Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Signed one is code 2. Positive-only table graphs preserve arbitrary zeroth values, including N=0. The unit and divisor-sum identities are proved, never embedded in definitions. The separate inverse family proves the general unit-at-one criterion; multiplicative-function closure remains open.
Exact theorem in conservative defined notation
∀ N. ∀ F. ∀ U. ∀ n. ∀ z. ArithTable(N,F) → ConstantOneTable(N,U) → ¬n = 0 → Le(n,N) → (DirichletSum(F,U,n,z) → DivisorSum(F,n,z)) ∧ (DivisorSum(F,n,z) → DirichletSum(F,U,n,z))
Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Original expanded first-order statement
forall N F U n z. (exists dst_positive_code_ones_sum_input dst_positive_scale_ones_sum_input dst_negative_code_ones_sum_input dst_negative_scale_ones_sum_input. (((F) = (((((dst_positive_code_ones_sum_input) + (dst_positive_scale_ones_sum_input)) * S ((dst_positive_code_ones_sum_input) + (dst_positive_scale_ones_sum_input)) + ((dst_positive_scale_ones_sum_input) + (dst_positive_scale_ones_sum_input))) + (((dst_negative_code_ones_sum_input) + (dst_negative_scale_ones_sum_input)) * S ((dst_negative_code_ones_sum_input) + (dst_negative_scale_ones_sum_input)) + ((dst_negative_scale_ones_sum_input) + (dst_negative_scale_ones_sum_input)))) * S ((((dst_positive_code_ones_sum_input) + (dst_positive_scale_ones_sum_input)) * S ((dst_positive_code_ones_sum_input) + (dst_positive_scale_ones_sum_input)) + ((dst_positive_scale_ones_sum_input) + (dst_positive_scale_ones_sum_input))) + (((dst_negative_code_ones_sum_input) + (dst_negative_scale_ones_sum_input)) * S ((dst_negative_code_ones_sum_input) + (dst_negative_scale_ones_sum_input)) + ((dst_negative_scale_ones_sum_input) + (dst_negative_scale_ones_sum_input)))) + ((((dst_negative_code_ones_sum_input) + (dst_negative_scale_ones_sum_input)) * S ((dst_negative_code_ones_sum_input) + (dst_negative_scale_ones_sum_input)) + ((dst_negative_scale_ones_sum_input) + (dst_negative_scale_ones_sum_input))) + (((dst_negative_code_ones_sum_input) + (dst_negative_scale_ones_sum_input)) * S ((dst_negative_code_ones_sum_input) + (dst_negative_scale_ones_sum_input)) + ((dst_negative_scale_ones_sum_input) + (dst_negative_scale_ones_sum_input)))))) /\ (forall dst_index_ones_sum_input. (exists pvs_le_gap_ones_sum_inputdomain. pvs_le_gap_ones_sum_inputdomain + (dst_index_ones_sum_input) = (N)) -> exists dst_positive_ones_sum_input dst_negative_ones_sum_input dst_value_ones_sum_input. ((((exists ff_h_pvs_ones_sum_inputentrypositive. ff_h_pvs_ones_sum_inputentrypositive + S (dst_positive_ones_sum_input) = S ((S (dst_index_ones_sum_input)) * dst_positive_scale_ones_sum_input)) /\ exists ff_q_pvs_ones_sum_inputentrypositive. dst_positive_code_ones_sum_input = ff_q_pvs_ones_sum_inputentrypositive * S ((S (dst_index_ones_sum_input)) * dst_positive_scale_ones_sum_input) + (dst_positive_ones_sum_input))) /\ (((((exists ff_h_pvs_ones_sum_inputentrynegative. ff_h_pvs_ones_sum_inputentrynegative + S (dst_negative_ones_sum_input) = S ((S (dst_index_ones_sum_input)) * dst_negative_scale_ones_sum_input)) /\ exists ff_q_pvs_ones_sum_inputentrynegative. dst_negative_code_ones_sum_input = ff_q_pvs_ones_sum_inputentrynegative * S ((S (dst_index_ones_sum_input)) * dst_negative_scale_ones_sum_input) + (dst_negative_ones_sum_input))) /\ (exists ge_balance_positive_ones_sum_inputentryvalue ge_balance_negative_ones_sum_inputentryvalue. (((((dst_value_ones_sum_input) = 2 * (ge_balance_positive_ones_sum_inputentryvalue) /\ (ge_balance_negative_ones_sum_inputentryvalue) = 0) \/ exists ge_signed_half_ones_sum_inputentryvaluedecode. (((dst_value_ones_sum_input) = 2 * ge_signed_half_ones_sum_inputentryvaluedecode + 1 /\ (ge_balance_positive_ones_sum_inputentryvalue) = 0) /\ (ge_balance_negative_ones_sum_inputentryvalue) = S ge_signed_half_ones_sum_inputentryvaluedecode))) /\ ((dst_positive_ones_sum_input) + ge_balance_negative_ones_sum_inputentryvalue = (dst_negative_ones_sum_input) + ge_balance_positive_ones_sum_inputentryvalue))))))))) -> (((exists dst_positive_code_ones_sum_onestable dst_positive_scale_ones_sum_onestable dst_negative_code_ones_sum_onestable dst_negative_scale_ones_sum_onestable. (((U) = (((((dst_positive_code_ones_sum_onestable) + (dst_positive_scale_ones_sum_onestable)) * S ((dst_positive_code_ones_sum_onestable) + (dst_positive_scale_ones_sum_onestable)) + ((dst_positive_scale_ones_sum_onestable) + (dst_positive_scale_ones_sum_onestable))) + (((dst_negative_code_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)) * S ((dst_negative_code_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)) + ((dst_negative_scale_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)))) * S ((((dst_positive_code_ones_sum_onestable) + (dst_positive_scale_ones_sum_onestable)) * S ((dst_positive_code_ones_sum_onestable) + (dst_positive_scale_ones_sum_onestable)) + ((dst_positive_scale_ones_sum_onestable) + (dst_positive_scale_ones_sum_onestable))) + (((dst_negative_code_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)) * S ((dst_negative_code_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)) + ((dst_negative_scale_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)))) + ((((dst_negative_code_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)) * S ((dst_negative_code_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)) + ((dst_negative_scale_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable))) + (((dst_negative_code_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)) * S ((dst_negative_code_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)) + ((dst_negative_scale_ones_sum_onestable) + (dst_negative_scale_ones_sum_onestable)))))) /\ (forall dst_index_ones_sum_onestable. (exists pvs_le_gap_ones_sum_onestabledomain. pvs_le_gap_ones_sum_onestabledomain + (dst_index_ones_sum_onestable) = (N)) -> exists dst_positive_ones_sum_onestable dst_negative_ones_sum_onestable dst_value_ones_sum_onestable. ((((exists ff_h_pvs_ones_sum_onestableentrypositive. ff_h_pvs_ones_sum_onestableentrypositive + S (dst_positive_ones_sum_onestable) = S ((S (dst_index_ones_sum_onestable)) * dst_positive_scale_ones_sum_onestable)) /\ exists ff_q_pvs_ones_sum_onestableentrypositive. dst_positive_code_ones_sum_onestable = ff_q_pvs_ones_sum_onestableentrypositive * S ((S (dst_index_ones_sum_onestable)) * dst_positive_scale_ones_sum_onestable) + (dst_positive_ones_sum_onestable))) /\ (((((exists ff_h_pvs_ones_sum_onestableentrynegative. ff_h_pvs_ones_sum_onestableentrynegative + S (dst_negative_ones_sum_onestable) = S ((S (dst_index_ones_sum_onestable)) * dst_negative_scale_ones_sum_onestable)) /\ exists ff_q_pvs_ones_sum_onestableentrynegative. dst_negative_code_ones_sum_onestable = ff_q_pvs_ones_sum_onestableentrynegative * S ((S (dst_index_ones_sum_onestable)) * dst_negative_scale_ones_sum_onestable) + (dst_negative_ones_sum_onestable))) /\ (exists ge_balance_positive_ones_sum_onestableentryvalue ge_balance_negative_ones_sum_onestableentryvalue. (((((dst_value_ones_sum_onestable) = 2 * (ge_balance_positive_ones_sum_onestableentryvalue) /\ (ge_balance_negative_ones_sum_onestableentryvalue) = 0) \/ exists ge_signed_half_ones_sum_onestableentryvaluedecode. (((dst_value_ones_sum_onestable) = 2 * ge_signed_half_ones_sum_onestableentryvaluedecode + 1 /\ (ge_balance_positive_ones_sum_onestableentryvalue) = 0) /\ (ge_balance_negative_ones_sum_onestableentryvalue) = S ge_signed_half_ones_sum_onestableentryvaluedecode))) /\ ((dst_positive_ones_sum_onestable) + ge_balance_negative_ones_sum_onestableentryvalue = (dst_negative_ones_sum_onestable) + ge_balance_positive_ones_sum_onestableentryvalue))))))))) /\ (forall du_index_ones_sum_ones du_value_ones_sum_ones. ~(du_index_ones_sum_ones=0) -> (exists pvs_le_gap_ones_sum_onesbound. pvs_le_gap_ones_sum_onesbound + (du_index_ones_sum_ones) = (N)) -> (exists dst_positive_code_ones_sum_onesentry dst_positive_scale_ones_sum_onesentry dst_negative_code_ones_sum_onesentry dst_negative_scale_ones_sum_onesentry dst_positive_ones_sum_onesentry dst_negative_ones_sum_onesentry. (((U) = (((((dst_positive_code_ones_sum_onesentry) + (dst_positive_scale_ones_sum_onesentry)) * S ((dst_positive_code_ones_sum_onesentry) + (dst_positive_scale_ones_sum_onesentry)) + ((dst_positive_scale_ones_sum_onesentry) + (dst_positive_scale_ones_sum_onesentry))) + (((dst_negative_code_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)) * S ((dst_negative_code_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)) + ((dst_negative_scale_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)))) * S ((((dst_positive_code_ones_sum_onesentry) + (dst_positive_scale_ones_sum_onesentry)) * S ((dst_positive_code_ones_sum_onesentry) + (dst_positive_scale_ones_sum_onesentry)) + ((dst_positive_scale_ones_sum_onesentry) + (dst_positive_scale_ones_sum_onesentry))) + (((dst_negative_code_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)) * S ((dst_negative_code_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)) + ((dst_negative_scale_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)))) + ((((dst_negative_code_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)) * S ((dst_negative_code_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)) + ((dst_negative_scale_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry))) + (((dst_negative_code_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)) * S ((dst_negative_code_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)) + ((dst_negative_scale_ones_sum_onesentry) + (dst_negative_scale_ones_sum_onesentry)))))) /\ (((((exists ff_h_pvs_ones_sum_onesentrypositive. ff_h_pvs_ones_sum_onesentrypositive + S (dst_positive_ones_sum_onesentry) = S ((S (du_index_ones_sum_ones)) * dst_positive_scale_ones_sum_onesentry)) /\ exists ff_q_pvs_ones_sum_onesentrypositive. dst_positive_code_ones_sum_onesentry = ff_q_pvs_ones_sum_onesentrypositive * S ((S (du_index_ones_sum_ones)) * dst_positive_scale_ones_sum_onesentry) + (dst_positive_ones_sum_onesentry))) /\ (((((exists ff_h_pvs_ones_sum_onesentrynegative. ff_h_pvs_ones_sum_onesentrynegative + S (dst_negative_ones_sum_onesentry) = S ((S (du_index_ones_sum_ones)) * dst_negative_scale_ones_sum_onesentry)) /\ exists ff_q_pvs_ones_sum_onesentrynegative. dst_negative_code_ones_sum_onesentry = ff_q_pvs_ones_sum_onesentrynegative * S ((S (du_index_ones_sum_ones)) * dst_negative_scale_ones_sum_onesentry) + (dst_negative_ones_sum_onesentry))) /\ (exists ge_balance_positive_ones_sum_onesentryvalue ge_balance_negative_ones_sum_onesentryvalue. (((((du_value_ones_sum_ones) = 2 * (ge_balance_positive_ones_sum_onesentryvalue) /\ (ge_balance_negative_ones_sum_onesentryvalue) = 0) \/ exists ge_signed_half_ones_sum_onesentryvaluedecode. (((du_value_ones_sum_ones) = 2 * ge_signed_half_ones_sum_onesentryvaluedecode + 1 /\ (ge_balance_positive_ones_sum_onesentryvalue) = 0) /\ (ge_balance_negative_ones_sum_onesentryvalue) = S ge_signed_half_ones_sum_onesentryvaluedecode))) /\ ((dst_positive_ones_sum_onesentry) + ge_balance_negative_ones_sum_onesentryvalue = (dst_negative_ones_sum_onesentry) + ge_balance_positive_ones_sum_onesentryvalue))))))))) -> du_value_ones_sum_ones=2))) -> ~(n=0) -> (exists pvs_le_gap_ones_sum_bound. pvs_le_gap_ones_sum_bound + (n) = (N)) -> ((((((~((n)=0)) /\ (exists dc_mask_ones_sum_resultconvolution. ((((exists dst_positive_code_ones_sum_resultconvolutionmasktable dst_positive_scale_ones_sum_resultconvolutionmasktable dst_negative_code_ones_sum_resultconvolutionmasktable dst_negative_scale_ones_sum_resultconvolutionmasktable. (((dc_mask_ones_sum_resultconvolution) = (((((dst_positive_code_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_positive_code_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable)) + ((dst_positive_scale_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable))) + (((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) + ((dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)))) * S ((((dst_positive_code_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_positive_code_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable)) + ((dst_positive_scale_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable))) + (((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) + ((dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)))) + ((((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) + ((dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable))) + (((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) + ((dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)))))) /\ (forall dst_index_ones_sum_resultconvolutionmasktable. (exists pvs_le_gap_ones_sum_resultconvolutionmasktabledomain. pvs_le_gap_ones_sum_resultconvolutionmasktabledomain + (dst_index_ones_sum_resultconvolutionmasktable) = (n)) -> exists dst_positive_ones_sum_resultconvolutionmasktable dst_negative_ones_sum_resultconvolutionmasktable dst_value_ones_sum_resultconvolutionmasktable. ((((exists ff_h_pvs_ones_sum_resultconvolutionmasktableentrypositive. ff_h_pvs_ones_sum_resultconvolutionmasktableentrypositive + S (dst_positive_ones_sum_resultconvolutionmasktable) = S ((S (dst_index_ones_sum_resultconvolutionmasktable)) * dst_positive_scale_ones_sum_resultconvolutionmasktable)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmasktableentrypositive. dst_positive_code_ones_sum_resultconvolutionmasktable = ff_q_pvs_ones_sum_resultconvolutionmasktableentrypositive * S ((S (dst_index_ones_sum_resultconvolutionmasktable)) * dst_positive_scale_ones_sum_resultconvolutionmasktable) + (dst_positive_ones_sum_resultconvolutionmasktable))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmasktableentrynegative. ff_h_pvs_ones_sum_resultconvolutionmasktableentrynegative + S (dst_negative_ones_sum_resultconvolutionmasktable) = S ((S (dst_index_ones_sum_resultconvolutionmasktable)) * dst_negative_scale_ones_sum_resultconvolutionmasktable)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmasktableentrynegative. dst_negative_code_ones_sum_resultconvolutionmasktable = ff_q_pvs_ones_sum_resultconvolutionmasktableentrynegative * S ((S (dst_index_ones_sum_resultconvolutionmasktable)) * dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_ones_sum_resultconvolutionmasktable))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionmasktableentryvalue ge_balance_negative_ones_sum_resultconvolutionmasktableentryvalue. (((((dst_value_ones_sum_resultconvolutionmasktable) = 2 * (ge_balance_positive_ones_sum_resultconvolutionmasktableentryvalue) /\ (ge_balance_negative_ones_sum_resultconvolutionmasktableentryvalue) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmasktableentryvaluedecode. (((dst_value_ones_sum_resultconvolutionmasktable) = 2 * ge_signed_half_ones_sum_resultconvolutionmasktableentryvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionmasktableentryvalue) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionmasktableentryvalue) = S ge_signed_half_ones_sum_resultconvolutionmasktableentryvaluedecode))) /\ ((dst_positive_ones_sum_resultconvolutionmasktable) + ge_balance_negative_ones_sum_resultconvolutionmasktableentryvalue = (dst_negative_ones_sum_resultconvolutionmasktable) + ge_balance_positive_ones_sum_resultconvolutionmasktableentryvalue))))))))) /\ (forall dc_index_ones_sum_resultconvolutionmask dc_value_ones_sum_resultconvolutionmask. (exists pvs_le_gap_ones_sum_resultconvolutionmaskdomain. pvs_le_gap_ones_sum_resultconvolutionmaskdomain + (dc_index_ones_sum_resultconvolutionmask) = (n)) -> (exists dst_positive_code_ones_sum_resultconvolutionmasklookup dst_positive_scale_ones_sum_resultconvolutionmasklookup dst_negative_code_ones_sum_resultconvolutionmasklookup dst_negative_scale_ones_sum_resultconvolutionmasklookup dst_positive_ones_sum_resultconvolutionmasklookup dst_negative_ones_sum_resultconvolutionmasklookup. (((dc_mask_ones_sum_resultconvolution) = (((((dst_positive_code_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_positive_code_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_positive_scale_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup))) + (((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)))) * S ((((dst_positive_code_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_positive_code_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_positive_scale_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup))) + (((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)))) + ((((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup))) + (((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)))))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmasklookuppositive. ff_h_pvs_ones_sum_resultconvolutionmasklookuppositive + S (dst_positive_ones_sum_resultconvolutionmasklookup) = S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_positive_scale_ones_sum_resultconvolutionmasklookup)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmasklookuppositive. dst_positive_code_ones_sum_resultconvolutionmasklookup = ff_q_pvs_ones_sum_resultconvolutionmasklookuppositive * S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_positive_scale_ones_sum_resultconvolutionmasklookup) + (dst_positive_ones_sum_resultconvolutionmasklookup))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmasklookupnegative. ff_h_pvs_ones_sum_resultconvolutionmasklookupnegative + S (dst_negative_ones_sum_resultconvolutionmasklookup) = S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_negative_scale_ones_sum_resultconvolutionmasklookup)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmasklookupnegative. dst_negative_code_ones_sum_resultconvolutionmasklookup = ff_q_pvs_ones_sum_resultconvolutionmasklookupnegative * S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_ones_sum_resultconvolutionmasklookup))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionmasklookupvalue ge_balance_negative_ones_sum_resultconvolutionmasklookupvalue. (((((dc_value_ones_sum_resultconvolutionmask) = 2 * (ge_balance_positive_ones_sum_resultconvolutionmasklookupvalue) /\ (ge_balance_negative_ones_sum_resultconvolutionmasklookupvalue) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmasklookupvaluedecode. (((dc_value_ones_sum_resultconvolutionmask) = 2 * ge_signed_half_ones_sum_resultconvolutionmasklookupvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionmasklookupvalue) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionmasklookupvalue) = S ge_signed_half_ones_sum_resultconvolutionmasklookupvaluedecode))) /\ ((dst_positive_ones_sum_resultconvolutionmasklookup) + ge_balance_negative_ones_sum_resultconvolutionmasklookupvalue = (dst_negative_ones_sum_resultconvolutionmasklookup) + ge_balance_positive_ones_sum_resultconvolutionmasklookupvalue))))))))) -> ((((~((dc_index_ones_sum_resultconvolutionmask)=0)) /\ (exists dc_quotient_ones_sum_resultconvolutionmaskentry dc_left_ones_sum_resultconvolutionmaskentry dc_right_ones_sum_resultconvolutionmaskentry. (((n)=(dc_index_ones_sum_resultconvolutionmask)*dc_quotient_ones_sum_resultconvolutionmaskentry) /\ (((exists dst_positive_code_ones_sum_resultconvolutionmaskentryleft dst_positive_scale_ones_sum_resultconvolutionmaskentryleft dst_negative_code_ones_sum_resultconvolutionmaskentryleft dst_negative_scale_ones_sum_resultconvolutionmaskentryleft dst_positive_ones_sum_resultconvolutionmaskentryleft dst_negative_ones_sum_resultconvolutionmaskentryleft. (((F) = (((((dst_positive_code_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_positive_code_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_positive_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)))) * S ((((dst_positive_code_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_positive_code_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_positive_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)))) + ((((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)))))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmaskentryleftpositive. ff_h_pvs_ones_sum_resultconvolutionmaskentryleftpositive + S (dst_positive_ones_sum_resultconvolutionmaskentryleft) = S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmaskentryleftpositive. dst_positive_code_ones_sum_resultconvolutionmaskentryleft = ff_q_pvs_ones_sum_resultconvolutionmaskentryleftpositive * S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_positive_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_ones_sum_resultconvolutionmaskentryleft))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmaskentryleftnegative. ff_h_pvs_ones_sum_resultconvolutionmaskentryleftnegative + S (dst_negative_ones_sum_resultconvolutionmaskentryleft) = S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmaskentryleftnegative. dst_negative_code_ones_sum_resultconvolutionmaskentryleft = ff_q_pvs_ones_sum_resultconvolutionmaskentryleftnegative * S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_ones_sum_resultconvolutionmaskentryleft))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionmaskentryleftvalue ge_balance_negative_ones_sum_resultconvolutionmaskentryleftvalue. (((((dc_left_ones_sum_resultconvolutionmaskentry) = 2 * (ge_balance_positive_ones_sum_resultconvolutionmaskentryleftvalue) /\ (ge_balance_negative_ones_sum_resultconvolutionmaskentryleftvalue) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryleftvaluedecode. (((dc_left_ones_sum_resultconvolutionmaskentry) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionmaskentryleftvalue) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionmaskentryleftvalue) = S ge_signed_half_ones_sum_resultconvolutionmaskentryleftvaluedecode))) /\ ((dst_positive_ones_sum_resultconvolutionmaskentryleft) + ge_balance_negative_ones_sum_resultconvolutionmaskentryleftvalue = (dst_negative_ones_sum_resultconvolutionmaskentryleft) + ge_balance_positive_ones_sum_resultconvolutionmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_ones_sum_resultconvolutionmaskentryright dst_positive_scale_ones_sum_resultconvolutionmaskentryright dst_negative_code_ones_sum_resultconvolutionmaskentryright dst_negative_scale_ones_sum_resultconvolutionmaskentryright dst_positive_ones_sum_resultconvolutionmaskentryright dst_negative_ones_sum_resultconvolutionmaskentryright. (((U) = (((((dst_positive_code_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_positive_code_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_positive_scale_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)))) * S ((((dst_positive_code_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_positive_code_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_positive_scale_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)))) + ((((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)))))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmaskentryrightpositive. ff_h_pvs_ones_sum_resultconvolutionmaskentryrightpositive + S (dst_positive_ones_sum_resultconvolutionmaskentryright) = S ((S (dc_quotient_ones_sum_resultconvolutionmaskentry)) * dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmaskentryrightpositive. dst_positive_code_ones_sum_resultconvolutionmaskentryright = ff_q_pvs_ones_sum_resultconvolutionmaskentryrightpositive * S ((S (dc_quotient_ones_sum_resultconvolutionmaskentry)) * dst_positive_scale_ones_sum_resultconvolutionmaskentryright) + (dst_positive_ones_sum_resultconvolutionmaskentryright))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmaskentryrightnegative. ff_h_pvs_ones_sum_resultconvolutionmaskentryrightnegative + S (dst_negative_ones_sum_resultconvolutionmaskentryright) = S ((S (dc_quotient_ones_sum_resultconvolutionmaskentry)) * dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmaskentryrightnegative. dst_negative_code_ones_sum_resultconvolutionmaskentryright = ff_q_pvs_ones_sum_resultconvolutionmaskentryrightnegative * S ((S (dc_quotient_ones_sum_resultconvolutionmaskentry)) * dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_ones_sum_resultconvolutionmaskentryright))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionmaskentryrightvalue ge_balance_negative_ones_sum_resultconvolutionmaskentryrightvalue. (((((dc_right_ones_sum_resultconvolutionmaskentry) = 2 * (ge_balance_positive_ones_sum_resultconvolutionmaskentryrightvalue) /\ (ge_balance_negative_ones_sum_resultconvolutionmaskentryrightvalue) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryrightvaluedecode. (((dc_right_ones_sum_resultconvolutionmaskentry) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionmaskentryrightvalue) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionmaskentryrightvalue) = S ge_signed_half_ones_sum_resultconvolutionmaskentryrightvaluedecode))) /\ ((dst_positive_ones_sum_resultconvolutionmaskentryright) + ge_balance_negative_ones_sum_resultconvolutionmaskentryrightvalue = (dst_negative_ones_sum_resultconvolutionmaskentryright) + ge_balance_positive_ones_sum_resultconvolutionmaskentryrightvalue))))))))) /\ (exists sto_ap_ones_sum_resultconvolutionmaskentryproduct sto_an_ones_sum_resultconvolutionmaskentryproduct sto_bp_ones_sum_resultconvolutionmaskentryproduct sto_bn_ones_sum_resultconvolutionmaskentryproduct sto_cp_ones_sum_resultconvolutionmaskentryproduct sto_cn_ones_sum_resultconvolutionmaskentryproduct. (((((dc_left_ones_sum_resultconvolutionmaskentry) = 2 * (sto_ap_ones_sum_resultconvolutionmaskentryproduct) /\ (sto_an_ones_sum_resultconvolutionmaskentryproduct) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryproductleft. (((dc_left_ones_sum_resultconvolutionmaskentry) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryproductleft + 1 /\ (sto_ap_ones_sum_resultconvolutionmaskentryproduct) = 0) /\ (sto_an_ones_sum_resultconvolutionmaskentryproduct) = S ge_signed_half_ones_sum_resultconvolutionmaskentryproductleft))) /\ ((((((dc_right_ones_sum_resultconvolutionmaskentry) = 2 * (sto_bp_ones_sum_resultconvolutionmaskentryproduct) /\ (sto_bn_ones_sum_resultconvolutionmaskentryproduct) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryproductright. (((dc_right_ones_sum_resultconvolutionmaskentry) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryproductright + 1 /\ (sto_bp_ones_sum_resultconvolutionmaskentryproduct) = 0) /\ (sto_bn_ones_sum_resultconvolutionmaskentryproduct) = S ge_signed_half_ones_sum_resultconvolutionmaskentryproductright))) /\ ((((((dc_value_ones_sum_resultconvolutionmask) = 2 * (sto_cp_ones_sum_resultconvolutionmaskentryproduct) /\ (sto_cn_ones_sum_resultconvolutionmaskentryproduct) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryproductoutput. (((dc_value_ones_sum_resultconvolutionmask) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryproductoutput + 1 /\ (sto_cp_ones_sum_resultconvolutionmaskentryproduct) = 0) /\ (sto_cn_ones_sum_resultconvolutionmaskentryproduct) = S ge_signed_half_ones_sum_resultconvolutionmaskentryproductoutput))) /\ ((sto_ap_ones_sum_resultconvolutionmaskentryproduct * sto_bp_ones_sum_resultconvolutionmaskentryproduct + sto_an_ones_sum_resultconvolutionmaskentryproduct * sto_bn_ones_sum_resultconvolutionmaskentryproduct) + sto_cn_ones_sum_resultconvolutionmaskentryproduct = (sto_ap_ones_sum_resultconvolutionmaskentryproduct * sto_bn_ones_sum_resultconvolutionmaskentryproduct + sto_an_ones_sum_resultconvolutionmaskentryproduct * sto_bp_ones_sum_resultconvolutionmaskentryproduct) + sto_cp_ones_sum_resultconvolutionmaskentryproduct))))))))))))))) \/ ((((dc_index_ones_sum_resultconvolutionmask)=0 \/ ~(exists pvs_factor_ones_sum_resultconvolutionmaskentrynondivisor. (n) = (dc_index_ones_sum_resultconvolutionmask) * pvs_factor_ones_sum_resultconvolutionmaskentrynondivisor)) /\ ((dc_value_ones_sum_resultconvolutionmask)=0))))))) /\ (exists dst_positive_code_ones_sum_resultconvolutionfold dst_positive_scale_ones_sum_resultconvolutionfold dst_negative_code_ones_sum_resultconvolutionfold dst_negative_scale_ones_sum_resultconvolutionfold dst_positive_sum_ones_sum_resultconvolutionfold dst_negative_sum_ones_sum_resultconvolutionfold. (((dc_mask_ones_sum_resultconvolution) = (((((dst_positive_code_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold)) * S ((dst_positive_code_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold)) + ((dst_positive_scale_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold))) + (((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) * S ((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) + ((dst_negative_scale_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)))) * S ((((dst_positive_code_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold)) * S ((dst_positive_code_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold)) + ((dst_positive_scale_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold))) + (((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) * S ((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) + ((dst_negative_scale_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)))) + ((((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) * S ((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) + ((dst_negative_scale_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold))) + (((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) * S ((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) + ((dst_negative_scale_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)))))) /\ (((exists fs_u_dst_ones_sum_resultconvolutionfoldpositive fs_v_dst_ones_sum_resultconvolutionfoldpositive. ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_start. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_start. fs_u_dst_ones_sum_resultconvolutionfoldpositive = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_start * S ((S (0)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive) + (0))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_terminal. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_terminal + S (dst_positive_sum_ones_sum_resultconvolutionfold) = S ((S (S (n))) * fs_v_dst_ones_sum_resultconvolutionfoldpositive)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_terminal. fs_u_dst_ones_sum_resultconvolutionfoldpositive = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_ones_sum_resultconvolutionfoldpositive) + (dst_positive_sum_ones_sum_resultconvolutionfold))) /\ forall fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps. (exists fs_lt_dst_ones_sum_resultconvolutionfoldpositive_body_steps_bound. fs_lt_dst_ones_sum_resultconvolutionfoldpositive_body_steps_bound + S fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps = S (n)) -> exists fs_a_dst_ones_sum_resultconvolutionfoldpositive_body_steps fs_r_dst_ones_sum_resultconvolutionfoldpositive_body_steps fs_s_dst_ones_sum_resultconvolutionfoldpositive_body_steps. ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_summand. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_summand + S (fs_a_dst_ones_sum_resultconvolutionfoldpositive_body_steps) = S ((S (fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * dst_positive_scale_ones_sum_resultconvolutionfold)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_summand. dst_positive_code_ones_sum_resultconvolutionfold = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_summand * S ((S (fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * dst_positive_scale_ones_sum_resultconvolutionfold) + (fs_a_dst_ones_sum_resultconvolutionfoldpositive_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_partial. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_partial + S (fs_r_dst_ones_sum_resultconvolutionfoldpositive_body_steps) = S ((S (fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_partial. fs_u_dst_ones_sum_resultconvolutionfoldpositive = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_partial * S ((S (fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive) + (fs_r_dst_ones_sum_resultconvolutionfoldpositive_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_successor. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_successor + S (fs_s_dst_ones_sum_resultconvolutionfoldpositive_body_steps) = S ((S (S fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_successor. fs_u_dst_ones_sum_resultconvolutionfoldpositive = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_successor * S ((S (S fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive) + (fs_s_dst_ones_sum_resultconvolutionfoldpositive_body_steps))) /\ fs_s_dst_ones_sum_resultconvolutionfoldpositive_body_steps = fs_r_dst_ones_sum_resultconvolutionfoldpositive_body_steps + fs_a_dst_ones_sum_resultconvolutionfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_ones_sum_resultconvolutionfoldnegative fs_v_dst_ones_sum_resultconvolutionfoldnegative. ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_start. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_start. fs_u_dst_ones_sum_resultconvolutionfoldnegative = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_start * S ((S (0)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative) + (0))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_terminal. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_terminal + S (dst_negative_sum_ones_sum_resultconvolutionfold) = S ((S (S (n))) * fs_v_dst_ones_sum_resultconvolutionfoldnegative)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_terminal. fs_u_dst_ones_sum_resultconvolutionfoldnegative = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_ones_sum_resultconvolutionfoldnegative) + (dst_negative_sum_ones_sum_resultconvolutionfold))) /\ forall fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps. (exists fs_lt_dst_ones_sum_resultconvolutionfoldnegative_body_steps_bound. fs_lt_dst_ones_sum_resultconvolutionfoldnegative_body_steps_bound + S fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps = S (n)) -> exists fs_a_dst_ones_sum_resultconvolutionfoldnegative_body_steps fs_r_dst_ones_sum_resultconvolutionfoldnegative_body_steps fs_s_dst_ones_sum_resultconvolutionfoldnegative_body_steps. ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_summand. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_summand + S (fs_a_dst_ones_sum_resultconvolutionfoldnegative_body_steps) = S ((S (fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * dst_negative_scale_ones_sum_resultconvolutionfold)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_summand. dst_negative_code_ones_sum_resultconvolutionfold = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_summand * S ((S (fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * dst_negative_scale_ones_sum_resultconvolutionfold) + (fs_a_dst_ones_sum_resultconvolutionfoldnegative_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_partial. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_partial + S (fs_r_dst_ones_sum_resultconvolutionfoldnegative_body_steps) = S ((S (fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_partial. fs_u_dst_ones_sum_resultconvolutionfoldnegative = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_partial * S ((S (fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative) + (fs_r_dst_ones_sum_resultconvolutionfoldnegative_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_successor. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_successor + S (fs_s_dst_ones_sum_resultconvolutionfoldnegative_body_steps) = S ((S (S fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_successor. fs_u_dst_ones_sum_resultconvolutionfoldnegative = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_successor * S ((S (S fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative) + (fs_s_dst_ones_sum_resultconvolutionfoldnegative_body_steps))) /\ fs_s_dst_ones_sum_resultconvolutionfoldnegative_body_steps = fs_r_dst_ones_sum_resultconvolutionfoldnegative_body_steps + fs_a_dst_ones_sum_resultconvolutionfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionfoldresult ge_balance_negative_ones_sum_resultconvolutionfoldresult. (((((z) = 2 * (ge_balance_positive_ones_sum_resultconvolutionfoldresult) /\ (ge_balance_negative_ones_sum_resultconvolutionfoldresult) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionfoldresultdecode. (((z) = 2 * ge_signed_half_ones_sum_resultconvolutionfoldresultdecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionfoldresult) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionfoldresult) = S ge_signed_half_ones_sum_resultconvolutionfoldresultdecode))) /\ ((dst_positive_sum_ones_sum_resultconvolutionfold) + ge_balance_negative_ones_sum_resultconvolutionfoldresult = (dst_negative_sum_ones_sum_resultconvolutionfold) + ge_balance_positive_ones_sum_resultconvolutionfoldresult))))))))))))) -> (((~((n)=0)) /\ (exists dm_mask_table_ones_sum_resultdivisor. ((((exists dst_positive_code_ones_sum_resultdivisormasktable dst_positive_scale_ones_sum_resultdivisormasktable dst_negative_code_ones_sum_resultdivisormasktable dst_negative_scale_ones_sum_resultdivisormasktable. (((dm_mask_table_ones_sum_resultdivisor) = (((((dst_positive_code_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable)) * S ((dst_positive_code_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable)) + ((dst_positive_scale_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable))) + (((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) * S ((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) + ((dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)))) * S ((((dst_positive_code_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable)) * S ((dst_positive_code_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable)) + ((dst_positive_scale_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable))) + (((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) * S ((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) + ((dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)))) + ((((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) * S ((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) + ((dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable))) + (((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) * S ((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) + ((dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)))))) /\ (forall dst_index_ones_sum_resultdivisormasktable. (exists pvs_le_gap_ones_sum_resultdivisormasktabledomain. pvs_le_gap_ones_sum_resultdivisormasktabledomain + (dst_index_ones_sum_resultdivisormasktable) = (n)) -> exists dst_positive_ones_sum_resultdivisormasktable dst_negative_ones_sum_resultdivisormasktable dst_value_ones_sum_resultdivisormasktable. ((((exists ff_h_pvs_ones_sum_resultdivisormasktableentrypositive. ff_h_pvs_ones_sum_resultdivisormasktableentrypositive + S (dst_positive_ones_sum_resultdivisormasktable) = S ((S (dst_index_ones_sum_resultdivisormasktable)) * dst_positive_scale_ones_sum_resultdivisormasktable)) /\ exists ff_q_pvs_ones_sum_resultdivisormasktableentrypositive. dst_positive_code_ones_sum_resultdivisormasktable = ff_q_pvs_ones_sum_resultdivisormasktableentrypositive * S ((S (dst_index_ones_sum_resultdivisormasktable)) * dst_positive_scale_ones_sum_resultdivisormasktable) + (dst_positive_ones_sum_resultdivisormasktable))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormasktableentrynegative. ff_h_pvs_ones_sum_resultdivisormasktableentrynegative + S (dst_negative_ones_sum_resultdivisormasktable) = S ((S (dst_index_ones_sum_resultdivisormasktable)) * dst_negative_scale_ones_sum_resultdivisormasktable)) /\ exists ff_q_pvs_ones_sum_resultdivisormasktableentrynegative. dst_negative_code_ones_sum_resultdivisormasktable = ff_q_pvs_ones_sum_resultdivisormasktableentrynegative * S ((S (dst_index_ones_sum_resultdivisormasktable)) * dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_ones_sum_resultdivisormasktable))) /\ (exists ge_balance_positive_ones_sum_resultdivisormasktableentryvalue ge_balance_negative_ones_sum_resultdivisormasktableentryvalue. (((((dst_value_ones_sum_resultdivisormasktable) = 2 * (ge_balance_positive_ones_sum_resultdivisormasktableentryvalue) /\ (ge_balance_negative_ones_sum_resultdivisormasktableentryvalue) = 0) \/ exists ge_signed_half_ones_sum_resultdivisormasktableentryvaluedecode. (((dst_value_ones_sum_resultdivisormasktable) = 2 * ge_signed_half_ones_sum_resultdivisormasktableentryvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultdivisormasktableentryvalue) = 0) /\ (ge_balance_negative_ones_sum_resultdivisormasktableentryvalue) = S ge_signed_half_ones_sum_resultdivisormasktableentryvaluedecode))) /\ ((dst_positive_ones_sum_resultdivisormasktable) + ge_balance_negative_ones_sum_resultdivisormasktableentryvalue = (dst_negative_ones_sum_resultdivisormasktable) + ge_balance_positive_ones_sum_resultdivisormasktableentryvalue))))))))) /\ (forall dm_index_ones_sum_resultdivisormask dm_value_ones_sum_resultdivisormask. (exists pvs_le_gap_ones_sum_resultdivisormaskdomain. pvs_le_gap_ones_sum_resultdivisormaskdomain + (dm_index_ones_sum_resultdivisormask) = (n)) -> (exists dst_positive_code_ones_sum_resultdivisormasklookup dst_positive_scale_ones_sum_resultdivisormasklookup dst_negative_code_ones_sum_resultdivisormasklookup dst_negative_scale_ones_sum_resultdivisormasklookup dst_positive_ones_sum_resultdivisormasklookup dst_negative_ones_sum_resultdivisormasklookup. (((dm_mask_table_ones_sum_resultdivisor) = (((((dst_positive_code_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup)) * S ((dst_positive_code_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup)) + ((dst_positive_scale_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup))) + (((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) * S ((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) + ((dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)))) * S ((((dst_positive_code_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup)) * S ((dst_positive_code_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup)) + ((dst_positive_scale_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup))) + (((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) * S ((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) + ((dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)))) + ((((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) * S ((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) + ((dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup))) + (((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) * S ((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) + ((dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)))))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormasklookuppositive. ff_h_pvs_ones_sum_resultdivisormasklookuppositive + S (dst_positive_ones_sum_resultdivisormasklookup) = S ((S (dm_index_ones_sum_resultdivisormask)) * dst_positive_scale_ones_sum_resultdivisormasklookup)) /\ exists ff_q_pvs_ones_sum_resultdivisormasklookuppositive. dst_positive_code_ones_sum_resultdivisormasklookup = ff_q_pvs_ones_sum_resultdivisormasklookuppositive * S ((S (dm_index_ones_sum_resultdivisormask)) * dst_positive_scale_ones_sum_resultdivisormasklookup) + (dst_positive_ones_sum_resultdivisormasklookup))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormasklookupnegative. ff_h_pvs_ones_sum_resultdivisormasklookupnegative + S (dst_negative_ones_sum_resultdivisormasklookup) = S ((S (dm_index_ones_sum_resultdivisormask)) * dst_negative_scale_ones_sum_resultdivisormasklookup)) /\ exists ff_q_pvs_ones_sum_resultdivisormasklookupnegative. dst_negative_code_ones_sum_resultdivisormasklookup = ff_q_pvs_ones_sum_resultdivisormasklookupnegative * S ((S (dm_index_ones_sum_resultdivisormask)) * dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_ones_sum_resultdivisormasklookup))) /\ (exists ge_balance_positive_ones_sum_resultdivisormasklookupvalue ge_balance_negative_ones_sum_resultdivisormasklookupvalue. (((((dm_value_ones_sum_resultdivisormask) = 2 * (ge_balance_positive_ones_sum_resultdivisormasklookupvalue) /\ (ge_balance_negative_ones_sum_resultdivisormasklookupvalue) = 0) \/ exists ge_signed_half_ones_sum_resultdivisormasklookupvaluedecode. (((dm_value_ones_sum_resultdivisormask) = 2 * ge_signed_half_ones_sum_resultdivisormasklookupvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultdivisormasklookupvalue) = 0) /\ (ge_balance_negative_ones_sum_resultdivisormasklookupvalue) = S ge_signed_half_ones_sum_resultdivisormasklookupvaluedecode))) /\ ((dst_positive_ones_sum_resultdivisormasklookup) + ge_balance_negative_ones_sum_resultdivisormasklookupvalue = (dst_negative_ones_sum_resultdivisormasklookup) + ge_balance_positive_ones_sum_resultdivisormasklookupvalue))))))))) -> ((((~((dm_index_ones_sum_resultdivisormask)=0)) /\ (exists dm_quotient_ones_sum_resultdivisormaskentry. (((n)=(dm_index_ones_sum_resultdivisormask)*dm_quotient_ones_sum_resultdivisormaskentry) /\ (exists dst_positive_code_ones_sum_resultdivisormaskentryinput dst_positive_scale_ones_sum_resultdivisormaskentryinput dst_negative_code_ones_sum_resultdivisormaskentryinput dst_negative_scale_ones_sum_resultdivisormaskentryinput dst_positive_ones_sum_resultdivisormaskentryinput dst_negative_ones_sum_resultdivisormaskentryinput. (((F) = (((((dst_positive_code_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_positive_code_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_positive_scale_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput))) + (((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)))) * S ((((dst_positive_code_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_positive_code_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_positive_scale_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput))) + (((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)))) + ((((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput))) + (((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)))))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormaskentryinputpositive. ff_h_pvs_ones_sum_resultdivisormaskentryinputpositive + S (dst_positive_ones_sum_resultdivisormaskentryinput) = S ((S (dm_index_ones_sum_resultdivisormask)) * dst_positive_scale_ones_sum_resultdivisormaskentryinput)) /\ exists ff_q_pvs_ones_sum_resultdivisormaskentryinputpositive. dst_positive_code_ones_sum_resultdivisormaskentryinput = ff_q_pvs_ones_sum_resultdivisormaskentryinputpositive * S ((S (dm_index_ones_sum_resultdivisormask)) * dst_positive_scale_ones_sum_resultdivisormaskentryinput) + (dst_positive_ones_sum_resultdivisormaskentryinput))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormaskentryinputnegative. ff_h_pvs_ones_sum_resultdivisormaskentryinputnegative + S (dst_negative_ones_sum_resultdivisormaskentryinput) = S ((S (dm_index_ones_sum_resultdivisormask)) * dst_negative_scale_ones_sum_resultdivisormaskentryinput)) /\ exists ff_q_pvs_ones_sum_resultdivisormaskentryinputnegative. dst_negative_code_ones_sum_resultdivisormaskentryinput = ff_q_pvs_ones_sum_resultdivisormaskentryinputnegative * S ((S (dm_index_ones_sum_resultdivisormask)) * dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_ones_sum_resultdivisormaskentryinput))) /\ (exists ge_balance_positive_ones_sum_resultdivisormaskentryinputvalue ge_balance_negative_ones_sum_resultdivisormaskentryinputvalue. (((((dm_value_ones_sum_resultdivisormask) = 2 * (ge_balance_positive_ones_sum_resultdivisormaskentryinputvalue) /\ (ge_balance_negative_ones_sum_resultdivisormaskentryinputvalue) = 0) \/ exists ge_signed_half_ones_sum_resultdivisormaskentryinputvaluedecode. (((dm_value_ones_sum_resultdivisormask) = 2 * ge_signed_half_ones_sum_resultdivisormaskentryinputvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultdivisormaskentryinputvalue) = 0) /\ (ge_balance_negative_ones_sum_resultdivisormaskentryinputvalue) = S ge_signed_half_ones_sum_resultdivisormaskentryinputvaluedecode))) /\ ((dst_positive_ones_sum_resultdivisormaskentryinput) + ge_balance_negative_ones_sum_resultdivisormaskentryinputvalue = (dst_negative_ones_sum_resultdivisormaskentryinput) + ge_balance_positive_ones_sum_resultdivisormaskentryinputvalue))))))))))))) \/ ((((dm_index_ones_sum_resultdivisormask)=0 \/ ~(exists pvs_factor_ones_sum_resultdivisormaskentrynondivisor. (n) = (dm_index_ones_sum_resultdivisormask) * pvs_factor_ones_sum_resultdivisormaskentrynondivisor)) /\ ((dm_value_ones_sum_resultdivisormask)=0))))))) /\ (exists dst_positive_code_ones_sum_resultdivisorfold dst_positive_scale_ones_sum_resultdivisorfold dst_negative_code_ones_sum_resultdivisorfold dst_negative_scale_ones_sum_resultdivisorfold dst_positive_sum_ones_sum_resultdivisorfold dst_negative_sum_ones_sum_resultdivisorfold. (((dm_mask_table_ones_sum_resultdivisor) = (((((dst_positive_code_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold)) * S ((dst_positive_code_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold)) + ((dst_positive_scale_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold))) + (((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) * S ((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) + ((dst_negative_scale_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)))) * S ((((dst_positive_code_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold)) * S ((dst_positive_code_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold)) + ((dst_positive_scale_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold))) + (((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) * S ((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) + ((dst_negative_scale_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)))) + ((((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) * S ((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) + ((dst_negative_scale_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold))) + (((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) * S ((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) + ((dst_negative_scale_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)))))) /\ (((exists fs_u_dst_ones_sum_resultdivisorfoldpositive fs_v_dst_ones_sum_resultdivisorfoldpositive. ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_start. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_ones_sum_resultdivisorfoldpositive)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_start. fs_u_dst_ones_sum_resultdivisorfoldpositive = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_start * S ((S (0)) * fs_v_dst_ones_sum_resultdivisorfoldpositive) + (0))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_terminal. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_terminal + S (dst_positive_sum_ones_sum_resultdivisorfold) = S ((S (S (n))) * fs_v_dst_ones_sum_resultdivisorfoldpositive)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_terminal. fs_u_dst_ones_sum_resultdivisorfoldpositive = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_ones_sum_resultdivisorfoldpositive) + (dst_positive_sum_ones_sum_resultdivisorfold))) /\ forall fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps. (exists fs_lt_dst_ones_sum_resultdivisorfoldpositive_body_steps_bound. fs_lt_dst_ones_sum_resultdivisorfoldpositive_body_steps_bound + S fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps = S (n)) -> exists fs_a_dst_ones_sum_resultdivisorfoldpositive_body_steps fs_r_dst_ones_sum_resultdivisorfoldpositive_body_steps fs_s_dst_ones_sum_resultdivisorfoldpositive_body_steps. ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_summand. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_summand + S (fs_a_dst_ones_sum_resultdivisorfoldpositive_body_steps) = S ((S (fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * dst_positive_scale_ones_sum_resultdivisorfold)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_summand. dst_positive_code_ones_sum_resultdivisorfold = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_summand * S ((S (fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * dst_positive_scale_ones_sum_resultdivisorfold) + (fs_a_dst_ones_sum_resultdivisorfoldpositive_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_partial. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_partial + S (fs_r_dst_ones_sum_resultdivisorfoldpositive_body_steps) = S ((S (fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldpositive)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_partial. fs_u_dst_ones_sum_resultdivisorfoldpositive = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_partial * S ((S (fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldpositive) + (fs_r_dst_ones_sum_resultdivisorfoldpositive_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_successor. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_successor + S (fs_s_dst_ones_sum_resultdivisorfoldpositive_body_steps) = S ((S (S fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldpositive)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_successor. fs_u_dst_ones_sum_resultdivisorfoldpositive = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_successor * S ((S (S fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldpositive) + (fs_s_dst_ones_sum_resultdivisorfoldpositive_body_steps))) /\ fs_s_dst_ones_sum_resultdivisorfoldpositive_body_steps = fs_r_dst_ones_sum_resultdivisorfoldpositive_body_steps + fs_a_dst_ones_sum_resultdivisorfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_ones_sum_resultdivisorfoldnegative fs_v_dst_ones_sum_resultdivisorfoldnegative. ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_start. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_ones_sum_resultdivisorfoldnegative)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_start. fs_u_dst_ones_sum_resultdivisorfoldnegative = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_start * S ((S (0)) * fs_v_dst_ones_sum_resultdivisorfoldnegative) + (0))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_terminal. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_terminal + S (dst_negative_sum_ones_sum_resultdivisorfold) = S ((S (S (n))) * fs_v_dst_ones_sum_resultdivisorfoldnegative)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_terminal. fs_u_dst_ones_sum_resultdivisorfoldnegative = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_ones_sum_resultdivisorfoldnegative) + (dst_negative_sum_ones_sum_resultdivisorfold))) /\ forall fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps. (exists fs_lt_dst_ones_sum_resultdivisorfoldnegative_body_steps_bound. fs_lt_dst_ones_sum_resultdivisorfoldnegative_body_steps_bound + S fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps = S (n)) -> exists fs_a_dst_ones_sum_resultdivisorfoldnegative_body_steps fs_r_dst_ones_sum_resultdivisorfoldnegative_body_steps fs_s_dst_ones_sum_resultdivisorfoldnegative_body_steps. ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_summand. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_summand + S (fs_a_dst_ones_sum_resultdivisorfoldnegative_body_steps) = S ((S (fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * dst_negative_scale_ones_sum_resultdivisorfold)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_summand. dst_negative_code_ones_sum_resultdivisorfold = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_summand * S ((S (fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * dst_negative_scale_ones_sum_resultdivisorfold) + (fs_a_dst_ones_sum_resultdivisorfoldnegative_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_partial. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_partial + S (fs_r_dst_ones_sum_resultdivisorfoldnegative_body_steps) = S ((S (fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldnegative)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_partial. fs_u_dst_ones_sum_resultdivisorfoldnegative = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_partial * S ((S (fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldnegative) + (fs_r_dst_ones_sum_resultdivisorfoldnegative_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_successor. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_successor + S (fs_s_dst_ones_sum_resultdivisorfoldnegative_body_steps) = S ((S (S fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldnegative)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_successor. fs_u_dst_ones_sum_resultdivisorfoldnegative = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_successor * S ((S (S fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldnegative) + (fs_s_dst_ones_sum_resultdivisorfoldnegative_body_steps))) /\ fs_s_dst_ones_sum_resultdivisorfoldnegative_body_steps = fs_r_dst_ones_sum_resultdivisorfoldnegative_body_steps + fs_a_dst_ones_sum_resultdivisorfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_ones_sum_resultdivisorfoldresult ge_balance_negative_ones_sum_resultdivisorfoldresult. (((((z) = 2 * (ge_balance_positive_ones_sum_resultdivisorfoldresult) /\ (ge_balance_negative_ones_sum_resultdivisorfoldresult) = 0) \/ exists ge_signed_half_ones_sum_resultdivisorfoldresultdecode. (((z) = 2 * ge_signed_half_ones_sum_resultdivisorfoldresultdecode + 1 /\ (ge_balance_positive_ones_sum_resultdivisorfoldresult) = 0) /\ (ge_balance_negative_ones_sum_resultdivisorfoldresult) = S ge_signed_half_ones_sum_resultdivisorfoldresultdecode))) /\ ((dst_positive_sum_ones_sum_resultdivisorfold) + ge_balance_negative_ones_sum_resultdivisorfoldresult = (dst_negative_sum_ones_sum_resultdivisorfold) + ge_balance_positive_ones_sum_resultdivisorfoldresult)))))))))))))) /\ ((((~((n)=0)) /\ (exists dm_mask_table_ones_sum_resultdivisor. ((((exists dst_positive_code_ones_sum_resultdivisormasktable dst_positive_scale_ones_sum_resultdivisormasktable dst_negative_code_ones_sum_resultdivisormasktable dst_negative_scale_ones_sum_resultdivisormasktable. (((dm_mask_table_ones_sum_resultdivisor) = (((((dst_positive_code_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable)) * S ((dst_positive_code_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable)) + ((dst_positive_scale_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable))) + (((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) * S ((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) + ((dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)))) * S ((((dst_positive_code_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable)) * S ((dst_positive_code_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable)) + ((dst_positive_scale_ones_sum_resultdivisormasktable) + (dst_positive_scale_ones_sum_resultdivisormasktable))) + (((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) * S ((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) + ((dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)))) + ((((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) * S ((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) + ((dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable))) + (((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) * S ((dst_negative_code_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)) + ((dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_scale_ones_sum_resultdivisormasktable)))))) /\ (forall dst_index_ones_sum_resultdivisormasktable. (exists pvs_le_gap_ones_sum_resultdivisormasktabledomain. pvs_le_gap_ones_sum_resultdivisormasktabledomain + (dst_index_ones_sum_resultdivisormasktable) = (n)) -> exists dst_positive_ones_sum_resultdivisormasktable dst_negative_ones_sum_resultdivisormasktable dst_value_ones_sum_resultdivisormasktable. ((((exists ff_h_pvs_ones_sum_resultdivisormasktableentrypositive. ff_h_pvs_ones_sum_resultdivisormasktableentrypositive + S (dst_positive_ones_sum_resultdivisormasktable) = S ((S (dst_index_ones_sum_resultdivisormasktable)) * dst_positive_scale_ones_sum_resultdivisormasktable)) /\ exists ff_q_pvs_ones_sum_resultdivisormasktableentrypositive. dst_positive_code_ones_sum_resultdivisormasktable = ff_q_pvs_ones_sum_resultdivisormasktableentrypositive * S ((S (dst_index_ones_sum_resultdivisormasktable)) * dst_positive_scale_ones_sum_resultdivisormasktable) + (dst_positive_ones_sum_resultdivisormasktable))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormasktableentrynegative. ff_h_pvs_ones_sum_resultdivisormasktableentrynegative + S (dst_negative_ones_sum_resultdivisormasktable) = S ((S (dst_index_ones_sum_resultdivisormasktable)) * dst_negative_scale_ones_sum_resultdivisormasktable)) /\ exists ff_q_pvs_ones_sum_resultdivisormasktableentrynegative. dst_negative_code_ones_sum_resultdivisormasktable = ff_q_pvs_ones_sum_resultdivisormasktableentrynegative * S ((S (dst_index_ones_sum_resultdivisormasktable)) * dst_negative_scale_ones_sum_resultdivisormasktable) + (dst_negative_ones_sum_resultdivisormasktable))) /\ (exists ge_balance_positive_ones_sum_resultdivisormasktableentryvalue ge_balance_negative_ones_sum_resultdivisormasktableentryvalue. (((((dst_value_ones_sum_resultdivisormasktable) = 2 * (ge_balance_positive_ones_sum_resultdivisormasktableentryvalue) /\ (ge_balance_negative_ones_sum_resultdivisormasktableentryvalue) = 0) \/ exists ge_signed_half_ones_sum_resultdivisormasktableentryvaluedecode. (((dst_value_ones_sum_resultdivisormasktable) = 2 * ge_signed_half_ones_sum_resultdivisormasktableentryvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultdivisormasktableentryvalue) = 0) /\ (ge_balance_negative_ones_sum_resultdivisormasktableentryvalue) = S ge_signed_half_ones_sum_resultdivisormasktableentryvaluedecode))) /\ ((dst_positive_ones_sum_resultdivisormasktable) + ge_balance_negative_ones_sum_resultdivisormasktableentryvalue = (dst_negative_ones_sum_resultdivisormasktable) + ge_balance_positive_ones_sum_resultdivisormasktableentryvalue))))))))) /\ (forall dm_index_ones_sum_resultdivisormask dm_value_ones_sum_resultdivisormask. (exists pvs_le_gap_ones_sum_resultdivisormaskdomain. pvs_le_gap_ones_sum_resultdivisormaskdomain + (dm_index_ones_sum_resultdivisormask) = (n)) -> (exists dst_positive_code_ones_sum_resultdivisormasklookup dst_positive_scale_ones_sum_resultdivisormasklookup dst_negative_code_ones_sum_resultdivisormasklookup dst_negative_scale_ones_sum_resultdivisormasklookup dst_positive_ones_sum_resultdivisormasklookup dst_negative_ones_sum_resultdivisormasklookup. (((dm_mask_table_ones_sum_resultdivisor) = (((((dst_positive_code_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup)) * S ((dst_positive_code_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup)) + ((dst_positive_scale_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup))) + (((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) * S ((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) + ((dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)))) * S ((((dst_positive_code_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup)) * S ((dst_positive_code_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup)) + ((dst_positive_scale_ones_sum_resultdivisormasklookup) + (dst_positive_scale_ones_sum_resultdivisormasklookup))) + (((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) * S ((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) + ((dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)))) + ((((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) * S ((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) + ((dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup))) + (((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) * S ((dst_negative_code_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)) + ((dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_scale_ones_sum_resultdivisormasklookup)))))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormasklookuppositive. ff_h_pvs_ones_sum_resultdivisormasklookuppositive + S (dst_positive_ones_sum_resultdivisormasklookup) = S ((S (dm_index_ones_sum_resultdivisormask)) * dst_positive_scale_ones_sum_resultdivisormasklookup)) /\ exists ff_q_pvs_ones_sum_resultdivisormasklookuppositive. dst_positive_code_ones_sum_resultdivisormasklookup = ff_q_pvs_ones_sum_resultdivisormasklookuppositive * S ((S (dm_index_ones_sum_resultdivisormask)) * dst_positive_scale_ones_sum_resultdivisormasklookup) + (dst_positive_ones_sum_resultdivisormasklookup))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormasklookupnegative. ff_h_pvs_ones_sum_resultdivisormasklookupnegative + S (dst_negative_ones_sum_resultdivisormasklookup) = S ((S (dm_index_ones_sum_resultdivisormask)) * dst_negative_scale_ones_sum_resultdivisormasklookup)) /\ exists ff_q_pvs_ones_sum_resultdivisormasklookupnegative. dst_negative_code_ones_sum_resultdivisormasklookup = ff_q_pvs_ones_sum_resultdivisormasklookupnegative * S ((S (dm_index_ones_sum_resultdivisormask)) * dst_negative_scale_ones_sum_resultdivisormasklookup) + (dst_negative_ones_sum_resultdivisormasklookup))) /\ (exists ge_balance_positive_ones_sum_resultdivisormasklookupvalue ge_balance_negative_ones_sum_resultdivisormasklookupvalue. (((((dm_value_ones_sum_resultdivisormask) = 2 * (ge_balance_positive_ones_sum_resultdivisormasklookupvalue) /\ (ge_balance_negative_ones_sum_resultdivisormasklookupvalue) = 0) \/ exists ge_signed_half_ones_sum_resultdivisormasklookupvaluedecode. (((dm_value_ones_sum_resultdivisormask) = 2 * ge_signed_half_ones_sum_resultdivisormasklookupvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultdivisormasklookupvalue) = 0) /\ (ge_balance_negative_ones_sum_resultdivisormasklookupvalue) = S ge_signed_half_ones_sum_resultdivisormasklookupvaluedecode))) /\ ((dst_positive_ones_sum_resultdivisormasklookup) + ge_balance_negative_ones_sum_resultdivisormasklookupvalue = (dst_negative_ones_sum_resultdivisormasklookup) + ge_balance_positive_ones_sum_resultdivisormasklookupvalue))))))))) -> ((((~((dm_index_ones_sum_resultdivisormask)=0)) /\ (exists dm_quotient_ones_sum_resultdivisormaskentry. (((n)=(dm_index_ones_sum_resultdivisormask)*dm_quotient_ones_sum_resultdivisormaskentry) /\ (exists dst_positive_code_ones_sum_resultdivisormaskentryinput dst_positive_scale_ones_sum_resultdivisormaskentryinput dst_negative_code_ones_sum_resultdivisormaskentryinput dst_negative_scale_ones_sum_resultdivisormaskentryinput dst_positive_ones_sum_resultdivisormaskentryinput dst_negative_ones_sum_resultdivisormaskentryinput. (((F) = (((((dst_positive_code_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_positive_code_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_positive_scale_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput))) + (((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)))) * S ((((dst_positive_code_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_positive_code_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_positive_scale_ones_sum_resultdivisormaskentryinput) + (dst_positive_scale_ones_sum_resultdivisormaskentryinput))) + (((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)))) + ((((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput))) + (((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) * S ((dst_negative_code_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)) + ((dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_scale_ones_sum_resultdivisormaskentryinput)))))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormaskentryinputpositive. ff_h_pvs_ones_sum_resultdivisormaskentryinputpositive + S (dst_positive_ones_sum_resultdivisormaskentryinput) = S ((S (dm_index_ones_sum_resultdivisormask)) * dst_positive_scale_ones_sum_resultdivisormaskentryinput)) /\ exists ff_q_pvs_ones_sum_resultdivisormaskentryinputpositive. dst_positive_code_ones_sum_resultdivisormaskentryinput = ff_q_pvs_ones_sum_resultdivisormaskentryinputpositive * S ((S (dm_index_ones_sum_resultdivisormask)) * dst_positive_scale_ones_sum_resultdivisormaskentryinput) + (dst_positive_ones_sum_resultdivisormaskentryinput))) /\ (((((exists ff_h_pvs_ones_sum_resultdivisormaskentryinputnegative. ff_h_pvs_ones_sum_resultdivisormaskentryinputnegative + S (dst_negative_ones_sum_resultdivisormaskentryinput) = S ((S (dm_index_ones_sum_resultdivisormask)) * dst_negative_scale_ones_sum_resultdivisormaskentryinput)) /\ exists ff_q_pvs_ones_sum_resultdivisormaskentryinputnegative. dst_negative_code_ones_sum_resultdivisormaskentryinput = ff_q_pvs_ones_sum_resultdivisormaskentryinputnegative * S ((S (dm_index_ones_sum_resultdivisormask)) * dst_negative_scale_ones_sum_resultdivisormaskentryinput) + (dst_negative_ones_sum_resultdivisormaskentryinput))) /\ (exists ge_balance_positive_ones_sum_resultdivisormaskentryinputvalue ge_balance_negative_ones_sum_resultdivisormaskentryinputvalue. (((((dm_value_ones_sum_resultdivisormask) = 2 * (ge_balance_positive_ones_sum_resultdivisormaskentryinputvalue) /\ (ge_balance_negative_ones_sum_resultdivisormaskentryinputvalue) = 0) \/ exists ge_signed_half_ones_sum_resultdivisormaskentryinputvaluedecode. (((dm_value_ones_sum_resultdivisormask) = 2 * ge_signed_half_ones_sum_resultdivisormaskentryinputvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultdivisormaskentryinputvalue) = 0) /\ (ge_balance_negative_ones_sum_resultdivisormaskentryinputvalue) = S ge_signed_half_ones_sum_resultdivisormaskentryinputvaluedecode))) /\ ((dst_positive_ones_sum_resultdivisormaskentryinput) + ge_balance_negative_ones_sum_resultdivisormaskentryinputvalue = (dst_negative_ones_sum_resultdivisormaskentryinput) + ge_balance_positive_ones_sum_resultdivisormaskentryinputvalue))))))))))))) \/ ((((dm_index_ones_sum_resultdivisormask)=0 \/ ~(exists pvs_factor_ones_sum_resultdivisormaskentrynondivisor. (n) = (dm_index_ones_sum_resultdivisormask) * pvs_factor_ones_sum_resultdivisormaskentrynondivisor)) /\ ((dm_value_ones_sum_resultdivisormask)=0))))))) /\ (exists dst_positive_code_ones_sum_resultdivisorfold dst_positive_scale_ones_sum_resultdivisorfold dst_negative_code_ones_sum_resultdivisorfold dst_negative_scale_ones_sum_resultdivisorfold dst_positive_sum_ones_sum_resultdivisorfold dst_negative_sum_ones_sum_resultdivisorfold. (((dm_mask_table_ones_sum_resultdivisor) = (((((dst_positive_code_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold)) * S ((dst_positive_code_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold)) + ((dst_positive_scale_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold))) + (((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) * S ((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) + ((dst_negative_scale_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)))) * S ((((dst_positive_code_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold)) * S ((dst_positive_code_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold)) + ((dst_positive_scale_ones_sum_resultdivisorfold) + (dst_positive_scale_ones_sum_resultdivisorfold))) + (((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) * S ((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) + ((dst_negative_scale_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)))) + ((((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) * S ((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) + ((dst_negative_scale_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold))) + (((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) * S ((dst_negative_code_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)) + ((dst_negative_scale_ones_sum_resultdivisorfold) + (dst_negative_scale_ones_sum_resultdivisorfold)))))) /\ (((exists fs_u_dst_ones_sum_resultdivisorfoldpositive fs_v_dst_ones_sum_resultdivisorfoldpositive. ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_start. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_ones_sum_resultdivisorfoldpositive)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_start. fs_u_dst_ones_sum_resultdivisorfoldpositive = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_start * S ((S (0)) * fs_v_dst_ones_sum_resultdivisorfoldpositive) + (0))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_terminal. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_terminal + S (dst_positive_sum_ones_sum_resultdivisorfold) = S ((S (S (n))) * fs_v_dst_ones_sum_resultdivisorfoldpositive)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_terminal. fs_u_dst_ones_sum_resultdivisorfoldpositive = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_ones_sum_resultdivisorfoldpositive) + (dst_positive_sum_ones_sum_resultdivisorfold))) /\ forall fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps. (exists fs_lt_dst_ones_sum_resultdivisorfoldpositive_body_steps_bound. fs_lt_dst_ones_sum_resultdivisorfoldpositive_body_steps_bound + S fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps = S (n)) -> exists fs_a_dst_ones_sum_resultdivisorfoldpositive_body_steps fs_r_dst_ones_sum_resultdivisorfoldpositive_body_steps fs_s_dst_ones_sum_resultdivisorfoldpositive_body_steps. ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_summand. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_summand + S (fs_a_dst_ones_sum_resultdivisorfoldpositive_body_steps) = S ((S (fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * dst_positive_scale_ones_sum_resultdivisorfold)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_summand. dst_positive_code_ones_sum_resultdivisorfold = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_summand * S ((S (fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * dst_positive_scale_ones_sum_resultdivisorfold) + (fs_a_dst_ones_sum_resultdivisorfoldpositive_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_partial. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_partial + S (fs_r_dst_ones_sum_resultdivisorfoldpositive_body_steps) = S ((S (fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldpositive)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_partial. fs_u_dst_ones_sum_resultdivisorfoldpositive = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_partial * S ((S (fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldpositive) + (fs_r_dst_ones_sum_resultdivisorfoldpositive_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_successor. fs_h_dst_ones_sum_resultdivisorfoldpositive_body_steps_successor + S (fs_s_dst_ones_sum_resultdivisorfoldpositive_body_steps) = S ((S (S fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldpositive)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_successor. fs_u_dst_ones_sum_resultdivisorfoldpositive = fs_q_dst_ones_sum_resultdivisorfoldpositive_body_steps_successor * S ((S (S fs_i_dst_ones_sum_resultdivisorfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldpositive) + (fs_s_dst_ones_sum_resultdivisorfoldpositive_body_steps))) /\ fs_s_dst_ones_sum_resultdivisorfoldpositive_body_steps = fs_r_dst_ones_sum_resultdivisorfoldpositive_body_steps + fs_a_dst_ones_sum_resultdivisorfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_ones_sum_resultdivisorfoldnegative fs_v_dst_ones_sum_resultdivisorfoldnegative. ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_start. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_ones_sum_resultdivisorfoldnegative)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_start. fs_u_dst_ones_sum_resultdivisorfoldnegative = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_start * S ((S (0)) * fs_v_dst_ones_sum_resultdivisorfoldnegative) + (0))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_terminal. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_terminal + S (dst_negative_sum_ones_sum_resultdivisorfold) = S ((S (S (n))) * fs_v_dst_ones_sum_resultdivisorfoldnegative)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_terminal. fs_u_dst_ones_sum_resultdivisorfoldnegative = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_ones_sum_resultdivisorfoldnegative) + (dst_negative_sum_ones_sum_resultdivisorfold))) /\ forall fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps. (exists fs_lt_dst_ones_sum_resultdivisorfoldnegative_body_steps_bound. fs_lt_dst_ones_sum_resultdivisorfoldnegative_body_steps_bound + S fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps = S (n)) -> exists fs_a_dst_ones_sum_resultdivisorfoldnegative_body_steps fs_r_dst_ones_sum_resultdivisorfoldnegative_body_steps fs_s_dst_ones_sum_resultdivisorfoldnegative_body_steps. ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_summand. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_summand + S (fs_a_dst_ones_sum_resultdivisorfoldnegative_body_steps) = S ((S (fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * dst_negative_scale_ones_sum_resultdivisorfold)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_summand. dst_negative_code_ones_sum_resultdivisorfold = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_summand * S ((S (fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * dst_negative_scale_ones_sum_resultdivisorfold) + (fs_a_dst_ones_sum_resultdivisorfoldnegative_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_partial. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_partial + S (fs_r_dst_ones_sum_resultdivisorfoldnegative_body_steps) = S ((S (fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldnegative)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_partial. fs_u_dst_ones_sum_resultdivisorfoldnegative = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_partial * S ((S (fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldnegative) + (fs_r_dst_ones_sum_resultdivisorfoldnegative_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_successor. fs_h_dst_ones_sum_resultdivisorfoldnegative_body_steps_successor + S (fs_s_dst_ones_sum_resultdivisorfoldnegative_body_steps) = S ((S (S fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldnegative)) /\ exists fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_successor. fs_u_dst_ones_sum_resultdivisorfoldnegative = fs_q_dst_ones_sum_resultdivisorfoldnegative_body_steps_successor * S ((S (S fs_i_dst_ones_sum_resultdivisorfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultdivisorfoldnegative) + (fs_s_dst_ones_sum_resultdivisorfoldnegative_body_steps))) /\ fs_s_dst_ones_sum_resultdivisorfoldnegative_body_steps = fs_r_dst_ones_sum_resultdivisorfoldnegative_body_steps + fs_a_dst_ones_sum_resultdivisorfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_ones_sum_resultdivisorfoldresult ge_balance_negative_ones_sum_resultdivisorfoldresult. (((((z) = 2 * (ge_balance_positive_ones_sum_resultdivisorfoldresult) /\ (ge_balance_negative_ones_sum_resultdivisorfoldresult) = 0) \/ exists ge_signed_half_ones_sum_resultdivisorfoldresultdecode. (((z) = 2 * ge_signed_half_ones_sum_resultdivisorfoldresultdecode + 1 /\ (ge_balance_positive_ones_sum_resultdivisorfoldresult) = 0) /\ (ge_balance_negative_ones_sum_resultdivisorfoldresult) = S ge_signed_half_ones_sum_resultdivisorfoldresultdecode))) /\ ((dst_positive_sum_ones_sum_resultdivisorfold) + ge_balance_negative_ones_sum_resultdivisorfoldresult = (dst_negative_sum_ones_sum_resultdivisorfold) + ge_balance_positive_ones_sum_resultdivisorfoldresult))))))))))))) -> (((~((n)=0)) /\ (exists dc_mask_ones_sum_resultconvolution. ((((exists dst_positive_code_ones_sum_resultconvolutionmasktable dst_positive_scale_ones_sum_resultconvolutionmasktable dst_negative_code_ones_sum_resultconvolutionmasktable dst_negative_scale_ones_sum_resultconvolutionmasktable. (((dc_mask_ones_sum_resultconvolution) = (((((dst_positive_code_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_positive_code_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable)) + ((dst_positive_scale_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable))) + (((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) + ((dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)))) * S ((((dst_positive_code_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_positive_code_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable)) + ((dst_positive_scale_ones_sum_resultconvolutionmasktable) + (dst_positive_scale_ones_sum_resultconvolutionmasktable))) + (((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) + ((dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)))) + ((((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) + ((dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable))) + (((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) * S ((dst_negative_code_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)) + ((dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_scale_ones_sum_resultconvolutionmasktable)))))) /\ (forall dst_index_ones_sum_resultconvolutionmasktable. (exists pvs_le_gap_ones_sum_resultconvolutionmasktabledomain. pvs_le_gap_ones_sum_resultconvolutionmasktabledomain + (dst_index_ones_sum_resultconvolutionmasktable) = (n)) -> exists dst_positive_ones_sum_resultconvolutionmasktable dst_negative_ones_sum_resultconvolutionmasktable dst_value_ones_sum_resultconvolutionmasktable. ((((exists ff_h_pvs_ones_sum_resultconvolutionmasktableentrypositive. ff_h_pvs_ones_sum_resultconvolutionmasktableentrypositive + S (dst_positive_ones_sum_resultconvolutionmasktable) = S ((S (dst_index_ones_sum_resultconvolutionmasktable)) * dst_positive_scale_ones_sum_resultconvolutionmasktable)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmasktableentrypositive. dst_positive_code_ones_sum_resultconvolutionmasktable = ff_q_pvs_ones_sum_resultconvolutionmasktableentrypositive * S ((S (dst_index_ones_sum_resultconvolutionmasktable)) * dst_positive_scale_ones_sum_resultconvolutionmasktable) + (dst_positive_ones_sum_resultconvolutionmasktable))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmasktableentrynegative. ff_h_pvs_ones_sum_resultconvolutionmasktableentrynegative + S (dst_negative_ones_sum_resultconvolutionmasktable) = S ((S (dst_index_ones_sum_resultconvolutionmasktable)) * dst_negative_scale_ones_sum_resultconvolutionmasktable)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmasktableentrynegative. dst_negative_code_ones_sum_resultconvolutionmasktable = ff_q_pvs_ones_sum_resultconvolutionmasktableentrynegative * S ((S (dst_index_ones_sum_resultconvolutionmasktable)) * dst_negative_scale_ones_sum_resultconvolutionmasktable) + (dst_negative_ones_sum_resultconvolutionmasktable))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionmasktableentryvalue ge_balance_negative_ones_sum_resultconvolutionmasktableentryvalue. (((((dst_value_ones_sum_resultconvolutionmasktable) = 2 * (ge_balance_positive_ones_sum_resultconvolutionmasktableentryvalue) /\ (ge_balance_negative_ones_sum_resultconvolutionmasktableentryvalue) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmasktableentryvaluedecode. (((dst_value_ones_sum_resultconvolutionmasktable) = 2 * ge_signed_half_ones_sum_resultconvolutionmasktableentryvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionmasktableentryvalue) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionmasktableentryvalue) = S ge_signed_half_ones_sum_resultconvolutionmasktableentryvaluedecode))) /\ ((dst_positive_ones_sum_resultconvolutionmasktable) + ge_balance_negative_ones_sum_resultconvolutionmasktableentryvalue = (dst_negative_ones_sum_resultconvolutionmasktable) + ge_balance_positive_ones_sum_resultconvolutionmasktableentryvalue))))))))) /\ (forall dc_index_ones_sum_resultconvolutionmask dc_value_ones_sum_resultconvolutionmask. (exists pvs_le_gap_ones_sum_resultconvolutionmaskdomain. pvs_le_gap_ones_sum_resultconvolutionmaskdomain + (dc_index_ones_sum_resultconvolutionmask) = (n)) -> (exists dst_positive_code_ones_sum_resultconvolutionmasklookup dst_positive_scale_ones_sum_resultconvolutionmasklookup dst_negative_code_ones_sum_resultconvolutionmasklookup dst_negative_scale_ones_sum_resultconvolutionmasklookup dst_positive_ones_sum_resultconvolutionmasklookup dst_negative_ones_sum_resultconvolutionmasklookup. (((dc_mask_ones_sum_resultconvolution) = (((((dst_positive_code_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_positive_code_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_positive_scale_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup))) + (((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)))) * S ((((dst_positive_code_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_positive_code_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_positive_scale_ones_sum_resultconvolutionmasklookup) + (dst_positive_scale_ones_sum_resultconvolutionmasklookup))) + (((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)))) + ((((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup))) + (((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) * S ((dst_negative_code_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)) + ((dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_scale_ones_sum_resultconvolutionmasklookup)))))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmasklookuppositive. ff_h_pvs_ones_sum_resultconvolutionmasklookuppositive + S (dst_positive_ones_sum_resultconvolutionmasklookup) = S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_positive_scale_ones_sum_resultconvolutionmasklookup)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmasklookuppositive. dst_positive_code_ones_sum_resultconvolutionmasklookup = ff_q_pvs_ones_sum_resultconvolutionmasklookuppositive * S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_positive_scale_ones_sum_resultconvolutionmasklookup) + (dst_positive_ones_sum_resultconvolutionmasklookup))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmasklookupnegative. ff_h_pvs_ones_sum_resultconvolutionmasklookupnegative + S (dst_negative_ones_sum_resultconvolutionmasklookup) = S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_negative_scale_ones_sum_resultconvolutionmasklookup)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmasklookupnegative. dst_negative_code_ones_sum_resultconvolutionmasklookup = ff_q_pvs_ones_sum_resultconvolutionmasklookupnegative * S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_negative_scale_ones_sum_resultconvolutionmasklookup) + (dst_negative_ones_sum_resultconvolutionmasklookup))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionmasklookupvalue ge_balance_negative_ones_sum_resultconvolutionmasklookupvalue. (((((dc_value_ones_sum_resultconvolutionmask) = 2 * (ge_balance_positive_ones_sum_resultconvolutionmasklookupvalue) /\ (ge_balance_negative_ones_sum_resultconvolutionmasklookupvalue) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmasklookupvaluedecode. (((dc_value_ones_sum_resultconvolutionmask) = 2 * ge_signed_half_ones_sum_resultconvolutionmasklookupvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionmasklookupvalue) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionmasklookupvalue) = S ge_signed_half_ones_sum_resultconvolutionmasklookupvaluedecode))) /\ ((dst_positive_ones_sum_resultconvolutionmasklookup) + ge_balance_negative_ones_sum_resultconvolutionmasklookupvalue = (dst_negative_ones_sum_resultconvolutionmasklookup) + ge_balance_positive_ones_sum_resultconvolutionmasklookupvalue))))))))) -> ((((~((dc_index_ones_sum_resultconvolutionmask)=0)) /\ (exists dc_quotient_ones_sum_resultconvolutionmaskentry dc_left_ones_sum_resultconvolutionmaskentry dc_right_ones_sum_resultconvolutionmaskentry. (((n)=(dc_index_ones_sum_resultconvolutionmask)*dc_quotient_ones_sum_resultconvolutionmaskentry) /\ (((exists dst_positive_code_ones_sum_resultconvolutionmaskentryleft dst_positive_scale_ones_sum_resultconvolutionmaskentryleft dst_negative_code_ones_sum_resultconvolutionmaskentryleft dst_negative_scale_ones_sum_resultconvolutionmaskentryleft dst_positive_ones_sum_resultconvolutionmaskentryleft dst_negative_ones_sum_resultconvolutionmaskentryleft. (((F) = (((((dst_positive_code_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_positive_code_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_positive_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)))) * S ((((dst_positive_code_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_positive_code_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_positive_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryleft))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)))) + ((((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)))))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmaskentryleftpositive. ff_h_pvs_ones_sum_resultconvolutionmaskentryleftpositive + S (dst_positive_ones_sum_resultconvolutionmaskentryleft) = S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_positive_scale_ones_sum_resultconvolutionmaskentryleft)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmaskentryleftpositive. dst_positive_code_ones_sum_resultconvolutionmaskentryleft = ff_q_pvs_ones_sum_resultconvolutionmaskentryleftpositive * S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_positive_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_positive_ones_sum_resultconvolutionmaskentryleft))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmaskentryleftnegative. ff_h_pvs_ones_sum_resultconvolutionmaskentryleftnegative + S (dst_negative_ones_sum_resultconvolutionmaskentryleft) = S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_negative_scale_ones_sum_resultconvolutionmaskentryleft)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmaskentryleftnegative. dst_negative_code_ones_sum_resultconvolutionmaskentryleft = ff_q_pvs_ones_sum_resultconvolutionmaskentryleftnegative * S ((S (dc_index_ones_sum_resultconvolutionmask)) * dst_negative_scale_ones_sum_resultconvolutionmaskentryleft) + (dst_negative_ones_sum_resultconvolutionmaskentryleft))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionmaskentryleftvalue ge_balance_negative_ones_sum_resultconvolutionmaskentryleftvalue. (((((dc_left_ones_sum_resultconvolutionmaskentry) = 2 * (ge_balance_positive_ones_sum_resultconvolutionmaskentryleftvalue) /\ (ge_balance_negative_ones_sum_resultconvolutionmaskentryleftvalue) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryleftvaluedecode. (((dc_left_ones_sum_resultconvolutionmaskentry) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionmaskentryleftvalue) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionmaskentryleftvalue) = S ge_signed_half_ones_sum_resultconvolutionmaskentryleftvaluedecode))) /\ ((dst_positive_ones_sum_resultconvolutionmaskentryleft) + ge_balance_negative_ones_sum_resultconvolutionmaskentryleftvalue = (dst_negative_ones_sum_resultconvolutionmaskentryleft) + ge_balance_positive_ones_sum_resultconvolutionmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_ones_sum_resultconvolutionmaskentryright dst_positive_scale_ones_sum_resultconvolutionmaskentryright dst_negative_code_ones_sum_resultconvolutionmaskentryright dst_negative_scale_ones_sum_resultconvolutionmaskentryright dst_positive_ones_sum_resultconvolutionmaskentryright dst_negative_ones_sum_resultconvolutionmaskentryright. (((U) = (((((dst_positive_code_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_positive_code_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_positive_scale_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)))) * S ((((dst_positive_code_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_positive_code_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_positive_scale_ones_sum_resultconvolutionmaskentryright) + (dst_positive_scale_ones_sum_resultconvolutionmaskentryright))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)))) + ((((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright))) + (((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) * S ((dst_negative_code_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) + ((dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_scale_ones_sum_resultconvolutionmaskentryright)))))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmaskentryrightpositive. ff_h_pvs_ones_sum_resultconvolutionmaskentryrightpositive + S (dst_positive_ones_sum_resultconvolutionmaskentryright) = S ((S (dc_quotient_ones_sum_resultconvolutionmaskentry)) * dst_positive_scale_ones_sum_resultconvolutionmaskentryright)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmaskentryrightpositive. dst_positive_code_ones_sum_resultconvolutionmaskentryright = ff_q_pvs_ones_sum_resultconvolutionmaskentryrightpositive * S ((S (dc_quotient_ones_sum_resultconvolutionmaskentry)) * dst_positive_scale_ones_sum_resultconvolutionmaskentryright) + (dst_positive_ones_sum_resultconvolutionmaskentryright))) /\ (((((exists ff_h_pvs_ones_sum_resultconvolutionmaskentryrightnegative. ff_h_pvs_ones_sum_resultconvolutionmaskentryrightnegative + S (dst_negative_ones_sum_resultconvolutionmaskentryright) = S ((S (dc_quotient_ones_sum_resultconvolutionmaskentry)) * dst_negative_scale_ones_sum_resultconvolutionmaskentryright)) /\ exists ff_q_pvs_ones_sum_resultconvolutionmaskentryrightnegative. dst_negative_code_ones_sum_resultconvolutionmaskentryright = ff_q_pvs_ones_sum_resultconvolutionmaskentryrightnegative * S ((S (dc_quotient_ones_sum_resultconvolutionmaskentry)) * dst_negative_scale_ones_sum_resultconvolutionmaskentryright) + (dst_negative_ones_sum_resultconvolutionmaskentryright))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionmaskentryrightvalue ge_balance_negative_ones_sum_resultconvolutionmaskentryrightvalue. (((((dc_right_ones_sum_resultconvolutionmaskentry) = 2 * (ge_balance_positive_ones_sum_resultconvolutionmaskentryrightvalue) /\ (ge_balance_negative_ones_sum_resultconvolutionmaskentryrightvalue) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryrightvaluedecode. (((dc_right_ones_sum_resultconvolutionmaskentry) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionmaskentryrightvalue) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionmaskentryrightvalue) = S ge_signed_half_ones_sum_resultconvolutionmaskentryrightvaluedecode))) /\ ((dst_positive_ones_sum_resultconvolutionmaskentryright) + ge_balance_negative_ones_sum_resultconvolutionmaskentryrightvalue = (dst_negative_ones_sum_resultconvolutionmaskentryright) + ge_balance_positive_ones_sum_resultconvolutionmaskentryrightvalue))))))))) /\ (exists sto_ap_ones_sum_resultconvolutionmaskentryproduct sto_an_ones_sum_resultconvolutionmaskentryproduct sto_bp_ones_sum_resultconvolutionmaskentryproduct sto_bn_ones_sum_resultconvolutionmaskentryproduct sto_cp_ones_sum_resultconvolutionmaskentryproduct sto_cn_ones_sum_resultconvolutionmaskentryproduct. (((((dc_left_ones_sum_resultconvolutionmaskentry) = 2 * (sto_ap_ones_sum_resultconvolutionmaskentryproduct) /\ (sto_an_ones_sum_resultconvolutionmaskentryproduct) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryproductleft. (((dc_left_ones_sum_resultconvolutionmaskentry) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryproductleft + 1 /\ (sto_ap_ones_sum_resultconvolutionmaskentryproduct) = 0) /\ (sto_an_ones_sum_resultconvolutionmaskentryproduct) = S ge_signed_half_ones_sum_resultconvolutionmaskentryproductleft))) /\ ((((((dc_right_ones_sum_resultconvolutionmaskentry) = 2 * (sto_bp_ones_sum_resultconvolutionmaskentryproduct) /\ (sto_bn_ones_sum_resultconvolutionmaskentryproduct) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryproductright. (((dc_right_ones_sum_resultconvolutionmaskentry) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryproductright + 1 /\ (sto_bp_ones_sum_resultconvolutionmaskentryproduct) = 0) /\ (sto_bn_ones_sum_resultconvolutionmaskentryproduct) = S ge_signed_half_ones_sum_resultconvolutionmaskentryproductright))) /\ ((((((dc_value_ones_sum_resultconvolutionmask) = 2 * (sto_cp_ones_sum_resultconvolutionmaskentryproduct) /\ (sto_cn_ones_sum_resultconvolutionmaskentryproduct) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionmaskentryproductoutput. (((dc_value_ones_sum_resultconvolutionmask) = 2 * ge_signed_half_ones_sum_resultconvolutionmaskentryproductoutput + 1 /\ (sto_cp_ones_sum_resultconvolutionmaskentryproduct) = 0) /\ (sto_cn_ones_sum_resultconvolutionmaskentryproduct) = S ge_signed_half_ones_sum_resultconvolutionmaskentryproductoutput))) /\ ((sto_ap_ones_sum_resultconvolutionmaskentryproduct * sto_bp_ones_sum_resultconvolutionmaskentryproduct + sto_an_ones_sum_resultconvolutionmaskentryproduct * sto_bn_ones_sum_resultconvolutionmaskentryproduct) + sto_cn_ones_sum_resultconvolutionmaskentryproduct = (sto_ap_ones_sum_resultconvolutionmaskentryproduct * sto_bn_ones_sum_resultconvolutionmaskentryproduct + sto_an_ones_sum_resultconvolutionmaskentryproduct * sto_bp_ones_sum_resultconvolutionmaskentryproduct) + sto_cp_ones_sum_resultconvolutionmaskentryproduct))))))))))))))) \/ ((((dc_index_ones_sum_resultconvolutionmask)=0 \/ ~(exists pvs_factor_ones_sum_resultconvolutionmaskentrynondivisor. (n) = (dc_index_ones_sum_resultconvolutionmask) * pvs_factor_ones_sum_resultconvolutionmaskentrynondivisor)) /\ ((dc_value_ones_sum_resultconvolutionmask)=0))))))) /\ (exists dst_positive_code_ones_sum_resultconvolutionfold dst_positive_scale_ones_sum_resultconvolutionfold dst_negative_code_ones_sum_resultconvolutionfold dst_negative_scale_ones_sum_resultconvolutionfold dst_positive_sum_ones_sum_resultconvolutionfold dst_negative_sum_ones_sum_resultconvolutionfold. (((dc_mask_ones_sum_resultconvolution) = (((((dst_positive_code_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold)) * S ((dst_positive_code_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold)) + ((dst_positive_scale_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold))) + (((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) * S ((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) + ((dst_negative_scale_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)))) * S ((((dst_positive_code_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold)) * S ((dst_positive_code_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold)) + ((dst_positive_scale_ones_sum_resultconvolutionfold) + (dst_positive_scale_ones_sum_resultconvolutionfold))) + (((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) * S ((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) + ((dst_negative_scale_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)))) + ((((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) * S ((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) + ((dst_negative_scale_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold))) + (((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) * S ((dst_negative_code_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)) + ((dst_negative_scale_ones_sum_resultconvolutionfold) + (dst_negative_scale_ones_sum_resultconvolutionfold)))))) /\ (((exists fs_u_dst_ones_sum_resultconvolutionfoldpositive fs_v_dst_ones_sum_resultconvolutionfoldpositive. ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_start. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_start. fs_u_dst_ones_sum_resultconvolutionfoldpositive = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_start * S ((S (0)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive) + (0))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_terminal. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_terminal + S (dst_positive_sum_ones_sum_resultconvolutionfold) = S ((S (S (n))) * fs_v_dst_ones_sum_resultconvolutionfoldpositive)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_terminal. fs_u_dst_ones_sum_resultconvolutionfoldpositive = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_ones_sum_resultconvolutionfoldpositive) + (dst_positive_sum_ones_sum_resultconvolutionfold))) /\ forall fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps. (exists fs_lt_dst_ones_sum_resultconvolutionfoldpositive_body_steps_bound. fs_lt_dst_ones_sum_resultconvolutionfoldpositive_body_steps_bound + S fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps = S (n)) -> exists fs_a_dst_ones_sum_resultconvolutionfoldpositive_body_steps fs_r_dst_ones_sum_resultconvolutionfoldpositive_body_steps fs_s_dst_ones_sum_resultconvolutionfoldpositive_body_steps. ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_summand. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_summand + S (fs_a_dst_ones_sum_resultconvolutionfoldpositive_body_steps) = S ((S (fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * dst_positive_scale_ones_sum_resultconvolutionfold)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_summand. dst_positive_code_ones_sum_resultconvolutionfold = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_summand * S ((S (fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * dst_positive_scale_ones_sum_resultconvolutionfold) + (fs_a_dst_ones_sum_resultconvolutionfoldpositive_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_partial. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_partial + S (fs_r_dst_ones_sum_resultconvolutionfoldpositive_body_steps) = S ((S (fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_partial. fs_u_dst_ones_sum_resultconvolutionfoldpositive = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_partial * S ((S (fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive) + (fs_r_dst_ones_sum_resultconvolutionfoldpositive_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_successor. fs_h_dst_ones_sum_resultconvolutionfoldpositive_body_steps_successor + S (fs_s_dst_ones_sum_resultconvolutionfoldpositive_body_steps) = S ((S (S fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_successor. fs_u_dst_ones_sum_resultconvolutionfoldpositive = fs_q_dst_ones_sum_resultconvolutionfoldpositive_body_steps_successor * S ((S (S fs_i_dst_ones_sum_resultconvolutionfoldpositive_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldpositive) + (fs_s_dst_ones_sum_resultconvolutionfoldpositive_body_steps))) /\ fs_s_dst_ones_sum_resultconvolutionfoldpositive_body_steps = fs_r_dst_ones_sum_resultconvolutionfoldpositive_body_steps + fs_a_dst_ones_sum_resultconvolutionfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_ones_sum_resultconvolutionfoldnegative fs_v_dst_ones_sum_resultconvolutionfoldnegative. ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_start. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_start. fs_u_dst_ones_sum_resultconvolutionfoldnegative = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_start * S ((S (0)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative) + (0))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_terminal. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_terminal + S (dst_negative_sum_ones_sum_resultconvolutionfold) = S ((S (S (n))) * fs_v_dst_ones_sum_resultconvolutionfoldnegative)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_terminal. fs_u_dst_ones_sum_resultconvolutionfoldnegative = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_ones_sum_resultconvolutionfoldnegative) + (dst_negative_sum_ones_sum_resultconvolutionfold))) /\ forall fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps. (exists fs_lt_dst_ones_sum_resultconvolutionfoldnegative_body_steps_bound. fs_lt_dst_ones_sum_resultconvolutionfoldnegative_body_steps_bound + S fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps = S (n)) -> exists fs_a_dst_ones_sum_resultconvolutionfoldnegative_body_steps fs_r_dst_ones_sum_resultconvolutionfoldnegative_body_steps fs_s_dst_ones_sum_resultconvolutionfoldnegative_body_steps. ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_summand. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_summand + S (fs_a_dst_ones_sum_resultconvolutionfoldnegative_body_steps) = S ((S (fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * dst_negative_scale_ones_sum_resultconvolutionfold)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_summand. dst_negative_code_ones_sum_resultconvolutionfold = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_summand * S ((S (fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * dst_negative_scale_ones_sum_resultconvolutionfold) + (fs_a_dst_ones_sum_resultconvolutionfoldnegative_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_partial. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_partial + S (fs_r_dst_ones_sum_resultconvolutionfoldnegative_body_steps) = S ((S (fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_partial. fs_u_dst_ones_sum_resultconvolutionfoldnegative = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_partial * S ((S (fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative) + (fs_r_dst_ones_sum_resultconvolutionfoldnegative_body_steps))) /\ ((((exists fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_successor. fs_h_dst_ones_sum_resultconvolutionfoldnegative_body_steps_successor + S (fs_s_dst_ones_sum_resultconvolutionfoldnegative_body_steps) = S ((S (S fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative)) /\ exists fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_successor. fs_u_dst_ones_sum_resultconvolutionfoldnegative = fs_q_dst_ones_sum_resultconvolutionfoldnegative_body_steps_successor * S ((S (S fs_i_dst_ones_sum_resultconvolutionfoldnegative_body_steps)) * fs_v_dst_ones_sum_resultconvolutionfoldnegative) + (fs_s_dst_ones_sum_resultconvolutionfoldnegative_body_steps))) /\ fs_s_dst_ones_sum_resultconvolutionfoldnegative_body_steps = fs_r_dst_ones_sum_resultconvolutionfoldnegative_body_steps + fs_a_dst_ones_sum_resultconvolutionfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_ones_sum_resultconvolutionfoldresult ge_balance_negative_ones_sum_resultconvolutionfoldresult. (((((z) = 2 * (ge_balance_positive_ones_sum_resultconvolutionfoldresult) /\ (ge_balance_negative_ones_sum_resultconvolutionfoldresult) = 0) \/ exists ge_signed_half_ones_sum_resultconvolutionfoldresultdecode. (((z) = 2 * ge_signed_half_ones_sum_resultconvolutionfoldresultdecode + 1 /\ (ge_balance_positive_ones_sum_resultconvolutionfoldresult) = 0) /\ (ge_balance_negative_ones_sum_resultconvolutionfoldresult) = S ge_signed_half_ones_sum_resultconvolutionfoldresultdecode))) /\ ((dst_positive_sum_ones_sum_resultconvolutionfold) + ge_balance_negative_ones_sum_resultconvolutionfoldresult = (dst_negative_sum_ones_sum_resultconvolutionfold) + ge_balance_positive_ones_sum_resultconvolutionfoldresult))))))))))))))))Complete tactic proof in conservative notation
All 50 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
50 script commands · 16 reading checkpoints · 0 local claims
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.
Named ingredients (2)
01Fix variables and assumptionsL1–9
02Separate the logical casesL10–10
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L10
split
03Fix variables and assumptionsL11–11
Work with arbitrary variables or the premises of the current implication.
- L11
intro hs
04Separate the logical casesL12–15
05Use earlier factsL16–16
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L16
exact hn
06Construct an explicit witnessL17–17
Supply the displayed value, then prove that it has the required property.
- L17
exists x
07Separate the logical casesL18–18
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L18
split
08Use earlier factsL19–28
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L19
specialize dirichlet_constant_one_prefix_to_divisor_mask (N) - L20
specialize dirichlet_constant_one_prefix_to_divisor_mask (F) - L21
specialize dirichlet_constant_one_prefix_to_divisor_mask (U) - L22
specialize dirichlet_constant_one_prefix_to_divisor_mask (n) - L23
specialize dirichlet_constant_one_prefix_to_divisor_mask (n) - L24
specialize dirichlet_constant_one_prefix_to_divisor_mask (x) - L25
apply dirichlet_constant_one_prefix_to_divisor_mask - L26
exact hu - L27
exact hn - L28
exact hb
09Use earlier factsL29–30
10Fix variables and assumptionsL31–31
Work with arbitrary variables or the premises of the current implication.
- L31
intro hs
11Separate the logical casesL32–35
12Use earlier factsL36–36
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L36
exact hn
13Construct an explicit witnessL37–37
Supply the displayed value, then prove that it has the required property.
- L37
exists x
14Separate the logical casesL38–38
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L38
split
15Use earlier factsL39–48
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L39
specialize dirichlet_constant_one_prefix_from_divisor_mask (N) - L40
specialize dirichlet_constant_one_prefix_from_divisor_mask (F) - L41
specialize dirichlet_constant_one_prefix_from_divisor_mask (U) - L42
specialize dirichlet_constant_one_prefix_from_divisor_mask (n) - L43
specialize dirichlet_constant_one_prefix_from_divisor_mask (n) - L44
specialize dirichlet_constant_one_prefix_from_divisor_mask (x) - L45
apply dirichlet_constant_one_prefix_from_divisor_mask - L46
exact hu - L47
exact hn - L48
exact hb
Original defined command ledger · 50 lines
- 0001
intro N - 0002
intro F - 0003
intro U - 0004
intro n - 0005
intro z - 0006
intro hf - 0007
intro hu - 0008
intro hn - 0009
intro hb - 0010
split - 0011
intro hs - 0012
cases hs - 0013
cases hs_right - 0014
cases hs_right_witness - 0015
split - 0016
exact hn - 0017
exists x - 0018
split - 0019
specialize dirichlet_constant_one_prefix_to_divisor_mask (N) - 0020
specialize dirichlet_constant_one_prefix_to_divisor_mask (F) - 0021
specialize dirichlet_constant_one_prefix_to_divisor_mask (U) - 0022
specialize dirichlet_constant_one_prefix_to_divisor_mask (n) - 0023
specialize dirichlet_constant_one_prefix_to_divisor_mask (n) - 0024
specialize dirichlet_constant_one_prefix_to_divisor_mask (x) - 0025
apply dirichlet_constant_one_prefix_to_divisor_mask - 0026
exact hu - 0027
exact hn - 0028
exact hb - 0029
exact hs_right_witness_left - 0030
exact hs_right_witness_right - 0031
intro hs - 0032
cases hs - 0033
cases hs_right - 0034
cases hs_right_witness - 0035
split - 0036
exact hn - 0037
exists x - 0038
split - 0039
specialize dirichlet_constant_one_prefix_from_divisor_mask (N) - 0040
specialize dirichlet_constant_one_prefix_from_divisor_mask (F) - 0041
specialize dirichlet_constant_one_prefix_from_divisor_mask (U) - 0042
specialize dirichlet_constant_one_prefix_from_divisor_mask (n) - 0043
specialize dirichlet_constant_one_prefix_from_divisor_mask (n) - 0044
specialize dirichlet_constant_one_prefix_from_divisor_mask (x) - 0045
apply dirichlet_constant_one_prefix_from_divisor_mask - 0046
exact hu - 0047
exact hn - 0048
exact hb - 0049
exact hs_right_witness_left - 0050
exact hs_right_witness_right