Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Each retained summand has a witnessed n=d*q and actual signed multiplication. Zero and nondivisors contribute zero. Input and output values at zero are unrestricted; uniqueness is for positive represented values. The separate inverse family proves the unit-at-one criterion. Full G009 multiplicative-function closure is now admitted in the separate Alpha-v32 multiplicative-convolution family.
Exact theorem in conservative defined notation
∀ N. ∀ F. ∀ G. ∀ H. ∀ n. DirichletTable(N,F,G,H) → ¬n = 0 → Le(n,N) → ∃ x. ArithAt(H,n,x) ∧ DirichletSum(F,G,n,x)Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Original expanded first-order statement
forall N F G H n. (((exists dst_positive_code_table_lookup_sourceleft dst_positive_scale_table_lookup_sourceleft dst_negative_code_table_lookup_sourceleft dst_negative_scale_table_lookup_sourceleft. (((F) = (((((dst_positive_code_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft)) * S ((dst_positive_code_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft)) + ((dst_positive_scale_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft))) + (((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) * S ((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) + ((dst_negative_scale_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)))) * S ((((dst_positive_code_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft)) * S ((dst_positive_code_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft)) + ((dst_positive_scale_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft))) + (((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) * S ((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) + ((dst_negative_scale_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)))) + ((((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) * S ((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) + ((dst_negative_scale_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft))) + (((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) * S ((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) + ((dst_negative_scale_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)))))) /\ (forall dst_index_table_lookup_sourceleft. (exists pvs_le_gap_table_lookup_sourceleftdomain. pvs_le_gap_table_lookup_sourceleftdomain + (dst_index_table_lookup_sourceleft) = (N)) -> exists dst_positive_table_lookup_sourceleft dst_negative_table_lookup_sourceleft dst_value_table_lookup_sourceleft. ((((exists ff_h_pvs_table_lookup_sourceleftentrypositive. ff_h_pvs_table_lookup_sourceleftentrypositive + S (dst_positive_table_lookup_sourceleft) = S ((S (dst_index_table_lookup_sourceleft)) * dst_positive_scale_table_lookup_sourceleft)) /\ exists ff_q_pvs_table_lookup_sourceleftentrypositive. dst_positive_code_table_lookup_sourceleft = ff_q_pvs_table_lookup_sourceleftentrypositive * S ((S (dst_index_table_lookup_sourceleft)) * dst_positive_scale_table_lookup_sourceleft) + (dst_positive_table_lookup_sourceleft))) /\ (((((exists ff_h_pvs_table_lookup_sourceleftentrynegative. ff_h_pvs_table_lookup_sourceleftentrynegative + S (dst_negative_table_lookup_sourceleft) = S ((S (dst_index_table_lookup_sourceleft)) * dst_negative_scale_table_lookup_sourceleft)) /\ exists ff_q_pvs_table_lookup_sourceleftentrynegative. dst_negative_code_table_lookup_sourceleft = ff_q_pvs_table_lookup_sourceleftentrynegative * S ((S (dst_index_table_lookup_sourceleft)) * dst_negative_scale_table_lookup_sourceleft) + (dst_negative_table_lookup_sourceleft))) /\ (exists ge_balance_positive_table_lookup_sourceleftentryvalue ge_balance_negative_table_lookup_sourceleftentryvalue. (((((dst_value_table_lookup_sourceleft) = 2 * (ge_balance_positive_table_lookup_sourceleftentryvalue) /\ (ge_balance_negative_table_lookup_sourceleftentryvalue) = 0) \/ exists ge_signed_half_table_lookup_sourceleftentryvaluedecode. (((dst_value_table_lookup_sourceleft) = 2 * ge_signed_half_table_lookup_sourceleftentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourceleftentryvalue) = 0) /\ (ge_balance_negative_table_lookup_sourceleftentryvalue) = S ge_signed_half_table_lookup_sourceleftentryvaluedecode))) /\ ((dst_positive_table_lookup_sourceleft) + ge_balance_negative_table_lookup_sourceleftentryvalue = (dst_negative_table_lookup_sourceleft) + ge_balance_positive_table_lookup_sourceleftentryvalue))))))))) /\ (((exists dst_positive_code_table_lookup_sourceright dst_positive_scale_table_lookup_sourceright dst_negative_code_table_lookup_sourceright dst_negative_scale_table_lookup_sourceright. (((G) = (((((dst_positive_code_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright)) * S ((dst_positive_code_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright)) + ((dst_positive_scale_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright))) + (((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) * S ((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) + ((dst_negative_scale_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)))) * S ((((dst_positive_code_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright)) * S ((dst_positive_code_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright)) + ((dst_positive_scale_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright))) + (((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) * S ((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) + ((dst_negative_scale_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)))) + ((((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) * S ((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) + ((dst_negative_scale_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright))) + (((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) * S ((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) + ((dst_negative_scale_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)))))) /\ (forall dst_index_table_lookup_sourceright. (exists pvs_le_gap_table_lookup_sourcerightdomain. pvs_le_gap_table_lookup_sourcerightdomain + (dst_index_table_lookup_sourceright) = (N)) -> exists dst_positive_table_lookup_sourceright dst_negative_table_lookup_sourceright dst_value_table_lookup_sourceright. ((((exists ff_h_pvs_table_lookup_sourcerightentrypositive. ff_h_pvs_table_lookup_sourcerightentrypositive + S (dst_positive_table_lookup_sourceright) = S ((S (dst_index_table_lookup_sourceright)) * dst_positive_scale_table_lookup_sourceright)) /\ exists ff_q_pvs_table_lookup_sourcerightentrypositive. dst_positive_code_table_lookup_sourceright = ff_q_pvs_table_lookup_sourcerightentrypositive * S ((S (dst_index_table_lookup_sourceright)) * dst_positive_scale_table_lookup_sourceright) + (dst_positive_table_lookup_sourceright))) /\ (((((exists ff_h_pvs_table_lookup_sourcerightentrynegative. ff_h_pvs_table_lookup_sourcerightentrynegative + S (dst_negative_table_lookup_sourceright) = S ((S (dst_index_table_lookup_sourceright)) * dst_negative_scale_table_lookup_sourceright)) /\ exists ff_q_pvs_table_lookup_sourcerightentrynegative. dst_negative_code_table_lookup_sourceright = ff_q_pvs_table_lookup_sourcerightentrynegative * S ((S (dst_index_table_lookup_sourceright)) * dst_negative_scale_table_lookup_sourceright) + (dst_negative_table_lookup_sourceright))) /\ (exists ge_balance_positive_table_lookup_sourcerightentryvalue ge_balance_negative_table_lookup_sourcerightentryvalue. (((((dst_value_table_lookup_sourceright) = 2 * (ge_balance_positive_table_lookup_sourcerightentryvalue) /\ (ge_balance_negative_table_lookup_sourcerightentryvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcerightentryvaluedecode. (((dst_value_table_lookup_sourceright) = 2 * ge_signed_half_table_lookup_sourcerightentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcerightentryvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcerightentryvalue) = S ge_signed_half_table_lookup_sourcerightentryvaluedecode))) /\ ((dst_positive_table_lookup_sourceright) + ge_balance_negative_table_lookup_sourcerightentryvalue = (dst_negative_table_lookup_sourceright) + ge_balance_positive_table_lookup_sourcerightentryvalue))))))))) /\ (((exists dst_positive_code_table_lookup_sourcetable dst_positive_scale_table_lookup_sourcetable dst_negative_code_table_lookup_sourcetable dst_negative_scale_table_lookup_sourcetable. (((H) = (((((dst_positive_code_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable)) * S ((dst_positive_code_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable)) + ((dst_positive_scale_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable))) + (((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) * S ((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) + ((dst_negative_scale_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)))) * S ((((dst_positive_code_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable)) * S ((dst_positive_code_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable)) + ((dst_positive_scale_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable))) + (((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) * S ((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) + ((dst_negative_scale_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)))) + ((((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) * S ((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) + ((dst_negative_scale_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable))) + (((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) * S ((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) + ((dst_negative_scale_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)))))) /\ (forall dst_index_table_lookup_sourcetable. (exists pvs_le_gap_table_lookup_sourcetabledomain. pvs_le_gap_table_lookup_sourcetabledomain + (dst_index_table_lookup_sourcetable) = (N)) -> exists dst_positive_table_lookup_sourcetable dst_negative_table_lookup_sourcetable dst_value_table_lookup_sourcetable. ((((exists ff_h_pvs_table_lookup_sourcetableentrypositive. ff_h_pvs_table_lookup_sourcetableentrypositive + S (dst_positive_table_lookup_sourcetable) = S ((S (dst_index_table_lookup_sourcetable)) * dst_positive_scale_table_lookup_sourcetable)) /\ exists ff_q_pvs_table_lookup_sourcetableentrypositive. dst_positive_code_table_lookup_sourcetable = ff_q_pvs_table_lookup_sourcetableentrypositive * S ((S (dst_index_table_lookup_sourcetable)) * dst_positive_scale_table_lookup_sourcetable) + (dst_positive_table_lookup_sourcetable))) /\ (((((exists ff_h_pvs_table_lookup_sourcetableentrynegative. ff_h_pvs_table_lookup_sourcetableentrynegative + S (dst_negative_table_lookup_sourcetable) = S ((S (dst_index_table_lookup_sourcetable)) * dst_negative_scale_table_lookup_sourcetable)) /\ exists ff_q_pvs_table_lookup_sourcetableentrynegative. dst_negative_code_table_lookup_sourcetable = ff_q_pvs_table_lookup_sourcetableentrynegative * S ((S (dst_index_table_lookup_sourcetable)) * dst_negative_scale_table_lookup_sourcetable) + (dst_negative_table_lookup_sourcetable))) /\ (exists ge_balance_positive_table_lookup_sourcetableentryvalue ge_balance_negative_table_lookup_sourcetableentryvalue. (((((dst_value_table_lookup_sourcetable) = 2 * (ge_balance_positive_table_lookup_sourcetableentryvalue) /\ (ge_balance_negative_table_lookup_sourcetableentryvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcetableentryvaluedecode. (((dst_value_table_lookup_sourcetable) = 2 * ge_signed_half_table_lookup_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcetableentryvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcetableentryvalue) = S ge_signed_half_table_lookup_sourcetableentryvaluedecode))) /\ ((dst_positive_table_lookup_sourcetable) + ge_balance_negative_table_lookup_sourcetableentryvalue = (dst_negative_table_lookup_sourcetable) + ge_balance_positive_table_lookup_sourcetableentryvalue))))))))) /\ (forall dc_input_table_lookup_source dc_output_table_lookup_source. ~(dc_input_table_lookup_source=0) -> (exists pvs_le_gap_table_lookup_sourcedomain. pvs_le_gap_table_lookup_sourcedomain + (dc_input_table_lookup_source) = (N)) -> (exists dst_positive_code_table_lookup_sourcelookup dst_positive_scale_table_lookup_sourcelookup dst_negative_code_table_lookup_sourcelookup dst_negative_scale_table_lookup_sourcelookup dst_positive_table_lookup_sourcelookup dst_negative_table_lookup_sourcelookup. (((H) = (((((dst_positive_code_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup)) * S ((dst_positive_code_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup)) + ((dst_positive_scale_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup))) + (((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) * S ((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) + ((dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)))) * S ((((dst_positive_code_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup)) * S ((dst_positive_code_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup)) + ((dst_positive_scale_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup))) + (((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) * S ((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) + ((dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)))) + ((((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) * S ((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) + ((dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup))) + (((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) * S ((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) + ((dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)))))) /\ (((((exists ff_h_pvs_table_lookup_sourcelookuppositive. ff_h_pvs_table_lookup_sourcelookuppositive + S (dst_positive_table_lookup_sourcelookup) = S ((S (dc_input_table_lookup_source)) * dst_positive_scale_table_lookup_sourcelookup)) /\ exists ff_q_pvs_table_lookup_sourcelookuppositive. dst_positive_code_table_lookup_sourcelookup = ff_q_pvs_table_lookup_sourcelookuppositive * S ((S (dc_input_table_lookup_source)) * dst_positive_scale_table_lookup_sourcelookup) + (dst_positive_table_lookup_sourcelookup))) /\ (((((exists ff_h_pvs_table_lookup_sourcelookupnegative. ff_h_pvs_table_lookup_sourcelookupnegative + S (dst_negative_table_lookup_sourcelookup) = S ((S (dc_input_table_lookup_source)) * dst_negative_scale_table_lookup_sourcelookup)) /\ exists ff_q_pvs_table_lookup_sourcelookupnegative. dst_negative_code_table_lookup_sourcelookup = ff_q_pvs_table_lookup_sourcelookupnegative * S ((S (dc_input_table_lookup_source)) * dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_table_lookup_sourcelookup))) /\ (exists ge_balance_positive_table_lookup_sourcelookupvalue ge_balance_negative_table_lookup_sourcelookupvalue. (((((dc_output_table_lookup_source) = 2 * (ge_balance_positive_table_lookup_sourcelookupvalue) /\ (ge_balance_negative_table_lookup_sourcelookupvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcelookupvaluedecode. (((dc_output_table_lookup_source) = 2 * ge_signed_half_table_lookup_sourcelookupvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcelookupvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcelookupvalue) = S ge_signed_half_table_lookup_sourcelookupvaluedecode))) /\ ((dst_positive_table_lookup_sourcelookup) + ge_balance_negative_table_lookup_sourcelookupvalue = (dst_negative_table_lookup_sourcelookup) + ge_balance_positive_table_lookup_sourcelookupvalue))))))))) -> (((~((dc_input_table_lookup_source)=0)) /\ (exists dc_mask_table_lookup_sourcevalue. ((((exists dst_positive_code_table_lookup_sourcevaluemasktable dst_positive_scale_table_lookup_sourcevaluemasktable dst_negative_code_table_lookup_sourcevaluemasktable dst_negative_scale_table_lookup_sourcevaluemasktable. (((dc_mask_table_lookup_sourcevalue) = (((((dst_positive_code_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable)) * S ((dst_positive_code_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable)) + ((dst_positive_scale_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable))) + (((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) * S ((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) + ((dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)))) * S ((((dst_positive_code_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable)) * S ((dst_positive_code_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable)) + ((dst_positive_scale_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable))) + (((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) * S ((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) + ((dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)))) + ((((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) * S ((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) + ((dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable))) + (((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) * S ((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) + ((dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)))))) /\ (forall dst_index_table_lookup_sourcevaluemasktable. (exists pvs_le_gap_table_lookup_sourcevaluemasktabledomain. pvs_le_gap_table_lookup_sourcevaluemasktabledomain + (dst_index_table_lookup_sourcevaluemasktable) = (dc_input_table_lookup_source)) -> exists dst_positive_table_lookup_sourcevaluemasktable dst_negative_table_lookup_sourcevaluemasktable dst_value_table_lookup_sourcevaluemasktable. ((((exists ff_h_pvs_table_lookup_sourcevaluemasktableentrypositive. ff_h_pvs_table_lookup_sourcevaluemasktableentrypositive + S (dst_positive_table_lookup_sourcevaluemasktable) = S ((S (dst_index_table_lookup_sourcevaluemasktable)) * dst_positive_scale_table_lookup_sourcevaluemasktable)) /\ exists ff_q_pvs_table_lookup_sourcevaluemasktableentrypositive. dst_positive_code_table_lookup_sourcevaluemasktable = ff_q_pvs_table_lookup_sourcevaluemasktableentrypositive * S ((S (dst_index_table_lookup_sourcevaluemasktable)) * dst_positive_scale_table_lookup_sourcevaluemasktable) + (dst_positive_table_lookup_sourcevaluemasktable))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemasktableentrynegative. ff_h_pvs_table_lookup_sourcevaluemasktableentrynegative + S (dst_negative_table_lookup_sourcevaluemasktable) = S ((S (dst_index_table_lookup_sourcevaluemasktable)) * dst_negative_scale_table_lookup_sourcevaluemasktable)) /\ exists ff_q_pvs_table_lookup_sourcevaluemasktableentrynegative. dst_negative_code_table_lookup_sourcevaluemasktable = ff_q_pvs_table_lookup_sourcevaluemasktableentrynegative * S ((S (dst_index_table_lookup_sourcevaluemasktable)) * dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_table_lookup_sourcevaluemasktable))) /\ (exists ge_balance_positive_table_lookup_sourcevaluemasktableentryvalue ge_balance_negative_table_lookup_sourcevaluemasktableentryvalue. (((((dst_value_table_lookup_sourcevaluemasktable) = 2 * (ge_balance_positive_table_lookup_sourcevaluemasktableentryvalue) /\ (ge_balance_negative_table_lookup_sourcevaluemasktableentryvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemasktableentryvaluedecode. (((dst_value_table_lookup_sourcevaluemasktable) = 2 * ge_signed_half_table_lookup_sourcevaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluemasktableentryvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluemasktableentryvalue) = S ge_signed_half_table_lookup_sourcevaluemasktableentryvaluedecode))) /\ ((dst_positive_table_lookup_sourcevaluemasktable) + ge_balance_negative_table_lookup_sourcevaluemasktableentryvalue = (dst_negative_table_lookup_sourcevaluemasktable) + ge_balance_positive_table_lookup_sourcevaluemasktableentryvalue))))))))) /\ (forall dc_index_table_lookup_sourcevaluemask dc_value_table_lookup_sourcevaluemask. (exists pvs_le_gap_table_lookup_sourcevaluemaskdomain. pvs_le_gap_table_lookup_sourcevaluemaskdomain + (dc_index_table_lookup_sourcevaluemask) = (dc_input_table_lookup_source)) -> (exists dst_positive_code_table_lookup_sourcevaluemasklookup dst_positive_scale_table_lookup_sourcevaluemasklookup dst_negative_code_table_lookup_sourcevaluemasklookup dst_negative_scale_table_lookup_sourcevaluemasklookup dst_positive_table_lookup_sourcevaluemasklookup dst_negative_table_lookup_sourcevaluemasklookup. (((dc_mask_table_lookup_sourcevalue) = (((((dst_positive_code_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_positive_code_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup)) + ((dst_positive_scale_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup))) + (((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) + ((dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)))) * S ((((dst_positive_code_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_positive_code_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup)) + ((dst_positive_scale_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup))) + (((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) + ((dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)))) + ((((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) + ((dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup))) + (((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) + ((dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)))))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemasklookuppositive. ff_h_pvs_table_lookup_sourcevaluemasklookuppositive + S (dst_positive_table_lookup_sourcevaluemasklookup) = S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_positive_scale_table_lookup_sourcevaluemasklookup)) /\ exists ff_q_pvs_table_lookup_sourcevaluemasklookuppositive. dst_positive_code_table_lookup_sourcevaluemasklookup = ff_q_pvs_table_lookup_sourcevaluemasklookuppositive * S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_positive_scale_table_lookup_sourcevaluemasklookup) + (dst_positive_table_lookup_sourcevaluemasklookup))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemasklookupnegative. ff_h_pvs_table_lookup_sourcevaluemasklookupnegative + S (dst_negative_table_lookup_sourcevaluemasklookup) = S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_negative_scale_table_lookup_sourcevaluemasklookup)) /\ exists ff_q_pvs_table_lookup_sourcevaluemasklookupnegative. dst_negative_code_table_lookup_sourcevaluemasklookup = ff_q_pvs_table_lookup_sourcevaluemasklookupnegative * S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_table_lookup_sourcevaluemasklookup))) /\ (exists ge_balance_positive_table_lookup_sourcevaluemasklookupvalue ge_balance_negative_table_lookup_sourcevaluemasklookupvalue. (((((dc_value_table_lookup_sourcevaluemask) = 2 * (ge_balance_positive_table_lookup_sourcevaluemasklookupvalue) /\ (ge_balance_negative_table_lookup_sourcevaluemasklookupvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemasklookupvaluedecode. (((dc_value_table_lookup_sourcevaluemask) = 2 * ge_signed_half_table_lookup_sourcevaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluemasklookupvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluemasklookupvalue) = S ge_signed_half_table_lookup_sourcevaluemasklookupvaluedecode))) /\ ((dst_positive_table_lookup_sourcevaluemasklookup) + ge_balance_negative_table_lookup_sourcevaluemasklookupvalue = (dst_negative_table_lookup_sourcevaluemasklookup) + ge_balance_positive_table_lookup_sourcevaluemasklookupvalue))))))))) -> ((((~((dc_index_table_lookup_sourcevaluemask)=0)) /\ (exists dc_quotient_table_lookup_sourcevaluemaskentry dc_left_table_lookup_sourcevaluemaskentry dc_right_table_lookup_sourcevaluemaskentry. (((dc_input_table_lookup_source)=(dc_index_table_lookup_sourcevaluemask)*dc_quotient_table_lookup_sourcevaluemaskentry) /\ (((exists dst_positive_code_table_lookup_sourcevaluemaskentryleft dst_positive_scale_table_lookup_sourcevaluemaskentryleft dst_negative_code_table_lookup_sourcevaluemaskentryleft dst_negative_scale_table_lookup_sourcevaluemaskentryleft dst_positive_table_lookup_sourcevaluemaskentryleft dst_negative_table_lookup_sourcevaluemaskentryleft. (((F) = (((((dst_positive_code_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_positive_code_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_positive_scale_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)))) * S ((((dst_positive_code_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_positive_code_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_positive_scale_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)))) + ((((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemaskentryleftpositive. ff_h_pvs_table_lookup_sourcevaluemaskentryleftpositive + S (dst_positive_table_lookup_sourcevaluemaskentryleft) = S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) /\ exists ff_q_pvs_table_lookup_sourcevaluemaskentryleftpositive. dst_positive_code_table_lookup_sourcevaluemaskentryleft = ff_q_pvs_table_lookup_sourcevaluemaskentryleftpositive * S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_positive_scale_table_lookup_sourcevaluemaskentryleft) + (dst_positive_table_lookup_sourcevaluemaskentryleft))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemaskentryleftnegative. ff_h_pvs_table_lookup_sourcevaluemaskentryleftnegative + S (dst_negative_table_lookup_sourcevaluemaskentryleft) = S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) /\ exists ff_q_pvs_table_lookup_sourcevaluemaskentryleftnegative. dst_negative_code_table_lookup_sourcevaluemaskentryleft = ff_q_pvs_table_lookup_sourcevaluemaskentryleftnegative * S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_table_lookup_sourcevaluemaskentryleft))) /\ (exists ge_balance_positive_table_lookup_sourcevaluemaskentryleftvalue ge_balance_negative_table_lookup_sourcevaluemaskentryleftvalue. (((((dc_left_table_lookup_sourcevaluemaskentry) = 2 * (ge_balance_positive_table_lookup_sourcevaluemaskentryleftvalue) /\ (ge_balance_negative_table_lookup_sourcevaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryleftvaluedecode. (((dc_left_table_lookup_sourcevaluemaskentry) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluemaskentryleftvalue) = S ge_signed_half_table_lookup_sourcevaluemaskentryleftvaluedecode))) /\ ((dst_positive_table_lookup_sourcevaluemaskentryleft) + ge_balance_negative_table_lookup_sourcevaluemaskentryleftvalue = (dst_negative_table_lookup_sourcevaluemaskentryleft) + ge_balance_positive_table_lookup_sourcevaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_table_lookup_sourcevaluemaskentryright dst_positive_scale_table_lookup_sourcevaluemaskentryright dst_negative_code_table_lookup_sourcevaluemaskentryright dst_negative_scale_table_lookup_sourcevaluemaskentryright dst_positive_table_lookup_sourcevaluemaskentryright dst_negative_table_lookup_sourcevaluemaskentryright. (((G) = (((((dst_positive_code_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_positive_code_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_positive_scale_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)))) * S ((((dst_positive_code_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_positive_code_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_positive_scale_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)))) + ((((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)))))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemaskentryrightpositive. ff_h_pvs_table_lookup_sourcevaluemaskentryrightpositive + S (dst_positive_table_lookup_sourcevaluemaskentryright) = S ((S (dc_quotient_table_lookup_sourcevaluemaskentry)) * dst_positive_scale_table_lookup_sourcevaluemaskentryright)) /\ exists ff_q_pvs_table_lookup_sourcevaluemaskentryrightpositive. dst_positive_code_table_lookup_sourcevaluemaskentryright = ff_q_pvs_table_lookup_sourcevaluemaskentryrightpositive * S ((S (dc_quotient_table_lookup_sourcevaluemaskentry)) * dst_positive_scale_table_lookup_sourcevaluemaskentryright) + (dst_positive_table_lookup_sourcevaluemaskentryright))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemaskentryrightnegative. ff_h_pvs_table_lookup_sourcevaluemaskentryrightnegative + S (dst_negative_table_lookup_sourcevaluemaskentryright) = S ((S (dc_quotient_table_lookup_sourcevaluemaskentry)) * dst_negative_scale_table_lookup_sourcevaluemaskentryright)) /\ exists ff_q_pvs_table_lookup_sourcevaluemaskentryrightnegative. dst_negative_code_table_lookup_sourcevaluemaskentryright = ff_q_pvs_table_lookup_sourcevaluemaskentryrightnegative * S ((S (dc_quotient_table_lookup_sourcevaluemaskentry)) * dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_table_lookup_sourcevaluemaskentryright))) /\ (exists ge_balance_positive_table_lookup_sourcevaluemaskentryrightvalue ge_balance_negative_table_lookup_sourcevaluemaskentryrightvalue. (((((dc_right_table_lookup_sourcevaluemaskentry) = 2 * (ge_balance_positive_table_lookup_sourcevaluemaskentryrightvalue) /\ (ge_balance_negative_table_lookup_sourcevaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryrightvaluedecode. (((dc_right_table_lookup_sourcevaluemaskentry) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluemaskentryrightvalue) = S ge_signed_half_table_lookup_sourcevaluemaskentryrightvaluedecode))) /\ ((dst_positive_table_lookup_sourcevaluemaskentryright) + ge_balance_negative_table_lookup_sourcevaluemaskentryrightvalue = (dst_negative_table_lookup_sourcevaluemaskentryright) + ge_balance_positive_table_lookup_sourcevaluemaskentryrightvalue))))))))) /\ (exists sto_ap_table_lookup_sourcevaluemaskentryproduct sto_an_table_lookup_sourcevaluemaskentryproduct sto_bp_table_lookup_sourcevaluemaskentryproduct sto_bn_table_lookup_sourcevaluemaskentryproduct sto_cp_table_lookup_sourcevaluemaskentryproduct sto_cn_table_lookup_sourcevaluemaskentryproduct. (((((dc_left_table_lookup_sourcevaluemaskentry) = 2 * (sto_ap_table_lookup_sourcevaluemaskentryproduct) /\ (sto_an_table_lookup_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryproductleft. (((dc_left_table_lookup_sourcevaluemaskentry) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryproductleft + 1 /\ (sto_ap_table_lookup_sourcevaluemaskentryproduct) = 0) /\ (sto_an_table_lookup_sourcevaluemaskentryproduct) = S ge_signed_half_table_lookup_sourcevaluemaskentryproductleft))) /\ ((((((dc_right_table_lookup_sourcevaluemaskentry) = 2 * (sto_bp_table_lookup_sourcevaluemaskentryproduct) /\ (sto_bn_table_lookup_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryproductright. (((dc_right_table_lookup_sourcevaluemaskentry) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryproductright + 1 /\ (sto_bp_table_lookup_sourcevaluemaskentryproduct) = 0) /\ (sto_bn_table_lookup_sourcevaluemaskentryproduct) = S ge_signed_half_table_lookup_sourcevaluemaskentryproductright))) /\ ((((((dc_value_table_lookup_sourcevaluemask) = 2 * (sto_cp_table_lookup_sourcevaluemaskentryproduct) /\ (sto_cn_table_lookup_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryproductoutput. (((dc_value_table_lookup_sourcevaluemask) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryproductoutput + 1 /\ (sto_cp_table_lookup_sourcevaluemaskentryproduct) = 0) /\ (sto_cn_table_lookup_sourcevaluemaskentryproduct) = S ge_signed_half_table_lookup_sourcevaluemaskentryproductoutput))) /\ ((sto_ap_table_lookup_sourcevaluemaskentryproduct * sto_bp_table_lookup_sourcevaluemaskentryproduct + sto_an_table_lookup_sourcevaluemaskentryproduct * sto_bn_table_lookup_sourcevaluemaskentryproduct) + sto_cn_table_lookup_sourcevaluemaskentryproduct = (sto_ap_table_lookup_sourcevaluemaskentryproduct * sto_bn_table_lookup_sourcevaluemaskentryproduct + sto_an_table_lookup_sourcevaluemaskentryproduct * sto_bp_table_lookup_sourcevaluemaskentryproduct) + sto_cp_table_lookup_sourcevaluemaskentryproduct))))))))))))))) \/ ((((dc_index_table_lookup_sourcevaluemask)=0 \/ ~(exists pvs_factor_table_lookup_sourcevaluemaskentrynondivisor. (dc_input_table_lookup_source) = (dc_index_table_lookup_sourcevaluemask) * pvs_factor_table_lookup_sourcevaluemaskentrynondivisor)) /\ ((dc_value_table_lookup_sourcevaluemask)=0))))))) /\ (exists dst_positive_code_table_lookup_sourcevaluefold dst_positive_scale_table_lookup_sourcevaluefold dst_negative_code_table_lookup_sourcevaluefold dst_negative_scale_table_lookup_sourcevaluefold dst_positive_sum_table_lookup_sourcevaluefold dst_negative_sum_table_lookup_sourcevaluefold. (((dc_mask_table_lookup_sourcevalue) = (((((dst_positive_code_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold)) * S ((dst_positive_code_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold)) + ((dst_positive_scale_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold))) + (((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) * S ((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) + ((dst_negative_scale_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)))) * S ((((dst_positive_code_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold)) * S ((dst_positive_code_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold)) + ((dst_positive_scale_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold))) + (((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) * S ((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) + ((dst_negative_scale_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)))) + ((((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) * S ((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) + ((dst_negative_scale_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold))) + (((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) * S ((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) + ((dst_negative_scale_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)))))) /\ (((exists fs_u_dst_table_lookup_sourcevaluefoldpositive fs_v_dst_table_lookup_sourcevaluefoldpositive. ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_start. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_table_lookup_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_start. fs_u_dst_table_lookup_sourcevaluefoldpositive = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_table_lookup_sourcevaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_terminal. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_terminal + S (dst_positive_sum_table_lookup_sourcevaluefold) = S ((S (S (dc_input_table_lookup_source))) * fs_v_dst_table_lookup_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_terminal. fs_u_dst_table_lookup_sourcevaluefoldpositive = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_terminal * S ((S (S (dc_input_table_lookup_source))) * fs_v_dst_table_lookup_sourcevaluefoldpositive) + (dst_positive_sum_table_lookup_sourcevaluefold))) /\ forall fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps. (exists fs_lt_dst_table_lookup_sourcevaluefoldpositive_body_steps_bound. fs_lt_dst_table_lookup_sourcevaluefoldpositive_body_steps_bound + S fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps = S (dc_input_table_lookup_source)) -> exists fs_a_dst_table_lookup_sourcevaluefoldpositive_body_steps fs_r_dst_table_lookup_sourcevaluefoldpositive_body_steps fs_s_dst_table_lookup_sourcevaluefoldpositive_body_steps. ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_summand. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_summand + S (fs_a_dst_table_lookup_sourcevaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * dst_positive_scale_table_lookup_sourcevaluefold)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_summand. dst_positive_code_table_lookup_sourcevaluefold = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * dst_positive_scale_table_lookup_sourcevaluefold) + (fs_a_dst_table_lookup_sourcevaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_partial. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_partial + S (fs_r_dst_table_lookup_sourcevaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_partial. fs_u_dst_table_lookup_sourcevaluefoldpositive = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldpositive) + (fs_r_dst_table_lookup_sourcevaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_successor. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_successor + S (fs_s_dst_table_lookup_sourcevaluefoldpositive_body_steps) = S ((S (S fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_successor. fs_u_dst_table_lookup_sourcevaluefoldpositive = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldpositive) + (fs_s_dst_table_lookup_sourcevaluefoldpositive_body_steps))) /\ fs_s_dst_table_lookup_sourcevaluefoldpositive_body_steps = fs_r_dst_table_lookup_sourcevaluefoldpositive_body_steps + fs_a_dst_table_lookup_sourcevaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_table_lookup_sourcevaluefoldnegative fs_v_dst_table_lookup_sourcevaluefoldnegative. ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_start. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_table_lookup_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_start. fs_u_dst_table_lookup_sourcevaluefoldnegative = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_table_lookup_sourcevaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_terminal. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_terminal + S (dst_negative_sum_table_lookup_sourcevaluefold) = S ((S (S (dc_input_table_lookup_source))) * fs_v_dst_table_lookup_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_terminal. fs_u_dst_table_lookup_sourcevaluefoldnegative = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_terminal * S ((S (S (dc_input_table_lookup_source))) * fs_v_dst_table_lookup_sourcevaluefoldnegative) + (dst_negative_sum_table_lookup_sourcevaluefold))) /\ forall fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps. (exists fs_lt_dst_table_lookup_sourcevaluefoldnegative_body_steps_bound. fs_lt_dst_table_lookup_sourcevaluefoldnegative_body_steps_bound + S fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps = S (dc_input_table_lookup_source)) -> exists fs_a_dst_table_lookup_sourcevaluefoldnegative_body_steps fs_r_dst_table_lookup_sourcevaluefoldnegative_body_steps fs_s_dst_table_lookup_sourcevaluefoldnegative_body_steps. ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_summand. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_summand + S (fs_a_dst_table_lookup_sourcevaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * dst_negative_scale_table_lookup_sourcevaluefold)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_summand. dst_negative_code_table_lookup_sourcevaluefold = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * dst_negative_scale_table_lookup_sourcevaluefold) + (fs_a_dst_table_lookup_sourcevaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_partial. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_partial + S (fs_r_dst_table_lookup_sourcevaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_partial. fs_u_dst_table_lookup_sourcevaluefoldnegative = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldnegative) + (fs_r_dst_table_lookup_sourcevaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_successor. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_successor + S (fs_s_dst_table_lookup_sourcevaluefoldnegative_body_steps) = S ((S (S fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_successor. fs_u_dst_table_lookup_sourcevaluefoldnegative = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldnegative) + (fs_s_dst_table_lookup_sourcevaluefoldnegative_body_steps))) /\ fs_s_dst_table_lookup_sourcevaluefoldnegative_body_steps = fs_r_dst_table_lookup_sourcevaluefoldnegative_body_steps + fs_a_dst_table_lookup_sourcevaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_table_lookup_sourcevaluefoldresult ge_balance_negative_table_lookup_sourcevaluefoldresult. (((((dc_output_table_lookup_source) = 2 * (ge_balance_positive_table_lookup_sourcevaluefoldresult) /\ (ge_balance_negative_table_lookup_sourcevaluefoldresult) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluefoldresultdecode. (((dc_output_table_lookup_source) = 2 * ge_signed_half_table_lookup_sourcevaluefoldresultdecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluefoldresult) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluefoldresult) = S ge_signed_half_table_lookup_sourcevaluefoldresultdecode))) /\ ((dst_positive_sum_table_lookup_sourcevaluefold) + ge_balance_negative_table_lookup_sourcevaluefoldresult = (dst_negative_sum_table_lookup_sourcevaluefold) + ge_balance_positive_table_lookup_sourcevaluefoldresult)))))))))))))))))))) -> ~(n=0) -> (exists pvs_le_gap_table_lookup_bound. pvs_le_gap_table_lookup_bound + (n) = (N)) -> exists z. (exists dst_positive_code_table_lookup_entry dst_positive_scale_table_lookup_entry dst_negative_code_table_lookup_entry dst_negative_scale_table_lookup_entry dst_positive_table_lookup_entry dst_negative_table_lookup_entry. (((H) = (((((dst_positive_code_table_lookup_entry) + (dst_positive_scale_table_lookup_entry)) * S ((dst_positive_code_table_lookup_entry) + (dst_positive_scale_table_lookup_entry)) + ((dst_positive_scale_table_lookup_entry) + (dst_positive_scale_table_lookup_entry))) + (((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) * S ((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) + ((dst_negative_scale_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)))) * S ((((dst_positive_code_table_lookup_entry) + (dst_positive_scale_table_lookup_entry)) * S ((dst_positive_code_table_lookup_entry) + (dst_positive_scale_table_lookup_entry)) + ((dst_positive_scale_table_lookup_entry) + (dst_positive_scale_table_lookup_entry))) + (((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) * S ((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) + ((dst_negative_scale_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)))) + ((((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) * S ((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) + ((dst_negative_scale_table_lookup_entry) + (dst_negative_scale_table_lookup_entry))) + (((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) * S ((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) + ((dst_negative_scale_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)))))) /\ (((((exists ff_h_pvs_table_lookup_entrypositive. ff_h_pvs_table_lookup_entrypositive + S (dst_positive_table_lookup_entry) = S ((S (n)) * dst_positive_scale_table_lookup_entry)) /\ exists ff_q_pvs_table_lookup_entrypositive. dst_positive_code_table_lookup_entry = ff_q_pvs_table_lookup_entrypositive * S ((S (n)) * dst_positive_scale_table_lookup_entry) + (dst_positive_table_lookup_entry))) /\ (((((exists ff_h_pvs_table_lookup_entrynegative. ff_h_pvs_table_lookup_entrynegative + S (dst_negative_table_lookup_entry) = S ((S (n)) * dst_negative_scale_table_lookup_entry)) /\ exists ff_q_pvs_table_lookup_entrynegative. dst_negative_code_table_lookup_entry = ff_q_pvs_table_lookup_entrynegative * S ((S (n)) * dst_negative_scale_table_lookup_entry) + (dst_negative_table_lookup_entry))) /\ (exists ge_balance_positive_table_lookup_entryvalue ge_balance_negative_table_lookup_entryvalue. (((((z) = 2 * (ge_balance_positive_table_lookup_entryvalue) /\ (ge_balance_negative_table_lookup_entryvalue) = 0) \/ exists ge_signed_half_table_lookup_entryvaluedecode. (((z) = 2 * ge_signed_half_table_lookup_entryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_entryvalue) = 0) /\ (ge_balance_negative_table_lookup_entryvalue) = S ge_signed_half_table_lookup_entryvaluedecode))) /\ ((dst_positive_table_lookup_entry) + ge_balance_negative_table_lookup_entryvalue = (dst_negative_table_lookup_entry) + ge_balance_positive_table_lookup_entryvalue))))))))) /\ (((~((n)=0)) /\ (exists dc_mask_table_lookup_value. ((((exists dst_positive_code_table_lookup_valuemasktable dst_positive_scale_table_lookup_valuemasktable dst_negative_code_table_lookup_valuemasktable dst_negative_scale_table_lookup_valuemasktable. (((dc_mask_table_lookup_value) = (((((dst_positive_code_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable)) * S ((dst_positive_code_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable)) + ((dst_positive_scale_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable))) + (((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) * S ((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) + ((dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)))) * S ((((dst_positive_code_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable)) * S ((dst_positive_code_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable)) + ((dst_positive_scale_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable))) + (((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) * S ((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) + ((dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)))) + ((((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) * S ((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) + ((dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable))) + (((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) * S ((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) + ((dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)))))) /\ (forall dst_index_table_lookup_valuemasktable. (exists pvs_le_gap_table_lookup_valuemasktabledomain. pvs_le_gap_table_lookup_valuemasktabledomain + (dst_index_table_lookup_valuemasktable) = (n)) -> exists dst_positive_table_lookup_valuemasktable dst_negative_table_lookup_valuemasktable dst_value_table_lookup_valuemasktable. ((((exists ff_h_pvs_table_lookup_valuemasktableentrypositive. ff_h_pvs_table_lookup_valuemasktableentrypositive + S (dst_positive_table_lookup_valuemasktable) = S ((S (dst_index_table_lookup_valuemasktable)) * dst_positive_scale_table_lookup_valuemasktable)) /\ exists ff_q_pvs_table_lookup_valuemasktableentrypositive. dst_positive_code_table_lookup_valuemasktable = ff_q_pvs_table_lookup_valuemasktableentrypositive * S ((S (dst_index_table_lookup_valuemasktable)) * dst_positive_scale_table_lookup_valuemasktable) + (dst_positive_table_lookup_valuemasktable))) /\ (((((exists ff_h_pvs_table_lookup_valuemasktableentrynegative. ff_h_pvs_table_lookup_valuemasktableentrynegative + S (dst_negative_table_lookup_valuemasktable) = S ((S (dst_index_table_lookup_valuemasktable)) * dst_negative_scale_table_lookup_valuemasktable)) /\ exists ff_q_pvs_table_lookup_valuemasktableentrynegative. dst_negative_code_table_lookup_valuemasktable = ff_q_pvs_table_lookup_valuemasktableentrynegative * S ((S (dst_index_table_lookup_valuemasktable)) * dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_table_lookup_valuemasktable))) /\ (exists ge_balance_positive_table_lookup_valuemasktableentryvalue ge_balance_negative_table_lookup_valuemasktableentryvalue. (((((dst_value_table_lookup_valuemasktable) = 2 * (ge_balance_positive_table_lookup_valuemasktableentryvalue) /\ (ge_balance_negative_table_lookup_valuemasktableentryvalue) = 0) \/ exists ge_signed_half_table_lookup_valuemasktableentryvaluedecode. (((dst_value_table_lookup_valuemasktable) = 2 * ge_signed_half_table_lookup_valuemasktableentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_valuemasktableentryvalue) = 0) /\ (ge_balance_negative_table_lookup_valuemasktableentryvalue) = S ge_signed_half_table_lookup_valuemasktableentryvaluedecode))) /\ ((dst_positive_table_lookup_valuemasktable) + ge_balance_negative_table_lookup_valuemasktableentryvalue = (dst_negative_table_lookup_valuemasktable) + ge_balance_positive_table_lookup_valuemasktableentryvalue))))))))) /\ (forall dc_index_table_lookup_valuemask dc_value_table_lookup_valuemask. (exists pvs_le_gap_table_lookup_valuemaskdomain. pvs_le_gap_table_lookup_valuemaskdomain + (dc_index_table_lookup_valuemask) = (n)) -> (exists dst_positive_code_table_lookup_valuemasklookup dst_positive_scale_table_lookup_valuemasklookup dst_negative_code_table_lookup_valuemasklookup dst_negative_scale_table_lookup_valuemasklookup dst_positive_table_lookup_valuemasklookup dst_negative_table_lookup_valuemasklookup. (((dc_mask_table_lookup_value) = (((((dst_positive_code_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup)) * S ((dst_positive_code_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup)) + ((dst_positive_scale_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup))) + (((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) * S ((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) + ((dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)))) * S ((((dst_positive_code_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup)) * S ((dst_positive_code_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup)) + ((dst_positive_scale_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup))) + (((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) * S ((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) + ((dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)))) + ((((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) * S ((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) + ((dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup))) + (((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) * S ((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) + ((dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)))))) /\ (((((exists ff_h_pvs_table_lookup_valuemasklookuppositive. ff_h_pvs_table_lookup_valuemasklookuppositive + S (dst_positive_table_lookup_valuemasklookup) = S ((S (dc_index_table_lookup_valuemask)) * dst_positive_scale_table_lookup_valuemasklookup)) /\ exists ff_q_pvs_table_lookup_valuemasklookuppositive. dst_positive_code_table_lookup_valuemasklookup = ff_q_pvs_table_lookup_valuemasklookuppositive * S ((S (dc_index_table_lookup_valuemask)) * dst_positive_scale_table_lookup_valuemasklookup) + (dst_positive_table_lookup_valuemasklookup))) /\ (((((exists ff_h_pvs_table_lookup_valuemasklookupnegative. ff_h_pvs_table_lookup_valuemasklookupnegative + S (dst_negative_table_lookup_valuemasklookup) = S ((S (dc_index_table_lookup_valuemask)) * dst_negative_scale_table_lookup_valuemasklookup)) /\ exists ff_q_pvs_table_lookup_valuemasklookupnegative. dst_negative_code_table_lookup_valuemasklookup = ff_q_pvs_table_lookup_valuemasklookupnegative * S ((S (dc_index_table_lookup_valuemask)) * dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_table_lookup_valuemasklookup))) /\ (exists ge_balance_positive_table_lookup_valuemasklookupvalue ge_balance_negative_table_lookup_valuemasklookupvalue. (((((dc_value_table_lookup_valuemask) = 2 * (ge_balance_positive_table_lookup_valuemasklookupvalue) /\ (ge_balance_negative_table_lookup_valuemasklookupvalue) = 0) \/ exists ge_signed_half_table_lookup_valuemasklookupvaluedecode. (((dc_value_table_lookup_valuemask) = 2 * ge_signed_half_table_lookup_valuemasklookupvaluedecode + 1 /\ (ge_balance_positive_table_lookup_valuemasklookupvalue) = 0) /\ (ge_balance_negative_table_lookup_valuemasklookupvalue) = S ge_signed_half_table_lookup_valuemasklookupvaluedecode))) /\ ((dst_positive_table_lookup_valuemasklookup) + ge_balance_negative_table_lookup_valuemasklookupvalue = (dst_negative_table_lookup_valuemasklookup) + ge_balance_positive_table_lookup_valuemasklookupvalue))))))))) -> ((((~((dc_index_table_lookup_valuemask)=0)) /\ (exists dc_quotient_table_lookup_valuemaskentry dc_left_table_lookup_valuemaskentry dc_right_table_lookup_valuemaskentry. (((n)=(dc_index_table_lookup_valuemask)*dc_quotient_table_lookup_valuemaskentry) /\ (((exists dst_positive_code_table_lookup_valuemaskentryleft dst_positive_scale_table_lookup_valuemaskentryleft dst_negative_code_table_lookup_valuemaskentryleft dst_negative_scale_table_lookup_valuemaskentryleft dst_positive_table_lookup_valuemaskentryleft dst_negative_table_lookup_valuemaskentryleft. (((F) = (((((dst_positive_code_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft)) * S ((dst_positive_code_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft)) + ((dst_positive_scale_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft))) + (((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) * S ((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) + ((dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)))) * S ((((dst_positive_code_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft)) * S ((dst_positive_code_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft)) + ((dst_positive_scale_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft))) + (((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) * S ((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) + ((dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)))) + ((((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) * S ((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) + ((dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft))) + (((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) * S ((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) + ((dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)))))) /\ (((((exists ff_h_pvs_table_lookup_valuemaskentryleftpositive. ff_h_pvs_table_lookup_valuemaskentryleftpositive + S (dst_positive_table_lookup_valuemaskentryleft) = S ((S (dc_index_table_lookup_valuemask)) * dst_positive_scale_table_lookup_valuemaskentryleft)) /\ exists ff_q_pvs_table_lookup_valuemaskentryleftpositive. dst_positive_code_table_lookup_valuemaskentryleft = ff_q_pvs_table_lookup_valuemaskentryleftpositive * S ((S (dc_index_table_lookup_valuemask)) * dst_positive_scale_table_lookup_valuemaskentryleft) + (dst_positive_table_lookup_valuemaskentryleft))) /\ (((((exists ff_h_pvs_table_lookup_valuemaskentryleftnegative. ff_h_pvs_table_lookup_valuemaskentryleftnegative + S (dst_negative_table_lookup_valuemaskentryleft) = S ((S (dc_index_table_lookup_valuemask)) * dst_negative_scale_table_lookup_valuemaskentryleft)) /\ exists ff_q_pvs_table_lookup_valuemaskentryleftnegative. dst_negative_code_table_lookup_valuemaskentryleft = ff_q_pvs_table_lookup_valuemaskentryleftnegative * S ((S (dc_index_table_lookup_valuemask)) * dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_table_lookup_valuemaskentryleft))) /\ (exists ge_balance_positive_table_lookup_valuemaskentryleftvalue ge_balance_negative_table_lookup_valuemaskentryleftvalue. (((((dc_left_table_lookup_valuemaskentry) = 2 * (ge_balance_positive_table_lookup_valuemaskentryleftvalue) /\ (ge_balance_negative_table_lookup_valuemaskentryleftvalue) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryleftvaluedecode. (((dc_left_table_lookup_valuemaskentry) = 2 * ge_signed_half_table_lookup_valuemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_table_lookup_valuemaskentryleftvalue) = 0) /\ (ge_balance_negative_table_lookup_valuemaskentryleftvalue) = S ge_signed_half_table_lookup_valuemaskentryleftvaluedecode))) /\ ((dst_positive_table_lookup_valuemaskentryleft) + ge_balance_negative_table_lookup_valuemaskentryleftvalue = (dst_negative_table_lookup_valuemaskentryleft) + ge_balance_positive_table_lookup_valuemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_table_lookup_valuemaskentryright dst_positive_scale_table_lookup_valuemaskentryright dst_negative_code_table_lookup_valuemaskentryright dst_negative_scale_table_lookup_valuemaskentryright dst_positive_table_lookup_valuemaskentryright dst_negative_table_lookup_valuemaskentryright. (((G) = (((((dst_positive_code_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright)) * S ((dst_positive_code_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright)) + ((dst_positive_scale_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright))) + (((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) * S ((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) + ((dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)))) * S ((((dst_positive_code_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright)) * S ((dst_positive_code_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright)) + ((dst_positive_scale_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright))) + (((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) * S ((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) + ((dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)))) + ((((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) * S ((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) + ((dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright))) + (((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) * S ((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) + ((dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)))))) /\ (((((exists ff_h_pvs_table_lookup_valuemaskentryrightpositive. ff_h_pvs_table_lookup_valuemaskentryrightpositive + S (dst_positive_table_lookup_valuemaskentryright) = S ((S (dc_quotient_table_lookup_valuemaskentry)) * dst_positive_scale_table_lookup_valuemaskentryright)) /\ exists ff_q_pvs_table_lookup_valuemaskentryrightpositive. dst_positive_code_table_lookup_valuemaskentryright = ff_q_pvs_table_lookup_valuemaskentryrightpositive * S ((S (dc_quotient_table_lookup_valuemaskentry)) * dst_positive_scale_table_lookup_valuemaskentryright) + (dst_positive_table_lookup_valuemaskentryright))) /\ (((((exists ff_h_pvs_table_lookup_valuemaskentryrightnegative. ff_h_pvs_table_lookup_valuemaskentryrightnegative + S (dst_negative_table_lookup_valuemaskentryright) = S ((S (dc_quotient_table_lookup_valuemaskentry)) * dst_negative_scale_table_lookup_valuemaskentryright)) /\ exists ff_q_pvs_table_lookup_valuemaskentryrightnegative. dst_negative_code_table_lookup_valuemaskentryright = ff_q_pvs_table_lookup_valuemaskentryrightnegative * S ((S (dc_quotient_table_lookup_valuemaskentry)) * dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_table_lookup_valuemaskentryright))) /\ (exists ge_balance_positive_table_lookup_valuemaskentryrightvalue ge_balance_negative_table_lookup_valuemaskentryrightvalue. (((((dc_right_table_lookup_valuemaskentry) = 2 * (ge_balance_positive_table_lookup_valuemaskentryrightvalue) /\ (ge_balance_negative_table_lookup_valuemaskentryrightvalue) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryrightvaluedecode. (((dc_right_table_lookup_valuemaskentry) = 2 * ge_signed_half_table_lookup_valuemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_table_lookup_valuemaskentryrightvalue) = 0) /\ (ge_balance_negative_table_lookup_valuemaskentryrightvalue) = S ge_signed_half_table_lookup_valuemaskentryrightvaluedecode))) /\ ((dst_positive_table_lookup_valuemaskentryright) + ge_balance_negative_table_lookup_valuemaskentryrightvalue = (dst_negative_table_lookup_valuemaskentryright) + ge_balance_positive_table_lookup_valuemaskentryrightvalue))))))))) /\ (exists sto_ap_table_lookup_valuemaskentryproduct sto_an_table_lookup_valuemaskentryproduct sto_bp_table_lookup_valuemaskentryproduct sto_bn_table_lookup_valuemaskentryproduct sto_cp_table_lookup_valuemaskentryproduct sto_cn_table_lookup_valuemaskentryproduct. (((((dc_left_table_lookup_valuemaskentry) = 2 * (sto_ap_table_lookup_valuemaskentryproduct) /\ (sto_an_table_lookup_valuemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryproductleft. (((dc_left_table_lookup_valuemaskentry) = 2 * ge_signed_half_table_lookup_valuemaskentryproductleft + 1 /\ (sto_ap_table_lookup_valuemaskentryproduct) = 0) /\ (sto_an_table_lookup_valuemaskentryproduct) = S ge_signed_half_table_lookup_valuemaskentryproductleft))) /\ ((((((dc_right_table_lookup_valuemaskentry) = 2 * (sto_bp_table_lookup_valuemaskentryproduct) /\ (sto_bn_table_lookup_valuemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryproductright. (((dc_right_table_lookup_valuemaskentry) = 2 * ge_signed_half_table_lookup_valuemaskentryproductright + 1 /\ (sto_bp_table_lookup_valuemaskentryproduct) = 0) /\ (sto_bn_table_lookup_valuemaskentryproduct) = S ge_signed_half_table_lookup_valuemaskentryproductright))) /\ ((((((dc_value_table_lookup_valuemask) = 2 * (sto_cp_table_lookup_valuemaskentryproduct) /\ (sto_cn_table_lookup_valuemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryproductoutput. (((dc_value_table_lookup_valuemask) = 2 * ge_signed_half_table_lookup_valuemaskentryproductoutput + 1 /\ (sto_cp_table_lookup_valuemaskentryproduct) = 0) /\ (sto_cn_table_lookup_valuemaskentryproduct) = S ge_signed_half_table_lookup_valuemaskentryproductoutput))) /\ ((sto_ap_table_lookup_valuemaskentryproduct * sto_bp_table_lookup_valuemaskentryproduct + sto_an_table_lookup_valuemaskentryproduct * sto_bn_table_lookup_valuemaskentryproduct) + sto_cn_table_lookup_valuemaskentryproduct = (sto_ap_table_lookup_valuemaskentryproduct * sto_bn_table_lookup_valuemaskentryproduct + sto_an_table_lookup_valuemaskentryproduct * sto_bp_table_lookup_valuemaskentryproduct) + sto_cp_table_lookup_valuemaskentryproduct))))))))))))))) \/ ((((dc_index_table_lookup_valuemask)=0 \/ ~(exists pvs_factor_table_lookup_valuemaskentrynondivisor. (n) = (dc_index_table_lookup_valuemask) * pvs_factor_table_lookup_valuemaskentrynondivisor)) /\ ((dc_value_table_lookup_valuemask)=0))))))) /\ (exists dst_positive_code_table_lookup_valuefold dst_positive_scale_table_lookup_valuefold dst_negative_code_table_lookup_valuefold dst_negative_scale_table_lookup_valuefold dst_positive_sum_table_lookup_valuefold dst_negative_sum_table_lookup_valuefold. (((dc_mask_table_lookup_value) = (((((dst_positive_code_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold)) * S ((dst_positive_code_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold)) + ((dst_positive_scale_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold))) + (((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) * S ((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) + ((dst_negative_scale_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)))) * S ((((dst_positive_code_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold)) * S ((dst_positive_code_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold)) + ((dst_positive_scale_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold))) + (((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) * S ((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) + ((dst_negative_scale_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)))) + ((((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) * S ((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) + ((dst_negative_scale_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold))) + (((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) * S ((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) + ((dst_negative_scale_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)))))) /\ (((exists fs_u_dst_table_lookup_valuefoldpositive fs_v_dst_table_lookup_valuefoldpositive. ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_start. fs_h_dst_table_lookup_valuefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_table_lookup_valuefoldpositive)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_start. fs_u_dst_table_lookup_valuefoldpositive = fs_q_dst_table_lookup_valuefoldpositive_body_start * S ((S (0)) * fs_v_dst_table_lookup_valuefoldpositive) + (0))) /\ ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_terminal. fs_h_dst_table_lookup_valuefoldpositive_body_terminal + S (dst_positive_sum_table_lookup_valuefold) = S ((S (S (n))) * fs_v_dst_table_lookup_valuefoldpositive)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_terminal. fs_u_dst_table_lookup_valuefoldpositive = fs_q_dst_table_lookup_valuefoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_table_lookup_valuefoldpositive) + (dst_positive_sum_table_lookup_valuefold))) /\ forall fs_i_dst_table_lookup_valuefoldpositive_body_steps. (exists fs_lt_dst_table_lookup_valuefoldpositive_body_steps_bound. fs_lt_dst_table_lookup_valuefoldpositive_body_steps_bound + S fs_i_dst_table_lookup_valuefoldpositive_body_steps = S (n)) -> exists fs_a_dst_table_lookup_valuefoldpositive_body_steps fs_r_dst_table_lookup_valuefoldpositive_body_steps fs_s_dst_table_lookup_valuefoldpositive_body_steps. ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_steps_summand. fs_h_dst_table_lookup_valuefoldpositive_body_steps_summand + S (fs_a_dst_table_lookup_valuefoldpositive_body_steps) = S ((S (fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * dst_positive_scale_table_lookup_valuefold)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_steps_summand. dst_positive_code_table_lookup_valuefold = fs_q_dst_table_lookup_valuefoldpositive_body_steps_summand * S ((S (fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * dst_positive_scale_table_lookup_valuefold) + (fs_a_dst_table_lookup_valuefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_steps_partial. fs_h_dst_table_lookup_valuefoldpositive_body_steps_partial + S (fs_r_dst_table_lookup_valuefoldpositive_body_steps) = S ((S (fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * fs_v_dst_table_lookup_valuefoldpositive)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_steps_partial. fs_u_dst_table_lookup_valuefoldpositive = fs_q_dst_table_lookup_valuefoldpositive_body_steps_partial * S ((S (fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * fs_v_dst_table_lookup_valuefoldpositive) + (fs_r_dst_table_lookup_valuefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_steps_successor. fs_h_dst_table_lookup_valuefoldpositive_body_steps_successor + S (fs_s_dst_table_lookup_valuefoldpositive_body_steps) = S ((S (S fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * fs_v_dst_table_lookup_valuefoldpositive)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_steps_successor. fs_u_dst_table_lookup_valuefoldpositive = fs_q_dst_table_lookup_valuefoldpositive_body_steps_successor * S ((S (S fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * fs_v_dst_table_lookup_valuefoldpositive) + (fs_s_dst_table_lookup_valuefoldpositive_body_steps))) /\ fs_s_dst_table_lookup_valuefoldpositive_body_steps = fs_r_dst_table_lookup_valuefoldpositive_body_steps + fs_a_dst_table_lookup_valuefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_table_lookup_valuefoldnegative fs_v_dst_table_lookup_valuefoldnegative. ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_start. fs_h_dst_table_lookup_valuefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_table_lookup_valuefoldnegative)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_start. fs_u_dst_table_lookup_valuefoldnegative = fs_q_dst_table_lookup_valuefoldnegative_body_start * S ((S (0)) * fs_v_dst_table_lookup_valuefoldnegative) + (0))) /\ ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_terminal. fs_h_dst_table_lookup_valuefoldnegative_body_terminal + S (dst_negative_sum_table_lookup_valuefold) = S ((S (S (n))) * fs_v_dst_table_lookup_valuefoldnegative)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_terminal. fs_u_dst_table_lookup_valuefoldnegative = fs_q_dst_table_lookup_valuefoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_table_lookup_valuefoldnegative) + (dst_negative_sum_table_lookup_valuefold))) /\ forall fs_i_dst_table_lookup_valuefoldnegative_body_steps. (exists fs_lt_dst_table_lookup_valuefoldnegative_body_steps_bound. fs_lt_dst_table_lookup_valuefoldnegative_body_steps_bound + S fs_i_dst_table_lookup_valuefoldnegative_body_steps = S (n)) -> exists fs_a_dst_table_lookup_valuefoldnegative_body_steps fs_r_dst_table_lookup_valuefoldnegative_body_steps fs_s_dst_table_lookup_valuefoldnegative_body_steps. ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_steps_summand. fs_h_dst_table_lookup_valuefoldnegative_body_steps_summand + S (fs_a_dst_table_lookup_valuefoldnegative_body_steps) = S ((S (fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * dst_negative_scale_table_lookup_valuefold)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_steps_summand. dst_negative_code_table_lookup_valuefold = fs_q_dst_table_lookup_valuefoldnegative_body_steps_summand * S ((S (fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * dst_negative_scale_table_lookup_valuefold) + (fs_a_dst_table_lookup_valuefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_steps_partial. fs_h_dst_table_lookup_valuefoldnegative_body_steps_partial + S (fs_r_dst_table_lookup_valuefoldnegative_body_steps) = S ((S (fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * fs_v_dst_table_lookup_valuefoldnegative)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_steps_partial. fs_u_dst_table_lookup_valuefoldnegative = fs_q_dst_table_lookup_valuefoldnegative_body_steps_partial * S ((S (fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * fs_v_dst_table_lookup_valuefoldnegative) + (fs_r_dst_table_lookup_valuefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_steps_successor. fs_h_dst_table_lookup_valuefoldnegative_body_steps_successor + S (fs_s_dst_table_lookup_valuefoldnegative_body_steps) = S ((S (S fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * fs_v_dst_table_lookup_valuefoldnegative)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_steps_successor. fs_u_dst_table_lookup_valuefoldnegative = fs_q_dst_table_lookup_valuefoldnegative_body_steps_successor * S ((S (S fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * fs_v_dst_table_lookup_valuefoldnegative) + (fs_s_dst_table_lookup_valuefoldnegative_body_steps))) /\ fs_s_dst_table_lookup_valuefoldnegative_body_steps = fs_r_dst_table_lookup_valuefoldnegative_body_steps + fs_a_dst_table_lookup_valuefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_table_lookup_valuefoldresult ge_balance_negative_table_lookup_valuefoldresult. (((((z) = 2 * (ge_balance_positive_table_lookup_valuefoldresult) /\ (ge_balance_negative_table_lookup_valuefoldresult) = 0) \/ exists ge_signed_half_table_lookup_valuefoldresultdecode. (((z) = 2 * ge_signed_half_table_lookup_valuefoldresultdecode + 1 /\ (ge_balance_positive_table_lookup_valuefoldresult) = 0) /\ (ge_balance_negative_table_lookup_valuefoldresult) = S ge_signed_half_table_lookup_valuefoldresultdecode))) /\ ((dst_positive_sum_table_lookup_valuefold) + ge_balance_negative_table_lookup_valuefoldresult = (dst_negative_sum_table_lookup_valuefold) + ge_balance_positive_table_lookup_valuefoldresult)))))))))))))Complete tactic proof in conservative notation
All 28 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay script.
Read the argument
Proof checkpoints
28 script commands · 7 reading checkpoints · 1 local claims
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.
01Fix variables and assumptionsL1–8
02Separate the logical casesL9–11
03Establish hzL12–18
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply divisor signed table lookup.
- L12
have hz : ∃ z. ArithAt(H,n,z)Definitions: ArithAt(H,n,z)Original native command in the exact edition - L13
specialize divisor_signed_table_lookup (N) - L14
specialize divisor_signed_table_lookup (H) - L15
specialize divisor_signed_table_lookup (n) - L16
apply divisor_signed_table_lookup - L17
exact hc_right_right_left - L18
exact hbound
04Separate the logical casesL19–19
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L19
cases hz
05Construct an explicit witnessL20–20
Supply the displayed value, then prove that it has the required property.
- L20
exists x
06Separate the logical casesL21–21
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L21
split
Original defined command ledger · 28 lines
- 0001
intro N - 0002
intro F - 0003
intro G - 0004
intro H - 0005
intro n - 0006
intro hc - 0007
intro hn - 0008
intro hbound - 0009
cases hc - 0010
cases hc_right - 0011
cases hc_right_right - 0012
have hz : ∃ z. ArithAt(H,n,z) - 0013
specialize divisor_signed_table_lookup (N) - 0014
specialize divisor_signed_table_lookup (H) - 0015
specialize divisor_signed_table_lookup (n) - 0016
apply divisor_signed_table_lookup - 0017
exact hc_right_right_left - 0018
exact hbound - 0019
cases hz - 0020
exists x - 0021
split - 0022
exact hz_witness - 0023
specialize hc_right_right_right (n) - 0024
specialize hc_right_right_right (x) - 0025
apply hc_right_right_right - 0026
exact hn - 0027
exact hbound - 0028
exact hz_witness