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 A r s L M T V i j z. (((exists dst_positive_code_column_lookup_gridsource dst_positive_scale_column_lookup_gridsource dst_negative_code_column_lookup_gridsource dst_negative_scale_column_lookup_gridsource. (((A) = (((((dst_positive_code_column_lookup_gridsource) + (dst_positive_scale_column_lookup_gridsource)) * S ((dst_positive_code_column_lookup_gridsource) + (dst_positive_scale_column_lookup_gridsource)) + ((dst_positive_scale_column_lookup_gridsource) + (dst_positive_scale_column_lookup_gridsource))) + (((dst_negative_code_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)) * S ((dst_negative_code_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)) + ((dst_negative_scale_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)))) * S ((((dst_positive_code_column_lookup_gridsource) + (dst_positive_scale_column_lookup_gridsource)) * S ((dst_positive_code_column_lookup_gridsource) + (dst_positive_scale_column_lookup_gridsource)) + ((dst_positive_scale_column_lookup_gridsource) + (dst_positive_scale_column_lookup_gridsource))) + (((dst_negative_code_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)) * S ((dst_negative_code_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)) + ((dst_negative_scale_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)))) + ((((dst_negative_code_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)) * S ((dst_negative_code_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)) + ((dst_negative_scale_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource))) + (((dst_negative_code_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)) * S ((dst_negative_code_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)) + ((dst_negative_scale_column_lookup_gridsource) + (dst_negative_scale_column_lookup_gridsource)))))) /\ (forall dst_index_column_lookup_gridsource. (exists pvs_le_gap_column_lookup_gridsourcedomain. pvs_le_gap_column_lookup_gridsourcedomain + (dst_index_column_lookup_gridsource) = (0)) -> exists dst_positive_column_lookup_gridsource dst_negative_column_lookup_gridsource dst_value_column_lookup_gridsource. ((((exists ff_h_pvs_column_lookup_gridsourceentrypositive. ff_h_pvs_column_lookup_gridsourceentrypositive + S (dst_positive_column_lookup_gridsource) = S ((S (dst_index_column_lookup_gridsource)) * dst_positive_scale_column_lookup_gridsource)) /\ exists ff_q_pvs_column_lookup_gridsourceentrypositive. dst_positive_code_column_lookup_gridsource = ff_q_pvs_column_lookup_gridsourceentrypositive * S ((S (dst_index_column_lookup_gridsource)) * dst_positive_scale_column_lookup_gridsource) + (dst_positive_column_lookup_gridsource))) /\ (((((exists ff_h_pvs_column_lookup_gridsourceentrynegative. ff_h_pvs_column_lookup_gridsourceentrynegative + S (dst_negative_column_lookup_gridsource) = S ((S (dst_index_column_lookup_gridsource)) * dst_negative_scale_column_lookup_gridsource)) /\ exists ff_q_pvs_column_lookup_gridsourceentrynegative. dst_negative_code_column_lookup_gridsource = ff_q_pvs_column_lookup_gridsourceentrynegative * S ((S (dst_index_column_lookup_gridsource)) * dst_negative_scale_column_lookup_gridsource) + (dst_negative_column_lookup_gridsource))) /\ (exists ge_balance_positive_column_lookup_gridsourceentryvalue ge_balance_negative_column_lookup_gridsourceentryvalue. (((((dst_value_column_lookup_gridsource) = 2 * (ge_balance_positive_column_lookup_gridsourceentryvalue) /\ (ge_balance_negative_column_lookup_gridsourceentryvalue) = 0) \/ exists ge_signed_half_column_lookup_gridsourceentryvaluedecode. (((dst_value_column_lookup_gridsource) = 2 * ge_signed_half_column_lookup_gridsourceentryvaluedecode + 1 /\ (ge_balance_positive_column_lookup_gridsourceentryvalue) = 0) /\ (ge_balance_negative_column_lookup_gridsourceentryvalue) = S ge_signed_half_column_lookup_gridsourceentryvaluedecode))) /\ ((dst_positive_column_lookup_gridsource) + ge_balance_negative_column_lookup_gridsourceentryvalue = (dst_negative_column_lookup_gridsource) + ge_balance_positive_column_lookup_gridsourceentryvalue))))))))) /\ (((exists dst_positive_code_column_lookup_gridtable dst_positive_scale_column_lookup_gridtable dst_negative_code_column_lookup_gridtable dst_negative_scale_column_lookup_gridtable. (((T) = (((((dst_positive_code_column_lookup_gridtable) + (dst_positive_scale_column_lookup_gridtable)) * S ((dst_positive_code_column_lookup_gridtable) + (dst_positive_scale_column_lookup_gridtable)) + ((dst_positive_scale_column_lookup_gridtable) + (dst_positive_scale_column_lookup_gridtable))) + (((dst_negative_code_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)) * S ((dst_negative_code_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)) + ((dst_negative_scale_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)))) * S ((((dst_positive_code_column_lookup_gridtable) + (dst_positive_scale_column_lookup_gridtable)) * S ((dst_positive_code_column_lookup_gridtable) + (dst_positive_scale_column_lookup_gridtable)) + ((dst_positive_scale_column_lookup_gridtable) + (dst_positive_scale_column_lookup_gridtable))) + (((dst_negative_code_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)) * S ((dst_negative_code_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)) + ((dst_negative_scale_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)))) + ((((dst_negative_code_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)) * S ((dst_negative_code_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)) + ((dst_negative_scale_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable))) + (((dst_negative_code_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)) * S ((dst_negative_code_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)) + ((dst_negative_scale_column_lookup_gridtable) + (dst_negative_scale_column_lookup_gridtable)))))) /\ (forall dst_index_column_lookup_gridtable. (exists pvs_le_gap_column_lookup_gridtabledomain. pvs_le_gap_column_lookup_gridtabledomain + (dst_index_column_lookup_gridtable) = ((L)*(S (M)))) -> exists dst_positive_column_lookup_gridtable dst_negative_column_lookup_gridtable dst_value_column_lookup_gridtable. ((((exists ff_h_pvs_column_lookup_gridtableentrypositive. ff_h_pvs_column_lookup_gridtableentrypositive + S (dst_positive_column_lookup_gridtable) = S ((S (dst_index_column_lookup_gridtable)) * dst_positive_scale_column_lookup_gridtable)) /\ exists ff_q_pvs_column_lookup_gridtableentrypositive. dst_positive_code_column_lookup_gridtable = ff_q_pvs_column_lookup_gridtableentrypositive * S ((S (dst_index_column_lookup_gridtable)) * dst_positive_scale_column_lookup_gridtable) + (dst_positive_column_lookup_gridtable))) /\ (((((exists ff_h_pvs_column_lookup_gridtableentrynegative. ff_h_pvs_column_lookup_gridtableentrynegative + S (dst_negative_column_lookup_gridtable) = S ((S (dst_index_column_lookup_gridtable)) * dst_negative_scale_column_lookup_gridtable)) /\ exists ff_q_pvs_column_lookup_gridtableentrynegative. dst_negative_code_column_lookup_gridtable = ff_q_pvs_column_lookup_gridtableentrynegative * S ((S (dst_index_column_lookup_gridtable)) * dst_negative_scale_column_lookup_gridtable) + (dst_negative_column_lookup_gridtable))) /\ (exists ge_balance_positive_column_lookup_gridtableentryvalue ge_balance_negative_column_lookup_gridtableentryvalue. (((((dst_value_column_lookup_gridtable) = 2 * (ge_balance_positive_column_lookup_gridtableentryvalue) /\ (ge_balance_negative_column_lookup_gridtableentryvalue) = 0) \/ exists ge_signed_half_column_lookup_gridtableentryvaluedecode. (((dst_value_column_lookup_gridtable) = 2 * ge_signed_half_column_lookup_gridtableentryvaluedecode + 1 /\ (ge_balance_positive_column_lookup_gridtableentryvalue) = 0) /\ (ge_balance_negative_column_lookup_gridtableentryvalue) = S ge_signed_half_column_lookup_gridtableentryvaluedecode))) /\ ((dst_positive_column_lookup_gridtable) + ge_balance_negative_column_lookup_gridtableentryvalue = (dst_negative_column_lookup_gridtable) + ge_balance_positive_column_lookup_gridtableentryvalue))))))))) /\ (forall ssr_grid_row_column_lookup_grid ssr_grid_column_column_lookup_grid ssr_grid_value_column_lookup_grid. (exists pvs_gap_column_lookup_gridrow_bound. pvs_gap_column_lookup_gridrow_bound + S (ssr_grid_row_column_lookup_grid) = (L)) -> (exists pvs_gap_column_lookup_gridcolumn_bound. pvs_gap_column_lookup_gridcolumn_bound + S (ssr_grid_column_column_lookup_grid) = (M)) -> (exists dst_positive_code_column_lookup_gridlookup dst_positive_scale_column_lookup_gridlookup dst_negative_code_column_lookup_gridlookup dst_negative_scale_column_lookup_gridlookup dst_positive_column_lookup_gridlookup dst_negative_column_lookup_gridlookup. (((T) = (((((dst_positive_code_column_lookup_gridlookup) + (dst_positive_scale_column_lookup_gridlookup)) * S ((dst_positive_code_column_lookup_gridlookup) + (dst_positive_scale_column_lookup_gridlookup)) + ((dst_positive_scale_column_lookup_gridlookup) + (dst_positive_scale_column_lookup_gridlookup))) + (((dst_negative_code_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)) * S ((dst_negative_code_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)) + ((dst_negative_scale_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)))) * S ((((dst_positive_code_column_lookup_gridlookup) + (dst_positive_scale_column_lookup_gridlookup)) * S ((dst_positive_code_column_lookup_gridlookup) + (dst_positive_scale_column_lookup_gridlookup)) + ((dst_positive_scale_column_lookup_gridlookup) + (dst_positive_scale_column_lookup_gridlookup))) + (((dst_negative_code_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)) * S ((dst_negative_code_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)) + ((dst_negative_scale_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)))) + ((((dst_negative_code_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)) * S ((dst_negative_code_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)) + ((dst_negative_scale_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup))) + (((dst_negative_code_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)) * S ((dst_negative_code_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)) + ((dst_negative_scale_column_lookup_gridlookup) + (dst_negative_scale_column_lookup_gridlookup)))))) /\ (((((exists ff_h_pvs_column_lookup_gridlookuppositive. ff_h_pvs_column_lookup_gridlookuppositive + S (dst_positive_column_lookup_gridlookup) = S ((S (((S (M))*(ssr_grid_row_column_lookup_grid)+(ssr_grid_column_column_lookup_grid)))) * dst_positive_scale_column_lookup_gridlookup)) /\ exists ff_q_pvs_column_lookup_gridlookuppositive. dst_positive_code_column_lookup_gridlookup = ff_q_pvs_column_lookup_gridlookuppositive * S ((S (((S (M))*(ssr_grid_row_column_lookup_grid)+(ssr_grid_column_column_lookup_grid)))) * dst_positive_scale_column_lookup_gridlookup) + (dst_positive_column_lookup_gridlookup))) /\ (((((exists ff_h_pvs_column_lookup_gridlookupnegative. ff_h_pvs_column_lookup_gridlookupnegative + S (dst_negative_column_lookup_gridlookup) = S ((S (((S (M))*(ssr_grid_row_column_lookup_grid)+(ssr_grid_column_column_lookup_grid)))) * dst_negative_scale_column_lookup_gridlookup)) /\ exists ff_q_pvs_column_lookup_gridlookupnegative. dst_negative_code_column_lookup_gridlookup = ff_q_pvs_column_lookup_gridlookupnegative * S ((S (((S (M))*(ssr_grid_row_column_lookup_grid)+(ssr_grid_column_column_lookup_grid)))) * dst_negative_scale_column_lookup_gridlookup) + (dst_negative_column_lookup_gridlookup))) /\ (exists ge_balance_positive_column_lookup_gridlookupvalue ge_balance_negative_column_lookup_gridlookupvalue. (((((ssr_grid_value_column_lookup_grid) = 2 * (ge_balance_positive_column_lookup_gridlookupvalue) /\ (ge_balance_negative_column_lookup_gridlookupvalue) = 0) \/ exists ge_signed_half_column_lookup_gridlookupvaluedecode. (((ssr_grid_value_column_lookup_grid) = 2 * ge_signed_half_column_lookup_gridlookupvaluedecode + 1 /\ (ge_balance_positive_column_lookup_gridlookupvalue) = 0) /\ (ge_balance_negative_column_lookup_gridlookupvalue) = S ge_signed_half_column_lookup_gridlookupvaluedecode))) /\ ((dst_positive_column_lookup_gridlookup) + ge_balance_negative_column_lookup_gridlookupvalue = (dst_negative_column_lookup_gridlookup) + ge_balance_positive_column_lookup_gridlookupvalue))))))))) -> (exists ssr_entry_value_column_lookup_gridentry ssr_entry_image_column_lookup_gridentry. ((exists dst_positive_code_column_lookup_gridentrysource dst_positive_scale_column_lookup_gridentrysource dst_negative_code_column_lookup_gridentrysource dst_negative_scale_column_lookup_gridentrysource dst_positive_column_lookup_gridentrysource dst_negative_column_lookup_gridentrysource. (((A) = (((((dst_positive_code_column_lookup_gridentrysource) + (dst_positive_scale_column_lookup_gridentrysource)) * S ((dst_positive_code_column_lookup_gridentrysource) + (dst_positive_scale_column_lookup_gridentrysource)) + ((dst_positive_scale_column_lookup_gridentrysource) + (dst_positive_scale_column_lookup_gridentrysource))) + (((dst_negative_code_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)) * S ((dst_negative_code_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)) + ((dst_negative_scale_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)))) * S ((((dst_positive_code_column_lookup_gridentrysource) + (dst_positive_scale_column_lookup_gridentrysource)) * S ((dst_positive_code_column_lookup_gridentrysource) + (dst_positive_scale_column_lookup_gridentrysource)) + ((dst_positive_scale_column_lookup_gridentrysource) + (dst_positive_scale_column_lookup_gridentrysource))) + (((dst_negative_code_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)) * S ((dst_negative_code_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)) + ((dst_negative_scale_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)))) + ((((dst_negative_code_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)) * S ((dst_negative_code_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)) + ((dst_negative_scale_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource))) + (((dst_negative_code_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)) * S ((dst_negative_code_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)) + ((dst_negative_scale_column_lookup_gridentrysource) + (dst_negative_scale_column_lookup_gridentrysource)))))) /\ (((((exists ff_h_pvs_column_lookup_gridentrysourcepositive. ff_h_pvs_column_lookup_gridentrysourcepositive + S (dst_positive_column_lookup_gridentrysource) = S ((S (ssr_grid_row_column_lookup_grid)) * dst_positive_scale_column_lookup_gridentrysource)) /\ exists ff_q_pvs_column_lookup_gridentrysourcepositive. dst_positive_code_column_lookup_gridentrysource = ff_q_pvs_column_lookup_gridentrysourcepositive * S ((S (ssr_grid_row_column_lookup_grid)) * dst_positive_scale_column_lookup_gridentrysource) + (dst_positive_column_lookup_gridentrysource))) /\ (((((exists ff_h_pvs_column_lookup_gridentrysourcenegative. ff_h_pvs_column_lookup_gridentrysourcenegative + S (dst_negative_column_lookup_gridentrysource) = S ((S (ssr_grid_row_column_lookup_grid)) * dst_negative_scale_column_lookup_gridentrysource)) /\ exists ff_q_pvs_column_lookup_gridentrysourcenegative. dst_negative_code_column_lookup_gridentrysource = ff_q_pvs_column_lookup_gridentrysourcenegative * S ((S (ssr_grid_row_column_lookup_grid)) * dst_negative_scale_column_lookup_gridentrysource) + (dst_negative_column_lookup_gridentrysource))) /\ (exists ge_balance_positive_column_lookup_gridentrysourcevalue ge_balance_negative_column_lookup_gridentrysourcevalue. (((((ssr_entry_value_column_lookup_gridentry) = 2 * (ge_balance_positive_column_lookup_gridentrysourcevalue) /\ (ge_balance_negative_column_lookup_gridentrysourcevalue) = 0) \/ exists ge_signed_half_column_lookup_gridentrysourcevaluedecode. (((ssr_entry_value_column_lookup_gridentry) = 2 * ge_signed_half_column_lookup_gridentrysourcevaluedecode + 1 /\ (ge_balance_positive_column_lookup_gridentrysourcevalue) = 0) /\ (ge_balance_negative_column_lookup_gridentrysourcevalue) = S ge_signed_half_column_lookup_gridentrysourcevaluedecode))) /\ ((dst_positive_column_lookup_gridentrysource) + ge_balance_negative_column_lookup_gridentrysourcevalue = (dst_negative_column_lookup_gridentrysource) + ge_balance_positive_column_lookup_gridentrysourcevalue))))))))) /\ (((((exists ff_h_pvs_column_lookup_gridentrymap. ff_h_pvs_column_lookup_gridentrymap + S (ssr_entry_image_column_lookup_gridentry) = S ((S (ssr_grid_row_column_lookup_grid)) * s)) /\ exists ff_q_pvs_column_lookup_gridentrymap. r = ff_q_pvs_column_lookup_gridentrymap * S ((S (ssr_grid_row_column_lookup_grid)) * s) + (ssr_entry_image_column_lookup_gridentry))) /\ (((((ssr_grid_column_column_lookup_grid)=(ssr_entry_image_column_lookup_gridentry)) /\ ((ssr_grid_value_column_lookup_grid)=(ssr_entry_value_column_lookup_gridentry)))) \/ (((~((ssr_grid_column_column_lookup_grid)=(ssr_entry_image_column_lookup_gridentry))) /\ ((ssr_grid_value_column_lookup_grid)=0))))))))))))) -> (((exists dst_positive_code_column_lookup_slicesource_table dst_positive_scale_column_lookup_slicesource_table dst_negative_code_column_lookup_slicesource_table dst_negative_scale_column_lookup_slicesource_table. (((T) = (((((dst_positive_code_column_lookup_slicesource_table) + (dst_positive_scale_column_lookup_slicesource_table)) * S ((dst_positive_code_column_lookup_slicesource_table) + (dst_positive_scale_column_lookup_slicesource_table)) + ((dst_positive_scale_column_lookup_slicesource_table) + (dst_positive_scale_column_lookup_slicesource_table))) + (((dst_negative_code_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)) * S ((dst_negative_code_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)) + ((dst_negative_scale_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)))) * S ((((dst_positive_code_column_lookup_slicesource_table) + (dst_positive_scale_column_lookup_slicesource_table)) * S ((dst_positive_code_column_lookup_slicesource_table) + (dst_positive_scale_column_lookup_slicesource_table)) + ((dst_positive_scale_column_lookup_slicesource_table) + (dst_positive_scale_column_lookup_slicesource_table))) + (((dst_negative_code_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)) * S ((dst_negative_code_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)) + ((dst_negative_scale_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)))) + ((((dst_negative_code_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)) * S ((dst_negative_code_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)) + ((dst_negative_scale_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table))) + (((dst_negative_code_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)) * S ((dst_negative_code_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)) + ((dst_negative_scale_column_lookup_slicesource_table) + (dst_negative_scale_column_lookup_slicesource_table)))))) /\ (forall dst_index_column_lookup_slicesource_table. (exists pvs_le_gap_column_lookup_slicesource_tabledomain. pvs_le_gap_column_lookup_slicesource_tabledomain + (dst_index_column_lookup_slicesource_table) = (0)) -> exists dst_positive_column_lookup_slicesource_table dst_negative_column_lookup_slicesource_table dst_value_column_lookup_slicesource_table. ((((exists ff_h_pvs_column_lookup_slicesource_tableentrypositive. ff_h_pvs_column_lookup_slicesource_tableentrypositive + S (dst_positive_column_lookup_slicesource_table) = S ((S (dst_index_column_lookup_slicesource_table)) * dst_positive_scale_column_lookup_slicesource_table)) /\ exists ff_q_pvs_column_lookup_slicesource_tableentrypositive. dst_positive_code_column_lookup_slicesource_table = ff_q_pvs_column_lookup_slicesource_tableentrypositive * S ((S (dst_index_column_lookup_slicesource_table)) * dst_positive_scale_column_lookup_slicesource_table) + (dst_positive_column_lookup_slicesource_table))) /\ (((((exists ff_h_pvs_column_lookup_slicesource_tableentrynegative. ff_h_pvs_column_lookup_slicesource_tableentrynegative + S (dst_negative_column_lookup_slicesource_table) = S ((S (dst_index_column_lookup_slicesource_table)) * dst_negative_scale_column_lookup_slicesource_table)) /\ exists ff_q_pvs_column_lookup_slicesource_tableentrynegative. dst_negative_code_column_lookup_slicesource_table = ff_q_pvs_column_lookup_slicesource_tableentrynegative * S ((S (dst_index_column_lookup_slicesource_table)) * dst_negative_scale_column_lookup_slicesource_table) + (dst_negative_column_lookup_slicesource_table))) /\ (exists ge_balance_positive_column_lookup_slicesource_tableentryvalue ge_balance_negative_column_lookup_slicesource_tableentryvalue. (((((dst_value_column_lookup_slicesource_table) = 2 * (ge_balance_positive_column_lookup_slicesource_tableentryvalue) /\ (ge_balance_negative_column_lookup_slicesource_tableentryvalue) = 0) \/ exists ge_signed_half_column_lookup_slicesource_tableentryvaluedecode. (((dst_value_column_lookup_slicesource_table) = 2 * ge_signed_half_column_lookup_slicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_lookup_slicesource_tableentryvalue) = 0) /\ (ge_balance_negative_column_lookup_slicesource_tableentryvalue) = S ge_signed_half_column_lookup_slicesource_tableentryvaluedecode))) /\ ((dst_positive_column_lookup_slicesource_table) + ge_balance_negative_column_lookup_slicesource_tableentryvalue = (dst_negative_column_lookup_slicesource_table) + ge_balance_positive_column_lookup_slicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_column_lookup_sliceoutput_table dst_positive_scale_column_lookup_sliceoutput_table dst_negative_code_column_lookup_sliceoutput_table dst_negative_scale_column_lookup_sliceoutput_table. (((V) = (((((dst_positive_code_column_lookup_sliceoutput_table) + (dst_positive_scale_column_lookup_sliceoutput_table)) * S ((dst_positive_code_column_lookup_sliceoutput_table) + (dst_positive_scale_column_lookup_sliceoutput_table)) + ((dst_positive_scale_column_lookup_sliceoutput_table) + (dst_positive_scale_column_lookup_sliceoutput_table))) + (((dst_negative_code_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)) * S ((dst_negative_code_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)) + ((dst_negative_scale_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)))) * S ((((dst_positive_code_column_lookup_sliceoutput_table) + (dst_positive_scale_column_lookup_sliceoutput_table)) * S ((dst_positive_code_column_lookup_sliceoutput_table) + (dst_positive_scale_column_lookup_sliceoutput_table)) + ((dst_positive_scale_column_lookup_sliceoutput_table) + (dst_positive_scale_column_lookup_sliceoutput_table))) + (((dst_negative_code_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)) * S ((dst_negative_code_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)) + ((dst_negative_scale_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)))) + ((((dst_negative_code_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)) * S ((dst_negative_code_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)) + ((dst_negative_scale_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table))) + (((dst_negative_code_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)) * S ((dst_negative_code_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)) + ((dst_negative_scale_column_lookup_sliceoutput_table) + (dst_negative_scale_column_lookup_sliceoutput_table)))))) /\ (forall dst_index_column_lookup_sliceoutput_table. (exists pvs_le_gap_column_lookup_sliceoutput_tabledomain. pvs_le_gap_column_lookup_sliceoutput_tabledomain + (dst_index_column_lookup_sliceoutput_table) = (L)) -> exists dst_positive_column_lookup_sliceoutput_table dst_negative_column_lookup_sliceoutput_table dst_value_column_lookup_sliceoutput_table. ((((exists ff_h_pvs_column_lookup_sliceoutput_tableentrypositive. ff_h_pvs_column_lookup_sliceoutput_tableentrypositive + S (dst_positive_column_lookup_sliceoutput_table) = S ((S (dst_index_column_lookup_sliceoutput_table)) * dst_positive_scale_column_lookup_sliceoutput_table)) /\ exists ff_q_pvs_column_lookup_sliceoutput_tableentrypositive. dst_positive_code_column_lookup_sliceoutput_table = ff_q_pvs_column_lookup_sliceoutput_tableentrypositive * S ((S (dst_index_column_lookup_sliceoutput_table)) * dst_positive_scale_column_lookup_sliceoutput_table) + (dst_positive_column_lookup_sliceoutput_table))) /\ (((((exists ff_h_pvs_column_lookup_sliceoutput_tableentrynegative. ff_h_pvs_column_lookup_sliceoutput_tableentrynegative + S (dst_negative_column_lookup_sliceoutput_table) = S ((S (dst_index_column_lookup_sliceoutput_table)) * dst_negative_scale_column_lookup_sliceoutput_table)) /\ exists ff_q_pvs_column_lookup_sliceoutput_tableentrynegative. dst_negative_code_column_lookup_sliceoutput_table = ff_q_pvs_column_lookup_sliceoutput_tableentrynegative * S ((S (dst_index_column_lookup_sliceoutput_table)) * dst_negative_scale_column_lookup_sliceoutput_table) + (dst_negative_column_lookup_sliceoutput_table))) /\ (exists ge_balance_positive_column_lookup_sliceoutput_tableentryvalue ge_balance_negative_column_lookup_sliceoutput_tableentryvalue. (((((dst_value_column_lookup_sliceoutput_table) = 2 * (ge_balance_positive_column_lookup_sliceoutput_tableentryvalue) /\ (ge_balance_negative_column_lookup_sliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_column_lookup_sliceoutput_tableentryvaluedecode. (((dst_value_column_lookup_sliceoutput_table) = 2 * ge_signed_half_column_lookup_sliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_column_lookup_sliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_column_lookup_sliceoutput_tableentryvalue) = S ge_signed_half_column_lookup_sliceoutput_tableentryvaluedecode))) /\ ((dst_positive_column_lookup_sliceoutput_table) + ge_balance_negative_column_lookup_sliceoutput_tableentryvalue = (dst_negative_column_lookup_sliceoutput_table) + ge_balance_positive_column_lookup_sliceoutput_tableentryvalue))))))))) /\ (forall srs_index_column_lookup_slice. (exists pvs_gap_column_lookup_slicebound. pvs_gap_column_lookup_slicebound + S (srs_index_column_lookup_slice) = (L)) -> exists srs_value_column_lookup_slice. (((exists dst_positive_code_column_lookup_sliceentrysource dst_positive_scale_column_lookup_sliceentrysource dst_negative_code_column_lookup_sliceentrysource dst_negative_scale_column_lookup_sliceentrysource dst_positive_column_lookup_sliceentrysource dst_negative_column_lookup_sliceentrysource. (((T) = (((((dst_positive_code_column_lookup_sliceentrysource) + (dst_positive_scale_column_lookup_sliceentrysource)) * S ((dst_positive_code_column_lookup_sliceentrysource) + (dst_positive_scale_column_lookup_sliceentrysource)) + ((dst_positive_scale_column_lookup_sliceentrysource) + (dst_positive_scale_column_lookup_sliceentrysource))) + (((dst_negative_code_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)) * S ((dst_negative_code_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)) + ((dst_negative_scale_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)))) * S ((((dst_positive_code_column_lookup_sliceentrysource) + (dst_positive_scale_column_lookup_sliceentrysource)) * S ((dst_positive_code_column_lookup_sliceentrysource) + (dst_positive_scale_column_lookup_sliceentrysource)) + ((dst_positive_scale_column_lookup_sliceentrysource) + (dst_positive_scale_column_lookup_sliceentrysource))) + (((dst_negative_code_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)) * S ((dst_negative_code_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)) + ((dst_negative_scale_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)))) + ((((dst_negative_code_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)) * S ((dst_negative_code_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)) + ((dst_negative_scale_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource))) + (((dst_negative_code_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)) * S ((dst_negative_code_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)) + ((dst_negative_scale_column_lookup_sliceentrysource) + (dst_negative_scale_column_lookup_sliceentrysource)))))) /\ (((((exists ff_h_pvs_column_lookup_sliceentrysourcepositive. ff_h_pvs_column_lookup_sliceentrysourcepositive + S (dst_positive_column_lookup_sliceentrysource) = S ((S (((((0) + ((1) * (j)))) + ((S M) * (srs_index_column_lookup_slice))))) * dst_positive_scale_column_lookup_sliceentrysource)) /\ exists ff_q_pvs_column_lookup_sliceentrysourcepositive. dst_positive_code_column_lookup_sliceentrysource = ff_q_pvs_column_lookup_sliceentrysourcepositive * S ((S (((((0) + ((1) * (j)))) + ((S M) * (srs_index_column_lookup_slice))))) * dst_positive_scale_column_lookup_sliceentrysource) + (dst_positive_column_lookup_sliceentrysource))) /\ (((((exists ff_h_pvs_column_lookup_sliceentrysourcenegative. ff_h_pvs_column_lookup_sliceentrysourcenegative + S (dst_negative_column_lookup_sliceentrysource) = S ((S (((((0) + ((1) * (j)))) + ((S M) * (srs_index_column_lookup_slice))))) * dst_negative_scale_column_lookup_sliceentrysource)) /\ exists ff_q_pvs_column_lookup_sliceentrysourcenegative. dst_negative_code_column_lookup_sliceentrysource = ff_q_pvs_column_lookup_sliceentrysourcenegative * S ((S (((((0) + ((1) * (j)))) + ((S M) * (srs_index_column_lookup_slice))))) * dst_negative_scale_column_lookup_sliceentrysource) + (dst_negative_column_lookup_sliceentrysource))) /\ (exists ge_balance_positive_column_lookup_sliceentrysourcevalue ge_balance_negative_column_lookup_sliceentrysourcevalue. (((((srs_value_column_lookup_slice) = 2 * (ge_balance_positive_column_lookup_sliceentrysourcevalue) /\ (ge_balance_negative_column_lookup_sliceentrysourcevalue) = 0) \/ exists ge_signed_half_column_lookup_sliceentrysourcevaluedecode. (((srs_value_column_lookup_slice) = 2 * ge_signed_half_column_lookup_sliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_column_lookup_sliceentrysourcevalue) = 0) /\ (ge_balance_negative_column_lookup_sliceentrysourcevalue) = S ge_signed_half_column_lookup_sliceentrysourcevaluedecode))) /\ ((dst_positive_column_lookup_sliceentrysource) + ge_balance_negative_column_lookup_sliceentrysourcevalue = (dst_negative_column_lookup_sliceentrysource) + ge_balance_positive_column_lookup_sliceentrysourcevalue))))))))) /\ (exists dst_positive_code_column_lookup_sliceentryoutput dst_positive_scale_column_lookup_sliceentryoutput dst_negative_code_column_lookup_sliceentryoutput dst_negative_scale_column_lookup_sliceentryoutput dst_positive_column_lookup_sliceentryoutput dst_negative_column_lookup_sliceentryoutput. (((V) = (((((dst_positive_code_column_lookup_sliceentryoutput) + (dst_positive_scale_column_lookup_sliceentryoutput)) * S ((dst_positive_code_column_lookup_sliceentryoutput) + (dst_positive_scale_column_lookup_sliceentryoutput)) + ((dst_positive_scale_column_lookup_sliceentryoutput) + (dst_positive_scale_column_lookup_sliceentryoutput))) + (((dst_negative_code_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)) * S ((dst_negative_code_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)) + ((dst_negative_scale_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)))) * S ((((dst_positive_code_column_lookup_sliceentryoutput) + (dst_positive_scale_column_lookup_sliceentryoutput)) * S ((dst_positive_code_column_lookup_sliceentryoutput) + (dst_positive_scale_column_lookup_sliceentryoutput)) + ((dst_positive_scale_column_lookup_sliceentryoutput) + (dst_positive_scale_column_lookup_sliceentryoutput))) + (((dst_negative_code_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)) * S ((dst_negative_code_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)) + ((dst_negative_scale_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)))) + ((((dst_negative_code_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)) * S ((dst_negative_code_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)) + ((dst_negative_scale_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput))) + (((dst_negative_code_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)) * S ((dst_negative_code_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)) + ((dst_negative_scale_column_lookup_sliceentryoutput) + (dst_negative_scale_column_lookup_sliceentryoutput)))))) /\ (((((exists ff_h_pvs_column_lookup_sliceentryoutputpositive. ff_h_pvs_column_lookup_sliceentryoutputpositive + S (dst_positive_column_lookup_sliceentryoutput) = S ((S (srs_index_column_lookup_slice)) * dst_positive_scale_column_lookup_sliceentryoutput)) /\ exists ff_q_pvs_column_lookup_sliceentryoutputpositive. dst_positive_code_column_lookup_sliceentryoutput = ff_q_pvs_column_lookup_sliceentryoutputpositive * S ((S (srs_index_column_lookup_slice)) * dst_positive_scale_column_lookup_sliceentryoutput) + (dst_positive_column_lookup_sliceentryoutput))) /\ (((((exists ff_h_pvs_column_lookup_sliceentryoutputnegative. ff_h_pvs_column_lookup_sliceentryoutputnegative + S (dst_negative_column_lookup_sliceentryoutput) = S ((S (srs_index_column_lookup_slice)) * dst_negative_scale_column_lookup_sliceentryoutput)) /\ exists ff_q_pvs_column_lookup_sliceentryoutputnegative. dst_negative_code_column_lookup_sliceentryoutput = ff_q_pvs_column_lookup_sliceentryoutputnegative * S ((S (srs_index_column_lookup_slice)) * dst_negative_scale_column_lookup_sliceentryoutput) + (dst_negative_column_lookup_sliceentryoutput))) /\ (exists ge_balance_positive_column_lookup_sliceentryoutputvalue ge_balance_negative_column_lookup_sliceentryoutputvalue. (((((srs_value_column_lookup_slice) = 2 * (ge_balance_positive_column_lookup_sliceentryoutputvalue) /\ (ge_balance_negative_column_lookup_sliceentryoutputvalue) = 0) \/ exists ge_signed_half_column_lookup_sliceentryoutputvaluedecode. (((srs_value_column_lookup_slice) = 2 * ge_signed_half_column_lookup_sliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_column_lookup_sliceentryoutputvalue) = 0) /\ (ge_balance_negative_column_lookup_sliceentryoutputvalue) = S ge_signed_half_column_lookup_sliceentryoutputvaluedecode))) /\ ((dst_positive_column_lookup_sliceentryoutput) + ge_balance_negative_column_lookup_sliceentryoutputvalue = (dst_negative_column_lookup_sliceentryoutput) + ge_balance_positive_column_lookup_sliceentryoutputvalue)))))))))))))))) -> (exists pvs_gap_column_lookup_row. pvs_gap_column_lookup_row + S (i) = (L)) -> (exists pvs_gap_column_lookup_bound. pvs_gap_column_lookup_bound + S (j) = (M)) -> (exists dst_positive_code_column_lookup_value dst_positive_scale_column_lookup_value dst_negative_code_column_lookup_value dst_negative_scale_column_lookup_value dst_positive_column_lookup_value dst_negative_column_lookup_value. (((V) = (((((dst_positive_code_column_lookup_value) + (dst_positive_scale_column_lookup_value)) * S ((dst_positive_code_column_lookup_value) + (dst_positive_scale_column_lookup_value)) + ((dst_positive_scale_column_lookup_value) + (dst_positive_scale_column_lookup_value))) + (((dst_negative_code_column_lookup_value) + (dst_negative_scale_column_lookup_value)) * S ((dst_negative_code_column_lookup_value) + (dst_negative_scale_column_lookup_value)) + ((dst_negative_scale_column_lookup_value) + (dst_negative_scale_column_lookup_value)))) * S ((((dst_positive_code_column_lookup_value) + (dst_positive_scale_column_lookup_value)) * S ((dst_positive_code_column_lookup_value) + (dst_positive_scale_column_lookup_value)) + ((dst_positive_scale_column_lookup_value) + (dst_positive_scale_column_lookup_value))) + (((dst_negative_code_column_lookup_value) + (dst_negative_scale_column_lookup_value)) * S ((dst_negative_code_column_lookup_value) + (dst_negative_scale_column_lookup_value)) + ((dst_negative_scale_column_lookup_value) + (dst_negative_scale_column_lookup_value)))) + ((((dst_negative_code_column_lookup_value) + (dst_negative_scale_column_lookup_value)) * S ((dst_negative_code_column_lookup_value) + (dst_negative_scale_column_lookup_value)) + ((dst_negative_scale_column_lookup_value) + (dst_negative_scale_column_lookup_value))) + (((dst_negative_code_column_lookup_value) + (dst_negative_scale_column_lookup_value)) * S ((dst_negative_code_column_lookup_value) + (dst_negative_scale_column_lookup_value)) + ((dst_negative_scale_column_lookup_value) + (dst_negative_scale_column_lookup_value)))))) /\ (((((exists ff_h_pvs_column_lookup_valuepositive. ff_h_pvs_column_lookup_valuepositive + S (dst_positive_column_lookup_value) = S ((S (i)) * dst_positive_scale_column_lookup_value)) /\ exists ff_q_pvs_column_lookup_valuepositive. dst_positive_code_column_lookup_value = ff_q_pvs_column_lookup_valuepositive * S ((S (i)) * dst_positive_scale_column_lookup_value) + (dst_positive_column_lookup_value))) /\ (((((exists ff_h_pvs_column_lookup_valuenegative. ff_h_pvs_column_lookup_valuenegative + S (dst_negative_column_lookup_value) = S ((S (i)) * dst_negative_scale_column_lookup_value)) /\ exists ff_q_pvs_column_lookup_valuenegative. dst_negative_code_column_lookup_value = ff_q_pvs_column_lookup_valuenegative * S ((S (i)) * dst_negative_scale_column_lookup_value) + (dst_negative_column_lookup_value))) /\ (exists ge_balance_positive_column_lookup_valuevalue ge_balance_negative_column_lookup_valuevalue. (((((z) = 2 * (ge_balance_positive_column_lookup_valuevalue) /\ (ge_balance_negative_column_lookup_valuevalue) = 0) \/ exists ge_signed_half_column_lookup_valuevaluedecode. (((z) = 2 * ge_signed_half_column_lookup_valuevaluedecode + 1 /\ (ge_balance_positive_column_lookup_valuevalue) = 0) /\ (ge_balance_negative_column_lookup_valuevalue) = S ge_signed_half_column_lookup_valuevaluedecode))) /\ ((dst_positive_column_lookup_value) + ge_balance_negative_column_lookup_valuevalue = (dst_negative_column_lookup_value) + ge_balance_positive_column_lookup_valuevalue))))))))) -> (exists ssr_entry_value_column_lookup_entry ssr_entry_image_column_lookup_entry. ((exists dst_positive_code_column_lookup_entrysource dst_positive_scale_column_lookup_entrysource dst_negative_code_column_lookup_entrysource dst_negative_scale_column_lookup_entrysource dst_positive_column_lookup_entrysource dst_negative_column_lookup_entrysource. (((A) = (((((dst_positive_code_column_lookup_entrysource) + (dst_positive_scale_column_lookup_entrysource)) * S ((dst_positive_code_column_lookup_entrysource) + (dst_positive_scale_column_lookup_entrysource)) + ((dst_positive_scale_column_lookup_entrysource) + (dst_positive_scale_column_lookup_entrysource))) + (((dst_negative_code_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)) * S ((dst_negative_code_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)) + ((dst_negative_scale_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)))) * S ((((dst_positive_code_column_lookup_entrysource) + (dst_positive_scale_column_lookup_entrysource)) * S ((dst_positive_code_column_lookup_entrysource) + (dst_positive_scale_column_lookup_entrysource)) + ((dst_positive_scale_column_lookup_entrysource) + (dst_positive_scale_column_lookup_entrysource))) + (((dst_negative_code_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)) * S ((dst_negative_code_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)) + ((dst_negative_scale_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)))) + ((((dst_negative_code_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)) * S ((dst_negative_code_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)) + ((dst_negative_scale_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource))) + (((dst_negative_code_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)) * S ((dst_negative_code_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)) + ((dst_negative_scale_column_lookup_entrysource) + (dst_negative_scale_column_lookup_entrysource)))))) /\ (((((exists ff_h_pvs_column_lookup_entrysourcepositive. ff_h_pvs_column_lookup_entrysourcepositive + S (dst_positive_column_lookup_entrysource) = S ((S (i)) * dst_positive_scale_column_lookup_entrysource)) /\ exists ff_q_pvs_column_lookup_entrysourcepositive. dst_positive_code_column_lookup_entrysource = ff_q_pvs_column_lookup_entrysourcepositive * S ((S (i)) * dst_positive_scale_column_lookup_entrysource) + (dst_positive_column_lookup_entrysource))) /\ (((((exists ff_h_pvs_column_lookup_entrysourcenegative. ff_h_pvs_column_lookup_entrysourcenegative + S (dst_negative_column_lookup_entrysource) = S ((S (i)) * dst_negative_scale_column_lookup_entrysource)) /\ exists ff_q_pvs_column_lookup_entrysourcenegative. dst_negative_code_column_lookup_entrysource = ff_q_pvs_column_lookup_entrysourcenegative * S ((S (i)) * dst_negative_scale_column_lookup_entrysource) + (dst_negative_column_lookup_entrysource))) /\ (exists ge_balance_positive_column_lookup_entrysourcevalue ge_balance_negative_column_lookup_entrysourcevalue. (((((ssr_entry_value_column_lookup_entry) = 2 * (ge_balance_positive_column_lookup_entrysourcevalue) /\ (ge_balance_negative_column_lookup_entrysourcevalue) = 0) \/ exists ge_signed_half_column_lookup_entrysourcevaluedecode. (((ssr_entry_value_column_lookup_entry) = 2 * ge_signed_half_column_lookup_entrysourcevaluedecode + 1 /\ (ge_balance_positive_column_lookup_entrysourcevalue) = 0) /\ (ge_balance_negative_column_lookup_entrysourcevalue) = S ge_signed_half_column_lookup_entrysourcevaluedecode))) /\ ((dst_positive_column_lookup_entrysource) + ge_balance_negative_column_lookup_entrysourcevalue = (dst_negative_column_lookup_entrysource) + ge_balance_positive_column_lookup_entrysourcevalue))))))))) /\ (((((exists ff_h_pvs_column_lookup_entrymap. ff_h_pvs_column_lookup_entrymap + S (ssr_entry_image_column_lookup_entry) = S ((S (i)) * s)) /\ exists ff_q_pvs_column_lookup_entrymap. r = ff_q_pvs_column_lookup_entrymap * S ((S (i)) * s) + (ssr_entry_image_column_lookup_entry))) /\ (((((j)=(ssr_entry_image_column_lookup_entry)) /\ ((z)=(ssr_entry_value_column_lookup_entry)))) \/ (((~((j)=(ssr_entry_image_column_lookup_entry))) /\ ((z)=0))))))))Constructive proof overview
Generated structural guide
An actual affine column-slice entry is the same incidence cell after proved natural index commutation.
The unchanged tactic script uses 4 declared prerequisites and contains 46 exact native proof lines.
Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
signed_rectangular_slice_lookup Alpha theorem; checked-use authorized zero_add Stable theorem; checked-use authorized one_mul Stable theorem; checked-use authorized add_comm Stable theorem; checked-use authorizedDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–15
03Separate the logical casesL16–17
04Use earlier factsL18–23
05Establish hsL24–33
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed rectangular slice lookup.
- L24
have hs : ArithAt(T,0 + 1 · j + S M · i,z)Definitions: ArithAt - L25
specialize signed_rectangular_slice_lookup (T) - L26
specialize signed_rectangular_slice_lookup (V) - L27
specialize signed_rectangular_slice_lookup (((0) + ((1) * (j)))) - L28
specialize signed_rectangular_slice_lookup (S M) - L29
specialize signed_rectangular_slice_lookup (L) - L30
specialize signed_rectangular_slice_lookup (i) - L31
specialize signed_rectangular_slice_lookup (z) - L32
apply signed_rectangular_slice_lookup - L33
exact hv
06Use earlier factsL34–35
07Establish heL36–45
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply add comm.
08Use earlier factsL46–46
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L46
exact hs
Original exact command ledger · 46 lines
- 0001
intro A - 0002
intro r - 0003
intro s - 0004
intro L - 0005
intro M - 0006
intro T - 0007
intro V - 0008
intro i - 0009
intro j - 0010
intro z - 0011
intro hg - 0012
intro hv - 0013
intro hi - 0014
intro hj - 0015
intro hz - 0016
cases hg - 0017
cases hg_right - 0018
specialize hg_right_right (i) - 0019
specialize hg_right_right (j) - 0020
specialize hg_right_right (z) - 0021
apply hg_right_right - 0022
exact hi - 0023
exact hj - 0024
have hs : exists dst_positive_code_column_actual_source dst_positive_scale_column_actual_source dst_negative_code_column_actual_source dst_negative_scale_column_actual_source dst_positive_column_actual_source dst_negative_column_actual_source. (((T) = (((((dst_positive_code_column_actual_source) + (dst_positive_scale_column_actual_source)) * S ((dst_positive_code_column_actual_source) + (dst_positive_scale_column_actual_source)) + ((dst_positive_scale_column_actual_source) + (dst_positive_scale_column_actual_source))) + (((dst_negative_code_column_actual_source) + (dst_negative_scale_column_actual_source)) * S ((dst_negative_code_column_actual_source) + (dst_negative_scale_column_actual_source)) + ((dst_negative_scale_column_actual_source) + (dst_negative_scale_column_actual_source)))) * S ((((dst_positive_code_column_actual_source) + (dst_positive_scale_column_actual_source)) * S ((dst_positive_code_column_actual_source) + (dst_positive_scale_column_actual_source)) + ((dst_positive_scale_column_actual_source) + (dst_positive_scale_column_actual_source))) + (((dst_negative_code_column_actual_source) + (dst_negative_scale_column_actual_source)) * S ((dst_negative_code_column_actual_source) + (dst_negative_scale_column_actual_source)) + ((dst_negative_scale_column_actual_source) + (dst_negative_scale_column_actual_source)))) + ((((dst_negative_code_column_actual_source) + (dst_negative_scale_column_actual_source)) * S ((dst_negative_code_column_actual_source) + (dst_negative_scale_column_actual_source)) + ((dst_negative_scale_column_actual_source) + (dst_negative_scale_column_actual_source))) + (((dst_negative_code_column_actual_source) + (dst_negative_scale_column_actual_source)) * S ((dst_negative_code_column_actual_source) + (dst_negative_scale_column_actual_source)) + ((dst_negative_scale_column_actual_source) + (dst_negative_scale_column_actual_source)))))) /\ (((((exists ff_h_pvs_column_actual_sourcepositive. ff_h_pvs_column_actual_sourcepositive + S (dst_positive_column_actual_source) = S ((S (((((0) + ((1) * (j)))) + ((S M) * (i))))) * dst_positive_scale_column_actual_source)) /\ exists ff_q_pvs_column_actual_sourcepositive. dst_positive_code_column_actual_source = ff_q_pvs_column_actual_sourcepositive * S ((S (((((0) + ((1) * (j)))) + ((S M) * (i))))) * dst_positive_scale_column_actual_source) + (dst_positive_column_actual_source))) /\ (((((exists ff_h_pvs_column_actual_sourcenegative. ff_h_pvs_column_actual_sourcenegative + S (dst_negative_column_actual_source) = S ((S (((((0) + ((1) * (j)))) + ((S M) * (i))))) * dst_negative_scale_column_actual_source)) /\ exists ff_q_pvs_column_actual_sourcenegative. dst_negative_code_column_actual_source = ff_q_pvs_column_actual_sourcenegative * S ((S (((((0) + ((1) * (j)))) + ((S M) * (i))))) * dst_negative_scale_column_actual_source) + (dst_negative_column_actual_source))) /\ (exists ge_balance_positive_column_actual_sourcevalue ge_balance_negative_column_actual_sourcevalue. (((((z) = 2 * (ge_balance_positive_column_actual_sourcevalue) /\ (ge_balance_negative_column_actual_sourcevalue) = 0) \/ exists ge_signed_half_column_actual_sourcevaluedecode. (((z) = 2 * ge_signed_half_column_actual_sourcevaluedecode + 1 /\ (ge_balance_positive_column_actual_sourcevalue) = 0) /\ (ge_balance_negative_column_actual_sourcevalue) = S ge_signed_half_column_actual_sourcevaluedecode))) /\ ((dst_positive_column_actual_source) + ge_balance_negative_column_actual_sourcevalue = (dst_negative_column_actual_source) + ge_balance_positive_column_actual_sourcevalue)))))))) - 0025
specialize signed_rectangular_slice_lookup (T) - 0026
specialize signed_rectangular_slice_lookup (V) - 0027
specialize signed_rectangular_slice_lookup (((0) + ((1) * (j)))) - 0028
specialize signed_rectangular_slice_lookup (S M) - 0029
specialize signed_rectangular_slice_lookup (L) - 0030
specialize signed_rectangular_slice_lookup (i) - 0031
specialize signed_rectangular_slice_lookup (z) - 0032
apply signed_rectangular_slice_lookup - 0033
exact hv - 0034
exact hi - 0035
exact hz - 0036
have he : ((((0) + ((1) * (j)))) + ((S M) * (i)))=((S (M))*(i)+(j)) - 0037
specialize zero_add (1*j) - 0038
rewrite zero_add - 0039
specialize one_mul (j) - 0040
rewrite one_mul - 0041
apply add_comm - 0042
rewrite he at hs - 0043
rewrite he at hs - 0044
rewrite he at hs - 0045
rewrite he at hs - 0046
exact hs