DU0018

dirichlet_constant_one_sum_iff

Actual convolution with a constant-one table is equivalent to the independently defined signed divisor sum, with exactly the same constructed mask and fold.

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

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

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

  1. L1
    intro N
  2. L2
    intro F
  3. L3
    intro U
  4. L4
    intro n
  5. L5
    intro z
  6. L6
    intro hf
  7. L7
    intro hu
  8. L8
    intro hn
  9. L9
    intro hb
02Separate the logical casesL10–10

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

  1. L10
    split
03Fix variables and assumptionsL11–11

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

  1. L11
    intro hs
04Separate the logical casesL12–15

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

  1. L12
    cases hs
  2. L13
    cases hs_right
  3. L14
    cases hs_right_witness
  4. L15
    split
05Use earlier factsL16–16

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

  1. L16
    exact hn
06Construct an explicit witnessL17–17

Supply the displayed value, then prove that it has the required property.

  1. L17
    exists x
07Separate the logical casesL18–18

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

  1. L18
    split
08Use earlier factsL19–28

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

  1. L19
    specialize dirichlet_constant_one_prefix_to_divisor_mask (N)
  2. L20
    specialize dirichlet_constant_one_prefix_to_divisor_mask (F)
  3. L21
    specialize dirichlet_constant_one_prefix_to_divisor_mask (U)
  4. L22
    specialize dirichlet_constant_one_prefix_to_divisor_mask (n)
  5. L23
    specialize dirichlet_constant_one_prefix_to_divisor_mask (n)
  6. L24
    specialize dirichlet_constant_one_prefix_to_divisor_mask (x)
  7. L25
    apply dirichlet_constant_one_prefix_to_divisor_mask
  8. L26
    exact hu
  9. L27
    exact hn
  10. L28
    exact hb
09Use earlier factsL29–30

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

  1. L29
    exact hs_right_witness_left
  2. L30
    exact hs_right_witness_right
10Fix variables and assumptionsL31–31

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

  1. L31
    intro hs
11Separate the logical casesL32–35

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

  1. L32
    cases hs
  2. L33
    cases hs_right
  3. L34
    cases hs_right_witness
  4. L35
    split
12Use earlier factsL36–36

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

  1. L36
    exact hn
13Construct an explicit witnessL37–37

Supply the displayed value, then prove that it has the required property.

  1. L37
    exists x
14Separate the logical casesL38–38

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

  1. L38
    split
15Use earlier factsL39–48

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

  1. L39
    specialize dirichlet_constant_one_prefix_from_divisor_mask (N)
  2. L40
    specialize dirichlet_constant_one_prefix_from_divisor_mask (F)
  3. L41
    specialize dirichlet_constant_one_prefix_from_divisor_mask (U)
  4. L42
    specialize dirichlet_constant_one_prefix_from_divisor_mask (n)
  5. L43
    specialize dirichlet_constant_one_prefix_from_divisor_mask (n)
  6. L44
    specialize dirichlet_constant_one_prefix_from_divisor_mask (x)
  7. L45
    apply dirichlet_constant_one_prefix_from_divisor_mask
  8. L46
    exact hu
  9. L47
    exact hn
  10. L48
    exact hb
16Use earlier factsL49–50

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

  1. L49
    exact hs_right_witness_left
  2. L50
    exact hs_right_witness_right

Library-wide reading audit

Original defined command ledger · 50 lines
  1. 0001intro N
  2. 0002intro F
  3. 0003intro U
  4. 0004intro n
  5. 0005intro z
  6. 0006intro hf
  7. 0007intro hu
  8. 0008intro hn
  9. 0009intro hb
  10. 0010split
  11. 0011intro hs
  12. 0012cases hs
  13. 0013cases hs_right
  14. 0014cases hs_right_witness
  15. 0015split
  16. 0016exact hn
  17. 0017exists x
  18. 0018split
  19. 0019specialize dirichlet_constant_one_prefix_to_divisor_mask (N)
  20. 0020specialize dirichlet_constant_one_prefix_to_divisor_mask (F)
  21. 0021specialize dirichlet_constant_one_prefix_to_divisor_mask (U)
  22. 0022specialize dirichlet_constant_one_prefix_to_divisor_mask (n)
  23. 0023specialize dirichlet_constant_one_prefix_to_divisor_mask (n)
  24. 0024specialize dirichlet_constant_one_prefix_to_divisor_mask (x)
  25. 0025apply dirichlet_constant_one_prefix_to_divisor_mask
  26. 0026exact hu
  27. 0027exact hn
  28. 0028exact hb
  29. 0029exact hs_right_witness_left
  30. 0030exact hs_right_witness_right
  31. 0031intro hs
  32. 0032cases hs
  33. 0033cases hs_right
  34. 0034cases hs_right_witness
  35. 0035split
  36. 0036exact hn
  37. 0037exists x
  38. 0038split
  39. 0039specialize dirichlet_constant_one_prefix_from_divisor_mask (N)
  40. 0040specialize dirichlet_constant_one_prefix_from_divisor_mask (F)
  41. 0041specialize dirichlet_constant_one_prefix_from_divisor_mask (U)
  42. 0042specialize dirichlet_constant_one_prefix_from_divisor_mask (n)
  43. 0043specialize dirichlet_constant_one_prefix_from_divisor_mask (n)
  44. 0044specialize dirichlet_constant_one_prefix_from_divisor_mask (x)
  45. 0045apply dirichlet_constant_one_prefix_from_divisor_mask
  46. 0046exact hu
  47. 0047exact hn
  48. 0048exact hb
  49. 0049exact hs_right_witness_left
  50. 0050exact hs_right_witness_right