WS0004

signed_table_add_restrict

Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

Restrict the strict pointwise window from S l to l while retaining genuine input and output table certificates.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.

Exact expanded first-order arithmetic statement

forall F G H 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)))))))))))))))))))

Constructive proof overview

Generated structural guide

Restrict the strict pointwise window from S l to l while retaining genuine input and output table certificates.

The unchanged tactic script uses 2 declared prerequisites and contains 34 exact native proof lines.

Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

WS0001 signed_table_domain_resize le_succ Stable theorem; checked-use authorized

Direct dependents

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.

Read the argument

Proof checkpoints

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.

Named ingredients (1)
01Fix variables and assumptionsL1–5

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro F
  2. L2
    intro G
  3. L3
    intro H
  4. L4
    intro l
  5. L5
    intro h
02Separate the logical casesL6–9

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L6
    cases h
  2. L7
    cases h_right
  3. L8
    cases h_right_right
  4. L9
    split
03Use earlier factsL10–14

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L10
    specialize signed_table_domain_resize (S l)
  2. L11
    specialize signed_table_domain_resize (l)
  3. L12
    specialize signed_table_domain_resize (F)
  4. L13
    apply signed_table_domain_resize
  5. L14
    exact h_left
04Separate the logical casesL15–15

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L15
    split
05Use earlier factsL16–20

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L16
    specialize signed_table_domain_resize (S l)
  2. L17
    specialize signed_table_domain_resize (l)
  3. L18
    specialize signed_table_domain_resize (G)
  4. L19
    apply signed_table_domain_resize
  5. L20
    exact h_right_left
06Separate the logical casesL21–21

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L21
    split
07Use earlier factsL22–26

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L22
    specialize signed_table_domain_resize (S l)
  2. L23
    specialize signed_table_domain_resize (l)
  3. L24
    specialize signed_table_domain_resize (H)
  4. L25
    apply signed_table_domain_resize
  5. L26
    exact h_right_right_left
08Fix variables and assumptionsL27–28

Work with arbitrary variables or the premises of the current implication.

  1. L27
    intro i
  2. L28
    intro hi
09Use earlier factsL29–34

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L29
    specialize h_right_right_right (i)
  2. L30
    apply h_right_right_right
  3. L31
    specialize le_succ (S i)
  4. L32
    specialize le_succ (l)
  5. L33
    apply le_succ
  6. L34
    exact hi

Library-wide reading audit

Original exact command ledger · 34 lines
  1. 0001intro F
  2. 0002intro G
  3. 0003intro H
  4. 0004intro l
  5. 0005intro h
  6. 0006cases h
  7. 0007cases h_right
  8. 0008cases h_right_right
  9. 0009split
  10. 0010specialize signed_table_domain_resize (S l)
  11. 0011specialize signed_table_domain_resize (l)
  12. 0012specialize signed_table_domain_resize (F)
  13. 0013apply signed_table_domain_resize
  14. 0014exact h_left
  15. 0015split
  16. 0016specialize signed_table_domain_resize (S l)
  17. 0017specialize signed_table_domain_resize (l)
  18. 0018specialize signed_table_domain_resize (G)
  19. 0019apply signed_table_domain_resize
  20. 0020exact h_right_left
  21. 0021split
  22. 0022specialize signed_table_domain_resize (S l)
  23. 0023specialize signed_table_domain_resize (l)
  24. 0024specialize signed_table_domain_resize (H)
  25. 0025apply signed_table_domain_resize
  26. 0026exact h_right_right_left
  27. 0027intro i
  28. 0028intro hi
  29. 0029specialize h_right_right_right (i)
  30. 0030apply h_right_right_right
  31. 0031specialize le_succ (S i)
  32. 0032specialize le_succ (l)
  33. 0033apply le_succ
  34. 0034exact hi