentryleft) + (dst_positive_scale_add_restrict_outputentriesentryleft)) + ((dst_positive_scale_add_restrict_outputentriesentryleft) + (dst_positive_scale_add_restrict_outputentriesentryleft))) + (((dst_negative_code_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)) * S ((dst_negative_code_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)) + ((dst_negative_scale_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)))) + ((((dst_negative_code_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)) * S ((dst_negative_code_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)) + ((dst_negative_scale_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft))) + (((dst_negative_code_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)) * S ((dst_negative_code_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)) + ((dst_negative_scale_add_restrict_outputentriesentryleft) + (dst_negative_scale_add_restrict_outputentriesentryleft)))))) /\ (((((exists ff_h_pvs_add_restrict_outputentriesentryleftpositive. ff_h_pvs_add_restrict_outputentriesentryleftpositive + S (dst_positive_add_restrict_outputentriesentryleft) = S ((S (sto_index_add_restrict_outputentries)) * dst_positive_scale_add_restrict_outputentriesentryleft)) /\ exists ff_q_pvs_add_restrict_outputentriesentryleftpositive. dst_positive_code_add_restrict_outputentriesentryleft = ff_q_pvs_add_restrict_outputentriesentryleftpositive * S ((S (sto_index_add_restrict_outputentries)) * dst_positive_scale_add_restrict_outputentriesentryleft) + (dst_positive_add_restrict_outputentriesentryleft))) /\ (((((exists ff_h_pvs_add_restrict_outputentriesentryleftnegative. ff_h_pvs_add_restrict_outputentriesentryleftnegative + S (dst_negative_add_restrict_outputentriesentryleft) = S ((S (sto_index_add_restrict_outputentries)) * dst_negative_scale_add_restrict_outputentriesentryleft)) /\ exists ff_q_pvs_add_restrict_outputentriesentryleftnegative. dst_negative_code_add_restrict_outputentriesentryleft = ff_q_pvs_add_restrict_outputentriesentryleftnegative * S ((S (sto_index_add_restrict_outputentries)) * dst_negative_scale_add_restrict_outputentriesentryleft) + (dst_negative_add_restrict_outputentriesentryleft))) /\ (exists ge_balance_positive_add_restrict_outputentriesentryleftvalue ge_balance_negative_add_restrict_outputentriesentryleftvalue. (((((sto_left_add_restrict_outputentries) = 2 * (ge_balance_positive_add_restrict_outputentriesentryleftvalue) /\ (ge_balance_negative_add_restrict_outputentriesentryleftvalue) = 0) \/ exists ge_signed_half_add_restrict_outputentriesentryleftvaluedecode. (((sto_left_add_restrict_outputentries) = 2 * ge_signed_half_add_restrict_outputentriesentryleftvaluedecode + 1 /\ (ge_balance_positive_add_restrict_outputentriesentryleftvalue) = 0) /\ (ge_balance_negative_add_restrict_outputentriesentryleftvalue) = S ge_signed_half_add_restrict_outputentriesentryleftvaluedecode))) /\ ((dst_positive_add_restrict_outputentriesentryleft) + ge_balance_negative_add_restrict_outputentriesentryleftvalue = (dst_negative_add_restrict_outputentriesentryleft) + ge_balance_positive_add_restrict_outputentriesentryleftvalue))))))))) /\ (((exists dst_positive_code_add_restrict_outputentriesentryright dst_positive_scale_add_restrict_outputentriesentryright dst_negative_code_add_restrict_outputentriesentryright dst_negative_scale_add_restrict_outputentriesentryright dst_positive_add_restrict_outputentriesentryright dst_negative_add_restrict_outputentriesentryright. (((G) = (((((dst_positive_code_add_restrict_outputentriesentryright) + (dst_positive_scale_add_restrict_outputentriesentryright)) * S ((dst_positive_code_add_restrict_outputentriesentryright) + (dst_positive_scale_add_restrict_outputentriesentryright)) + ((dst_positive_scale_add_restrict_outputentriesentryright) + (dst_positive_scale_add_restrict_outputentriesentryright))) + (((dst_negative_code_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)) * S ((dst_negative_code_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)) + ((dst_negative_scale_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)))) * S ((((dst_positive_code_add_restrict_outputentriesentryright) + (dst_positive_scale_add_restrict_outputentriesentryright)) * S ((dst_positive_code_add_restrict_outputentriesentryright) + (dst_positive_scale_add_restrict_outputentriesentryright)) + ((dst_positive_scale_add_restrict_outputentriesentryright) + (dst_positive_scale_add_restrict_outputentriesentryright))) + (((dst_negative_code_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)) * S ((dst_negative_code_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)) + ((dst_negative_scale_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)))) + ((((dst_negative_code_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)) * S ((dst_negative_code_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)) + ((dst_negative_scale_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright))) + (((dst_negative_code_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)) * S ((dst_negative_code_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)) + ((dst_negative_scale_add_restrict_outputentriesentryright) + (dst_negative_scale_add_restrict_outputentriesentryright)))))) /\ (((((exists ff_h_pvs_add_restrict_outputentriesentryrightpositive. ff_h_pvs_add_restrict_outputentriesentryrightpositive + S (dst_positive_add_restrict_outputentriesentryright) = S ((S (sto_index_add_restrict_outputentries)) * dst_positive_scale_add_restrict_outputentriesentryright)) /\ exists ff_q_pvs_add_restrict_outputentriesentryrightpositive. dst_positive_code_add_restrict_outputentriesentryright = ff_q_pvs_add_restrict_outputentriesentryrightpositive * S ((S (sto_index_add_restrict_outputentries)) * dst_positive_scale_add_restrict_outputentriesentryright) + (dst_positive_add_restrict_outputentriesentryright))) /\ (((((exists ff_h_pvs_add_restrict_outputentriesentryrightnegative. ff_h_pvs_add_restrict_outputentriesentryrightnegative + S (dst_negative_add_restrict_outputentriesentryright) = S ((S (sto_index_add_restrict_outputentries)) * dst_negative_scale_add_restrict_outputentriesentryright)) /\ exists ff_q_pvs_add_restrict_outputentriesentryrightnegative. dst_negative_code_add_restrict_outputentriesentryright = ff_q_pvs_add_restrict_outputentriesentryrightnegative * S ((S (sto_index_add_restrict_outputentries)) * dst_negative_scale_add_restrict_outputentriesentryright) + (dst_negative_add_restrict_outputentriesentryright))) /\ (exists ge_balance_positive_add_restrict_outputentriesentryrightvalue ge_balance_negative_add_restrict_outputentriesentryrightvalue. (((((sto_right_add_restrict_outputentries) = 2 * (ge_balance_positive_add_restrict_outputentriesentryrightvalue) /\ (ge_balance_negative_add_restrict_outputentriesentryrightvalue) = 0) \/ exists ge_signed_half_add_restrict_outputentriesentryrightvaluedecode. (((sto_right_add_restrict_outputentries) = 2 * ge_signed_half_add_restrict_outputentriesentryrightvaluedecode + 1 /\ (ge_balance_positive_add_restrict_outputentriesentryrightvalue) = 0) /\ (ge_balance_negative_add_restrict_outputentriesentryrightvalue) = S ge_signed_half_add_restrict_outputentriesentryrightvaluedecode))) /\ ((dst_positive_add_restrict_outputentriesentryright) + ge_balance_negative_add_restrict_outputentriesentryrightvalue = (dst_negative_add_restrict_outputentriesentryright) + ge_balance_positive_add_restrict_outputentriesentryrightvalue))))))))) /\ (((exists dst_positive_code_add_restrict_outputentriesentryoutput dst_positive_scale_add_restrict_outputentriesentryoutput dst_negative_code_add_restrict_outputentriesentryoutput dst_negative_scale_add_restrict_outputentriesentryoutput dst_positive_add_restrict_outputentriesentryoutput dst_negative_add_restrict_outputentriesentryoutput. (((H) = (((((dst_positive_code_add_restrict_outputentriesentryoutput) + (dst_positive_scale_add_restrict_outputentriesentryoutput)) * S ((dst_positive_code_add_restrict_outputentriesentryoutput) + (dst_positive_scale_add_restrict_outputentriesentryoutput)) + ((dst_positive_scale_add_restrict_outputentriesentryoutput) + (dst_positive_scale_add_restrict_outputentriesentryoutput))) + (((dst_negative_code_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)) * S ((dst_negative_code_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)) + ((dst_negative_scale_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)))) * S ((((dst_positive_code_add_restrict_outputentriesentryoutput) + (dst_positive_scale_add_restrict_outputentriesentryoutput)) * S ((dst_positive_code_add_restrict_outputentriesentryoutput) + (dst_positive_scale_add_restrict_outputentriesentryoutput)) + ((dst_positive_scale_add_restrict_outputentriesentryoutput) + (dst_positive_scale_add_restrict_outputentriesentryoutput))) + (((dst_negative_code_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)) * S ((dst_negative_code_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)) + ((dst_negative_scale_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)))) + ((((dst_negative_code_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)) * S ((dst_negative_code_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)) + ((dst_negative_scale_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput))) + (((dst_negative_code_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)) * S ((dst_negative_code_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)) + ((dst_negative_scale_add_restrict_outputentriesentryoutput) + (dst_negative_scale_add_restrict_outputentriesentryoutput)))))) /\ (((((exists ff_h_pvs_add_restrict_outputentriesentryoutputpositive. ff_h_pvs_add_restrict_outputentriesentryoutputpositive + S (dst_positive_add_restrict_outputentriesentryoutput) = S ((S (sto_index_add_restrict_outputentries)) * dst_positive_scale_add_restrict_outputentriesentryoutput)) /\ exists ff_q_pvs_add_restrict_outputentriesentryoutputpositive. dst_positive_code_add_restrict_outputentriesentryoutput = ff_q_pvs_add_restrict_outputentriesentryoutputpositive * S ((S (sto_index_add_restrict_outputentries)) * dst_positive_scale_add_restrict_outputentriesentryoutput) + (dst_positive_add_restrict_outputentriesentryoutput))) /\ (((((exists ff_h_pvs_add_restrict_outputentriesentryoutputnegative. ff_h_pvs_add_restrict_outputentriesentryoutputnegative + S (dst_negative_add_restrict_outputentriesentryoutput) = S ((S (sto_index_add_restrict_outputentries)) * dst_negative_scale_add_restrict_outputentriesentryoutput)) /\ exists ff_q_pvs_add_restrict_outputentriesentryoutputnegative. dst_negative_code_add_restrict_outputentriesentryoutput = ff_q_pvs_add_restrict_outputentriesentryoutputnegative * S ((S (sto_index_add_restrict_outputentries)) * dst_negative_scale_add_restrict_outputentriesentryoutput) + (dst_negative_add_restrict_outputentriesentryoutput))) /\ (exists ge_balance_positive_add_restrict_outputentriesentryoutputvalue ge_balance_negative_add_restrict_outputentriesentryoutputvalue. (((((sto_output_add_restrict_outputentries) = 2 * (ge_balance_positive_add_restrict_outputentriesentryoutputvalue) /\ (ge_balance_negative_add_restrict_outputentriesentryoutputvalue) = 0) \/ exists ge_signed_half_add_restrict_outputentriesentryoutputvaluedecode. (((sto_output_add_restrict_outputentries) = 2 * ge_signed_half_add_restrict_outputentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_add_restrict_outputentriesentryoutputvalue) = 0) /\ (ge_balance_negative_add_restrict_outputentriesentryoutputvalue) = S ge_signed_half_add_restrict_outputentriesentryoutputvaluedecode))) /\ ((dst_positive_add_restrict_outputentriesentryoutput) + ge_balance_negative_add_restrict_outputentriesentryoutputvalue = (dst_negative_add_restrict_outputentriesentryoutput) + ge_balance_positive_add_restrict_outputentriesentryoutputvalue))))))))) /\ (exists dsa_ap_add_restrict_outputentriesentryoperation dsa_an_add_restrict_outputentriesentryoperation dsa_bp_add_restrict_outputentriesentryoperation dsa_bn_add_restrict_outputentriesentryoperation dsa_cp_add_restrict_outputentriesentryoperation dsa_cn_add_restrict_outputentriesentryoperation. (((((sto_left_add_restrict_outputentries) = 2 * (dsa_ap_add_restrict_outputentriesentryoperation) /\ (dsa_an_add_restrict_outputentriesentryoperation) = 0) \/ exists ge_signed_half_add_restrict_outputentriesentryoperationleft. (((sto_left_add_restrict_outputentries) = 2 * ge_signed_half_add_restrict_outputentriesentryoperationleft + 1 /\ (dsa_ap_add_restrict_outputentriesentryoperation) = 0) /\ (dsa_an_add_restrict_outputentriesentryoperation) = S ge_signed_half_add_restrict_outputentriesentryoperationleft))) /\ ((((((sto_right_add_restrict_outputentries) = 2 * (dsa_bp_add_restrict_outputentriesentryoperation) /\ (dsa_bn_add_restrict_outputentriesentryoperation) = 0) \/ exists ge_signed_half_add_restrict_outputentriesentryoperationright. (((sto_right_add_restrict_outputentries) = 2 * ge_signed_half_add_restrict_outputentriesentryoperationright + 1 /\ (dsa_bp_add_restrict_outputentriesentryoperation) = 0) /\ (dsa_bn_add_restrict_outputentriesentryoperation) = S ge_signed_half_add_restrict_outputentriesentryoperationright))) /\ ((((((sto_output_add_restrict_outputentries) = 2 * (dsa_cp_add_restrict_outputentriesentryoperation) /\ (dsa_cn_add_restrict_outputentriesentryoperation) = 0) \/ exists ge_signed_half_add_restrict_outputentriesentryoperationoutput. (((sto_output_add_restrict_outputentries) = 2 * ge_signed_half_add_restrict_outputentriesentryoperationoutput + 1 /\ (dsa_cp_add_restrict_outputentriesentryoperation) = 0) /\ (dsa_cn_add_restrict_outputentriesentryoperation) = S ge_signed_half_add_restrict_outputentriesentryoperationoutput))) /\ ((dsa_ap_add_restrict_outputentriesentryoperation + dsa_bp_add_restrict_outputentriesentryoperation) + dsa_cn_add_restrict_outputentriesentryoperation = (dsa_an_add_restrict_outputentriesentryoperation + dsa_bn_add_restrict_outputentriesentryoperation) + dsa_cp_add_restrict_outputentriesentryoperation)))))))))))))))))))Complete tactic proof in conservative notation
All 34 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
34 script commands · 9 reading checkpoints · 0 local claims
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.
Named ingredients (1)
01Fix variables and assumptionsL1–5
02Separate the logical casesL6–9
03Use earlier factsL10–14
04Separate the logical casesL15–15
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L15
split
05Use earlier factsL16–20
06Separate the logical casesL21–21
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L21
split
07Use earlier factsL22–26
08Fix variables and assumptionsL27–28
Original defined command ledger · 34 lines
- 0001
intro F - 0002
intro G - 0003
intro H - 0004
intro l - 0005
intro h - 0006
cases h - 0007
cases h_right - 0008
cases h_right_right - 0009
split - 0010
specialize signed_table_domain_resize (S l) - 0011
specialize signed_table_domain_resize (l) - 0012
specialize signed_table_domain_resize (F) - 0013
apply signed_table_domain_resize - 0014
exact h_left - 0015
split - 0016
specialize signed_table_domain_resize (S l) - 0017
specialize signed_table_domain_resize (l) - 0018
specialize signed_table_domain_resize (G) - 0019
apply signed_table_domain_resize - 0020
exact h_right_left - 0021
split - 0022
specialize signed_table_domain_resize (S l) - 0023
specialize signed_table_domain_resize (l) - 0024
specialize signed_table_domain_resize (H) - 0025
apply signed_table_domain_resize - 0026
exact h_right_right_left - 0027
intro i - 0028
intro hi - 0029
specialize h_right_right_right (i) - 0030
apply h_right_right_right - 0031
specialize le_succ (S i) - 0032
specialize le_succ (l) - 0033
apply le_succ - 0034
exact hi