DF0015

dirichlet_grid_row_slice

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

An actual row slice supplies the exact factor-row values; every affine coordinate is transported by a proved natural equality.

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 n T a V. (((exists dst_positive_code_dirichlet_grid_row_slice_gridtable dst_positive_scale_dirichlet_grid_row_slice_gridtable dst_negative_code_dirichlet_grid_row_slice_gridtable dst_negative_scale_dirichlet_grid_row_slice_gridtable. (((T) = (((((dst_positive_code_dirichlet_grid_row_slice_gridtable) + (dst_positive_scale_dirichlet_grid_row_slice_gridtable)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridtable) + (dst_positive_scale_dirichlet_grid_row_slice_gridtable)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridtable) + (dst_positive_scale_dirichlet_grid_row_slice_gridtable))) + (((dst_negative_code_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_gridtable) + (dst_positive_scale_dirichlet_grid_row_slice_gridtable)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridtable) + (dst_positive_scale_dirichlet_grid_row_slice_gridtable)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridtable) + (dst_positive_scale_dirichlet_grid_row_slice_gridtable))) + (((dst_negative_code_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)))) + ((((dst_negative_code_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable))) + (((dst_negative_code_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridtable) + (dst_negative_scale_dirichlet_grid_row_slice_gridtable)))))) /\ (forall dst_index_dirichlet_grid_row_slice_gridtable. (exists pvs_le_gap_dirichlet_grid_row_slice_gridtabledomain. pvs_le_gap_dirichlet_grid_row_slice_gridtabledomain + (dst_index_dirichlet_grid_row_slice_gridtable) = ((S (n))*(S (n)))) -> exists dst_positive_dirichlet_grid_row_slice_gridtable dst_negative_dirichlet_grid_row_slice_gridtable dst_value_dirichlet_grid_row_slice_gridtable. ((((exists ff_h_pvs_dirichlet_grid_row_slice_gridtableentrypositive. ff_h_pvs_dirichlet_grid_row_slice_gridtableentrypositive + S (dst_positive_dirichlet_grid_row_slice_gridtable) = S ((S (dst_index_dirichlet_grid_row_slice_gridtable)) * dst_positive_scale_dirichlet_grid_row_slice_gridtable)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridtableentrypositive. dst_positive_code_dirichlet_grid_row_slice_gridtable = ff_q_pvs_dirichlet_grid_row_slice_gridtableentrypositive * S ((S (dst_index_dirichlet_grid_row_slice_gridtable)) * dst_positive_scale_dirichlet_grid_row_slice_gridtable) + (dst_positive_dirichlet_grid_row_slice_gridtable))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_gridtableentrynegative. ff_h_pvs_dirichlet_grid_row_slice_gridtableentrynegative + S (dst_negative_dirichlet_grid_row_slice_gridtable) = S ((S (dst_index_dirichlet_grid_row_slice_gridtable)) * dst_negative_scale_dirichlet_grid_row_slice_gridtable)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridtableentrynegative. dst_negative_code_dirichlet_grid_row_slice_gridtable = ff_q_pvs_dirichlet_grid_row_slice_gridtableentrynegative * S ((S (dst_index_dirichlet_grid_row_slice_gridtable)) * dst_negative_scale_dirichlet_grid_row_slice_gridtable) + (dst_negative_dirichlet_grid_row_slice_gridtable))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_gridtableentryvalue ge_balance_negative_dirichlet_grid_row_slice_gridtableentryvalue. (((((dst_value_dirichlet_grid_row_slice_gridtable) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_gridtableentryvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridtableentryvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridtableentryvaluedecode. (((dst_value_dirichlet_grid_row_slice_gridtable) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridtableentryvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_gridtableentryvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridtableentryvalue) = S ge_signed_half_dirichlet_grid_row_slice_gridtableentryvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_gridtable) + ge_balance_negative_dirichlet_grid_row_slice_gridtableentryvalue = (dst_negative_dirichlet_grid_row_slice_gridtable) + ge_balance_positive_dirichlet_grid_row_slice_gridtableentryvalue))))))))) /\ (forall dfg_grid_row_dirichlet_grid_row_slice_grid dfg_grid_column_dirichlet_grid_row_slice_grid dfg_grid_value_dirichlet_grid_row_slice_grid. (exists pvs_le_gap_dirichlet_grid_row_slice_gridrow. pvs_le_gap_dirichlet_grid_row_slice_gridrow + (dfg_grid_row_dirichlet_grid_row_slice_grid) = (n)) -> (exists pvs_le_gap_dirichlet_grid_row_slice_gridcolumn. pvs_le_gap_dirichlet_grid_row_slice_gridcolumn + (dfg_grid_column_dirichlet_grid_row_slice_grid) = (n)) -> (exists dst_positive_code_dirichlet_grid_row_slice_gridlookup dst_positive_scale_dirichlet_grid_row_slice_gridlookup dst_negative_code_dirichlet_grid_row_slice_gridlookup dst_negative_scale_dirichlet_grid_row_slice_gridlookup dst_positive_dirichlet_grid_row_slice_gridlookup dst_negative_dirichlet_grid_row_slice_gridlookup. (((T) = (((((dst_positive_code_dirichlet_grid_row_slice_gridlookup) + (dst_positive_scale_dirichlet_grid_row_slice_gridlookup)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridlookup) + (dst_positive_scale_dirichlet_grid_row_slice_gridlookup)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridlookup) + (dst_positive_scale_dirichlet_grid_row_slice_gridlookup))) + (((dst_negative_code_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_gridlookup) + (dst_positive_scale_dirichlet_grid_row_slice_gridlookup)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridlookup) + (dst_positive_scale_dirichlet_grid_row_slice_gridlookup)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridlookup) + (dst_positive_scale_dirichlet_grid_row_slice_gridlookup))) + (((dst_negative_code_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)))) + ((((dst_negative_code_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup))) + (((dst_negative_code_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridlookup) + (dst_negative_scale_dirichlet_grid_row_slice_gridlookup)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_gridlookuppositive. ff_h_pvs_dirichlet_grid_row_slice_gridlookuppositive + S (dst_positive_dirichlet_grid_row_slice_gridlookup) = S ((S ((S (n))*(dfg_grid_row_dirichlet_grid_row_slice_grid)+(dfg_grid_column_dirichlet_grid_row_slice_grid))) * dst_positive_scale_dirichlet_grid_row_slice_gridlookup)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridlookuppositive. dst_positive_code_dirichlet_grid_row_slice_gridlookup = ff_q_pvs_dirichlet_grid_row_slice_gridlookuppositive * S ((S ((S (n))*(dfg_grid_row_dirichlet_grid_row_slice_grid)+(dfg_grid_column_dirichlet_grid_row_slice_grid))) * dst_positive_scale_dirichlet_grid_row_slice_gridlookup) + (dst_positive_dirichlet_grid_row_slice_gridlookup))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_gridlookupnegative. ff_h_pvs_dirichlet_grid_row_slice_gridlookupnegative + S (dst_negative_dirichlet_grid_row_slice_gridlookup) = S ((S ((S (n))*(dfg_grid_row_dirichlet_grid_row_slice_grid)+(dfg_grid_column_dirichlet_grid_row_slice_grid))) * dst_negative_scale_dirichlet_grid_row_slice_gridlookup)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridlookupnegative. dst_negative_code_dirichlet_grid_row_slice_gridlookup = ff_q_pvs_dirichlet_grid_row_slice_gridlookupnegative * S ((S ((S (n))*(dfg_grid_row_dirichlet_grid_row_slice_grid)+(dfg_grid_column_dirichlet_grid_row_slice_grid))) * dst_negative_scale_dirichlet_grid_row_slice_gridlookup) + (dst_negative_dirichlet_grid_row_slice_gridlookup))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_gridlookupvalue ge_balance_negative_dirichlet_grid_row_slice_gridlookupvalue. (((((dfg_grid_value_dirichlet_grid_row_slice_grid) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_gridlookupvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridlookupvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridlookupvaluedecode. (((dfg_grid_value_dirichlet_grid_row_slice_grid) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridlookupvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_gridlookupvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridlookupvalue) = S ge_signed_half_dirichlet_grid_row_slice_gridlookupvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_gridlookup) + ge_balance_negative_dirichlet_grid_row_slice_gridlookupvalue = (dst_negative_dirichlet_grid_row_slice_gridlookup) + ge_balance_positive_dirichlet_grid_row_slice_gridlookupvalue))))))))) -> ((((~((dfg_grid_row_dirichlet_grid_row_slice_grid)=0)) /\ (((~((dfg_grid_column_dirichlet_grid_row_slice_grid)=0)) /\ (exists dfg_middle_dirichlet_grid_row_slice_gridentry dfg_first_dirichlet_grid_row_slice_gridentry dfg_last_dirichlet_grid_row_slice_gridentry dfg_value_dirichlet_grid_row_slice_gridentry. (((n)=((dfg_grid_row_dirichlet_grid_row_slice_grid)*(dfg_grid_column_dirichlet_grid_row_slice_grid))*dfg_middle_dirichlet_grid_row_slice_gridentry) /\ (((exists dst_positive_code_dirichlet_grid_row_slice_gridentryfirst dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst dst_negative_code_dirichlet_grid_row_slice_gridentryfirst dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst dst_positive_dirichlet_grid_row_slice_gridentryfirst dst_negative_dirichlet_grid_row_slice_gridentryfirst. (((F) = (((((dst_positive_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst))) + (((dst_negative_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst))) + (((dst_negative_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)))) + ((((dst_negative_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst))) + (((dst_negative_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_gridentryfirstpositive. ff_h_pvs_dirichlet_grid_row_slice_gridentryfirstpositive + S (dst_positive_dirichlet_grid_row_slice_gridentryfirst) = S ((S (dfg_grid_row_dirichlet_grid_row_slice_grid)) * dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridentryfirstpositive. dst_positive_code_dirichlet_grid_row_slice_gridentryfirst = ff_q_pvs_dirichlet_grid_row_slice_gridentryfirstpositive * S ((S (dfg_grid_row_dirichlet_grid_row_slice_grid)) * dst_positive_scale_dirichlet_grid_row_slice_gridentryfirst) + (dst_positive_dirichlet_grid_row_slice_gridentryfirst))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_gridentryfirstnegative. ff_h_pvs_dirichlet_grid_row_slice_gridentryfirstnegative + S (dst_negative_dirichlet_grid_row_slice_gridentryfirst) = S ((S (dfg_grid_row_dirichlet_grid_row_slice_grid)) * dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridentryfirstnegative. dst_negative_code_dirichlet_grid_row_slice_gridentryfirst = ff_q_pvs_dirichlet_grid_row_slice_gridentryfirstnegative * S ((S (dfg_grid_row_dirichlet_grid_row_slice_grid)) * dst_negative_scale_dirichlet_grid_row_slice_gridentryfirst) + (dst_negative_dirichlet_grid_row_slice_gridentryfirst))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_gridentryfirstvalue ge_balance_negative_dirichlet_grid_row_slice_gridentryfirstvalue. (((((dfg_first_dirichlet_grid_row_slice_gridentry) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_gridentryfirstvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridentryfirstvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridentryfirstvaluedecode. (((dfg_first_dirichlet_grid_row_slice_gridentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridentryfirstvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_gridentryfirstvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridentryfirstvalue) = S ge_signed_half_dirichlet_grid_row_slice_gridentryfirstvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_gridentryfirst) + ge_balance_negative_dirichlet_grid_row_slice_gridentryfirstvalue = (dst_negative_dirichlet_grid_row_slice_gridentryfirst) + ge_balance_positive_dirichlet_grid_row_slice_gridentryfirstvalue))))))))) /\ (((exists dst_positive_code_dirichlet_grid_row_slice_gridentrylast dst_positive_scale_dirichlet_grid_row_slice_gridentrylast dst_negative_code_dirichlet_grid_row_slice_gridentrylast dst_negative_scale_dirichlet_grid_row_slice_gridentrylast dst_positive_dirichlet_grid_row_slice_gridentrylast dst_negative_dirichlet_grid_row_slice_gridentrylast. (((H) = (((((dst_positive_code_dirichlet_grid_row_slice_gridentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrylast)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrylast)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrylast))) + (((dst_negative_code_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_gridentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrylast)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrylast)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrylast))) + (((dst_negative_code_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)))) + ((((dst_negative_code_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast))) + (((dst_negative_code_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_gridentrylastpositive. ff_h_pvs_dirichlet_grid_row_slice_gridentrylastpositive + S (dst_positive_dirichlet_grid_row_slice_gridentrylast) = S ((S (dfg_grid_column_dirichlet_grid_row_slice_grid)) * dst_positive_scale_dirichlet_grid_row_slice_gridentrylast)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridentrylastpositive. dst_positive_code_dirichlet_grid_row_slice_gridentrylast = ff_q_pvs_dirichlet_grid_row_slice_gridentrylastpositive * S ((S (dfg_grid_column_dirichlet_grid_row_slice_grid)) * dst_positive_scale_dirichlet_grid_row_slice_gridentrylast) + (dst_positive_dirichlet_grid_row_slice_gridentrylast))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_gridentrylastnegative. ff_h_pvs_dirichlet_grid_row_slice_gridentrylastnegative + S (dst_negative_dirichlet_grid_row_slice_gridentrylast) = S ((S (dfg_grid_column_dirichlet_grid_row_slice_grid)) * dst_negative_scale_dirichlet_grid_row_slice_gridentrylast)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridentrylastnegative. dst_negative_code_dirichlet_grid_row_slice_gridentrylast = ff_q_pvs_dirichlet_grid_row_slice_gridentrylastnegative * S ((S (dfg_grid_column_dirichlet_grid_row_slice_grid)) * dst_negative_scale_dirichlet_grid_row_slice_gridentrylast) + (dst_negative_dirichlet_grid_row_slice_gridentrylast))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_gridentrylastvalue ge_balance_negative_dirichlet_grid_row_slice_gridentrylastvalue. (((((dfg_last_dirichlet_grid_row_slice_gridentry) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_gridentrylastvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridentrylastvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridentrylastvaluedecode. (((dfg_last_dirichlet_grid_row_slice_gridentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridentrylastvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_gridentrylastvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridentrylastvalue) = S ge_signed_half_dirichlet_grid_row_slice_gridentrylastvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_gridentrylast) + ge_balance_negative_dirichlet_grid_row_slice_gridentrylastvalue = (dst_negative_dirichlet_grid_row_slice_gridentrylast) + ge_balance_positive_dirichlet_grid_row_slice_gridentrylastvalue))))))))) /\ (((exists dst_positive_code_dirichlet_grid_row_slice_gridentrymiddle dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle dst_positive_dirichlet_grid_row_slice_gridentrymiddle dst_negative_dirichlet_grid_row_slice_gridentrymiddle. (((G) = (((((dst_positive_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle))) + (((dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle)) * S ((dst_positive_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle)) + ((dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle))) + (((dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)))) + ((((dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle))) + (((dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)) * S ((dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)) + ((dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_gridentrymiddlepositive. ff_h_pvs_dirichlet_grid_row_slice_gridentrymiddlepositive + S (dst_positive_dirichlet_grid_row_slice_gridentrymiddle) = S ((S (dfg_middle_dirichlet_grid_row_slice_gridentry)) * dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridentrymiddlepositive. dst_positive_code_dirichlet_grid_row_slice_gridentrymiddle = ff_q_pvs_dirichlet_grid_row_slice_gridentrymiddlepositive * S ((S (dfg_middle_dirichlet_grid_row_slice_gridentry)) * dst_positive_scale_dirichlet_grid_row_slice_gridentrymiddle) + (dst_positive_dirichlet_grid_row_slice_gridentrymiddle))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_gridentrymiddlenegative. ff_h_pvs_dirichlet_grid_row_slice_gridentrymiddlenegative + S (dst_negative_dirichlet_grid_row_slice_gridentrymiddle) = S ((S (dfg_middle_dirichlet_grid_row_slice_gridentry)) * dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_gridentrymiddlenegative. dst_negative_code_dirichlet_grid_row_slice_gridentrymiddle = ff_q_pvs_dirichlet_grid_row_slice_gridentrymiddlenegative * S ((S (dfg_middle_dirichlet_grid_row_slice_gridentry)) * dst_negative_scale_dirichlet_grid_row_slice_gridentrymiddle) + (dst_negative_dirichlet_grid_row_slice_gridentrymiddle))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_gridentrymiddlevalue ge_balance_negative_dirichlet_grid_row_slice_gridentrymiddlevalue. (((((dfg_value_dirichlet_grid_row_slice_gridentry) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_gridentrymiddlevalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridentrymiddlevalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridentrymiddlevaluedecode. (((dfg_value_dirichlet_grid_row_slice_gridentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridentrymiddlevaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_gridentrymiddlevalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_gridentrymiddlevalue) = S ge_signed_half_dirichlet_grid_row_slice_gridentrymiddlevaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_gridentrymiddle) + ge_balance_negative_dirichlet_grid_row_slice_gridentrymiddlevalue = (dst_negative_dirichlet_grid_row_slice_gridentrymiddle) + ge_balance_positive_dirichlet_grid_row_slice_gridentrymiddlevalue))))))))) /\ (exists dfg_inner_dirichlet_grid_row_slice_gridentryproduct. ((exists sto_ap_dirichlet_grid_row_slice_gridentryproductinner sto_an_dirichlet_grid_row_slice_gridentryproductinner sto_bp_dirichlet_grid_row_slice_gridentryproductinner sto_bn_dirichlet_grid_row_slice_gridentryproductinner sto_cp_dirichlet_grid_row_slice_gridentryproductinner sto_cn_dirichlet_grid_row_slice_gridentryproductinner. (((((dfg_last_dirichlet_grid_row_slice_gridentry) = 2 * (sto_ap_dirichlet_grid_row_slice_gridentryproductinner) /\ (sto_an_dirichlet_grid_row_slice_gridentryproductinner) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridentryproductinnerleft. (((dfg_last_dirichlet_grid_row_slice_gridentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridentryproductinnerleft + 1 /\ (sto_ap_dirichlet_grid_row_slice_gridentryproductinner) = 0) /\ (sto_an_dirichlet_grid_row_slice_gridentryproductinner) = S ge_signed_half_dirichlet_grid_row_slice_gridentryproductinnerleft))) /\ ((((((dfg_value_dirichlet_grid_row_slice_gridentry) = 2 * (sto_bp_dirichlet_grid_row_slice_gridentryproductinner) /\ (sto_bn_dirichlet_grid_row_slice_gridentryproductinner) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridentryproductinnerright. (((dfg_value_dirichlet_grid_row_slice_gridentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridentryproductinnerright + 1 /\ (sto_bp_dirichlet_grid_row_slice_gridentryproductinner) = 0) /\ (sto_bn_dirichlet_grid_row_slice_gridentryproductinner) = S ge_signed_half_dirichlet_grid_row_slice_gridentryproductinnerright))) /\ ((((((dfg_inner_dirichlet_grid_row_slice_gridentryproduct) = 2 * (sto_cp_dirichlet_grid_row_slice_gridentryproductinner) /\ (sto_cn_dirichlet_grid_row_slice_gridentryproductinner) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridentryproductinneroutput. (((dfg_inner_dirichlet_grid_row_slice_gridentryproduct) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridentryproductinneroutput + 1 /\ (sto_cp_dirichlet_grid_row_slice_gridentryproductinner) = 0) /\ (sto_cn_dirichlet_grid_row_slice_gridentryproductinner) = S ge_signed_half_dirichlet_grid_row_slice_gridentryproductinneroutput))) /\ ((sto_ap_dirichlet_grid_row_slice_gridentryproductinner * sto_bp_dirichlet_grid_row_slice_gridentryproductinner + sto_an_dirichlet_grid_row_slice_gridentryproductinner * sto_bn_dirichlet_grid_row_slice_gridentryproductinner) + sto_cn_dirichlet_grid_row_slice_gridentryproductinner = (sto_ap_dirichlet_grid_row_slice_gridentryproductinner * sto_bn_dirichlet_grid_row_slice_gridentryproductinner + sto_an_dirichlet_grid_row_slice_gridentryproductinner * sto_bp_dirichlet_grid_row_slice_gridentryproductinner) + sto_cp_dirichlet_grid_row_slice_gridentryproductinner))))))) /\ (exists sto_ap_dirichlet_grid_row_slice_gridentryproductouter sto_an_dirichlet_grid_row_slice_gridentryproductouter sto_bp_dirichlet_grid_row_slice_gridentryproductouter sto_bn_dirichlet_grid_row_slice_gridentryproductouter sto_cp_dirichlet_grid_row_slice_gridentryproductouter sto_cn_dirichlet_grid_row_slice_gridentryproductouter. (((((dfg_first_dirichlet_grid_row_slice_gridentry) = 2 * (sto_ap_dirichlet_grid_row_slice_gridentryproductouter) /\ (sto_an_dirichlet_grid_row_slice_gridentryproductouter) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridentryproductouterleft. (((dfg_first_dirichlet_grid_row_slice_gridentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridentryproductouterleft + 1 /\ (sto_ap_dirichlet_grid_row_slice_gridentryproductouter) = 0) /\ (sto_an_dirichlet_grid_row_slice_gridentryproductouter) = S ge_signed_half_dirichlet_grid_row_slice_gridentryproductouterleft))) /\ ((((((dfg_inner_dirichlet_grid_row_slice_gridentryproduct) = 2 * (sto_bp_dirichlet_grid_row_slice_gridentryproductouter) /\ (sto_bn_dirichlet_grid_row_slice_gridentryproductouter) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridentryproductouterright. (((dfg_inner_dirichlet_grid_row_slice_gridentryproduct) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridentryproductouterright + 1 /\ (sto_bp_dirichlet_grid_row_slice_gridentryproductouter) = 0) /\ (sto_bn_dirichlet_grid_row_slice_gridentryproductouter) = S ge_signed_half_dirichlet_grid_row_slice_gridentryproductouterright))) /\ ((((((dfg_grid_value_dirichlet_grid_row_slice_grid) = 2 * (sto_cp_dirichlet_grid_row_slice_gridentryproductouter) /\ (sto_cn_dirichlet_grid_row_slice_gridentryproductouter) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_gridentryproductouteroutput. (((dfg_grid_value_dirichlet_grid_row_slice_grid) = 2 * ge_signed_half_dirichlet_grid_row_slice_gridentryproductouteroutput + 1 /\ (sto_cp_dirichlet_grid_row_slice_gridentryproductouter) = 0) /\ (sto_cn_dirichlet_grid_row_slice_gridentryproductouter) = S ge_signed_half_dirichlet_grid_row_slice_gridentryproductouteroutput))) /\ ((sto_ap_dirichlet_grid_row_slice_gridentryproductouter * sto_bp_dirichlet_grid_row_slice_gridentryproductouter + sto_an_dirichlet_grid_row_slice_gridentryproductouter * sto_bn_dirichlet_grid_row_slice_gridentryproductouter) + sto_cn_dirichlet_grid_row_slice_gridentryproductouter = (sto_ap_dirichlet_grid_row_slice_gridentryproductouter * sto_bn_dirichlet_grid_row_slice_gridentryproductouter + sto_an_dirichlet_grid_row_slice_gridentryproductouter * sto_bp_dirichlet_grid_row_slice_gridentryproductouter) + sto_cp_dirichlet_grid_row_slice_gridentryproductouter))))))))))))))))))))) \/ ((((dfg_grid_row_dirichlet_grid_row_slice_grid)=0 \/ ((dfg_grid_column_dirichlet_grid_row_slice_grid)=0 \/ ~(exists pvs_factor_dirichlet_grid_row_slice_gridentryomittednondivisor. (n) = ((dfg_grid_row_dirichlet_grid_row_slice_grid)*(dfg_grid_column_dirichlet_grid_row_slice_grid)) * pvs_factor_dirichlet_grid_row_slice_gridentryomittednondivisor))) /\ ((dfg_grid_value_dirichlet_grid_row_slice_grid)=0))))))) -> (exists pvs_le_gap_dirichlet_grid_row_slice_bound. pvs_le_gap_dirichlet_grid_row_slice_bound + (a) = (n)) -> (((exists dst_positive_code_dirichlet_grid_row_slice_slicesource_table dst_positive_scale_dirichlet_grid_row_slice_slicesource_table dst_negative_code_dirichlet_grid_row_slice_slicesource_table dst_negative_scale_dirichlet_grid_row_slice_slicesource_table. (((T) = (((((dst_positive_code_dirichlet_grid_row_slice_slicesource_table) + (dst_positive_scale_dirichlet_grid_row_slice_slicesource_table)) * S ((dst_positive_code_dirichlet_grid_row_slice_slicesource_table) + (dst_positive_scale_dirichlet_grid_row_slice_slicesource_table)) + ((dst_positive_scale_dirichlet_grid_row_slice_slicesource_table) + (dst_positive_scale_dirichlet_grid_row_slice_slicesource_table))) + (((dst_negative_code_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)) * S ((dst_negative_code_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)) + ((dst_negative_scale_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_slicesource_table) + (dst_positive_scale_dirichlet_grid_row_slice_slicesource_table)) * S ((dst_positive_code_dirichlet_grid_row_slice_slicesource_table) + (dst_positive_scale_dirichlet_grid_row_slice_slicesource_table)) + ((dst_positive_scale_dirichlet_grid_row_slice_slicesource_table) + (dst_positive_scale_dirichlet_grid_row_slice_slicesource_table))) + (((dst_negative_code_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)) * S ((dst_negative_code_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)) + ((dst_negative_scale_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)))) + ((((dst_negative_code_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)) * S ((dst_negative_code_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)) + ((dst_negative_scale_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table))) + (((dst_negative_code_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)) * S ((dst_negative_code_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)) + ((dst_negative_scale_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)))))) /\ (forall dst_index_dirichlet_grid_row_slice_slicesource_table. (exists pvs_le_gap_dirichlet_grid_row_slice_slicesource_tabledomain. pvs_le_gap_dirichlet_grid_row_slice_slicesource_tabledomain + (dst_index_dirichlet_grid_row_slice_slicesource_table) = (0)) -> exists dst_positive_dirichlet_grid_row_slice_slicesource_table dst_negative_dirichlet_grid_row_slice_slicesource_table dst_value_dirichlet_grid_row_slice_slicesource_table. ((((exists ff_h_pvs_dirichlet_grid_row_slice_slicesource_tableentrypositive. ff_h_pvs_dirichlet_grid_row_slice_slicesource_tableentrypositive + S (dst_positive_dirichlet_grid_row_slice_slicesource_table) = S ((S (dst_index_dirichlet_grid_row_slice_slicesource_table)) * dst_positive_scale_dirichlet_grid_row_slice_slicesource_table)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_slicesource_tableentrypositive. dst_positive_code_dirichlet_grid_row_slice_slicesource_table = ff_q_pvs_dirichlet_grid_row_slice_slicesource_tableentrypositive * S ((S (dst_index_dirichlet_grid_row_slice_slicesource_table)) * dst_positive_scale_dirichlet_grid_row_slice_slicesource_table) + (dst_positive_dirichlet_grid_row_slice_slicesource_table))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_slicesource_tableentrynegative. ff_h_pvs_dirichlet_grid_row_slice_slicesource_tableentrynegative + S (dst_negative_dirichlet_grid_row_slice_slicesource_table) = S ((S (dst_index_dirichlet_grid_row_slice_slicesource_table)) * dst_negative_scale_dirichlet_grid_row_slice_slicesource_table)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_slicesource_tableentrynegative. dst_negative_code_dirichlet_grid_row_slice_slicesource_table = ff_q_pvs_dirichlet_grid_row_slice_slicesource_tableentrynegative * S ((S (dst_index_dirichlet_grid_row_slice_slicesource_table)) * dst_negative_scale_dirichlet_grid_row_slice_slicesource_table) + (dst_negative_dirichlet_grid_row_slice_slicesource_table))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_slicesource_tableentryvalue ge_balance_negative_dirichlet_grid_row_slice_slicesource_tableentryvalue. (((((dst_value_dirichlet_grid_row_slice_slicesource_table) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_slicesource_tableentryvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_slicesource_tableentryvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_slicesource_tableentryvaluedecode. (((dst_value_dirichlet_grid_row_slice_slicesource_table) = 2 * ge_signed_half_dirichlet_grid_row_slice_slicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_slicesource_tableentryvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_slicesource_tableentryvalue) = S ge_signed_half_dirichlet_grid_row_slice_slicesource_tableentryvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_slicesource_table) + ge_balance_negative_dirichlet_grid_row_slice_slicesource_tableentryvalue = (dst_negative_dirichlet_grid_row_slice_slicesource_table) + ge_balance_positive_dirichlet_grid_row_slice_slicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_dirichlet_grid_row_slice_sliceoutput_table dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table. (((V) = (((((dst_positive_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table)) * S ((dst_positive_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table)) + ((dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table) + (dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table))) + (((dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table)) * S ((dst_positive_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table)) + ((dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table) + (dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table))) + (((dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)))) + ((((dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table))) + (((dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)))))) /\ (forall dst_index_dirichlet_grid_row_slice_sliceoutput_table. (exists pvs_le_gap_dirichlet_grid_row_slice_sliceoutput_tabledomain. pvs_le_gap_dirichlet_grid_row_slice_sliceoutput_tabledomain + (dst_index_dirichlet_grid_row_slice_sliceoutput_table) = (S n)) -> exists dst_positive_dirichlet_grid_row_slice_sliceoutput_table dst_negative_dirichlet_grid_row_slice_sliceoutput_table dst_value_dirichlet_grid_row_slice_sliceoutput_table. ((((exists ff_h_pvs_dirichlet_grid_row_slice_sliceoutput_tableentrypositive. ff_h_pvs_dirichlet_grid_row_slice_sliceoutput_tableentrypositive + S (dst_positive_dirichlet_grid_row_slice_sliceoutput_table) = S ((S (dst_index_dirichlet_grid_row_slice_sliceoutput_table)) * dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_sliceoutput_tableentrypositive. dst_positive_code_dirichlet_grid_row_slice_sliceoutput_table = ff_q_pvs_dirichlet_grid_row_slice_sliceoutput_tableentrypositive * S ((S (dst_index_dirichlet_grid_row_slice_sliceoutput_table)) * dst_positive_scale_dirichlet_grid_row_slice_sliceoutput_table) + (dst_positive_dirichlet_grid_row_slice_sliceoutput_table))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_sliceoutput_tableentrynegative. ff_h_pvs_dirichlet_grid_row_slice_sliceoutput_tableentrynegative + S (dst_negative_dirichlet_grid_row_slice_sliceoutput_table) = S ((S (dst_index_dirichlet_grid_row_slice_sliceoutput_table)) * dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_sliceoutput_tableentrynegative. dst_negative_code_dirichlet_grid_row_slice_sliceoutput_table = ff_q_pvs_dirichlet_grid_row_slice_sliceoutput_tableentrynegative * S ((S (dst_index_dirichlet_grid_row_slice_sliceoutput_table)) * dst_negative_scale_dirichlet_grid_row_slice_sliceoutput_table) + (dst_negative_dirichlet_grid_row_slice_sliceoutput_table))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_sliceoutput_tableentryvalue ge_balance_negative_dirichlet_grid_row_slice_sliceoutput_tableentryvalue. (((((dst_value_dirichlet_grid_row_slice_sliceoutput_table) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_sliceoutput_tableentryvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_sliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_sliceoutput_tableentryvaluedecode. (((dst_value_dirichlet_grid_row_slice_sliceoutput_table) = 2 * ge_signed_half_dirichlet_grid_row_slice_sliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_sliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_sliceoutput_tableentryvalue) = S ge_signed_half_dirichlet_grid_row_slice_sliceoutput_tableentryvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_sliceoutput_table) + ge_balance_negative_dirichlet_grid_row_slice_sliceoutput_tableentryvalue = (dst_negative_dirichlet_grid_row_slice_sliceoutput_table) + ge_balance_positive_dirichlet_grid_row_slice_sliceoutput_tableentryvalue))))))))) /\ (forall srs_index_dirichlet_grid_row_slice_slice. (exists pvs_gap_dirichlet_grid_row_slice_slicebound. pvs_gap_dirichlet_grid_row_slice_slicebound + S (srs_index_dirichlet_grid_row_slice_slice) = (S n)) -> exists srs_value_dirichlet_grid_row_slice_slice. (((exists dst_positive_code_dirichlet_grid_row_slice_sliceentrysource dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource dst_negative_code_dirichlet_grid_row_slice_sliceentrysource dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource dst_positive_dirichlet_grid_row_slice_sliceentrysource dst_negative_dirichlet_grid_row_slice_sliceentrysource. (((T) = (((((dst_positive_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource)) * S ((dst_positive_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource)) + ((dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource))) + (((dst_negative_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource)) * S ((dst_positive_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource)) + ((dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource))) + (((dst_negative_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)))) + ((((dst_negative_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource))) + (((dst_negative_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_sliceentrysourcepositive. ff_h_pvs_dirichlet_grid_row_slice_sliceentrysourcepositive + S (dst_positive_dirichlet_grid_row_slice_sliceentrysource) = S ((S (((0+(S n)*a) + ((1) * (srs_index_dirichlet_grid_row_slice_slice))))) * dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_sliceentrysourcepositive. dst_positive_code_dirichlet_grid_row_slice_sliceentrysource = ff_q_pvs_dirichlet_grid_row_slice_sliceentrysourcepositive * S ((S (((0+(S n)*a) + ((1) * (srs_index_dirichlet_grid_row_slice_slice))))) * dst_positive_scale_dirichlet_grid_row_slice_sliceentrysource) + (dst_positive_dirichlet_grid_row_slice_sliceentrysource))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_sliceentrysourcenegative. ff_h_pvs_dirichlet_grid_row_slice_sliceentrysourcenegative + S (dst_negative_dirichlet_grid_row_slice_sliceentrysource) = S ((S (((0+(S n)*a) + ((1) * (srs_index_dirichlet_grid_row_slice_slice))))) * dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_sliceentrysourcenegative. dst_negative_code_dirichlet_grid_row_slice_sliceentrysource = ff_q_pvs_dirichlet_grid_row_slice_sliceentrysourcenegative * S ((S (((0+(S n)*a) + ((1) * (srs_index_dirichlet_grid_row_slice_slice))))) * dst_negative_scale_dirichlet_grid_row_slice_sliceentrysource) + (dst_negative_dirichlet_grid_row_slice_sliceentrysource))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_sliceentrysourcevalue ge_balance_negative_dirichlet_grid_row_slice_sliceentrysourcevalue. (((((srs_value_dirichlet_grid_row_slice_slice) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_sliceentrysourcevalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_sliceentrysourcevalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_sliceentrysourcevaluedecode. (((srs_value_dirichlet_grid_row_slice_slice) = 2 * ge_signed_half_dirichlet_grid_row_slice_sliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_sliceentrysourcevalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_sliceentrysourcevalue) = S ge_signed_half_dirichlet_grid_row_slice_sliceentrysourcevaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_sliceentrysource) + ge_balance_negative_dirichlet_grid_row_slice_sliceentrysourcevalue = (dst_negative_dirichlet_grid_row_slice_sliceentrysource) + ge_balance_positive_dirichlet_grid_row_slice_sliceentrysourcevalue))))))))) /\ (exists dst_positive_code_dirichlet_grid_row_slice_sliceentryoutput dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput dst_positive_dirichlet_grid_row_slice_sliceentryoutput dst_negative_dirichlet_grid_row_slice_sliceentryoutput. (((V) = (((((dst_positive_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput)) * S ((dst_positive_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput)) + ((dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput))) + (((dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput)) * S ((dst_positive_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput)) + ((dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput) + (dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput))) + (((dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)))) + ((((dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput))) + (((dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)) * S ((dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)) + ((dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_sliceentryoutputpositive. ff_h_pvs_dirichlet_grid_row_slice_sliceentryoutputpositive + S (dst_positive_dirichlet_grid_row_slice_sliceentryoutput) = S ((S (srs_index_dirichlet_grid_row_slice_slice)) * dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_sliceentryoutputpositive. dst_positive_code_dirichlet_grid_row_slice_sliceentryoutput = ff_q_pvs_dirichlet_grid_row_slice_sliceentryoutputpositive * S ((S (srs_index_dirichlet_grid_row_slice_slice)) * dst_positive_scale_dirichlet_grid_row_slice_sliceentryoutput) + (dst_positive_dirichlet_grid_row_slice_sliceentryoutput))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_sliceentryoutputnegative. ff_h_pvs_dirichlet_grid_row_slice_sliceentryoutputnegative + S (dst_negative_dirichlet_grid_row_slice_sliceentryoutput) = S ((S (srs_index_dirichlet_grid_row_slice_slice)) * dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_sliceentryoutputnegative. dst_negative_code_dirichlet_grid_row_slice_sliceentryoutput = ff_q_pvs_dirichlet_grid_row_slice_sliceentryoutputnegative * S ((S (srs_index_dirichlet_grid_row_slice_slice)) * dst_negative_scale_dirichlet_grid_row_slice_sliceentryoutput) + (dst_negative_dirichlet_grid_row_slice_sliceentryoutput))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_sliceentryoutputvalue ge_balance_negative_dirichlet_grid_row_slice_sliceentryoutputvalue. (((((srs_value_dirichlet_grid_row_slice_slice) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_sliceentryoutputvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_sliceentryoutputvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_sliceentryoutputvaluedecode. (((srs_value_dirichlet_grid_row_slice_slice) = 2 * ge_signed_half_dirichlet_grid_row_slice_sliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_sliceentryoutputvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_sliceentryoutputvalue) = S ge_signed_half_dirichlet_grid_row_slice_sliceentryoutputvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_sliceentryoutput) + ge_balance_negative_dirichlet_grid_row_slice_sliceentryoutputvalue = (dst_negative_dirichlet_grid_row_slice_sliceentryoutput) + ge_balance_positive_dirichlet_grid_row_slice_sliceentryoutputvalue)))))))))))))))) -> (((exists dst_positive_code_dirichlet_grid_row_slice_resulttable dst_positive_scale_dirichlet_grid_row_slice_resulttable dst_negative_code_dirichlet_grid_row_slice_resulttable dst_negative_scale_dirichlet_grid_row_slice_resulttable. (((V) = (((((dst_positive_code_dirichlet_grid_row_slice_resulttable) + (dst_positive_scale_dirichlet_grid_row_slice_resulttable)) * S ((dst_positive_code_dirichlet_grid_row_slice_resulttable) + (dst_positive_scale_dirichlet_grid_row_slice_resulttable)) + ((dst_positive_scale_dirichlet_grid_row_slice_resulttable) + (dst_positive_scale_dirichlet_grid_row_slice_resulttable))) + (((dst_negative_code_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)) * S ((dst_negative_code_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)) + ((dst_negative_scale_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_resulttable) + (dst_positive_scale_dirichlet_grid_row_slice_resulttable)) * S ((dst_positive_code_dirichlet_grid_row_slice_resulttable) + (dst_positive_scale_dirichlet_grid_row_slice_resulttable)) + ((dst_positive_scale_dirichlet_grid_row_slice_resulttable) + (dst_positive_scale_dirichlet_grid_row_slice_resulttable))) + (((dst_negative_code_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)) * S ((dst_negative_code_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)) + ((dst_negative_scale_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)))) + ((((dst_negative_code_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)) * S ((dst_negative_code_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)) + ((dst_negative_scale_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable))) + (((dst_negative_code_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)) * S ((dst_negative_code_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)) + ((dst_negative_scale_dirichlet_grid_row_slice_resulttable) + (dst_negative_scale_dirichlet_grid_row_slice_resulttable)))))) /\ (forall dst_index_dirichlet_grid_row_slice_resulttable. (exists pvs_le_gap_dirichlet_grid_row_slice_resulttabledomain. pvs_le_gap_dirichlet_grid_row_slice_resulttabledomain + (dst_index_dirichlet_grid_row_slice_resulttable) = (S (n))) -> exists dst_positive_dirichlet_grid_row_slice_resulttable dst_negative_dirichlet_grid_row_slice_resulttable dst_value_dirichlet_grid_row_slice_resulttable. ((((exists ff_h_pvs_dirichlet_grid_row_slice_resulttableentrypositive. ff_h_pvs_dirichlet_grid_row_slice_resulttableentrypositive + S (dst_positive_dirichlet_grid_row_slice_resulttable) = S ((S (dst_index_dirichlet_grid_row_slice_resulttable)) * dst_positive_scale_dirichlet_grid_row_slice_resulttable)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resulttableentrypositive. dst_positive_code_dirichlet_grid_row_slice_resulttable = ff_q_pvs_dirichlet_grid_row_slice_resulttableentrypositive * S ((S (dst_index_dirichlet_grid_row_slice_resulttable)) * dst_positive_scale_dirichlet_grid_row_slice_resulttable) + (dst_positive_dirichlet_grid_row_slice_resulttable))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_resulttableentrynegative. ff_h_pvs_dirichlet_grid_row_slice_resulttableentrynegative + S (dst_negative_dirichlet_grid_row_slice_resulttable) = S ((S (dst_index_dirichlet_grid_row_slice_resulttable)) * dst_negative_scale_dirichlet_grid_row_slice_resulttable)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resulttableentrynegative. dst_negative_code_dirichlet_grid_row_slice_resulttable = ff_q_pvs_dirichlet_grid_row_slice_resulttableentrynegative * S ((S (dst_index_dirichlet_grid_row_slice_resulttable)) * dst_negative_scale_dirichlet_grid_row_slice_resulttable) + (dst_negative_dirichlet_grid_row_slice_resulttable))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_resulttableentryvalue ge_balance_negative_dirichlet_grid_row_slice_resulttableentryvalue. (((((dst_value_dirichlet_grid_row_slice_resulttable) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_resulttableentryvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_resulttableentryvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resulttableentryvaluedecode. (((dst_value_dirichlet_grid_row_slice_resulttable) = 2 * ge_signed_half_dirichlet_grid_row_slice_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_resulttableentryvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_resulttableentryvalue) = S ge_signed_half_dirichlet_grid_row_slice_resulttableentryvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_resulttable) + ge_balance_negative_dirichlet_grid_row_slice_resulttableentryvalue = (dst_negative_dirichlet_grid_row_slice_resulttable) + ge_balance_positive_dirichlet_grid_row_slice_resulttableentryvalue))))))))) /\ (forall dfg_factor_column_dirichlet_grid_row_slice_result dfg_factor_value_dirichlet_grid_row_slice_result. (exists pvs_le_gap_dirichlet_grid_row_slice_resultbound. pvs_le_gap_dirichlet_grid_row_slice_resultbound + (dfg_factor_column_dirichlet_grid_row_slice_result) = (n)) -> (exists dst_positive_code_dirichlet_grid_row_slice_resultlookup dst_positive_scale_dirichlet_grid_row_slice_resultlookup dst_negative_code_dirichlet_grid_row_slice_resultlookup dst_negative_scale_dirichlet_grid_row_slice_resultlookup dst_positive_dirichlet_grid_row_slice_resultlookup dst_negative_dirichlet_grid_row_slice_resultlookup. (((V) = (((((dst_positive_code_dirichlet_grid_row_slice_resultlookup) + (dst_positive_scale_dirichlet_grid_row_slice_resultlookup)) * S ((dst_positive_code_dirichlet_grid_row_slice_resultlookup) + (dst_positive_scale_dirichlet_grid_row_slice_resultlookup)) + ((dst_positive_scale_dirichlet_grid_row_slice_resultlookup) + (dst_positive_scale_dirichlet_grid_row_slice_resultlookup))) + (((dst_negative_code_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_resultlookup) + (dst_positive_scale_dirichlet_grid_row_slice_resultlookup)) * S ((dst_positive_code_dirichlet_grid_row_slice_resultlookup) + (dst_positive_scale_dirichlet_grid_row_slice_resultlookup)) + ((dst_positive_scale_dirichlet_grid_row_slice_resultlookup) + (dst_positive_scale_dirichlet_grid_row_slice_resultlookup))) + (((dst_negative_code_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)))) + ((((dst_negative_code_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup))) + (((dst_negative_code_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultlookup) + (dst_negative_scale_dirichlet_grid_row_slice_resultlookup)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_resultlookuppositive. ff_h_pvs_dirichlet_grid_row_slice_resultlookuppositive + S (dst_positive_dirichlet_grid_row_slice_resultlookup) = S ((S (dfg_factor_column_dirichlet_grid_row_slice_result)) * dst_positive_scale_dirichlet_grid_row_slice_resultlookup)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resultlookuppositive. dst_positive_code_dirichlet_grid_row_slice_resultlookup = ff_q_pvs_dirichlet_grid_row_slice_resultlookuppositive * S ((S (dfg_factor_column_dirichlet_grid_row_slice_result)) * dst_positive_scale_dirichlet_grid_row_slice_resultlookup) + (dst_positive_dirichlet_grid_row_slice_resultlookup))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_resultlookupnegative. ff_h_pvs_dirichlet_grid_row_slice_resultlookupnegative + S (dst_negative_dirichlet_grid_row_slice_resultlookup) = S ((S (dfg_factor_column_dirichlet_grid_row_slice_result)) * dst_negative_scale_dirichlet_grid_row_slice_resultlookup)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resultlookupnegative. dst_negative_code_dirichlet_grid_row_slice_resultlookup = ff_q_pvs_dirichlet_grid_row_slice_resultlookupnegative * S ((S (dfg_factor_column_dirichlet_grid_row_slice_result)) * dst_negative_scale_dirichlet_grid_row_slice_resultlookup) + (dst_negative_dirichlet_grid_row_slice_resultlookup))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_resultlookupvalue ge_balance_negative_dirichlet_grid_row_slice_resultlookupvalue. (((((dfg_factor_value_dirichlet_grid_row_slice_result) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_resultlookupvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_resultlookupvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultlookupvaluedecode. (((dfg_factor_value_dirichlet_grid_row_slice_result) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultlookupvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_resultlookupvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_resultlookupvalue) = S ge_signed_half_dirichlet_grid_row_slice_resultlookupvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_resultlookup) + ge_balance_negative_dirichlet_grid_row_slice_resultlookupvalue = (dst_negative_dirichlet_grid_row_slice_resultlookup) + ge_balance_positive_dirichlet_grid_row_slice_resultlookupvalue))))))))) -> ((((~((a)=0)) /\ (((~((dfg_factor_column_dirichlet_grid_row_slice_result)=0)) /\ (exists dfg_middle_dirichlet_grid_row_slice_resultentry dfg_first_dirichlet_grid_row_slice_resultentry dfg_last_dirichlet_grid_row_slice_resultentry dfg_value_dirichlet_grid_row_slice_resultentry. (((n)=((a)*(dfg_factor_column_dirichlet_grid_row_slice_result))*dfg_middle_dirichlet_grid_row_slice_resultentry) /\ (((exists dst_positive_code_dirichlet_grid_row_slice_resultentryfirst dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst dst_negative_code_dirichlet_grid_row_slice_resultentryfirst dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst dst_positive_dirichlet_grid_row_slice_resultentryfirst dst_negative_dirichlet_grid_row_slice_resultentryfirst. (((F) = (((((dst_positive_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst)) * S ((dst_positive_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst)) + ((dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst))) + (((dst_negative_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst)) * S ((dst_positive_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst)) + ((dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst) + (dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst))) + (((dst_negative_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)))) + ((((dst_negative_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst))) + (((dst_negative_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_resultentryfirstpositive. ff_h_pvs_dirichlet_grid_row_slice_resultentryfirstpositive + S (dst_positive_dirichlet_grid_row_slice_resultentryfirst) = S ((S (a)) * dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resultentryfirstpositive. dst_positive_code_dirichlet_grid_row_slice_resultentryfirst = ff_q_pvs_dirichlet_grid_row_slice_resultentryfirstpositive * S ((S (a)) * dst_positive_scale_dirichlet_grid_row_slice_resultentryfirst) + (dst_positive_dirichlet_grid_row_slice_resultentryfirst))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_resultentryfirstnegative. ff_h_pvs_dirichlet_grid_row_slice_resultentryfirstnegative + S (dst_negative_dirichlet_grid_row_slice_resultentryfirst) = S ((S (a)) * dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resultentryfirstnegative. dst_negative_code_dirichlet_grid_row_slice_resultentryfirst = ff_q_pvs_dirichlet_grid_row_slice_resultentryfirstnegative * S ((S (a)) * dst_negative_scale_dirichlet_grid_row_slice_resultentryfirst) + (dst_negative_dirichlet_grid_row_slice_resultentryfirst))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_resultentryfirstvalue ge_balance_negative_dirichlet_grid_row_slice_resultentryfirstvalue. (((((dfg_first_dirichlet_grid_row_slice_resultentry) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_resultentryfirstvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_resultentryfirstvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultentryfirstvaluedecode. (((dfg_first_dirichlet_grid_row_slice_resultentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultentryfirstvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_resultentryfirstvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_resultentryfirstvalue) = S ge_signed_half_dirichlet_grid_row_slice_resultentryfirstvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_resultentryfirst) + ge_balance_negative_dirichlet_grid_row_slice_resultentryfirstvalue = (dst_negative_dirichlet_grid_row_slice_resultentryfirst) + ge_balance_positive_dirichlet_grid_row_slice_resultentryfirstvalue))))))))) /\ (((exists dst_positive_code_dirichlet_grid_row_slice_resultentrylast dst_positive_scale_dirichlet_grid_row_slice_resultentrylast dst_negative_code_dirichlet_grid_row_slice_resultentrylast dst_negative_scale_dirichlet_grid_row_slice_resultentrylast dst_positive_dirichlet_grid_row_slice_resultentrylast dst_negative_dirichlet_grid_row_slice_resultentrylast. (((H) = (((((dst_positive_code_dirichlet_grid_row_slice_resultentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrylast)) * S ((dst_positive_code_dirichlet_grid_row_slice_resultentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrylast)) + ((dst_positive_scale_dirichlet_grid_row_slice_resultentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrylast))) + (((dst_negative_code_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_resultentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrylast)) * S ((dst_positive_code_dirichlet_grid_row_slice_resultentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrylast)) + ((dst_positive_scale_dirichlet_grid_row_slice_resultentrylast) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrylast))) + (((dst_negative_code_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)))) + ((((dst_negative_code_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast))) + (((dst_negative_code_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_resultentrylastpositive. ff_h_pvs_dirichlet_grid_row_slice_resultentrylastpositive + S (dst_positive_dirichlet_grid_row_slice_resultentrylast) = S ((S (dfg_factor_column_dirichlet_grid_row_slice_result)) * dst_positive_scale_dirichlet_grid_row_slice_resultentrylast)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resultentrylastpositive. dst_positive_code_dirichlet_grid_row_slice_resultentrylast = ff_q_pvs_dirichlet_grid_row_slice_resultentrylastpositive * S ((S (dfg_factor_column_dirichlet_grid_row_slice_result)) * dst_positive_scale_dirichlet_grid_row_slice_resultentrylast) + (dst_positive_dirichlet_grid_row_slice_resultentrylast))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_resultentrylastnegative. ff_h_pvs_dirichlet_grid_row_slice_resultentrylastnegative + S (dst_negative_dirichlet_grid_row_slice_resultentrylast) = S ((S (dfg_factor_column_dirichlet_grid_row_slice_result)) * dst_negative_scale_dirichlet_grid_row_slice_resultentrylast)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resultentrylastnegative. dst_negative_code_dirichlet_grid_row_slice_resultentrylast = ff_q_pvs_dirichlet_grid_row_slice_resultentrylastnegative * S ((S (dfg_factor_column_dirichlet_grid_row_slice_result)) * dst_negative_scale_dirichlet_grid_row_slice_resultentrylast) + (dst_negative_dirichlet_grid_row_slice_resultentrylast))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_resultentrylastvalue ge_balance_negative_dirichlet_grid_row_slice_resultentrylastvalue. (((((dfg_last_dirichlet_grid_row_slice_resultentry) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_resultentrylastvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_resultentrylastvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultentrylastvaluedecode. (((dfg_last_dirichlet_grid_row_slice_resultentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultentrylastvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_resultentrylastvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_resultentrylastvalue) = S ge_signed_half_dirichlet_grid_row_slice_resultentrylastvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_resultentrylast) + ge_balance_negative_dirichlet_grid_row_slice_resultentrylastvalue = (dst_negative_dirichlet_grid_row_slice_resultentrylast) + ge_balance_positive_dirichlet_grid_row_slice_resultentrylastvalue))))))))) /\ (((exists dst_positive_code_dirichlet_grid_row_slice_resultentrymiddle dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle dst_positive_dirichlet_grid_row_slice_resultentrymiddle dst_negative_dirichlet_grid_row_slice_resultentrymiddle. (((G) = (((((dst_positive_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle)) * S ((dst_positive_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle)) + ((dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle))) + (((dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle)) * S ((dst_positive_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle)) + ((dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle) + (dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle))) + (((dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)))) + ((((dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle))) + (((dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)) * S ((dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)) + ((dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_resultentrymiddlepositive. ff_h_pvs_dirichlet_grid_row_slice_resultentrymiddlepositive + S (dst_positive_dirichlet_grid_row_slice_resultentrymiddle) = S ((S (dfg_middle_dirichlet_grid_row_slice_resultentry)) * dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resultentrymiddlepositive. dst_positive_code_dirichlet_grid_row_slice_resultentrymiddle = ff_q_pvs_dirichlet_grid_row_slice_resultentrymiddlepositive * S ((S (dfg_middle_dirichlet_grid_row_slice_resultentry)) * dst_positive_scale_dirichlet_grid_row_slice_resultentrymiddle) + (dst_positive_dirichlet_grid_row_slice_resultentrymiddle))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_resultentrymiddlenegative. ff_h_pvs_dirichlet_grid_row_slice_resultentrymiddlenegative + S (dst_negative_dirichlet_grid_row_slice_resultentrymiddle) = S ((S (dfg_middle_dirichlet_grid_row_slice_resultentry)) * dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_resultentrymiddlenegative. dst_negative_code_dirichlet_grid_row_slice_resultentrymiddle = ff_q_pvs_dirichlet_grid_row_slice_resultentrymiddlenegative * S ((S (dfg_middle_dirichlet_grid_row_slice_resultentry)) * dst_negative_scale_dirichlet_grid_row_slice_resultentrymiddle) + (dst_negative_dirichlet_grid_row_slice_resultentrymiddle))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_resultentrymiddlevalue ge_balance_negative_dirichlet_grid_row_slice_resultentrymiddlevalue. (((((dfg_value_dirichlet_grid_row_slice_resultentry) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_resultentrymiddlevalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_resultentrymiddlevalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultentrymiddlevaluedecode. (((dfg_value_dirichlet_grid_row_slice_resultentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultentrymiddlevaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_resultentrymiddlevalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_resultentrymiddlevalue) = S ge_signed_half_dirichlet_grid_row_slice_resultentrymiddlevaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_resultentrymiddle) + ge_balance_negative_dirichlet_grid_row_slice_resultentrymiddlevalue = (dst_negative_dirichlet_grid_row_slice_resultentrymiddle) + ge_balance_positive_dirichlet_grid_row_slice_resultentrymiddlevalue))))))))) /\ (exists dfg_inner_dirichlet_grid_row_slice_resultentryproduct. ((exists sto_ap_dirichlet_grid_row_slice_resultentryproductinner sto_an_dirichlet_grid_row_slice_resultentryproductinner sto_bp_dirichlet_grid_row_slice_resultentryproductinner sto_bn_dirichlet_grid_row_slice_resultentryproductinner sto_cp_dirichlet_grid_row_slice_resultentryproductinner sto_cn_dirichlet_grid_row_slice_resultentryproductinner. (((((dfg_last_dirichlet_grid_row_slice_resultentry) = 2 * (sto_ap_dirichlet_grid_row_slice_resultentryproductinner) /\ (sto_an_dirichlet_grid_row_slice_resultentryproductinner) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultentryproductinnerleft. (((dfg_last_dirichlet_grid_row_slice_resultentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultentryproductinnerleft + 1 /\ (sto_ap_dirichlet_grid_row_slice_resultentryproductinner) = 0) /\ (sto_an_dirichlet_grid_row_slice_resultentryproductinner) = S ge_signed_half_dirichlet_grid_row_slice_resultentryproductinnerleft))) /\ ((((((dfg_value_dirichlet_grid_row_slice_resultentry) = 2 * (sto_bp_dirichlet_grid_row_slice_resultentryproductinner) /\ (sto_bn_dirichlet_grid_row_slice_resultentryproductinner) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultentryproductinnerright. (((dfg_value_dirichlet_grid_row_slice_resultentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultentryproductinnerright + 1 /\ (sto_bp_dirichlet_grid_row_slice_resultentryproductinner) = 0) /\ (sto_bn_dirichlet_grid_row_slice_resultentryproductinner) = S ge_signed_half_dirichlet_grid_row_slice_resultentryproductinnerright))) /\ ((((((dfg_inner_dirichlet_grid_row_slice_resultentryproduct) = 2 * (sto_cp_dirichlet_grid_row_slice_resultentryproductinner) /\ (sto_cn_dirichlet_grid_row_slice_resultentryproductinner) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultentryproductinneroutput. (((dfg_inner_dirichlet_grid_row_slice_resultentryproduct) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultentryproductinneroutput + 1 /\ (sto_cp_dirichlet_grid_row_slice_resultentryproductinner) = 0) /\ (sto_cn_dirichlet_grid_row_slice_resultentryproductinner) = S ge_signed_half_dirichlet_grid_row_slice_resultentryproductinneroutput))) /\ ((sto_ap_dirichlet_grid_row_slice_resultentryproductinner * sto_bp_dirichlet_grid_row_slice_resultentryproductinner + sto_an_dirichlet_grid_row_slice_resultentryproductinner * sto_bn_dirichlet_grid_row_slice_resultentryproductinner) + sto_cn_dirichlet_grid_row_slice_resultentryproductinner = (sto_ap_dirichlet_grid_row_slice_resultentryproductinner * sto_bn_dirichlet_grid_row_slice_resultentryproductinner + sto_an_dirichlet_grid_row_slice_resultentryproductinner * sto_bp_dirichlet_grid_row_slice_resultentryproductinner) + sto_cp_dirichlet_grid_row_slice_resultentryproductinner))))))) /\ (exists sto_ap_dirichlet_grid_row_slice_resultentryproductouter sto_an_dirichlet_grid_row_slice_resultentryproductouter sto_bp_dirichlet_grid_row_slice_resultentryproductouter sto_bn_dirichlet_grid_row_slice_resultentryproductouter sto_cp_dirichlet_grid_row_slice_resultentryproductouter sto_cn_dirichlet_grid_row_slice_resultentryproductouter. (((((dfg_first_dirichlet_grid_row_slice_resultentry) = 2 * (sto_ap_dirichlet_grid_row_slice_resultentryproductouter) /\ (sto_an_dirichlet_grid_row_slice_resultentryproductouter) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultentryproductouterleft. (((dfg_first_dirichlet_grid_row_slice_resultentry) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultentryproductouterleft + 1 /\ (sto_ap_dirichlet_grid_row_slice_resultentryproductouter) = 0) /\ (sto_an_dirichlet_grid_row_slice_resultentryproductouter) = S ge_signed_half_dirichlet_grid_row_slice_resultentryproductouterleft))) /\ ((((((dfg_inner_dirichlet_grid_row_slice_resultentryproduct) = 2 * (sto_bp_dirichlet_grid_row_slice_resultentryproductouter) /\ (sto_bn_dirichlet_grid_row_slice_resultentryproductouter) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultentryproductouterright. (((dfg_inner_dirichlet_grid_row_slice_resultentryproduct) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultentryproductouterright + 1 /\ (sto_bp_dirichlet_grid_row_slice_resultentryproductouter) = 0) /\ (sto_bn_dirichlet_grid_row_slice_resultentryproductouter) = S ge_signed_half_dirichlet_grid_row_slice_resultentryproductouterright))) /\ ((((((dfg_factor_value_dirichlet_grid_row_slice_result) = 2 * (sto_cp_dirichlet_grid_row_slice_resultentryproductouter) /\ (sto_cn_dirichlet_grid_row_slice_resultentryproductouter) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_resultentryproductouteroutput. (((dfg_factor_value_dirichlet_grid_row_slice_result) = 2 * ge_signed_half_dirichlet_grid_row_slice_resultentryproductouteroutput + 1 /\ (sto_cp_dirichlet_grid_row_slice_resultentryproductouter) = 0) /\ (sto_cn_dirichlet_grid_row_slice_resultentryproductouter) = S ge_signed_half_dirichlet_grid_row_slice_resultentryproductouteroutput))) /\ ((sto_ap_dirichlet_grid_row_slice_resultentryproductouter * sto_bp_dirichlet_grid_row_slice_resultentryproductouter + sto_an_dirichlet_grid_row_slice_resultentryproductouter * sto_bn_dirichlet_grid_row_slice_resultentryproductouter) + sto_cn_dirichlet_grid_row_slice_resultentryproductouter = (sto_ap_dirichlet_grid_row_slice_resultentryproductouter * sto_bn_dirichlet_grid_row_slice_resultentryproductouter + sto_an_dirichlet_grid_row_slice_resultentryproductouter * sto_bp_dirichlet_grid_row_slice_resultentryproductouter) + sto_cp_dirichlet_grid_row_slice_resultentryproductouter))))))))))))))))))))) \/ ((((a)=0 \/ ((dfg_factor_column_dirichlet_grid_row_slice_result)=0 \/ ~(exists pvs_factor_dirichlet_grid_row_slice_resultentryomittednondivisor. (n) = ((a)*(dfg_factor_column_dirichlet_grid_row_slice_result)) * pvs_factor_dirichlet_grid_row_slice_resultentryomittednondivisor))) /\ ((dfg_factor_value_dirichlet_grid_row_slice_result)=0)))))))

Constructive proof overview

Generated structural guide

An actual row slice supplies the exact factor-row values; every affine coordinate is transported by a proved natural equality.

The unchanged tactic script uses 5 declared prerequisites and contains 54 exact native proof lines.

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

Proof neighborhood

Direct dependencies

signed_rectangular_slice_lookup Alpha theorem; checked-use authorized succ_le_succ Stable theorem; checked-use authorized zero_add Stable theorem; checked-use authorized one_mul Stable theorem; checked-use authorized DF000F dirichlet_grid_table_lookup

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

54 script commands · 9 reading checkpoints · 2 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)

Long local formulas use this family’s existing definitions. Each new abbreviation was expanded back to the identical native formula, including its free-variable context. The original edition is preserved below.

01Fix variables and assumptionsL1–10

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 n
  5. L5
    intro T
  6. L6
    intro a
  7. L7
    intro V
  8. L8
    intro hg
  9. L9
    intro ha
  10. L10
    intro hs
02Separate the logical casesL11–13

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

  1. L11
    split
  2. L12
    cases hs
  3. L13
    cases hs_right
03Use earlier factsL14–14

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

  1. L14
    exact hs_right_left
04Fix variables and assumptionsL15–18

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

  1. L15
    intro e
  2. L16
    intro z
  3. L17
    intro he
  4. L18
    intro hz
05Establish hlL19–28

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed rectangular slice lookup.

  1. L19
    have hl : ArithAt(T,0 + S n · a + 1 · e,z)Definitions: ArithAt
  2. L20
    specialize signed_rectangular_slice_lookup (T)
  3. L21
    specialize signed_rectangular_slice_lookup (V)
  4. L22
    specialize signed_rectangular_slice_lookup (0+(S n)*a)
  5. L23
    specialize signed_rectangular_slice_lookup (1)
  6. L24
    specialize signed_rectangular_slice_lookup (S n)
  7. L25
    specialize signed_rectangular_slice_lookup (e)
  8. L26
    specialize signed_rectangular_slice_lookup (z)
  9. L27
    apply signed_rectangular_slice_lookup
  10. L28
    exact hs
06Use earlier factsL29–33

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

  1. L29
    specialize succ_le_succ (e)
  2. L30
    specialize succ_le_succ (n)
  3. L31
    apply succ_le_succ
  4. L32
    exact he
  5. L33
    exact hz
07Establish hindexL34–43

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply zero add.

  1. L34
    have hindex : (0+(S n)*a)+(1)*e=(S (n))*(a)+(e)
  2. L35
    congr
  3. L36
    apply zero_add
  4. L37
    apply one_mul
  5. L38
    rewrite hindex at hl
  6. L39
    rewrite hindex at hl
  7. L40
    rewrite hindex at hl
  8. L41
    rewrite hindex at hl
  9. L42
    specialize dirichlet_grid_table_lookup (F)
  10. L43
    specialize dirichlet_grid_table_lookup (G)
08Use earlier factsL44–53

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

  1. L44
    specialize dirichlet_grid_table_lookup (H)
  2. L45
    specialize dirichlet_grid_table_lookup (n)
  3. L46
    specialize dirichlet_grid_table_lookup (T)
  4. L47
    specialize dirichlet_grid_table_lookup (a)
  5. L48
    specialize dirichlet_grid_table_lookup (e)
  6. L49
    specialize dirichlet_grid_table_lookup (z)
  7. L50
    apply dirichlet_grid_table_lookup
  8. L51
    exact hg
  9. L52
    exact ha
  10. L53
    exact he
09Use earlier factsL54–54

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

  1. L54
    exact hl

Library-wide reading audit

Original exact command ledger · 54 lines
  1. 0001intro F
  2. 0002intro G
  3. 0003intro H
  4. 0004intro n
  5. 0005intro T
  6. 0006intro a
  7. 0007intro V
  8. 0008intro hg
  9. 0009intro ha
  10. 0010intro hs
  11. 0011split
  12. 0012cases hs
  13. 0013cases hs_right
  14. 0014exact hs_right_left
  15. 0015intro e
  16. 0016intro z
  17. 0017intro he
  18. 0018intro hz
  19. 0019have hl : exists dst_positive_code_dirichlet_grid_row_slice_source_entry dst_positive_scale_dirichlet_grid_row_slice_source_entry dst_negative_code_dirichlet_grid_row_slice_source_entry dst_negative_scale_dirichlet_grid_row_slice_source_entry dst_positive_dirichlet_grid_row_slice_source_entry dst_negative_dirichlet_grid_row_slice_source_entry. (((T) = (((((dst_positive_code_dirichlet_grid_row_slice_source_entry) + (dst_positive_scale_dirichlet_grid_row_slice_source_entry)) * S ((dst_positive_code_dirichlet_grid_row_slice_source_entry) + (dst_positive_scale_dirichlet_grid_row_slice_source_entry)) + ((dst_positive_scale_dirichlet_grid_row_slice_source_entry) + (dst_positive_scale_dirichlet_grid_row_slice_source_entry))) + (((dst_negative_code_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)) * S ((dst_negative_code_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)) + ((dst_negative_scale_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)))) * S ((((dst_positive_code_dirichlet_grid_row_slice_source_entry) + (dst_positive_scale_dirichlet_grid_row_slice_source_entry)) * S ((dst_positive_code_dirichlet_grid_row_slice_source_entry) + (dst_positive_scale_dirichlet_grid_row_slice_source_entry)) + ((dst_positive_scale_dirichlet_grid_row_slice_source_entry) + (dst_positive_scale_dirichlet_grid_row_slice_source_entry))) + (((dst_negative_code_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)) * S ((dst_negative_code_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)) + ((dst_negative_scale_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)))) + ((((dst_negative_code_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)) * S ((dst_negative_code_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)) + ((dst_negative_scale_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry))) + (((dst_negative_code_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)) * S ((dst_negative_code_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)) + ((dst_negative_scale_dirichlet_grid_row_slice_source_entry) + (dst_negative_scale_dirichlet_grid_row_slice_source_entry)))))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_source_entrypositive. ff_h_pvs_dirichlet_grid_row_slice_source_entrypositive + S (dst_positive_dirichlet_grid_row_slice_source_entry) = S ((S ((0+(S n)*a)+(1)*e)) * dst_positive_scale_dirichlet_grid_row_slice_source_entry)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_source_entrypositive. dst_positive_code_dirichlet_grid_row_slice_source_entry = ff_q_pvs_dirichlet_grid_row_slice_source_entrypositive * S ((S ((0+(S n)*a)+(1)*e)) * dst_positive_scale_dirichlet_grid_row_slice_source_entry) + (dst_positive_dirichlet_grid_row_slice_source_entry))) /\ (((((exists ff_h_pvs_dirichlet_grid_row_slice_source_entrynegative. ff_h_pvs_dirichlet_grid_row_slice_source_entrynegative + S (dst_negative_dirichlet_grid_row_slice_source_entry) = S ((S ((0+(S n)*a)+(1)*e)) * dst_negative_scale_dirichlet_grid_row_slice_source_entry)) /\ exists ff_q_pvs_dirichlet_grid_row_slice_source_entrynegative. dst_negative_code_dirichlet_grid_row_slice_source_entry = ff_q_pvs_dirichlet_grid_row_slice_source_entrynegative * S ((S ((0+(S n)*a)+(1)*e)) * dst_negative_scale_dirichlet_grid_row_slice_source_entry) + (dst_negative_dirichlet_grid_row_slice_source_entry))) /\ (exists ge_balance_positive_dirichlet_grid_row_slice_source_entryvalue ge_balance_negative_dirichlet_grid_row_slice_source_entryvalue. (((((z) = 2 * (ge_balance_positive_dirichlet_grid_row_slice_source_entryvalue) /\ (ge_balance_negative_dirichlet_grid_row_slice_source_entryvalue) = 0) \/ exists ge_signed_half_dirichlet_grid_row_slice_source_entryvaluedecode. (((z) = 2 * ge_signed_half_dirichlet_grid_row_slice_source_entryvaluedecode + 1 /\ (ge_balance_positive_dirichlet_grid_row_slice_source_entryvalue) = 0) /\ (ge_balance_negative_dirichlet_grid_row_slice_source_entryvalue) = S ge_signed_half_dirichlet_grid_row_slice_source_entryvaluedecode))) /\ ((dst_positive_dirichlet_grid_row_slice_source_entry) + ge_balance_negative_dirichlet_grid_row_slice_source_entryvalue = (dst_negative_dirichlet_grid_row_slice_source_entry) + ge_balance_positive_dirichlet_grid_row_slice_source_entryvalue))))))))
  20. 0020specialize signed_rectangular_slice_lookup (T)
  21. 0021specialize signed_rectangular_slice_lookup (V)
  22. 0022specialize signed_rectangular_slice_lookup (0+(S n)*a)
  23. 0023specialize signed_rectangular_slice_lookup (1)
  24. 0024specialize signed_rectangular_slice_lookup (S n)
  25. 0025specialize signed_rectangular_slice_lookup (e)
  26. 0026specialize signed_rectangular_slice_lookup (z)
  27. 0027apply signed_rectangular_slice_lookup
  28. 0028exact hs
  29. 0029specialize succ_le_succ (e)
  30. 0030specialize succ_le_succ (n)
  31. 0031apply succ_le_succ
  32. 0032exact he
  33. 0033exact hz
  34. 0034have hindex : (0+(S n)*a)+(1)*e=(S (n))*(a)+(e)
  35. 0035congr
  36. 0036apply zero_add
  37. 0037apply one_mul
  38. 0038rewrite hindex at hl
  39. 0039rewrite hindex at hl
  40. 0040rewrite hindex at hl
  41. 0041rewrite hindex at hl
  42. 0042specialize dirichlet_grid_table_lookup (F)
  43. 0043specialize dirichlet_grid_table_lookup (G)
  44. 0044specialize dirichlet_grid_table_lookup (H)
  45. 0045specialize dirichlet_grid_table_lookup (n)
  46. 0046specialize dirichlet_grid_table_lookup (T)
  47. 0047specialize dirichlet_grid_table_lookup (a)
  48. 0048specialize dirichlet_grid_table_lookup (e)
  49. 0049specialize dirichlet_grid_table_lookup (z)
  50. 0050apply dirichlet_grid_table_lookup
  51. 0051exact hg
  52. 0052exact ha
  53. 0053exact he
  54. 0054exact hl