Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Exact expanded first-order arithmetic statement
forall F G a b z. (exists dst_positive_code_one_first dst_positive_scale_one_first dst_negative_code_one_first dst_negative_scale_one_first dst_positive_one_first dst_negative_one_first. (((F) = (((((dst_positive_code_one_first) + (dst_positive_scale_one_first)) * S ((dst_positive_code_one_first) + (dst_positive_scale_one_first)) + ((dst_positive_scale_one_first) + (dst_positive_scale_one_first))) + (((dst_negative_code_one_first) + (dst_negative_scale_one_first)) * S ((dst_negative_code_one_first) + (dst_negative_scale_one_first)) + ((dst_negative_scale_one_first) + (dst_negative_scale_one_first)))) * S ((((dst_positive_code_one_first) + (dst_positive_scale_one_first)) * S ((dst_positive_code_one_first) + (dst_positive_scale_one_first)) + ((dst_positive_scale_one_first) + (dst_positive_scale_one_first))) + (((dst_negative_code_one_first) + (dst_negative_scale_one_first)) * S ((dst_negative_code_one_first) + (dst_negative_scale_one_first)) + ((dst_negative_scale_one_first) + (dst_negative_scale_one_first)))) + ((((dst_negative_code_one_first) + (dst_negative_scale_one_first)) * S ((dst_negative_code_one_first) + (dst_negative_scale_one_first)) + ((dst_negative_scale_one_first) + (dst_negative_scale_one_first))) + (((dst_negative_code_one_first) + (dst_negative_scale_one_first)) * S ((dst_negative_code_one_first) + (dst_negative_scale_one_first)) + ((dst_negative_scale_one_first) + (dst_negative_scale_one_first)))))) /\ (((((exists ff_h_pvs_one_firstpositive. ff_h_pvs_one_firstpositive + S (dst_positive_one_first) = S ((S (1)) * dst_positive_scale_one_first)) /\ exists ff_q_pvs_one_firstpositive. dst_positive_code_one_first = ff_q_pvs_one_firstpositive * S ((S (1)) * dst_positive_scale_one_first) + (dst_positive_one_first))) /\ (((((exists ff_h_pvs_one_firstnegative. ff_h_pvs_one_firstnegative + S (dst_negative_one_first) = S ((S (1)) * dst_negative_scale_one_first)) /\ exists ff_q_pvs_one_firstnegative. dst_negative_code_one_first = ff_q_pvs_one_firstnegative * S ((S (1)) * dst_negative_scale_one_first) + (dst_negative_one_first))) /\ (exists ge_balance_positive_one_firstvalue ge_balance_negative_one_firstvalue. (((((a) = 2 * (ge_balance_positive_one_firstvalue) /\ (ge_balance_negative_one_firstvalue) = 0) \/ exists ge_signed_half_one_firstvaluedecode. (((a) = 2 * ge_signed_half_one_firstvaluedecode + 1 /\ (ge_balance_positive_one_firstvalue) = 0) /\ (ge_balance_negative_one_firstvalue) = S ge_signed_half_one_firstvaluedecode))) /\ ((dst_positive_one_first) + ge_balance_negative_one_firstvalue = (dst_negative_one_first) + ge_balance_positive_one_firstvalue))))))))) -> (exists dst_positive_code_one_second dst_positive_scale_one_second dst_negative_code_one_second dst_negative_scale_one_second dst_positive_one_second dst_negative_one_second. (((G) = (((((dst_positive_code_one_second) + (dst_positive_scale_one_second)) * S ((dst_positive_code_one_second) + (dst_positive_scale_one_second)) + ((dst_positive_scale_one_second) + (dst_positive_scale_one_second))) + (((dst_negative_code_one_second) + (dst_negative_scale_one_second)) * S ((dst_negative_code_one_second) + (dst_negative_scale_one_second)) + ((dst_negative_scale_one_second) + (dst_negative_scale_one_second)))) * S ((((dst_positive_code_one_second) + (dst_positive_scale_one_second)) * S ((dst_positive_code_one_second) + (dst_positive_scale_one_second)) + ((dst_positive_scale_one_second) + (dst_positive_scale_one_second))) + (((dst_negative_code_one_second) + (dst_negative_scale_one_second)) * S ((dst_negative_code_one_second) + (dst_negative_scale_one_second)) + ((dst_negative_scale_one_second) + (dst_negative_scale_one_second)))) + ((((dst_negative_code_one_second) + (dst_negative_scale_one_second)) * S ((dst_negative_code_one_second) + (dst_negative_scale_one_second)) + ((dst_negative_scale_one_second) + (dst_negative_scale_one_second))) + (((dst_negative_code_one_second) + (dst_negative_scale_one_second)) * S ((dst_negative_code_one_second) + (dst_negative_scale_one_second)) + ((dst_negative_scale_one_second) + (dst_negative_scale_one_second)))))) /\ (((((exists ff_h_pvs_one_secondpositive. ff_h_pvs_one_secondpositive + S (dst_positive_one_second) = S ((S (1)) * dst_positive_scale_one_second)) /\ exists ff_q_pvs_one_secondpositive. dst_positive_code_one_second = ff_q_pvs_one_secondpositive * S ((S (1)) * dst_positive_scale_one_second) + (dst_positive_one_second))) /\ (((((exists ff_h_pvs_one_secondnegative. ff_h_pvs_one_secondnegative + S (dst_negative_one_second) = S ((S (1)) * dst_negative_scale_one_second)) /\ exists ff_q_pvs_one_secondnegative. dst_negative_code_one_second = ff_q_pvs_one_secondnegative * S ((S (1)) * dst_negative_scale_one_second) + (dst_negative_one_second))) /\ (exists ge_balance_positive_one_secondvalue ge_balance_negative_one_secondvalue. (((((b) = 2 * (ge_balance_positive_one_secondvalue) /\ (ge_balance_negative_one_secondvalue) = 0) \/ exists ge_signed_half_one_secondvaluedecode. (((b) = 2 * ge_signed_half_one_secondvaluedecode + 1 /\ (ge_balance_positive_one_secondvalue) = 0) /\ (ge_balance_negative_one_secondvalue) = S ge_signed_half_one_secondvaluedecode))) /\ ((dst_positive_one_second) + ge_balance_negative_one_secondvalue = (dst_negative_one_second) + ge_balance_positive_one_secondvalue))))))))) -> (((((~((1)=0)) /\ (exists dc_mask_one_convolution. ((((exists dst_positive_code_one_convolutionmasktable dst_positive_scale_one_convolutionmasktable dst_negative_code_one_convolutionmasktable dst_negative_scale_one_convolutionmasktable. (((dc_mask_one_convolution) = (((((dst_positive_code_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable)) * S ((dst_positive_code_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable)) + ((dst_positive_scale_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable))) + (((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) * S ((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) + ((dst_negative_scale_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)))) * S ((((dst_positive_code_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable)) * S ((dst_positive_code_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable)) + ((dst_positive_scale_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable))) + (((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) * S ((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) + ((dst_negative_scale_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)))) + ((((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) * S ((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) + ((dst_negative_scale_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable))) + (((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) * S ((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) + ((dst_negative_scale_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)))))) /\ (forall dst_index_one_convolutionmasktable. (exists pvs_le_gap_one_convolutionmasktabledomain. pvs_le_gap_one_convolutionmasktabledomain + (dst_index_one_convolutionmasktable) = (1)) -> exists dst_positive_one_convolutionmasktable dst_negative_one_convolutionmasktable dst_value_one_convolutionmasktable. ((((exists ff_h_pvs_one_convolutionmasktableentrypositive. ff_h_pvs_one_convolutionmasktableentrypositive + S (dst_positive_one_convolutionmasktable) = S ((S (dst_index_one_convolutionmasktable)) * dst_positive_scale_one_convolutionmasktable)) /\ exists ff_q_pvs_one_convolutionmasktableentrypositive. dst_positive_code_one_convolutionmasktable = ff_q_pvs_one_convolutionmasktableentrypositive * S ((S (dst_index_one_convolutionmasktable)) * dst_positive_scale_one_convolutionmasktable) + (dst_positive_one_convolutionmasktable))) /\ (((((exists ff_h_pvs_one_convolutionmasktableentrynegative. ff_h_pvs_one_convolutionmasktableentrynegative + S (dst_negative_one_convolutionmasktable) = S ((S (dst_index_one_convolutionmasktable)) * dst_negative_scale_one_convolutionmasktable)) /\ exists ff_q_pvs_one_convolutionmasktableentrynegative. dst_negative_code_one_convolutionmasktable = ff_q_pvs_one_convolutionmasktableentrynegative * S ((S (dst_index_one_convolutionmasktable)) * dst_negative_scale_one_convolutionmasktable) + (dst_negative_one_convolutionmasktable))) /\ (exists ge_balance_positive_one_convolutionmasktableentryvalue ge_balance_negative_one_convolutionmasktableentryvalue. (((((dst_value_one_convolutionmasktable) = 2 * (ge_balance_positive_one_convolutionmasktableentryvalue) /\ (ge_balance_negative_one_convolutionmasktableentryvalue) = 0) \/ exists ge_signed_half_one_convolutionmasktableentryvaluedecode. (((dst_value_one_convolutionmasktable) = 2 * ge_signed_half_one_convolutionmasktableentryvaluedecode + 1 /\ (ge_balance_positive_one_convolutionmasktableentryvalue) = 0) /\ (ge_balance_negative_one_convolutionmasktableentryvalue) = S ge_signed_half_one_convolutionmasktableentryvaluedecode))) /\ ((dst_positive_one_convolutionmasktable) + ge_balance_negative_one_convolutionmasktableentryvalue = (dst_negative_one_convolutionmasktable) + ge_balance_positive_one_convolutionmasktableentryvalue))))))))) /\ (forall dc_index_one_convolutionmask dc_value_one_convolutionmask. (exists pvs_le_gap_one_convolutionmaskdomain. pvs_le_gap_one_convolutionmaskdomain + (dc_index_one_convolutionmask) = (1)) -> (exists dst_positive_code_one_convolutionmasklookup dst_positive_scale_one_convolutionmasklookup dst_negative_code_one_convolutionmasklookup dst_negative_scale_one_convolutionmasklookup dst_positive_one_convolutionmasklookup dst_negative_one_convolutionmasklookup. (((dc_mask_one_convolution) = (((((dst_positive_code_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup)) * S ((dst_positive_code_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup)) + ((dst_positive_scale_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup))) + (((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) * S ((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) + ((dst_negative_scale_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)))) * S ((((dst_positive_code_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup)) * S ((dst_positive_code_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup)) + ((dst_positive_scale_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup))) + (((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) * S ((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) + ((dst_negative_scale_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)))) + ((((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) * S ((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) + ((dst_negative_scale_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup))) + (((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) * S ((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) + ((dst_negative_scale_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)))))) /\ (((((exists ff_h_pvs_one_convolutionmasklookuppositive. ff_h_pvs_one_convolutionmasklookuppositive + S (dst_positive_one_convolutionmasklookup) = S ((S (dc_index_one_convolutionmask)) * dst_positive_scale_one_convolutionmasklookup)) /\ exists ff_q_pvs_one_convolutionmasklookuppositive. dst_positive_code_one_convolutionmasklookup = ff_q_pvs_one_convolutionmasklookuppositive * S ((S (dc_index_one_convolutionmask)) * dst_positive_scale_one_convolutionmasklookup) + (dst_positive_one_convolutionmasklookup))) /\ (((((exists ff_h_pvs_one_convolutionmasklookupnegative. ff_h_pvs_one_convolutionmasklookupnegative + S (dst_negative_one_convolutionmasklookup) = S ((S (dc_index_one_convolutionmask)) * dst_negative_scale_one_convolutionmasklookup)) /\ exists ff_q_pvs_one_convolutionmasklookupnegative. dst_negative_code_one_convolutionmasklookup = ff_q_pvs_one_convolutionmasklookupnegative * S ((S (dc_index_one_convolutionmask)) * dst_negative_scale_one_convolutionmasklookup) + (dst_negative_one_convolutionmasklookup))) /\ (exists ge_balance_positive_one_convolutionmasklookupvalue ge_balance_negative_one_convolutionmasklookupvalue. (((((dc_value_one_convolutionmask) = 2 * (ge_balance_positive_one_convolutionmasklookupvalue) /\ (ge_balance_negative_one_convolutionmasklookupvalue) = 0) \/ exists ge_signed_half_one_convolutionmasklookupvaluedecode. (((dc_value_one_convolutionmask) = 2 * ge_signed_half_one_convolutionmasklookupvaluedecode + 1 /\ (ge_balance_positive_one_convolutionmasklookupvalue) = 0) /\ (ge_balance_negative_one_convolutionmasklookupvalue) = S ge_signed_half_one_convolutionmasklookupvaluedecode))) /\ ((dst_positive_one_convolutionmasklookup) + ge_balance_negative_one_convolutionmasklookupvalue = (dst_negative_one_convolutionmasklookup) + ge_balance_positive_one_convolutionmasklookupvalue))))))))) -> ((((~((dc_index_one_convolutionmask)=0)) /\ (exists dc_quotient_one_convolutionmaskentry dc_left_one_convolutionmaskentry dc_right_one_convolutionmaskentry. (((1)=(dc_index_one_convolutionmask)*dc_quotient_one_convolutionmaskentry) /\ (((exists dst_positive_code_one_convolutionmaskentryleft dst_positive_scale_one_convolutionmaskentryleft dst_negative_code_one_convolutionmaskentryleft dst_negative_scale_one_convolutionmaskentryleft dst_positive_one_convolutionmaskentryleft dst_negative_one_convolutionmaskentryleft. (((F) = (((((dst_positive_code_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft)) * S ((dst_positive_code_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft)) + ((dst_positive_scale_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft))) + (((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) * S ((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) + ((dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)))) * S ((((dst_positive_code_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft)) * S ((dst_positive_code_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft)) + ((dst_positive_scale_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft))) + (((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) * S ((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) + ((dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)))) + ((((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) * S ((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) + ((dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft))) + (((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) * S ((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) + ((dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)))))) /\ (((((exists ff_h_pvs_one_convolutionmaskentryleftpositive. ff_h_pvs_one_convolutionmaskentryleftpositive + S (dst_positive_one_convolutionmaskentryleft) = S ((S (dc_index_one_convolutionmask)) * dst_positive_scale_one_convolutionmaskentryleft)) /\ exists ff_q_pvs_one_convolutionmaskentryleftpositive. dst_positive_code_one_convolutionmaskentryleft = ff_q_pvs_one_convolutionmaskentryleftpositive * S ((S (dc_index_one_convolutionmask)) * dst_positive_scale_one_convolutionmaskentryleft) + (dst_positive_one_convolutionmaskentryleft))) /\ (((((exists ff_h_pvs_one_convolutionmaskentryleftnegative. ff_h_pvs_one_convolutionmaskentryleftnegative + S (dst_negative_one_convolutionmaskentryleft) = S ((S (dc_index_one_convolutionmask)) * dst_negative_scale_one_convolutionmaskentryleft)) /\ exists ff_q_pvs_one_convolutionmaskentryleftnegative. dst_negative_code_one_convolutionmaskentryleft = ff_q_pvs_one_convolutionmaskentryleftnegative * S ((S (dc_index_one_convolutionmask)) * dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_one_convolutionmaskentryleft))) /\ (exists ge_balance_positive_one_convolutionmaskentryleftvalue ge_balance_negative_one_convolutionmaskentryleftvalue. (((((dc_left_one_convolutionmaskentry) = 2 * (ge_balance_positive_one_convolutionmaskentryleftvalue) /\ (ge_balance_negative_one_convolutionmaskentryleftvalue) = 0) \/ exists ge_signed_half_one_convolutionmaskentryleftvaluedecode. (((dc_left_one_convolutionmaskentry) = 2 * ge_signed_half_one_convolutionmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_one_convolutionmaskentryleftvalue) = 0) /\ (ge_balance_negative_one_convolutionmaskentryleftvalue) = S ge_signed_half_one_convolutionmaskentryleftvaluedecode))) /\ ((dst_positive_one_convolutionmaskentryleft) + ge_balance_negative_one_convolutionmaskentryleftvalue = (dst_negative_one_convolutionmaskentryleft) + ge_balance_positive_one_convolutionmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_one_convolutionmaskentryright dst_positive_scale_one_convolutionmaskentryright dst_negative_code_one_convolutionmaskentryright dst_negative_scale_one_convolutionmaskentryright dst_positive_one_convolutionmaskentryright dst_negative_one_convolutionmaskentryright. (((G) = (((((dst_positive_code_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright)) * S ((dst_positive_code_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright)) + ((dst_positive_scale_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright))) + (((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) * S ((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) + ((dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)))) * S ((((dst_positive_code_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright)) * S ((dst_positive_code_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright)) + ((dst_positive_scale_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright))) + (((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) * S ((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) + ((dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)))) + ((((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) * S ((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) + ((dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright))) + (((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) * S ((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) + ((dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)))))) /\ (((((exists ff_h_pvs_one_convolutionmaskentryrightpositive. ff_h_pvs_one_convolutionmaskentryrightpositive + S (dst_positive_one_convolutionmaskentryright) = S ((S (dc_quotient_one_convolutionmaskentry)) * dst_positive_scale_one_convolutionmaskentryright)) /\ exists ff_q_pvs_one_convolutionmaskentryrightpositive. dst_positive_code_one_convolutionmaskentryright = ff_q_pvs_one_convolutionmaskentryrightpositive * S ((S (dc_quotient_one_convolutionmaskentry)) * dst_positive_scale_one_convolutionmaskentryright) + (dst_positive_one_convolutionmaskentryright))) /\ (((((exists ff_h_pvs_one_convolutionmaskentryrightnegative. ff_h_pvs_one_convolutionmaskentryrightnegative + S (dst_negative_one_convolutionmaskentryright) = S ((S (dc_quotient_one_convolutionmaskentry)) * dst_negative_scale_one_convolutionmaskentryright)) /\ exists ff_q_pvs_one_convolutionmaskentryrightnegative. dst_negative_code_one_convolutionmaskentryright = ff_q_pvs_one_convolutionmaskentryrightnegative * S ((S (dc_quotient_one_convolutionmaskentry)) * dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_one_convolutionmaskentryright))) /\ (exists ge_balance_positive_one_convolutionmaskentryrightvalue ge_balance_negative_one_convolutionmaskentryrightvalue. (((((dc_right_one_convolutionmaskentry) = 2 * (ge_balance_positive_one_convolutionmaskentryrightvalue) /\ (ge_balance_negative_one_convolutionmaskentryrightvalue) = 0) \/ exists ge_signed_half_one_convolutionmaskentryrightvaluedecode. (((dc_right_one_convolutionmaskentry) = 2 * ge_signed_half_one_convolutionmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_one_convolutionmaskentryrightvalue) = 0) /\ (ge_balance_negative_one_convolutionmaskentryrightvalue) = S ge_signed_half_one_convolutionmaskentryrightvaluedecode))) /\ ((dst_positive_one_convolutionmaskentryright) + ge_balance_negative_one_convolutionmaskentryrightvalue = (dst_negative_one_convolutionmaskentryright) + ge_balance_positive_one_convolutionmaskentryrightvalue))))))))) /\ (exists sto_ap_one_convolutionmaskentryproduct sto_an_one_convolutionmaskentryproduct sto_bp_one_convolutionmaskentryproduct sto_bn_one_convolutionmaskentryproduct sto_cp_one_convolutionmaskentryproduct sto_cn_one_convolutionmaskentryproduct. (((((dc_left_one_convolutionmaskentry) = 2 * (sto_ap_one_convolutionmaskentryproduct) /\ (sto_an_one_convolutionmaskentryproduct) = 0) \/ exists ge_signed_half_one_convolutionmaskentryproductleft. (((dc_left_one_convolutionmaskentry) = 2 * ge_signed_half_one_convolutionmaskentryproductleft + 1 /\ (sto_ap_one_convolutionmaskentryproduct) = 0) /\ (sto_an_one_convolutionmaskentryproduct) = S ge_signed_half_one_convolutionmaskentryproductleft))) /\ ((((((dc_right_one_convolutionmaskentry) = 2 * (sto_bp_one_convolutionmaskentryproduct) /\ (sto_bn_one_convolutionmaskentryproduct) = 0) \/ exists ge_signed_half_one_convolutionmaskentryproductright. (((dc_right_one_convolutionmaskentry) = 2 * ge_signed_half_one_convolutionmaskentryproductright + 1 /\ (sto_bp_one_convolutionmaskentryproduct) = 0) /\ (sto_bn_one_convolutionmaskentryproduct) = S ge_signed_half_one_convolutionmaskentryproductright))) /\ ((((((dc_value_one_convolutionmask) = 2 * (sto_cp_one_convolutionmaskentryproduct) /\ (sto_cn_one_convolutionmaskentryproduct) = 0) \/ exists ge_signed_half_one_convolutionmaskentryproductoutput. (((dc_value_one_convolutionmask) = 2 * ge_signed_half_one_convolutionmaskentryproductoutput + 1 /\ (sto_cp_one_convolutionmaskentryproduct) = 0) /\ (sto_cn_one_convolutionmaskentryproduct) = S ge_signed_half_one_convolutionmaskentryproductoutput))) /\ ((sto_ap_one_convolutionmaskentryproduct * sto_bp_one_convolutionmaskentryproduct + sto_an_one_convolutionmaskentryproduct * sto_bn_one_convolutionmaskentryproduct) + sto_cn_one_convolutionmaskentryproduct = (sto_ap_one_convolutionmaskentryproduct * sto_bn_one_convolutionmaskentryproduct + sto_an_one_convolutionmaskentryproduct * sto_bp_one_convolutionmaskentryproduct) + sto_cp_one_convolutionmaskentryproduct))))))))))))))) \/ ((((dc_index_one_convolutionmask)=0 \/ ~(exists pvs_factor_one_convolutionmaskentrynondivisor. (1) = (dc_index_one_convolutionmask) * pvs_factor_one_convolutionmaskentrynondivisor)) /\ ((dc_value_one_convolutionmask)=0))))))) /\ (exists dst_positive_code_one_convolutionfold dst_positive_scale_one_convolutionfold dst_negative_code_one_convolutionfold dst_negative_scale_one_convolutionfold dst_positive_sum_one_convolutionfold dst_negative_sum_one_convolutionfold. (((dc_mask_one_convolution) = (((((dst_positive_code_one_convolutionfold) + (dst_positive_scale_one_convolutionfold)) * S ((dst_positive_code_one_convolutionfold) + (dst_positive_scale_one_convolutionfold)) + ((dst_positive_scale_one_convolutionfold) + (dst_positive_scale_one_convolutionfold))) + (((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) * S ((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) + ((dst_negative_scale_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)))) * S ((((dst_positive_code_one_convolutionfold) + (dst_positive_scale_one_convolutionfold)) * S ((dst_positive_code_one_convolutionfold) + (dst_positive_scale_one_convolutionfold)) + ((dst_positive_scale_one_convolutionfold) + (dst_positive_scale_one_convolutionfold))) + (((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) * S ((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) + ((dst_negative_scale_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)))) + ((((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) * S ((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) + ((dst_negative_scale_one_convolutionfold) + (dst_negative_scale_one_convolutionfold))) + (((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) * S ((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) + ((dst_negative_scale_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)))))) /\ (((exists fs_u_dst_one_convolutionfoldpositive fs_v_dst_one_convolutionfoldpositive. ((((exists fs_h_dst_one_convolutionfoldpositive_body_start. fs_h_dst_one_convolutionfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_one_convolutionfoldpositive)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_start. fs_u_dst_one_convolutionfoldpositive = fs_q_dst_one_convolutionfoldpositive_body_start * S ((S (0)) * fs_v_dst_one_convolutionfoldpositive) + (0))) /\ ((((exists fs_h_dst_one_convolutionfoldpositive_body_terminal. fs_h_dst_one_convolutionfoldpositive_body_terminal + S (dst_positive_sum_one_convolutionfold) = S ((S (S (1))) * fs_v_dst_one_convolutionfoldpositive)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_terminal. fs_u_dst_one_convolutionfoldpositive = fs_q_dst_one_convolutionfoldpositive_body_terminal * S ((S (S (1))) * fs_v_dst_one_convolutionfoldpositive) + (dst_positive_sum_one_convolutionfold))) /\ forall fs_i_dst_one_convolutionfoldpositive_body_steps. (exists fs_lt_dst_one_convolutionfoldpositive_body_steps_bound. fs_lt_dst_one_convolutionfoldpositive_body_steps_bound + S fs_i_dst_one_convolutionfoldpositive_body_steps = S (1)) -> exists fs_a_dst_one_convolutionfoldpositive_body_steps fs_r_dst_one_convolutionfoldpositive_body_steps fs_s_dst_one_convolutionfoldpositive_body_steps. ((((exists fs_h_dst_one_convolutionfoldpositive_body_steps_summand. fs_h_dst_one_convolutionfoldpositive_body_steps_summand + S (fs_a_dst_one_convolutionfoldpositive_body_steps) = S ((S (fs_i_dst_one_convolutionfoldpositive_body_steps)) * dst_positive_scale_one_convolutionfold)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_steps_summand. dst_positive_code_one_convolutionfold = fs_q_dst_one_convolutionfoldpositive_body_steps_summand * S ((S (fs_i_dst_one_convolutionfoldpositive_body_steps)) * dst_positive_scale_one_convolutionfold) + (fs_a_dst_one_convolutionfoldpositive_body_steps))) /\ ((((exists fs_h_dst_one_convolutionfoldpositive_body_steps_partial. fs_h_dst_one_convolutionfoldpositive_body_steps_partial + S (fs_r_dst_one_convolutionfoldpositive_body_steps) = S ((S (fs_i_dst_one_convolutionfoldpositive_body_steps)) * fs_v_dst_one_convolutionfoldpositive)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_steps_partial. fs_u_dst_one_convolutionfoldpositive = fs_q_dst_one_convolutionfoldpositive_body_steps_partial * S ((S (fs_i_dst_one_convolutionfoldpositive_body_steps)) * fs_v_dst_one_convolutionfoldpositive) + (fs_r_dst_one_convolutionfoldpositive_body_steps))) /\ ((((exists fs_h_dst_one_convolutionfoldpositive_body_steps_successor. fs_h_dst_one_convolutionfoldpositive_body_steps_successor + S (fs_s_dst_one_convolutionfoldpositive_body_steps) = S ((S (S fs_i_dst_one_convolutionfoldpositive_body_steps)) * fs_v_dst_one_convolutionfoldpositive)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_steps_successor. fs_u_dst_one_convolutionfoldpositive = fs_q_dst_one_convolutionfoldpositive_body_steps_successor * S ((S (S fs_i_dst_one_convolutionfoldpositive_body_steps)) * fs_v_dst_one_convolutionfoldpositive) + (fs_s_dst_one_convolutionfoldpositive_body_steps))) /\ fs_s_dst_one_convolutionfoldpositive_body_steps = fs_r_dst_one_convolutionfoldpositive_body_steps + fs_a_dst_one_convolutionfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_one_convolutionfoldnegative fs_v_dst_one_convolutionfoldnegative. ((((exists fs_h_dst_one_convolutionfoldnegative_body_start. fs_h_dst_one_convolutionfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_one_convolutionfoldnegative)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_start. fs_u_dst_one_convolutionfoldnegative = fs_q_dst_one_convolutionfoldnegative_body_start * S ((S (0)) * fs_v_dst_one_convolutionfoldnegative) + (0))) /\ ((((exists fs_h_dst_one_convolutionfoldnegative_body_terminal. fs_h_dst_one_convolutionfoldnegative_body_terminal + S (dst_negative_sum_one_convolutionfold) = S ((S (S (1))) * fs_v_dst_one_convolutionfoldnegative)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_terminal. fs_u_dst_one_convolutionfoldnegative = fs_q_dst_one_convolutionfoldnegative_body_terminal * S ((S (S (1))) * fs_v_dst_one_convolutionfoldnegative) + (dst_negative_sum_one_convolutionfold))) /\ forall fs_i_dst_one_convolutionfoldnegative_body_steps. (exists fs_lt_dst_one_convolutionfoldnegative_body_steps_bound. fs_lt_dst_one_convolutionfoldnegative_body_steps_bound + S fs_i_dst_one_convolutionfoldnegative_body_steps = S (1)) -> exists fs_a_dst_one_convolutionfoldnegative_body_steps fs_r_dst_one_convolutionfoldnegative_body_steps fs_s_dst_one_convolutionfoldnegative_body_steps. ((((exists fs_h_dst_one_convolutionfoldnegative_body_steps_summand. fs_h_dst_one_convolutionfoldnegative_body_steps_summand + S (fs_a_dst_one_convolutionfoldnegative_body_steps) = S ((S (fs_i_dst_one_convolutionfoldnegative_body_steps)) * dst_negative_scale_one_convolutionfold)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_steps_summand. dst_negative_code_one_convolutionfold = fs_q_dst_one_convolutionfoldnegative_body_steps_summand * S ((S (fs_i_dst_one_convolutionfoldnegative_body_steps)) * dst_negative_scale_one_convolutionfold) + (fs_a_dst_one_convolutionfoldnegative_body_steps))) /\ ((((exists fs_h_dst_one_convolutionfoldnegative_body_steps_partial. fs_h_dst_one_convolutionfoldnegative_body_steps_partial + S (fs_r_dst_one_convolutionfoldnegative_body_steps) = S ((S (fs_i_dst_one_convolutionfoldnegative_body_steps)) * fs_v_dst_one_convolutionfoldnegative)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_steps_partial. fs_u_dst_one_convolutionfoldnegative = fs_q_dst_one_convolutionfoldnegative_body_steps_partial * S ((S (fs_i_dst_one_convolutionfoldnegative_body_steps)) * fs_v_dst_one_convolutionfoldnegative) + (fs_r_dst_one_convolutionfoldnegative_body_steps))) /\ ((((exists fs_h_dst_one_convolutionfoldnegative_body_steps_successor. fs_h_dst_one_convolutionfoldnegative_body_steps_successor + S (fs_s_dst_one_convolutionfoldnegative_body_steps) = S ((S (S fs_i_dst_one_convolutionfoldnegative_body_steps)) * fs_v_dst_one_convolutionfoldnegative)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_steps_successor. fs_u_dst_one_convolutionfoldnegative = fs_q_dst_one_convolutionfoldnegative_body_steps_successor * S ((S (S fs_i_dst_one_convolutionfoldnegative_body_steps)) * fs_v_dst_one_convolutionfoldnegative) + (fs_s_dst_one_convolutionfoldnegative_body_steps))) /\ fs_s_dst_one_convolutionfoldnegative_body_steps = fs_r_dst_one_convolutionfoldnegative_body_steps + fs_a_dst_one_convolutionfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_one_convolutionfoldresult ge_balance_negative_one_convolutionfoldresult. (((((z) = 2 * (ge_balance_positive_one_convolutionfoldresult) /\ (ge_balance_negative_one_convolutionfoldresult) = 0) \/ exists ge_signed_half_one_convolutionfoldresultdecode. (((z) = 2 * ge_signed_half_one_convolutionfoldresultdecode + 1 /\ (ge_balance_positive_one_convolutionfoldresult) = 0) /\ (ge_balance_negative_one_convolutionfoldresult) = S ge_signed_half_one_convolutionfoldresultdecode))) /\ ((dst_positive_sum_one_convolutionfold) + ge_balance_negative_one_convolutionfoldresult = (dst_negative_sum_one_convolutionfold) + ge_balance_positive_one_convolutionfoldresult))))))))))))) -> (exists sto_ap_one_product sto_an_one_product sto_bp_one_product sto_bn_one_product sto_cp_one_product sto_cn_one_product. (((((a) = 2 * (sto_ap_one_product) /\ (sto_an_one_product) = 0) \/ exists ge_signed_half_one_productleft. (((a) = 2 * ge_signed_half_one_productleft + 1 /\ (sto_ap_one_product) = 0) /\ (sto_an_one_product) = S ge_signed_half_one_productleft))) /\ ((((((b) = 2 * (sto_bp_one_product) /\ (sto_bn_one_product) = 0) \/ exists ge_signed_half_one_productright. (((b) = 2 * ge_signed_half_one_productright + 1 /\ (sto_bp_one_product) = 0) /\ (sto_bn_one_product) = S ge_signed_half_one_productright))) /\ ((((((z) = 2 * (sto_cp_one_product) /\ (sto_cn_one_product) = 0) \/ exists ge_signed_half_one_productoutput. (((z) = 2 * ge_signed_half_one_productoutput + 1 /\ (sto_cp_one_product) = 0) /\ (sto_cn_one_product) = S ge_signed_half_one_productoutput))) /\ ((sto_ap_one_product * sto_bp_one_product + sto_an_one_product * sto_bn_one_product) + sto_cn_one_product = (sto_ap_one_product * sto_bn_one_product + sto_an_one_product * sto_bp_one_product) + sto_cp_one_product)))))))) /\ ((exists sto_ap_one_product sto_an_one_product sto_bp_one_product sto_bn_one_product sto_cp_one_product sto_cn_one_product. (((((a) = 2 * (sto_ap_one_product) /\ (sto_an_one_product) = 0) \/ exists ge_signed_half_one_productleft. (((a) = 2 * ge_signed_half_one_productleft + 1 /\ (sto_ap_one_product) = 0) /\ (sto_an_one_product) = S ge_signed_half_one_productleft))) /\ ((((((b) = 2 * (sto_bp_one_product) /\ (sto_bn_one_product) = 0) \/ exists ge_signed_half_one_productright. (((b) = 2 * ge_signed_half_one_productright + 1 /\ (sto_bp_one_product) = 0) /\ (sto_bn_one_product) = S ge_signed_half_one_productright))) /\ ((((((z) = 2 * (sto_cp_one_product) /\ (sto_cn_one_product) = 0) \/ exists ge_signed_half_one_productoutput. (((z) = 2 * ge_signed_half_one_productoutput + 1 /\ (sto_cp_one_product) = 0) /\ (sto_cn_one_product) = S ge_signed_half_one_productoutput))) /\ ((sto_ap_one_product * sto_bp_one_product + sto_an_one_product * sto_bn_one_product) + sto_cn_one_product = (sto_ap_one_product * sto_bn_one_product + sto_an_one_product * sto_bp_one_product) + sto_cp_one_product))))))) -> (((~((1)=0)) /\ (exists dc_mask_one_convolution. ((((exists dst_positive_code_one_convolutionmasktable dst_positive_scale_one_convolutionmasktable dst_negative_code_one_convolutionmasktable dst_negative_scale_one_convolutionmasktable. (((dc_mask_one_convolution) = (((((dst_positive_code_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable)) * S ((dst_positive_code_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable)) + ((dst_positive_scale_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable))) + (((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) * S ((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) + ((dst_negative_scale_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)))) * S ((((dst_positive_code_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable)) * S ((dst_positive_code_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable)) + ((dst_positive_scale_one_convolutionmasktable) + (dst_positive_scale_one_convolutionmasktable))) + (((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) * S ((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) + ((dst_negative_scale_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)))) + ((((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) * S ((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) + ((dst_negative_scale_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable))) + (((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) * S ((dst_negative_code_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)) + ((dst_negative_scale_one_convolutionmasktable) + (dst_negative_scale_one_convolutionmasktable)))))) /\ (forall dst_index_one_convolutionmasktable. (exists pvs_le_gap_one_convolutionmasktabledomain. pvs_le_gap_one_convolutionmasktabledomain + (dst_index_one_convolutionmasktable) = (1)) -> exists dst_positive_one_convolutionmasktable dst_negative_one_convolutionmasktable dst_value_one_convolutionmasktable. ((((exists ff_h_pvs_one_convolutionmasktableentrypositive. ff_h_pvs_one_convolutionmasktableentrypositive + S (dst_positive_one_convolutionmasktable) = S ((S (dst_index_one_convolutionmasktable)) * dst_positive_scale_one_convolutionmasktable)) /\ exists ff_q_pvs_one_convolutionmasktableentrypositive. dst_positive_code_one_convolutionmasktable = ff_q_pvs_one_convolutionmasktableentrypositive * S ((S (dst_index_one_convolutionmasktable)) * dst_positive_scale_one_convolutionmasktable) + (dst_positive_one_convolutionmasktable))) /\ (((((exists ff_h_pvs_one_convolutionmasktableentrynegative. ff_h_pvs_one_convolutionmasktableentrynegative + S (dst_negative_one_convolutionmasktable) = S ((S (dst_index_one_convolutionmasktable)) * dst_negative_scale_one_convolutionmasktable)) /\ exists ff_q_pvs_one_convolutionmasktableentrynegative. dst_negative_code_one_convolutionmasktable = ff_q_pvs_one_convolutionmasktableentrynegative * S ((S (dst_index_one_convolutionmasktable)) * dst_negative_scale_one_convolutionmasktable) + (dst_negative_one_convolutionmasktable))) /\ (exists ge_balance_positive_one_convolutionmasktableentryvalue ge_balance_negative_one_convolutionmasktableentryvalue. (((((dst_value_one_convolutionmasktable) = 2 * (ge_balance_positive_one_convolutionmasktableentryvalue) /\ (ge_balance_negative_one_convolutionmasktableentryvalue) = 0) \/ exists ge_signed_half_one_convolutionmasktableentryvaluedecode. (((dst_value_one_convolutionmasktable) = 2 * ge_signed_half_one_convolutionmasktableentryvaluedecode + 1 /\ (ge_balance_positive_one_convolutionmasktableentryvalue) = 0) /\ (ge_balance_negative_one_convolutionmasktableentryvalue) = S ge_signed_half_one_convolutionmasktableentryvaluedecode))) /\ ((dst_positive_one_convolutionmasktable) + ge_balance_negative_one_convolutionmasktableentryvalue = (dst_negative_one_convolutionmasktable) + ge_balance_positive_one_convolutionmasktableentryvalue))))))))) /\ (forall dc_index_one_convolutionmask dc_value_one_convolutionmask. (exists pvs_le_gap_one_convolutionmaskdomain. pvs_le_gap_one_convolutionmaskdomain + (dc_index_one_convolutionmask) = (1)) -> (exists dst_positive_code_one_convolutionmasklookup dst_positive_scale_one_convolutionmasklookup dst_negative_code_one_convolutionmasklookup dst_negative_scale_one_convolutionmasklookup dst_positive_one_convolutionmasklookup dst_negative_one_convolutionmasklookup. (((dc_mask_one_convolution) = (((((dst_positive_code_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup)) * S ((dst_positive_code_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup)) + ((dst_positive_scale_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup))) + (((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) * S ((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) + ((dst_negative_scale_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)))) * S ((((dst_positive_code_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup)) * S ((dst_positive_code_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup)) + ((dst_positive_scale_one_convolutionmasklookup) + (dst_positive_scale_one_convolutionmasklookup))) + (((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) * S ((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) + ((dst_negative_scale_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)))) + ((((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) * S ((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) + ((dst_negative_scale_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup))) + (((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) * S ((dst_negative_code_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)) + ((dst_negative_scale_one_convolutionmasklookup) + (dst_negative_scale_one_convolutionmasklookup)))))) /\ (((((exists ff_h_pvs_one_convolutionmasklookuppositive. ff_h_pvs_one_convolutionmasklookuppositive + S (dst_positive_one_convolutionmasklookup) = S ((S (dc_index_one_convolutionmask)) * dst_positive_scale_one_convolutionmasklookup)) /\ exists ff_q_pvs_one_convolutionmasklookuppositive. dst_positive_code_one_convolutionmasklookup = ff_q_pvs_one_convolutionmasklookuppositive * S ((S (dc_index_one_convolutionmask)) * dst_positive_scale_one_convolutionmasklookup) + (dst_positive_one_convolutionmasklookup))) /\ (((((exists ff_h_pvs_one_convolutionmasklookupnegative. ff_h_pvs_one_convolutionmasklookupnegative + S (dst_negative_one_convolutionmasklookup) = S ((S (dc_index_one_convolutionmask)) * dst_negative_scale_one_convolutionmasklookup)) /\ exists ff_q_pvs_one_convolutionmasklookupnegative. dst_negative_code_one_convolutionmasklookup = ff_q_pvs_one_convolutionmasklookupnegative * S ((S (dc_index_one_convolutionmask)) * dst_negative_scale_one_convolutionmasklookup) + (dst_negative_one_convolutionmasklookup))) /\ (exists ge_balance_positive_one_convolutionmasklookupvalue ge_balance_negative_one_convolutionmasklookupvalue. (((((dc_value_one_convolutionmask) = 2 * (ge_balance_positive_one_convolutionmasklookupvalue) /\ (ge_balance_negative_one_convolutionmasklookupvalue) = 0) \/ exists ge_signed_half_one_convolutionmasklookupvaluedecode. (((dc_value_one_convolutionmask) = 2 * ge_signed_half_one_convolutionmasklookupvaluedecode + 1 /\ (ge_balance_positive_one_convolutionmasklookupvalue) = 0) /\ (ge_balance_negative_one_convolutionmasklookupvalue) = S ge_signed_half_one_convolutionmasklookupvaluedecode))) /\ ((dst_positive_one_convolutionmasklookup) + ge_balance_negative_one_convolutionmasklookupvalue = (dst_negative_one_convolutionmasklookup) + ge_balance_positive_one_convolutionmasklookupvalue))))))))) -> ((((~((dc_index_one_convolutionmask)=0)) /\ (exists dc_quotient_one_convolutionmaskentry dc_left_one_convolutionmaskentry dc_right_one_convolutionmaskentry. (((1)=(dc_index_one_convolutionmask)*dc_quotient_one_convolutionmaskentry) /\ (((exists dst_positive_code_one_convolutionmaskentryleft dst_positive_scale_one_convolutionmaskentryleft dst_negative_code_one_convolutionmaskentryleft dst_negative_scale_one_convolutionmaskentryleft dst_positive_one_convolutionmaskentryleft dst_negative_one_convolutionmaskentryleft. (((F) = (((((dst_positive_code_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft)) * S ((dst_positive_code_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft)) + ((dst_positive_scale_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft))) + (((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) * S ((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) + ((dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)))) * S ((((dst_positive_code_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft)) * S ((dst_positive_code_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft)) + ((dst_positive_scale_one_convolutionmaskentryleft) + (dst_positive_scale_one_convolutionmaskentryleft))) + (((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) * S ((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) + ((dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)))) + ((((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) * S ((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) + ((dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft))) + (((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) * S ((dst_negative_code_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)) + ((dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_scale_one_convolutionmaskentryleft)))))) /\ (((((exists ff_h_pvs_one_convolutionmaskentryleftpositive. ff_h_pvs_one_convolutionmaskentryleftpositive + S (dst_positive_one_convolutionmaskentryleft) = S ((S (dc_index_one_convolutionmask)) * dst_positive_scale_one_convolutionmaskentryleft)) /\ exists ff_q_pvs_one_convolutionmaskentryleftpositive. dst_positive_code_one_convolutionmaskentryleft = ff_q_pvs_one_convolutionmaskentryleftpositive * S ((S (dc_index_one_convolutionmask)) * dst_positive_scale_one_convolutionmaskentryleft) + (dst_positive_one_convolutionmaskentryleft))) /\ (((((exists ff_h_pvs_one_convolutionmaskentryleftnegative. ff_h_pvs_one_convolutionmaskentryleftnegative + S (dst_negative_one_convolutionmaskentryleft) = S ((S (dc_index_one_convolutionmask)) * dst_negative_scale_one_convolutionmaskentryleft)) /\ exists ff_q_pvs_one_convolutionmaskentryleftnegative. dst_negative_code_one_convolutionmaskentryleft = ff_q_pvs_one_convolutionmaskentryleftnegative * S ((S (dc_index_one_convolutionmask)) * dst_negative_scale_one_convolutionmaskentryleft) + (dst_negative_one_convolutionmaskentryleft))) /\ (exists ge_balance_positive_one_convolutionmaskentryleftvalue ge_balance_negative_one_convolutionmaskentryleftvalue. (((((dc_left_one_convolutionmaskentry) = 2 * (ge_balance_positive_one_convolutionmaskentryleftvalue) /\ (ge_balance_negative_one_convolutionmaskentryleftvalue) = 0) \/ exists ge_signed_half_one_convolutionmaskentryleftvaluedecode. (((dc_left_one_convolutionmaskentry) = 2 * ge_signed_half_one_convolutionmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_one_convolutionmaskentryleftvalue) = 0) /\ (ge_balance_negative_one_convolutionmaskentryleftvalue) = S ge_signed_half_one_convolutionmaskentryleftvaluedecode))) /\ ((dst_positive_one_convolutionmaskentryleft) + ge_balance_negative_one_convolutionmaskentryleftvalue = (dst_negative_one_convolutionmaskentryleft) + ge_balance_positive_one_convolutionmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_one_convolutionmaskentryright dst_positive_scale_one_convolutionmaskentryright dst_negative_code_one_convolutionmaskentryright dst_negative_scale_one_convolutionmaskentryright dst_positive_one_convolutionmaskentryright dst_negative_one_convolutionmaskentryright. (((G) = (((((dst_positive_code_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright)) * S ((dst_positive_code_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright)) + ((dst_positive_scale_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright))) + (((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) * S ((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) + ((dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)))) * S ((((dst_positive_code_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright)) * S ((dst_positive_code_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright)) + ((dst_positive_scale_one_convolutionmaskentryright) + (dst_positive_scale_one_convolutionmaskentryright))) + (((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) * S ((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) + ((dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)))) + ((((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) * S ((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) + ((dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright))) + (((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) * S ((dst_negative_code_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)) + ((dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_scale_one_convolutionmaskentryright)))))) /\ (((((exists ff_h_pvs_one_convolutionmaskentryrightpositive. ff_h_pvs_one_convolutionmaskentryrightpositive + S (dst_positive_one_convolutionmaskentryright) = S ((S (dc_quotient_one_convolutionmaskentry)) * dst_positive_scale_one_convolutionmaskentryright)) /\ exists ff_q_pvs_one_convolutionmaskentryrightpositive. dst_positive_code_one_convolutionmaskentryright = ff_q_pvs_one_convolutionmaskentryrightpositive * S ((S (dc_quotient_one_convolutionmaskentry)) * dst_positive_scale_one_convolutionmaskentryright) + (dst_positive_one_convolutionmaskentryright))) /\ (((((exists ff_h_pvs_one_convolutionmaskentryrightnegative. ff_h_pvs_one_convolutionmaskentryrightnegative + S (dst_negative_one_convolutionmaskentryright) = S ((S (dc_quotient_one_convolutionmaskentry)) * dst_negative_scale_one_convolutionmaskentryright)) /\ exists ff_q_pvs_one_convolutionmaskentryrightnegative. dst_negative_code_one_convolutionmaskentryright = ff_q_pvs_one_convolutionmaskentryrightnegative * S ((S (dc_quotient_one_convolutionmaskentry)) * dst_negative_scale_one_convolutionmaskentryright) + (dst_negative_one_convolutionmaskentryright))) /\ (exists ge_balance_positive_one_convolutionmaskentryrightvalue ge_balance_negative_one_convolutionmaskentryrightvalue. (((((dc_right_one_convolutionmaskentry) = 2 * (ge_balance_positive_one_convolutionmaskentryrightvalue) /\ (ge_balance_negative_one_convolutionmaskentryrightvalue) = 0) \/ exists ge_signed_half_one_convolutionmaskentryrightvaluedecode. (((dc_right_one_convolutionmaskentry) = 2 * ge_signed_half_one_convolutionmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_one_convolutionmaskentryrightvalue) = 0) /\ (ge_balance_negative_one_convolutionmaskentryrightvalue) = S ge_signed_half_one_convolutionmaskentryrightvaluedecode))) /\ ((dst_positive_one_convolutionmaskentryright) + ge_balance_negative_one_convolutionmaskentryrightvalue = (dst_negative_one_convolutionmaskentryright) + ge_balance_positive_one_convolutionmaskentryrightvalue))))))))) /\ (exists sto_ap_one_convolutionmaskentryproduct sto_an_one_convolutionmaskentryproduct sto_bp_one_convolutionmaskentryproduct sto_bn_one_convolutionmaskentryproduct sto_cp_one_convolutionmaskentryproduct sto_cn_one_convolutionmaskentryproduct. (((((dc_left_one_convolutionmaskentry) = 2 * (sto_ap_one_convolutionmaskentryproduct) /\ (sto_an_one_convolutionmaskentryproduct) = 0) \/ exists ge_signed_half_one_convolutionmaskentryproductleft. (((dc_left_one_convolutionmaskentry) = 2 * ge_signed_half_one_convolutionmaskentryproductleft + 1 /\ (sto_ap_one_convolutionmaskentryproduct) = 0) /\ (sto_an_one_convolutionmaskentryproduct) = S ge_signed_half_one_convolutionmaskentryproductleft))) /\ ((((((dc_right_one_convolutionmaskentry) = 2 * (sto_bp_one_convolutionmaskentryproduct) /\ (sto_bn_one_convolutionmaskentryproduct) = 0) \/ exists ge_signed_half_one_convolutionmaskentryproductright. (((dc_right_one_convolutionmaskentry) = 2 * ge_signed_half_one_convolutionmaskentryproductright + 1 /\ (sto_bp_one_convolutionmaskentryproduct) = 0) /\ (sto_bn_one_convolutionmaskentryproduct) = S ge_signed_half_one_convolutionmaskentryproductright))) /\ ((((((dc_value_one_convolutionmask) = 2 * (sto_cp_one_convolutionmaskentryproduct) /\ (sto_cn_one_convolutionmaskentryproduct) = 0) \/ exists ge_signed_half_one_convolutionmaskentryproductoutput. (((dc_value_one_convolutionmask) = 2 * ge_signed_half_one_convolutionmaskentryproductoutput + 1 /\ (sto_cp_one_convolutionmaskentryproduct) = 0) /\ (sto_cn_one_convolutionmaskentryproduct) = S ge_signed_half_one_convolutionmaskentryproductoutput))) /\ ((sto_ap_one_convolutionmaskentryproduct * sto_bp_one_convolutionmaskentryproduct + sto_an_one_convolutionmaskentryproduct * sto_bn_one_convolutionmaskentryproduct) + sto_cn_one_convolutionmaskentryproduct = (sto_ap_one_convolutionmaskentryproduct * sto_bn_one_convolutionmaskentryproduct + sto_an_one_convolutionmaskentryproduct * sto_bp_one_convolutionmaskentryproduct) + sto_cp_one_convolutionmaskentryproduct))))))))))))))) \/ ((((dc_index_one_convolutionmask)=0 \/ ~(exists pvs_factor_one_convolutionmaskentrynondivisor. (1) = (dc_index_one_convolutionmask) * pvs_factor_one_convolutionmaskentrynondivisor)) /\ ((dc_value_one_convolutionmask)=0))))))) /\ (exists dst_positive_code_one_convolutionfold dst_positive_scale_one_convolutionfold dst_negative_code_one_convolutionfold dst_negative_scale_one_convolutionfold dst_positive_sum_one_convolutionfold dst_negative_sum_one_convolutionfold. (((dc_mask_one_convolution) = (((((dst_positive_code_one_convolutionfold) + (dst_positive_scale_one_convolutionfold)) * S ((dst_positive_code_one_convolutionfold) + (dst_positive_scale_one_convolutionfold)) + ((dst_positive_scale_one_convolutionfold) + (dst_positive_scale_one_convolutionfold))) + (((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) * S ((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) + ((dst_negative_scale_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)))) * S ((((dst_positive_code_one_convolutionfold) + (dst_positive_scale_one_convolutionfold)) * S ((dst_positive_code_one_convolutionfold) + (dst_positive_scale_one_convolutionfold)) + ((dst_positive_scale_one_convolutionfold) + (dst_positive_scale_one_convolutionfold))) + (((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) * S ((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) + ((dst_negative_scale_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)))) + ((((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) * S ((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) + ((dst_negative_scale_one_convolutionfold) + (dst_negative_scale_one_convolutionfold))) + (((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) * S ((dst_negative_code_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)) + ((dst_negative_scale_one_convolutionfold) + (dst_negative_scale_one_convolutionfold)))))) /\ (((exists fs_u_dst_one_convolutionfoldpositive fs_v_dst_one_convolutionfoldpositive. ((((exists fs_h_dst_one_convolutionfoldpositive_body_start. fs_h_dst_one_convolutionfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_one_convolutionfoldpositive)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_start. fs_u_dst_one_convolutionfoldpositive = fs_q_dst_one_convolutionfoldpositive_body_start * S ((S (0)) * fs_v_dst_one_convolutionfoldpositive) + (0))) /\ ((((exists fs_h_dst_one_convolutionfoldpositive_body_terminal. fs_h_dst_one_convolutionfoldpositive_body_terminal + S (dst_positive_sum_one_convolutionfold) = S ((S (S (1))) * fs_v_dst_one_convolutionfoldpositive)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_terminal. fs_u_dst_one_convolutionfoldpositive = fs_q_dst_one_convolutionfoldpositive_body_terminal * S ((S (S (1))) * fs_v_dst_one_convolutionfoldpositive) + (dst_positive_sum_one_convolutionfold))) /\ forall fs_i_dst_one_convolutionfoldpositive_body_steps. (exists fs_lt_dst_one_convolutionfoldpositive_body_steps_bound. fs_lt_dst_one_convolutionfoldpositive_body_steps_bound + S fs_i_dst_one_convolutionfoldpositive_body_steps = S (1)) -> exists fs_a_dst_one_convolutionfoldpositive_body_steps fs_r_dst_one_convolutionfoldpositive_body_steps fs_s_dst_one_convolutionfoldpositive_body_steps. ((((exists fs_h_dst_one_convolutionfoldpositive_body_steps_summand. fs_h_dst_one_convolutionfoldpositive_body_steps_summand + S (fs_a_dst_one_convolutionfoldpositive_body_steps) = S ((S (fs_i_dst_one_convolutionfoldpositive_body_steps)) * dst_positive_scale_one_convolutionfold)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_steps_summand. dst_positive_code_one_convolutionfold = fs_q_dst_one_convolutionfoldpositive_body_steps_summand * S ((S (fs_i_dst_one_convolutionfoldpositive_body_steps)) * dst_positive_scale_one_convolutionfold) + (fs_a_dst_one_convolutionfoldpositive_body_steps))) /\ ((((exists fs_h_dst_one_convolutionfoldpositive_body_steps_partial. fs_h_dst_one_convolutionfoldpositive_body_steps_partial + S (fs_r_dst_one_convolutionfoldpositive_body_steps) = S ((S (fs_i_dst_one_convolutionfoldpositive_body_steps)) * fs_v_dst_one_convolutionfoldpositive)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_steps_partial. fs_u_dst_one_convolutionfoldpositive = fs_q_dst_one_convolutionfoldpositive_body_steps_partial * S ((S (fs_i_dst_one_convolutionfoldpositive_body_steps)) * fs_v_dst_one_convolutionfoldpositive) + (fs_r_dst_one_convolutionfoldpositive_body_steps))) /\ ((((exists fs_h_dst_one_convolutionfoldpositive_body_steps_successor. fs_h_dst_one_convolutionfoldpositive_body_steps_successor + S (fs_s_dst_one_convolutionfoldpositive_body_steps) = S ((S (S fs_i_dst_one_convolutionfoldpositive_body_steps)) * fs_v_dst_one_convolutionfoldpositive)) /\ exists fs_q_dst_one_convolutionfoldpositive_body_steps_successor. fs_u_dst_one_convolutionfoldpositive = fs_q_dst_one_convolutionfoldpositive_body_steps_successor * S ((S (S fs_i_dst_one_convolutionfoldpositive_body_steps)) * fs_v_dst_one_convolutionfoldpositive) + (fs_s_dst_one_convolutionfoldpositive_body_steps))) /\ fs_s_dst_one_convolutionfoldpositive_body_steps = fs_r_dst_one_convolutionfoldpositive_body_steps + fs_a_dst_one_convolutionfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_one_convolutionfoldnegative fs_v_dst_one_convolutionfoldnegative. ((((exists fs_h_dst_one_convolutionfoldnegative_body_start. fs_h_dst_one_convolutionfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_one_convolutionfoldnegative)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_start. fs_u_dst_one_convolutionfoldnegative = fs_q_dst_one_convolutionfoldnegative_body_start * S ((S (0)) * fs_v_dst_one_convolutionfoldnegative) + (0))) /\ ((((exists fs_h_dst_one_convolutionfoldnegative_body_terminal. fs_h_dst_one_convolutionfoldnegative_body_terminal + S (dst_negative_sum_one_convolutionfold) = S ((S (S (1))) * fs_v_dst_one_convolutionfoldnegative)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_terminal. fs_u_dst_one_convolutionfoldnegative = fs_q_dst_one_convolutionfoldnegative_body_terminal * S ((S (S (1))) * fs_v_dst_one_convolutionfoldnegative) + (dst_negative_sum_one_convolutionfold))) /\ forall fs_i_dst_one_convolutionfoldnegative_body_steps. (exists fs_lt_dst_one_convolutionfoldnegative_body_steps_bound. fs_lt_dst_one_convolutionfoldnegative_body_steps_bound + S fs_i_dst_one_convolutionfoldnegative_body_steps = S (1)) -> exists fs_a_dst_one_convolutionfoldnegative_body_steps fs_r_dst_one_convolutionfoldnegative_body_steps fs_s_dst_one_convolutionfoldnegative_body_steps. ((((exists fs_h_dst_one_convolutionfoldnegative_body_steps_summand. fs_h_dst_one_convolutionfoldnegative_body_steps_summand + S (fs_a_dst_one_convolutionfoldnegative_body_steps) = S ((S (fs_i_dst_one_convolutionfoldnegative_body_steps)) * dst_negative_scale_one_convolutionfold)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_steps_summand. dst_negative_code_one_convolutionfold = fs_q_dst_one_convolutionfoldnegative_body_steps_summand * S ((S (fs_i_dst_one_convolutionfoldnegative_body_steps)) * dst_negative_scale_one_convolutionfold) + (fs_a_dst_one_convolutionfoldnegative_body_steps))) /\ ((((exists fs_h_dst_one_convolutionfoldnegative_body_steps_partial. fs_h_dst_one_convolutionfoldnegative_body_steps_partial + S (fs_r_dst_one_convolutionfoldnegative_body_steps) = S ((S (fs_i_dst_one_convolutionfoldnegative_body_steps)) * fs_v_dst_one_convolutionfoldnegative)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_steps_partial. fs_u_dst_one_convolutionfoldnegative = fs_q_dst_one_convolutionfoldnegative_body_steps_partial * S ((S (fs_i_dst_one_convolutionfoldnegative_body_steps)) * fs_v_dst_one_convolutionfoldnegative) + (fs_r_dst_one_convolutionfoldnegative_body_steps))) /\ ((((exists fs_h_dst_one_convolutionfoldnegative_body_steps_successor. fs_h_dst_one_convolutionfoldnegative_body_steps_successor + S (fs_s_dst_one_convolutionfoldnegative_body_steps) = S ((S (S fs_i_dst_one_convolutionfoldnegative_body_steps)) * fs_v_dst_one_convolutionfoldnegative)) /\ exists fs_q_dst_one_convolutionfoldnegative_body_steps_successor. fs_u_dst_one_convolutionfoldnegative = fs_q_dst_one_convolutionfoldnegative_body_steps_successor * S ((S (S fs_i_dst_one_convolutionfoldnegative_body_steps)) * fs_v_dst_one_convolutionfoldnegative) + (fs_s_dst_one_convolutionfoldnegative_body_steps))) /\ fs_s_dst_one_convolutionfoldnegative_body_steps = fs_r_dst_one_convolutionfoldnegative_body_steps + fs_a_dst_one_convolutionfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_one_convolutionfoldresult ge_balance_negative_one_convolutionfoldresult. (((((z) = 2 * (ge_balance_positive_one_convolutionfoldresult) /\ (ge_balance_negative_one_convolutionfoldresult) = 0) \/ exists ge_signed_half_one_convolutionfoldresultdecode. (((z) = 2 * ge_signed_half_one_convolutionfoldresultdecode + 1 /\ (ge_balance_positive_one_convolutionfoldresult) = 0) /\ (ge_balance_negative_one_convolutionfoldresult) = S ge_signed_half_one_convolutionfoldresultdecode))) /\ ((dst_positive_sum_one_convolutionfold) + ge_balance_negative_one_convolutionfoldresult = (dst_negative_sum_one_convolutionfold) + ge_balance_positive_one_convolutionfoldresult)))))))))))))))Constructive proof overview
Generated structural guide
Actual convolution at input one is exactly the actual signed product F(1)*G(1); both implications construct or inspect the real two-entry masked fold.
The unchanged tactic script uses 13 declared prerequisites and contains 125 exact native proof lines.
Alpha v34 checked-use ยท first admitted v31 ยท independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
DT0009 dirichlet_convolution_zero_prefix_sum dirichlet_convolution_prefix_restrict Alpha theorem; checked-use authorized zero_le Stable theorem; checked-use authorized divisor_signed_sum_successor_decompose Alpha theorem; checked-use authorized divisor_signed_sum_functional Alpha theorem; checked-use authorized signed_add_functional Alpha theorem; checked-use authorized signed_add_zero_left Alpha theorem; checked-use authorized DT0005 dirichlet_convolution_last_entry_iff dirichlet_convolution_prefix_lookup Alpha theorem; checked-use authorized le_refl Stable theorem; checked-use authorized arithmetic_signed_table_singleton Alpha theorem; checked-use authorized dirichlet_convolution_prefix_zero_constructor Alpha theorem; checked-use authorized DT0007 dirichlet_convolution_prefix_last_stepDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Named ingredients (3)
01Fix variables and assumptionsL1โ7
02Separate the logical casesL8โ8
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L8
split
03Fix variables and assumptionsL9โ9
Work with arbitrary variables or the premises of the current implication.
- L9
intro hc
04Separate the logical casesL10โ12
05Establish hzeroL13โ22
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet convolution zero prefix sum.
- L13
have hzero : SignedPrefixSum(x,1,0)Definitions: SignedPrefixSum - L14
specialize dirichlet_convolution_zero_prefix_sum (F) - L15
specialize dirichlet_convolution_zero_prefix_sum (G) - L16
specialize dirichlet_convolution_zero_prefix_sum (1) - L17
specialize dirichlet_convolution_zero_prefix_sum (x) - L18
apply dirichlet_convolution_zero_prefix_sum - L19
specialize dirichlet_convolution_prefix_restrict (F) - L20
specialize dirichlet_convolution_prefix_restrict (G) - L21
specialize dirichlet_convolution_prefix_restrict (1) - L22
specialize dirichlet_convolution_prefix_restrict (1)
06Use earlier factsL23โ28
Instantiate or apply named facts and discharge the corresponding proof obligations.
07Establish hdL29โ34
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply divisor signed sum successor decompose.
- L29
have hd : โ r. โ v. SignedPrefixSum(x,1,r) โง (ArithAt(x,1,v) โง SignedAdd(r,v,z))Definitions: SignedAddArithAtSignedPrefixSum - L30
specialize divisor_signed_sum_successor_decompose (x) - L31
specialize divisor_signed_sum_successor_decompose (1) - L32
specialize divisor_signed_sum_successor_decompose (z) - L33
apply divisor_signed_sum_successor_decompose - L34
exact hc_right_witness_right
08Separate the logical casesL35โ38
09Establish hr0L39โ48
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply divisor signed sum functional.
- L39
have hr0 : x1=0 - L40
specialize divisor_signed_sum_functional (x) - L41
specialize divisor_signed_sum_functional (1) - L42
specialize divisor_signed_sum_functional (x1) - L43
specialize divisor_signed_sum_functional (0) - L44
apply divisor_signed_sum_functional - L45
exact hd_witness_witness_left - L46
exact hzero - L47
rewrite hr0 at hd_witness_witness_right_right - L48
rewrite hr0 at hd_witness_witness_right_right
10Establish hvL49โ58
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply signed add functional.
- L49
have hv : x2=z - L50
symm - L51
specialize signed_add_functional (0) - L52
specialize signed_add_functional (x2) - L53
specialize signed_add_functional (z) - L54
specialize signed_add_functional (x2) - L55
apply signed_add_functional - L56
exact hd_witness_witness_right_right - L57
specialize signed_add_zero_left (x2) - L58
apply signed_add_zero_left
11Establish heL59โ68
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet convolution last entry iff.
- L59
have he : (DirichletEntry(F,G,1,1,x2) โ SignedMul(a,b,x2)) โง (SignedMul(a,b,x2) โ DirichletEntry(F,G,1,1,x2))Definitions: SignedMulDirichletEntry - L60
specialize dirichlet_convolution_last_entry_iff (F) - L61
specialize dirichlet_convolution_last_entry_iff (G) - L62
specialize dirichlet_convolution_last_entry_iff (1) - L63
specialize dirichlet_convolution_last_entry_iff (a) - L64
specialize dirichlet_convolution_last_entry_iff (b) - L65
specialize dirichlet_convolution_last_entry_iff (x2) - L66
apply dirichlet_convolution_last_entry_iff - L67
intro hn - L68
apply PA1
12Use earlier factsL69โ71
13Separate the logical casesL72โ72
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L72
cases he
14Establish hpL73โ82
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply he left.
- L73
have hp : SignedMul(a,b,x2)Definitions: SignedMul - L74
apply he_left - L75
specialize dirichlet_convolution_prefix_lookup (F) - L76
specialize dirichlet_convolution_prefix_lookup (G) - L77
specialize dirichlet_convolution_prefix_lookup (1) - L78
specialize dirichlet_convolution_prefix_lookup (1) - L79
specialize dirichlet_convolution_prefix_lookup (x) - L80
specialize dirichlet_convolution_prefix_lookup (1) - L81
specialize dirichlet_convolution_prefix_lookup (x2) - L82
apply dirichlet_convolution_prefix_lookup
15Use earlier factsL83โ86
16Calculate and transport equalitiesL87โ88
17Use earlier factsL89โ89
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L89
exact hp
18Fix variables and assumptionsL90โ90
Work with arbitrary variables or the premises of the current implication.
- L90
intro hp
19Establish hmL91โ93
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply arithmetic signed table singleton.
- L91
have hm : โ M. ArithTable(0,M) โง ArithAt(M,0,0)Definitions: ArithTableArithAt - L92
specialize arithmetic_signed_table_singleton (0) - L93
apply arithmetic_signed_table_singleton
20Separate the logical casesL94โ95
21Establish hprefixL96โ105
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet convolution prefix zero constructor.
- L96
have hprefix : DirichletPrefix(F,G,1,0,x)Definitions: DirichletPrefix - L97
specialize dirichlet_convolution_prefix_zero_constructor (F) - L98
specialize dirichlet_convolution_prefix_zero_constructor (G) - L99
specialize dirichlet_convolution_prefix_zero_constructor (1) - L100
specialize dirichlet_convolution_prefix_zero_constructor (x) - L101
apply dirichlet_convolution_prefix_zero_constructor - L102
exact hm_witness_left - L103
exact hm_witness_right - L104
specialize dirichlet_convolution_prefix_last_step (F) - L105
specialize dirichlet_convolution_prefix_last_step (G)
22Use earlier factsL106โ115
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L106
specialize dirichlet_convolution_prefix_last_step (0) - L107
specialize dirichlet_convolution_prefix_last_step (x) - L108
specialize dirichlet_convolution_prefix_last_step (0) - L109
specialize dirichlet_convolution_prefix_last_step (a) - L110
specialize dirichlet_convolution_prefix_last_step (b) - L111
specialize dirichlet_convolution_prefix_last_step (z) - L112
specialize dirichlet_convolution_prefix_last_step (z) - L113
apply dirichlet_convolution_prefix_last_step - L114
exact hprefix - L115
specialize dirichlet_convolution_zero_prefix_sum (F)
23Use earlier factsL116โ125
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L116
specialize dirichlet_convolution_zero_prefix_sum (G) - L117
specialize dirichlet_convolution_zero_prefix_sum (1) - L118
specialize dirichlet_convolution_zero_prefix_sum (x) - L119
apply dirichlet_convolution_zero_prefix_sum - L120
exact hprefix - L121
exact ha - L122
exact hb - L123
exact hp - L124
specialize signed_add_zero_left (z) - L125
apply signed_add_zero_left
Original exact command ledger ยท 125 lines
- 0001
intro F - 0002
intro G - 0003
intro a - 0004
intro b - 0005
intro z - 0006
intro ha - 0007
intro hb - 0008
split - 0009
intro hc - 0010
cases hc - 0011
cases hc_right - 0012
cases hc_right_witness - 0013
have hzero : exists dst_positive_code_one_zero_fold dst_positive_scale_one_zero_fold dst_negative_code_one_zero_fold dst_negative_scale_one_zero_fold dst_positive_sum_one_zero_fold dst_negative_sum_one_zero_fold. (((x) = (((((dst_positive_code_one_zero_fold) + (dst_positive_scale_one_zero_fold)) * S ((dst_positive_code_one_zero_fold) + (dst_positive_scale_one_zero_fold)) + ((dst_positive_scale_one_zero_fold) + (dst_positive_scale_one_zero_fold))) + (((dst_negative_code_one_zero_fold) + (dst_negative_scale_one_zero_fold)) * S ((dst_negative_code_one_zero_fold) + (dst_negative_scale_one_zero_fold)) + ((dst_negative_scale_one_zero_fold) + (dst_negative_scale_one_zero_fold)))) * S ((((dst_positive_code_one_zero_fold) + (dst_positive_scale_one_zero_fold)) * S ((dst_positive_code_one_zero_fold) + (dst_positive_scale_one_zero_fold)) + ((dst_positive_scale_one_zero_fold) + (dst_positive_scale_one_zero_fold))) + (((dst_negative_code_one_zero_fold) + (dst_negative_scale_one_zero_fold)) * S ((dst_negative_code_one_zero_fold) + (dst_negative_scale_one_zero_fold)) + ((dst_negative_scale_one_zero_fold) + (dst_negative_scale_one_zero_fold)))) + ((((dst_negative_code_one_zero_fold) + (dst_negative_scale_one_zero_fold)) * S ((dst_negative_code_one_zero_fold) + (dst_negative_scale_one_zero_fold)) + ((dst_negative_scale_one_zero_fold) + (dst_negative_scale_one_zero_fold))) + (((dst_negative_code_one_zero_fold) + (dst_negative_scale_one_zero_fold)) * S ((dst_negative_code_one_zero_fold) + (dst_negative_scale_one_zero_fold)) + ((dst_negative_scale_one_zero_fold) + (dst_negative_scale_one_zero_fold)))))) /\ (((exists fs_u_dst_one_zero_foldpositive fs_v_dst_one_zero_foldpositive. ((((exists fs_h_dst_one_zero_foldpositive_body_start. fs_h_dst_one_zero_foldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_one_zero_foldpositive)) /\ exists fs_q_dst_one_zero_foldpositive_body_start. fs_u_dst_one_zero_foldpositive = fs_q_dst_one_zero_foldpositive_body_start * S ((S (0)) * fs_v_dst_one_zero_foldpositive) + (0))) /\ ((((exists fs_h_dst_one_zero_foldpositive_body_terminal. fs_h_dst_one_zero_foldpositive_body_terminal + S (dst_positive_sum_one_zero_fold) = S ((S (1)) * fs_v_dst_one_zero_foldpositive)) /\ exists fs_q_dst_one_zero_foldpositive_body_terminal. fs_u_dst_one_zero_foldpositive = fs_q_dst_one_zero_foldpositive_body_terminal * S ((S (1)) * fs_v_dst_one_zero_foldpositive) + (dst_positive_sum_one_zero_fold))) /\ forall fs_i_dst_one_zero_foldpositive_body_steps. (exists fs_lt_dst_one_zero_foldpositive_body_steps_bound. fs_lt_dst_one_zero_foldpositive_body_steps_bound + S fs_i_dst_one_zero_foldpositive_body_steps = 1) -> exists fs_a_dst_one_zero_foldpositive_body_steps fs_r_dst_one_zero_foldpositive_body_steps fs_s_dst_one_zero_foldpositive_body_steps. ((((exists fs_h_dst_one_zero_foldpositive_body_steps_summand. fs_h_dst_one_zero_foldpositive_body_steps_summand + S (fs_a_dst_one_zero_foldpositive_body_steps) = S ((S (fs_i_dst_one_zero_foldpositive_body_steps)) * dst_positive_scale_one_zero_fold)) /\ exists fs_q_dst_one_zero_foldpositive_body_steps_summand. dst_positive_code_one_zero_fold = fs_q_dst_one_zero_foldpositive_body_steps_summand * S ((S (fs_i_dst_one_zero_foldpositive_body_steps)) * dst_positive_scale_one_zero_fold) + (fs_a_dst_one_zero_foldpositive_body_steps))) /\ ((((exists fs_h_dst_one_zero_foldpositive_body_steps_partial. fs_h_dst_one_zero_foldpositive_body_steps_partial + S (fs_r_dst_one_zero_foldpositive_body_steps) = S ((S (fs_i_dst_one_zero_foldpositive_body_steps)) * fs_v_dst_one_zero_foldpositive)) /\ exists fs_q_dst_one_zero_foldpositive_body_steps_partial. fs_u_dst_one_zero_foldpositive = fs_q_dst_one_zero_foldpositive_body_steps_partial * S ((S (fs_i_dst_one_zero_foldpositive_body_steps)) * fs_v_dst_one_zero_foldpositive) + (fs_r_dst_one_zero_foldpositive_body_steps))) /\ ((((exists fs_h_dst_one_zero_foldpositive_body_steps_successor. fs_h_dst_one_zero_foldpositive_body_steps_successor + S (fs_s_dst_one_zero_foldpositive_body_steps) = S ((S (S fs_i_dst_one_zero_foldpositive_body_steps)) * fs_v_dst_one_zero_foldpositive)) /\ exists fs_q_dst_one_zero_foldpositive_body_steps_successor. fs_u_dst_one_zero_foldpositive = fs_q_dst_one_zero_foldpositive_body_steps_successor * S ((S (S fs_i_dst_one_zero_foldpositive_body_steps)) * fs_v_dst_one_zero_foldpositive) + (fs_s_dst_one_zero_foldpositive_body_steps))) /\ fs_s_dst_one_zero_foldpositive_body_steps = fs_r_dst_one_zero_foldpositive_body_steps + fs_a_dst_one_zero_foldpositive_body_steps)))))) /\ (((exists fs_u_dst_one_zero_foldnegative fs_v_dst_one_zero_foldnegative. ((((exists fs_h_dst_one_zero_foldnegative_body_start. fs_h_dst_one_zero_foldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_one_zero_foldnegative)) /\ exists fs_q_dst_one_zero_foldnegative_body_start. fs_u_dst_one_zero_foldnegative = fs_q_dst_one_zero_foldnegative_body_start * S ((S (0)) * fs_v_dst_one_zero_foldnegative) + (0))) /\ ((((exists fs_h_dst_one_zero_foldnegative_body_terminal. fs_h_dst_one_zero_foldnegative_body_terminal + S (dst_negative_sum_one_zero_fold) = S ((S (1)) * fs_v_dst_one_zero_foldnegative)) /\ exists fs_q_dst_one_zero_foldnegative_body_terminal. fs_u_dst_one_zero_foldnegative = fs_q_dst_one_zero_foldnegative_body_terminal * S ((S (1)) * fs_v_dst_one_zero_foldnegative) + (dst_negative_sum_one_zero_fold))) /\ forall fs_i_dst_one_zero_foldnegative_body_steps. (exists fs_lt_dst_one_zero_foldnegative_body_steps_bound. fs_lt_dst_one_zero_foldnegative_body_steps_bound + S fs_i_dst_one_zero_foldnegative_body_steps = 1) -> exists fs_a_dst_one_zero_foldnegative_body_steps fs_r_dst_one_zero_foldnegative_body_steps fs_s_dst_one_zero_foldnegative_body_steps. ((((exists fs_h_dst_one_zero_foldnegative_body_steps_summand. fs_h_dst_one_zero_foldnegative_body_steps_summand + S (fs_a_dst_one_zero_foldnegative_body_steps) = S ((S (fs_i_dst_one_zero_foldnegative_body_steps)) * dst_negative_scale_one_zero_fold)) /\ exists fs_q_dst_one_zero_foldnegative_body_steps_summand. dst_negative_code_one_zero_fold = fs_q_dst_one_zero_foldnegative_body_steps_summand * S ((S (fs_i_dst_one_zero_foldnegative_body_steps)) * dst_negative_scale_one_zero_fold) + (fs_a_dst_one_zero_foldnegative_body_steps))) /\ ((((exists fs_h_dst_one_zero_foldnegative_body_steps_partial. fs_h_dst_one_zero_foldnegative_body_steps_partial + S (fs_r_dst_one_zero_foldnegative_body_steps) = S ((S (fs_i_dst_one_zero_foldnegative_body_steps)) * fs_v_dst_one_zero_foldnegative)) /\ exists fs_q_dst_one_zero_foldnegative_body_steps_partial. fs_u_dst_one_zero_foldnegative = fs_q_dst_one_zero_foldnegative_body_steps_partial * S ((S (fs_i_dst_one_zero_foldnegative_body_steps)) * fs_v_dst_one_zero_foldnegative) + (fs_r_dst_one_zero_foldnegative_body_steps))) /\ ((((exists fs_h_dst_one_zero_foldnegative_body_steps_successor. fs_h_dst_one_zero_foldnegative_body_steps_successor + S (fs_s_dst_one_zero_foldnegative_body_steps) = S ((S (S fs_i_dst_one_zero_foldnegative_body_steps)) * fs_v_dst_one_zero_foldnegative)) /\ exists fs_q_dst_one_zero_foldnegative_body_steps_successor. fs_u_dst_one_zero_foldnegative = fs_q_dst_one_zero_foldnegative_body_steps_successor * S ((S (S fs_i_dst_one_zero_foldnegative_body_steps)) * fs_v_dst_one_zero_foldnegative) + (fs_s_dst_one_zero_foldnegative_body_steps))) /\ fs_s_dst_one_zero_foldnegative_body_steps = fs_r_dst_one_zero_foldnegative_body_steps + fs_a_dst_one_zero_foldnegative_body_steps)))))) /\ (exists ge_balance_positive_one_zero_foldresult ge_balance_negative_one_zero_foldresult. (((((0) = 2 * (ge_balance_positive_one_zero_foldresult) /\ (ge_balance_negative_one_zero_foldresult) = 0) \/ exists ge_signed_half_one_zero_foldresultdecode. (((0) = 2 * ge_signed_half_one_zero_foldresultdecode + 1 /\ (ge_balance_positive_one_zero_foldresult) = 0) /\ (ge_balance_negative_one_zero_foldresult) = S ge_signed_half_one_zero_foldresultdecode))) /\ ((dst_positive_sum_one_zero_fold) + ge_balance_negative_one_zero_foldresult = (dst_negative_sum_one_zero_fold) + ge_balance_positive_one_zero_foldresult)))))))) - 0014
specialize dirichlet_convolution_zero_prefix_sum (F) - 0015
specialize dirichlet_convolution_zero_prefix_sum (G) - 0016
specialize dirichlet_convolution_zero_prefix_sum (1) - 0017
specialize dirichlet_convolution_zero_prefix_sum (x) - 0018
apply dirichlet_convolution_zero_prefix_sum - 0019
specialize dirichlet_convolution_prefix_restrict (F) - 0020
specialize dirichlet_convolution_prefix_restrict (G) - 0021
specialize dirichlet_convolution_prefix_restrict (1) - 0022
specialize dirichlet_convolution_prefix_restrict (1) - 0023
specialize dirichlet_convolution_prefix_restrict (0) - 0024
specialize dirichlet_convolution_prefix_restrict (x) - 0025
apply dirichlet_convolution_prefix_restrict - 0026
exact hc_right_witness_left - 0027
specialize zero_le (1) - 0028
apply zero_le - 0029
have hd : exists r v. (((exists dst_positive_code_one_previous_fold dst_positive_scale_one_previous_fold dst_negative_code_one_previous_fold dst_negative_scale_one_previous_fold dst_positive_sum_one_previous_fold dst_negative_sum_one_previous_fold. (((x) = (((((dst_positive_code_one_previous_fold) + (dst_positive_scale_one_previous_fold)) * S ((dst_positive_code_one_previous_fold) + (dst_positive_scale_one_previous_fold)) + ((dst_positive_scale_one_previous_fold) + (dst_positive_scale_one_previous_fold))) + (((dst_negative_code_one_previous_fold) + (dst_negative_scale_one_previous_fold)) * S ((dst_negative_code_one_previous_fold) + (dst_negative_scale_one_previous_fold)) + ((dst_negative_scale_one_previous_fold) + (dst_negative_scale_one_previous_fold)))) * S ((((dst_positive_code_one_previous_fold) + (dst_positive_scale_one_previous_fold)) * S ((dst_positive_code_one_previous_fold) + (dst_positive_scale_one_previous_fold)) + ((dst_positive_scale_one_previous_fold) + (dst_positive_scale_one_previous_fold))) + (((dst_negative_code_one_previous_fold) + (dst_negative_scale_one_previous_fold)) * S ((dst_negative_code_one_previous_fold) + (dst_negative_scale_one_previous_fold)) + ((dst_negative_scale_one_previous_fold) + (dst_negative_scale_one_previous_fold)))) + ((((dst_negative_code_one_previous_fold) + (dst_negative_scale_one_previous_fold)) * S ((dst_negative_code_one_previous_fold) + (dst_negative_scale_one_previous_fold)) + ((dst_negative_scale_one_previous_fold) + (dst_negative_scale_one_previous_fold))) + (((dst_negative_code_one_previous_fold) + (dst_negative_scale_one_previous_fold)) * S ((dst_negative_code_one_previous_fold) + (dst_negative_scale_one_previous_fold)) + ((dst_negative_scale_one_previous_fold) + (dst_negative_scale_one_previous_fold)))))) /\ (((exists fs_u_dst_one_previous_foldpositive fs_v_dst_one_previous_foldpositive. ((((exists fs_h_dst_one_previous_foldpositive_body_start. fs_h_dst_one_previous_foldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_one_previous_foldpositive)) /\ exists fs_q_dst_one_previous_foldpositive_body_start. fs_u_dst_one_previous_foldpositive = fs_q_dst_one_previous_foldpositive_body_start * S ((S (0)) * fs_v_dst_one_previous_foldpositive) + (0))) /\ ((((exists fs_h_dst_one_previous_foldpositive_body_terminal. fs_h_dst_one_previous_foldpositive_body_terminal + S (dst_positive_sum_one_previous_fold) = S ((S (1)) * fs_v_dst_one_previous_foldpositive)) /\ exists fs_q_dst_one_previous_foldpositive_body_terminal. fs_u_dst_one_previous_foldpositive = fs_q_dst_one_previous_foldpositive_body_terminal * S ((S (1)) * fs_v_dst_one_previous_foldpositive) + (dst_positive_sum_one_previous_fold))) /\ forall fs_i_dst_one_previous_foldpositive_body_steps. (exists fs_lt_dst_one_previous_foldpositive_body_steps_bound. fs_lt_dst_one_previous_foldpositive_body_steps_bound + S fs_i_dst_one_previous_foldpositive_body_steps = 1) -> exists fs_a_dst_one_previous_foldpositive_body_steps fs_r_dst_one_previous_foldpositive_body_steps fs_s_dst_one_previous_foldpositive_body_steps. ((((exists fs_h_dst_one_previous_foldpositive_body_steps_summand. fs_h_dst_one_previous_foldpositive_body_steps_summand + S (fs_a_dst_one_previous_foldpositive_body_steps) = S ((S (fs_i_dst_one_previous_foldpositive_body_steps)) * dst_positive_scale_one_previous_fold)) /\ exists fs_q_dst_one_previous_foldpositive_body_steps_summand. dst_positive_code_one_previous_fold = fs_q_dst_one_previous_foldpositive_body_steps_summand * S ((S (fs_i_dst_one_previous_foldpositive_body_steps)) * dst_positive_scale_one_previous_fold) + (fs_a_dst_one_previous_foldpositive_body_steps))) /\ ((((exists fs_h_dst_one_previous_foldpositive_body_steps_partial. fs_h_dst_one_previous_foldpositive_body_steps_partial + S (fs_r_dst_one_previous_foldpositive_body_steps) = S ((S (fs_i_dst_one_previous_foldpositive_body_steps)) * fs_v_dst_one_previous_foldpositive)) /\ exists fs_q_dst_one_previous_foldpositive_body_steps_partial. fs_u_dst_one_previous_foldpositive = fs_q_dst_one_previous_foldpositive_body_steps_partial * S ((S (fs_i_dst_one_previous_foldpositive_body_steps)) * fs_v_dst_one_previous_foldpositive) + (fs_r_dst_one_previous_foldpositive_body_steps))) /\ ((((exists fs_h_dst_one_previous_foldpositive_body_steps_successor. fs_h_dst_one_previous_foldpositive_body_steps_successor + S (fs_s_dst_one_previous_foldpositive_body_steps) = S ((S (S fs_i_dst_one_previous_foldpositive_body_steps)) * fs_v_dst_one_previous_foldpositive)) /\ exists fs_q_dst_one_previous_foldpositive_body_steps_successor. fs_u_dst_one_previous_foldpositive = fs_q_dst_one_previous_foldpositive_body_steps_successor * S ((S (S fs_i_dst_one_previous_foldpositive_body_steps)) * fs_v_dst_one_previous_foldpositive) + (fs_s_dst_one_previous_foldpositive_body_steps))) /\ fs_s_dst_one_previous_foldpositive_body_steps = fs_r_dst_one_previous_foldpositive_body_steps + fs_a_dst_one_previous_foldpositive_body_steps)))))) /\ (((exists fs_u_dst_one_previous_foldnegative fs_v_dst_one_previous_foldnegative. ((((exists fs_h_dst_one_previous_foldnegative_body_start. fs_h_dst_one_previous_foldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_one_previous_foldnegative)) /\ exists fs_q_dst_one_previous_foldnegative_body_start. fs_u_dst_one_previous_foldnegative = fs_q_dst_one_previous_foldnegative_body_start * S ((S (0)) * fs_v_dst_one_previous_foldnegative) + (0))) /\ ((((exists fs_h_dst_one_previous_foldnegative_body_terminal. fs_h_dst_one_previous_foldnegative_body_terminal + S (dst_negative_sum_one_previous_fold) = S ((S (1)) * fs_v_dst_one_previous_foldnegative)) /\ exists fs_q_dst_one_previous_foldnegative_body_terminal. fs_u_dst_one_previous_foldnegative = fs_q_dst_one_previous_foldnegative_body_terminal * S ((S (1)) * fs_v_dst_one_previous_foldnegative) + (dst_negative_sum_one_previous_fold))) /\ forall fs_i_dst_one_previous_foldnegative_body_steps. (exists fs_lt_dst_one_previous_foldnegative_body_steps_bound. fs_lt_dst_one_previous_foldnegative_body_steps_bound + S fs_i_dst_one_previous_foldnegative_body_steps = 1) -> exists fs_a_dst_one_previous_foldnegative_body_steps fs_r_dst_one_previous_foldnegative_body_steps fs_s_dst_one_previous_foldnegative_body_steps. ((((exists fs_h_dst_one_previous_foldnegative_body_steps_summand. fs_h_dst_one_previous_foldnegative_body_steps_summand + S (fs_a_dst_one_previous_foldnegative_body_steps) = S ((S (fs_i_dst_one_previous_foldnegative_body_steps)) * dst_negative_scale_one_previous_fold)) /\ exists fs_q_dst_one_previous_foldnegative_body_steps_summand. dst_negative_code_one_previous_fold = fs_q_dst_one_previous_foldnegative_body_steps_summand * S ((S (fs_i_dst_one_previous_foldnegative_body_steps)) * dst_negative_scale_one_previous_fold) + (fs_a_dst_one_previous_foldnegative_body_steps))) /\ ((((exists fs_h_dst_one_previous_foldnegative_body_steps_partial. fs_h_dst_one_previous_foldnegative_body_steps_partial + S (fs_r_dst_one_previous_foldnegative_body_steps) = S ((S (fs_i_dst_one_previous_foldnegative_body_steps)) * fs_v_dst_one_previous_foldnegative)) /\ exists fs_q_dst_one_previous_foldnegative_body_steps_partial. fs_u_dst_one_previous_foldnegative = fs_q_dst_one_previous_foldnegative_body_steps_partial * S ((S (fs_i_dst_one_previous_foldnegative_body_steps)) * fs_v_dst_one_previous_foldnegative) + (fs_r_dst_one_previous_foldnegative_body_steps))) /\ ((((exists fs_h_dst_one_previous_foldnegative_body_steps_successor. fs_h_dst_one_previous_foldnegative_body_steps_successor + S (fs_s_dst_one_previous_foldnegative_body_steps) = S ((S (S fs_i_dst_one_previous_foldnegative_body_steps)) * fs_v_dst_one_previous_foldnegative)) /\ exists fs_q_dst_one_previous_foldnegative_body_steps_successor. fs_u_dst_one_previous_foldnegative = fs_q_dst_one_previous_foldnegative_body_steps_successor * S ((S (S fs_i_dst_one_previous_foldnegative_body_steps)) * fs_v_dst_one_previous_foldnegative) + (fs_s_dst_one_previous_foldnegative_body_steps))) /\ fs_s_dst_one_previous_foldnegative_body_steps = fs_r_dst_one_previous_foldnegative_body_steps + fs_a_dst_one_previous_foldnegative_body_steps)))))) /\ (exists ge_balance_positive_one_previous_foldresult ge_balance_negative_one_previous_foldresult. (((((r) = 2 * (ge_balance_positive_one_previous_foldresult) /\ (ge_balance_negative_one_previous_foldresult) = 0) \/ exists ge_signed_half_one_previous_foldresultdecode. (((r) = 2 * ge_signed_half_one_previous_foldresultdecode + 1 /\ (ge_balance_positive_one_previous_foldresult) = 0) /\ (ge_balance_negative_one_previous_foldresult) = S ge_signed_half_one_previous_foldresultdecode))) /\ ((dst_positive_sum_one_previous_fold) + ge_balance_negative_one_previous_foldresult = (dst_negative_sum_one_previous_fold) + ge_balance_positive_one_previous_foldresult))))))))) /\ (((exists dst_positive_code_one_endpoint_lookup dst_positive_scale_one_endpoint_lookup dst_negative_code_one_endpoint_lookup dst_negative_scale_one_endpoint_lookup dst_positive_one_endpoint_lookup dst_negative_one_endpoint_lookup. (((x) = (((((dst_positive_code_one_endpoint_lookup) + (dst_positive_scale_one_endpoint_lookup)) * S ((dst_positive_code_one_endpoint_lookup) + (dst_positive_scale_one_endpoint_lookup)) + ((dst_positive_scale_one_endpoint_lookup) + (dst_positive_scale_one_endpoint_lookup))) + (((dst_negative_code_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)) * S ((dst_negative_code_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)) + ((dst_negative_scale_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)))) * S ((((dst_positive_code_one_endpoint_lookup) + (dst_positive_scale_one_endpoint_lookup)) * S ((dst_positive_code_one_endpoint_lookup) + (dst_positive_scale_one_endpoint_lookup)) + ((dst_positive_scale_one_endpoint_lookup) + (dst_positive_scale_one_endpoint_lookup))) + (((dst_negative_code_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)) * S ((dst_negative_code_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)) + ((dst_negative_scale_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)))) + ((((dst_negative_code_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)) * S ((dst_negative_code_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)) + ((dst_negative_scale_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup))) + (((dst_negative_code_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)) * S ((dst_negative_code_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)) + ((dst_negative_scale_one_endpoint_lookup) + (dst_negative_scale_one_endpoint_lookup)))))) /\ (((((exists ff_h_pvs_one_endpoint_lookuppositive. ff_h_pvs_one_endpoint_lookuppositive + S (dst_positive_one_endpoint_lookup) = S ((S (1)) * dst_positive_scale_one_endpoint_lookup)) /\ exists ff_q_pvs_one_endpoint_lookuppositive. dst_positive_code_one_endpoint_lookup = ff_q_pvs_one_endpoint_lookuppositive * S ((S (1)) * dst_positive_scale_one_endpoint_lookup) + (dst_positive_one_endpoint_lookup))) /\ (((((exists ff_h_pvs_one_endpoint_lookupnegative. ff_h_pvs_one_endpoint_lookupnegative + S (dst_negative_one_endpoint_lookup) = S ((S (1)) * dst_negative_scale_one_endpoint_lookup)) /\ exists ff_q_pvs_one_endpoint_lookupnegative. dst_negative_code_one_endpoint_lookup = ff_q_pvs_one_endpoint_lookupnegative * S ((S (1)) * dst_negative_scale_one_endpoint_lookup) + (dst_negative_one_endpoint_lookup))) /\ (exists ge_balance_positive_one_endpoint_lookupvalue ge_balance_negative_one_endpoint_lookupvalue. (((((v) = 2 * (ge_balance_positive_one_endpoint_lookupvalue) /\ (ge_balance_negative_one_endpoint_lookupvalue) = 0) \/ exists ge_signed_half_one_endpoint_lookupvaluedecode. (((v) = 2 * ge_signed_half_one_endpoint_lookupvaluedecode + 1 /\ (ge_balance_positive_one_endpoint_lookupvalue) = 0) /\ (ge_balance_negative_one_endpoint_lookupvalue) = S ge_signed_half_one_endpoint_lookupvaluedecode))) /\ ((dst_positive_one_endpoint_lookup) + ge_balance_negative_one_endpoint_lookupvalue = (dst_negative_one_endpoint_lookup) + ge_balance_positive_one_endpoint_lookupvalue))))))))) /\ (exists dsa_ap_one_fold_add dsa_an_one_fold_add dsa_bp_one_fold_add dsa_bn_one_fold_add dsa_cp_one_fold_add dsa_cn_one_fold_add. (((((r) = 2 * (dsa_ap_one_fold_add) /\ (dsa_an_one_fold_add) = 0) \/ exists ge_signed_half_one_fold_addleft. (((r) = 2 * ge_signed_half_one_fold_addleft + 1 /\ (dsa_ap_one_fold_add) = 0) /\ (dsa_an_one_fold_add) = S ge_signed_half_one_fold_addleft))) /\ ((((((v) = 2 * (dsa_bp_one_fold_add) /\ (dsa_bn_one_fold_add) = 0) \/ exists ge_signed_half_one_fold_addright. (((v) = 2 * ge_signed_half_one_fold_addright + 1 /\ (dsa_bp_one_fold_add) = 0) /\ (dsa_bn_one_fold_add) = S ge_signed_half_one_fold_addright))) /\ ((((((z) = 2 * (dsa_cp_one_fold_add) /\ (dsa_cn_one_fold_add) = 0) \/ exists ge_signed_half_one_fold_addoutput. (((z) = 2 * ge_signed_half_one_fold_addoutput + 1 /\ (dsa_cp_one_fold_add) = 0) /\ (dsa_cn_one_fold_add) = S ge_signed_half_one_fold_addoutput))) /\ ((dsa_ap_one_fold_add + dsa_bp_one_fold_add) + dsa_cn_one_fold_add = (dsa_an_one_fold_add + dsa_bn_one_fold_add) + dsa_cp_one_fold_add))))))))))) - 0030
specialize divisor_signed_sum_successor_decompose (x) - 0031
specialize divisor_signed_sum_successor_decompose (1) - 0032
specialize divisor_signed_sum_successor_decompose (z) - 0033
apply divisor_signed_sum_successor_decompose - 0034
exact hc_right_witness_right - 0035
cases hd - 0036
cases hd_witness - 0037
cases hd_witness_witness - 0038
cases hd_witness_witness_right - 0039
have hr0 : x1=0 - 0040
specialize divisor_signed_sum_functional (x) - 0041
specialize divisor_signed_sum_functional (1) - 0042
specialize divisor_signed_sum_functional (x1) - 0043
specialize divisor_signed_sum_functional (0) - 0044
apply divisor_signed_sum_functional - 0045
exact hd_witness_witness_left - 0046
exact hzero - 0047
rewrite hr0 at hd_witness_witness_right_right - 0048
rewrite hr0 at hd_witness_witness_right_right - 0049
have hv : x2=z - 0050
symm - 0051
specialize signed_add_functional (0) - 0052
specialize signed_add_functional (x2) - 0053
specialize signed_add_functional (z) - 0054
specialize signed_add_functional (x2) - 0055
apply signed_add_functional - 0056
exact hd_witness_witness_right_right - 0057
specialize signed_add_zero_left (x2) - 0058
apply signed_add_zero_left - 0059
have he : ((((((~((1)=0)) /\ (exists dc_quotient_one_actual_entry dc_left_one_actual_entry dc_right_one_actual_entry. (((1)=(1)*dc_quotient_one_actual_entry) /\ (((exists dst_positive_code_one_actual_entryleft dst_positive_scale_one_actual_entryleft dst_negative_code_one_actual_entryleft dst_negative_scale_one_actual_entryleft dst_positive_one_actual_entryleft dst_negative_one_actual_entryleft. (((F) = (((((dst_positive_code_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft)) * S ((dst_positive_code_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft)) + ((dst_positive_scale_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft))) + (((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) * S ((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) + ((dst_negative_scale_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)))) * S ((((dst_positive_code_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft)) * S ((dst_positive_code_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft)) + ((dst_positive_scale_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft))) + (((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) * S ((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) + ((dst_negative_scale_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)))) + ((((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) * S ((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) + ((dst_negative_scale_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft))) + (((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) * S ((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) + ((dst_negative_scale_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)))))) /\ (((((exists ff_h_pvs_one_actual_entryleftpositive. ff_h_pvs_one_actual_entryleftpositive + S (dst_positive_one_actual_entryleft) = S ((S (1)) * dst_positive_scale_one_actual_entryleft)) /\ exists ff_q_pvs_one_actual_entryleftpositive. dst_positive_code_one_actual_entryleft = ff_q_pvs_one_actual_entryleftpositive * S ((S (1)) * dst_positive_scale_one_actual_entryleft) + (dst_positive_one_actual_entryleft))) /\ (((((exists ff_h_pvs_one_actual_entryleftnegative. ff_h_pvs_one_actual_entryleftnegative + S (dst_negative_one_actual_entryleft) = S ((S (1)) * dst_negative_scale_one_actual_entryleft)) /\ exists ff_q_pvs_one_actual_entryleftnegative. dst_negative_code_one_actual_entryleft = ff_q_pvs_one_actual_entryleftnegative * S ((S (1)) * dst_negative_scale_one_actual_entryleft) + (dst_negative_one_actual_entryleft))) /\ (exists ge_balance_positive_one_actual_entryleftvalue ge_balance_negative_one_actual_entryleftvalue. (((((dc_left_one_actual_entry) = 2 * (ge_balance_positive_one_actual_entryleftvalue) /\ (ge_balance_negative_one_actual_entryleftvalue) = 0) \/ exists ge_signed_half_one_actual_entryleftvaluedecode. (((dc_left_one_actual_entry) = 2 * ge_signed_half_one_actual_entryleftvaluedecode + 1 /\ (ge_balance_positive_one_actual_entryleftvalue) = 0) /\ (ge_balance_negative_one_actual_entryleftvalue) = S ge_signed_half_one_actual_entryleftvaluedecode))) /\ ((dst_positive_one_actual_entryleft) + ge_balance_negative_one_actual_entryleftvalue = (dst_negative_one_actual_entryleft) + ge_balance_positive_one_actual_entryleftvalue))))))))) /\ (((exists dst_positive_code_one_actual_entryright dst_positive_scale_one_actual_entryright dst_negative_code_one_actual_entryright dst_negative_scale_one_actual_entryright dst_positive_one_actual_entryright dst_negative_one_actual_entryright. (((G) = (((((dst_positive_code_one_actual_entryright) + (dst_positive_scale_one_actual_entryright)) * S ((dst_positive_code_one_actual_entryright) + (dst_positive_scale_one_actual_entryright)) + ((dst_positive_scale_one_actual_entryright) + (dst_positive_scale_one_actual_entryright))) + (((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) * S ((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) + ((dst_negative_scale_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)))) * S ((((dst_positive_code_one_actual_entryright) + (dst_positive_scale_one_actual_entryright)) * S ((dst_positive_code_one_actual_entryright) + (dst_positive_scale_one_actual_entryright)) + ((dst_positive_scale_one_actual_entryright) + (dst_positive_scale_one_actual_entryright))) + (((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) * S ((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) + ((dst_negative_scale_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)))) + ((((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) * S ((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) + ((dst_negative_scale_one_actual_entryright) + (dst_negative_scale_one_actual_entryright))) + (((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) * S ((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) + ((dst_negative_scale_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)))))) /\ (((((exists ff_h_pvs_one_actual_entryrightpositive. ff_h_pvs_one_actual_entryrightpositive + S (dst_positive_one_actual_entryright) = S ((S (dc_quotient_one_actual_entry)) * dst_positive_scale_one_actual_entryright)) /\ exists ff_q_pvs_one_actual_entryrightpositive. dst_positive_code_one_actual_entryright = ff_q_pvs_one_actual_entryrightpositive * S ((S (dc_quotient_one_actual_entry)) * dst_positive_scale_one_actual_entryright) + (dst_positive_one_actual_entryright))) /\ (((((exists ff_h_pvs_one_actual_entryrightnegative. ff_h_pvs_one_actual_entryrightnegative + S (dst_negative_one_actual_entryright) = S ((S (dc_quotient_one_actual_entry)) * dst_negative_scale_one_actual_entryright)) /\ exists ff_q_pvs_one_actual_entryrightnegative. dst_negative_code_one_actual_entryright = ff_q_pvs_one_actual_entryrightnegative * S ((S (dc_quotient_one_actual_entry)) * dst_negative_scale_one_actual_entryright) + (dst_negative_one_actual_entryright))) /\ (exists ge_balance_positive_one_actual_entryrightvalue ge_balance_negative_one_actual_entryrightvalue. (((((dc_right_one_actual_entry) = 2 * (ge_balance_positive_one_actual_entryrightvalue) /\ (ge_balance_negative_one_actual_entryrightvalue) = 0) \/ exists ge_signed_half_one_actual_entryrightvaluedecode. (((dc_right_one_actual_entry) = 2 * ge_signed_half_one_actual_entryrightvaluedecode + 1 /\ (ge_balance_positive_one_actual_entryrightvalue) = 0) /\ (ge_balance_negative_one_actual_entryrightvalue) = S ge_signed_half_one_actual_entryrightvaluedecode))) /\ ((dst_positive_one_actual_entryright) + ge_balance_negative_one_actual_entryrightvalue = (dst_negative_one_actual_entryright) + ge_balance_positive_one_actual_entryrightvalue))))))))) /\ (exists sto_ap_one_actual_entryproduct sto_an_one_actual_entryproduct sto_bp_one_actual_entryproduct sto_bn_one_actual_entryproduct sto_cp_one_actual_entryproduct sto_cn_one_actual_entryproduct. (((((dc_left_one_actual_entry) = 2 * (sto_ap_one_actual_entryproduct) /\ (sto_an_one_actual_entryproduct) = 0) \/ exists ge_signed_half_one_actual_entryproductleft. (((dc_left_one_actual_entry) = 2 * ge_signed_half_one_actual_entryproductleft + 1 /\ (sto_ap_one_actual_entryproduct) = 0) /\ (sto_an_one_actual_entryproduct) = S ge_signed_half_one_actual_entryproductleft))) /\ ((((((dc_right_one_actual_entry) = 2 * (sto_bp_one_actual_entryproduct) /\ (sto_bn_one_actual_entryproduct) = 0) \/ exists ge_signed_half_one_actual_entryproductright. (((dc_right_one_actual_entry) = 2 * ge_signed_half_one_actual_entryproductright + 1 /\ (sto_bp_one_actual_entryproduct) = 0) /\ (sto_bn_one_actual_entryproduct) = S ge_signed_half_one_actual_entryproductright))) /\ ((((((x2) = 2 * (sto_cp_one_actual_entryproduct) /\ (sto_cn_one_actual_entryproduct) = 0) \/ exists ge_signed_half_one_actual_entryproductoutput. (((x2) = 2 * ge_signed_half_one_actual_entryproductoutput + 1 /\ (sto_cp_one_actual_entryproduct) = 0) /\ (sto_cn_one_actual_entryproduct) = S ge_signed_half_one_actual_entryproductoutput))) /\ ((sto_ap_one_actual_entryproduct * sto_bp_one_actual_entryproduct + sto_an_one_actual_entryproduct * sto_bn_one_actual_entryproduct) + sto_cn_one_actual_entryproduct = (sto_ap_one_actual_entryproduct * sto_bn_one_actual_entryproduct + sto_an_one_actual_entryproduct * sto_bp_one_actual_entryproduct) + sto_cp_one_actual_entryproduct))))))))))))))) \/ ((((1)=0 \/ ~(exists pvs_factor_one_actual_entrynondivisor. (1) = (1) * pvs_factor_one_actual_entrynondivisor)) /\ ((x2)=0)))) -> (exists sto_ap_one_actual_product sto_an_one_actual_product sto_bp_one_actual_product sto_bn_one_actual_product sto_cp_one_actual_product sto_cn_one_actual_product. (((((a) = 2 * (sto_ap_one_actual_product) /\ (sto_an_one_actual_product) = 0) \/ exists ge_signed_half_one_actual_productleft. (((a) = 2 * ge_signed_half_one_actual_productleft + 1 /\ (sto_ap_one_actual_product) = 0) /\ (sto_an_one_actual_product) = S ge_signed_half_one_actual_productleft))) /\ ((((((b) = 2 * (sto_bp_one_actual_product) /\ (sto_bn_one_actual_product) = 0) \/ exists ge_signed_half_one_actual_productright. (((b) = 2 * ge_signed_half_one_actual_productright + 1 /\ (sto_bp_one_actual_product) = 0) /\ (sto_bn_one_actual_product) = S ge_signed_half_one_actual_productright))) /\ ((((((x2) = 2 * (sto_cp_one_actual_product) /\ (sto_cn_one_actual_product) = 0) \/ exists ge_signed_half_one_actual_productoutput. (((x2) = 2 * ge_signed_half_one_actual_productoutput + 1 /\ (sto_cp_one_actual_product) = 0) /\ (sto_cn_one_actual_product) = S ge_signed_half_one_actual_productoutput))) /\ ((sto_ap_one_actual_product * sto_bp_one_actual_product + sto_an_one_actual_product * sto_bn_one_actual_product) + sto_cn_one_actual_product = (sto_ap_one_actual_product * sto_bn_one_actual_product + sto_an_one_actual_product * sto_bp_one_actual_product) + sto_cp_one_actual_product)))))))) /\ ((exists sto_ap_one_actual_product sto_an_one_actual_product sto_bp_one_actual_product sto_bn_one_actual_product sto_cp_one_actual_product sto_cn_one_actual_product. (((((a) = 2 * (sto_ap_one_actual_product) /\ (sto_an_one_actual_product) = 0) \/ exists ge_signed_half_one_actual_productleft. (((a) = 2 * ge_signed_half_one_actual_productleft + 1 /\ (sto_ap_one_actual_product) = 0) /\ (sto_an_one_actual_product) = S ge_signed_half_one_actual_productleft))) /\ ((((((b) = 2 * (sto_bp_one_actual_product) /\ (sto_bn_one_actual_product) = 0) \/ exists ge_signed_half_one_actual_productright. (((b) = 2 * ge_signed_half_one_actual_productright + 1 /\ (sto_bp_one_actual_product) = 0) /\ (sto_bn_one_actual_product) = S ge_signed_half_one_actual_productright))) /\ ((((((x2) = 2 * (sto_cp_one_actual_product) /\ (sto_cn_one_actual_product) = 0) \/ exists ge_signed_half_one_actual_productoutput. (((x2) = 2 * ge_signed_half_one_actual_productoutput + 1 /\ (sto_cp_one_actual_product) = 0) /\ (sto_cn_one_actual_product) = S ge_signed_half_one_actual_productoutput))) /\ ((sto_ap_one_actual_product * sto_bp_one_actual_product + sto_an_one_actual_product * sto_bn_one_actual_product) + sto_cn_one_actual_product = (sto_ap_one_actual_product * sto_bn_one_actual_product + sto_an_one_actual_product * sto_bp_one_actual_product) + sto_cp_one_actual_product))))))) -> ((((~((1)=0)) /\ (exists dc_quotient_one_actual_entry dc_left_one_actual_entry dc_right_one_actual_entry. (((1)=(1)*dc_quotient_one_actual_entry) /\ (((exists dst_positive_code_one_actual_entryleft dst_positive_scale_one_actual_entryleft dst_negative_code_one_actual_entryleft dst_negative_scale_one_actual_entryleft dst_positive_one_actual_entryleft dst_negative_one_actual_entryleft. (((F) = (((((dst_positive_code_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft)) * S ((dst_positive_code_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft)) + ((dst_positive_scale_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft))) + (((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) * S ((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) + ((dst_negative_scale_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)))) * S ((((dst_positive_code_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft)) * S ((dst_positive_code_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft)) + ((dst_positive_scale_one_actual_entryleft) + (dst_positive_scale_one_actual_entryleft))) + (((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) * S ((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) + ((dst_negative_scale_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)))) + ((((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) * S ((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) + ((dst_negative_scale_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft))) + (((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) * S ((dst_negative_code_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)) + ((dst_negative_scale_one_actual_entryleft) + (dst_negative_scale_one_actual_entryleft)))))) /\ (((((exists ff_h_pvs_one_actual_entryleftpositive. ff_h_pvs_one_actual_entryleftpositive + S (dst_positive_one_actual_entryleft) = S ((S (1)) * dst_positive_scale_one_actual_entryleft)) /\ exists ff_q_pvs_one_actual_entryleftpositive. dst_positive_code_one_actual_entryleft = ff_q_pvs_one_actual_entryleftpositive * S ((S (1)) * dst_positive_scale_one_actual_entryleft) + (dst_positive_one_actual_entryleft))) /\ (((((exists ff_h_pvs_one_actual_entryleftnegative. ff_h_pvs_one_actual_entryleftnegative + S (dst_negative_one_actual_entryleft) = S ((S (1)) * dst_negative_scale_one_actual_entryleft)) /\ exists ff_q_pvs_one_actual_entryleftnegative. dst_negative_code_one_actual_entryleft = ff_q_pvs_one_actual_entryleftnegative * S ((S (1)) * dst_negative_scale_one_actual_entryleft) + (dst_negative_one_actual_entryleft))) /\ (exists ge_balance_positive_one_actual_entryleftvalue ge_balance_negative_one_actual_entryleftvalue. (((((dc_left_one_actual_entry) = 2 * (ge_balance_positive_one_actual_entryleftvalue) /\ (ge_balance_negative_one_actual_entryleftvalue) = 0) \/ exists ge_signed_half_one_actual_entryleftvaluedecode. (((dc_left_one_actual_entry) = 2 * ge_signed_half_one_actual_entryleftvaluedecode + 1 /\ (ge_balance_positive_one_actual_entryleftvalue) = 0) /\ (ge_balance_negative_one_actual_entryleftvalue) = S ge_signed_half_one_actual_entryleftvaluedecode))) /\ ((dst_positive_one_actual_entryleft) + ge_balance_negative_one_actual_entryleftvalue = (dst_negative_one_actual_entryleft) + ge_balance_positive_one_actual_entryleftvalue))))))))) /\ (((exists dst_positive_code_one_actual_entryright dst_positive_scale_one_actual_entryright dst_negative_code_one_actual_entryright dst_negative_scale_one_actual_entryright dst_positive_one_actual_entryright dst_negative_one_actual_entryright. (((G) = (((((dst_positive_code_one_actual_entryright) + (dst_positive_scale_one_actual_entryright)) * S ((dst_positive_code_one_actual_entryright) + (dst_positive_scale_one_actual_entryright)) + ((dst_positive_scale_one_actual_entryright) + (dst_positive_scale_one_actual_entryright))) + (((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) * S ((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) + ((dst_negative_scale_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)))) * S ((((dst_positive_code_one_actual_entryright) + (dst_positive_scale_one_actual_entryright)) * S ((dst_positive_code_one_actual_entryright) + (dst_positive_scale_one_actual_entryright)) + ((dst_positive_scale_one_actual_entryright) + (dst_positive_scale_one_actual_entryright))) + (((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) * S ((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) + ((dst_negative_scale_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)))) + ((((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) * S ((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) + ((dst_negative_scale_one_actual_entryright) + (dst_negative_scale_one_actual_entryright))) + (((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) * S ((dst_negative_code_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)) + ((dst_negative_scale_one_actual_entryright) + (dst_negative_scale_one_actual_entryright)))))) /\ (((((exists ff_h_pvs_one_actual_entryrightpositive. ff_h_pvs_one_actual_entryrightpositive + S (dst_positive_one_actual_entryright) = S ((S (dc_quotient_one_actual_entry)) * dst_positive_scale_one_actual_entryright)) /\ exists ff_q_pvs_one_actual_entryrightpositive. dst_positive_code_one_actual_entryright = ff_q_pvs_one_actual_entryrightpositive * S ((S (dc_quotient_one_actual_entry)) * dst_positive_scale_one_actual_entryright) + (dst_positive_one_actual_entryright))) /\ (((((exists ff_h_pvs_one_actual_entryrightnegative. ff_h_pvs_one_actual_entryrightnegative + S (dst_negative_one_actual_entryright) = S ((S (dc_quotient_one_actual_entry)) * dst_negative_scale_one_actual_entryright)) /\ exists ff_q_pvs_one_actual_entryrightnegative. dst_negative_code_one_actual_entryright = ff_q_pvs_one_actual_entryrightnegative * S ((S (dc_quotient_one_actual_entry)) * dst_negative_scale_one_actual_entryright) + (dst_negative_one_actual_entryright))) /\ (exists ge_balance_positive_one_actual_entryrightvalue ge_balance_negative_one_actual_entryrightvalue. (((((dc_right_one_actual_entry) = 2 * (ge_balance_positive_one_actual_entryrightvalue) /\ (ge_balance_negative_one_actual_entryrightvalue) = 0) \/ exists ge_signed_half_one_actual_entryrightvaluedecode. (((dc_right_one_actual_entry) = 2 * ge_signed_half_one_actual_entryrightvaluedecode + 1 /\ (ge_balance_positive_one_actual_entryrightvalue) = 0) /\ (ge_balance_negative_one_actual_entryrightvalue) = S ge_signed_half_one_actual_entryrightvaluedecode))) /\ ((dst_positive_one_actual_entryright) + ge_balance_negative_one_actual_entryrightvalue = (dst_negative_one_actual_entryright) + ge_balance_positive_one_actual_entryrightvalue))))))))) /\ (exists sto_ap_one_actual_entryproduct sto_an_one_actual_entryproduct sto_bp_one_actual_entryproduct sto_bn_one_actual_entryproduct sto_cp_one_actual_entryproduct sto_cn_one_actual_entryproduct. (((((dc_left_one_actual_entry) = 2 * (sto_ap_one_actual_entryproduct) /\ (sto_an_one_actual_entryproduct) = 0) \/ exists ge_signed_half_one_actual_entryproductleft. (((dc_left_one_actual_entry) = 2 * ge_signed_half_one_actual_entryproductleft + 1 /\ (sto_ap_one_actual_entryproduct) = 0) /\ (sto_an_one_actual_entryproduct) = S ge_signed_half_one_actual_entryproductleft))) /\ ((((((dc_right_one_actual_entry) = 2 * (sto_bp_one_actual_entryproduct) /\ (sto_bn_one_actual_entryproduct) = 0) \/ exists ge_signed_half_one_actual_entryproductright. (((dc_right_one_actual_entry) = 2 * ge_signed_half_one_actual_entryproductright + 1 /\ (sto_bp_one_actual_entryproduct) = 0) /\ (sto_bn_one_actual_entryproduct) = S ge_signed_half_one_actual_entryproductright))) /\ ((((((x2) = 2 * (sto_cp_one_actual_entryproduct) /\ (sto_cn_one_actual_entryproduct) = 0) \/ exists ge_signed_half_one_actual_entryproductoutput. (((x2) = 2 * ge_signed_half_one_actual_entryproductoutput + 1 /\ (sto_cp_one_actual_entryproduct) = 0) /\ (sto_cn_one_actual_entryproduct) = S ge_signed_half_one_actual_entryproductoutput))) /\ ((sto_ap_one_actual_entryproduct * sto_bp_one_actual_entryproduct + sto_an_one_actual_entryproduct * sto_bn_one_actual_entryproduct) + sto_cn_one_actual_entryproduct = (sto_ap_one_actual_entryproduct * sto_bn_one_actual_entryproduct + sto_an_one_actual_entryproduct * sto_bp_one_actual_entryproduct) + sto_cp_one_actual_entryproduct))))))))))))))) \/ ((((1)=0 \/ ~(exists pvs_factor_one_actual_entrynondivisor. (1) = (1) * pvs_factor_one_actual_entrynondivisor)) /\ ((x2)=0)))))) - 0060
specialize dirichlet_convolution_last_entry_iff (F) - 0061
specialize dirichlet_convolution_last_entry_iff (G) - 0062
specialize dirichlet_convolution_last_entry_iff (1) - 0063
specialize dirichlet_convolution_last_entry_iff (a) - 0064
specialize dirichlet_convolution_last_entry_iff (b) - 0065
specialize dirichlet_convolution_last_entry_iff (x2) - 0066
apply dirichlet_convolution_last_entry_iff - 0067
intro hn - 0068
apply PA1 - 0069
exact hn - 0070
exact ha - 0071
exact hb - 0072
cases he - 0073
have hp : exists sto_ap_one_actual_product sto_an_one_actual_product sto_bp_one_actual_product sto_bn_one_actual_product sto_cp_one_actual_product sto_cn_one_actual_product. (((((a) = 2 * (sto_ap_one_actual_product) /\ (sto_an_one_actual_product) = 0) \/ exists ge_signed_half_one_actual_productleft. (((a) = 2 * ge_signed_half_one_actual_productleft + 1 /\ (sto_ap_one_actual_product) = 0) /\ (sto_an_one_actual_product) = S ge_signed_half_one_actual_productleft))) /\ ((((((b) = 2 * (sto_bp_one_actual_product) /\ (sto_bn_one_actual_product) = 0) \/ exists ge_signed_half_one_actual_productright. (((b) = 2 * ge_signed_half_one_actual_productright + 1 /\ (sto_bp_one_actual_product) = 0) /\ (sto_bn_one_actual_product) = S ge_signed_half_one_actual_productright))) /\ ((((((x2) = 2 * (sto_cp_one_actual_product) /\ (sto_cn_one_actual_product) = 0) \/ exists ge_signed_half_one_actual_productoutput. (((x2) = 2 * ge_signed_half_one_actual_productoutput + 1 /\ (sto_cp_one_actual_product) = 0) /\ (sto_cn_one_actual_product) = S ge_signed_half_one_actual_productoutput))) /\ ((sto_ap_one_actual_product * sto_bp_one_actual_product + sto_an_one_actual_product * sto_bn_one_actual_product) + sto_cn_one_actual_product = (sto_ap_one_actual_product * sto_bn_one_actual_product + sto_an_one_actual_product * sto_bp_one_actual_product) + sto_cp_one_actual_product)))))) - 0074
apply he_left - 0075
specialize dirichlet_convolution_prefix_lookup (F) - 0076
specialize dirichlet_convolution_prefix_lookup (G) - 0077
specialize dirichlet_convolution_prefix_lookup (1) - 0078
specialize dirichlet_convolution_prefix_lookup (1) - 0079
specialize dirichlet_convolution_prefix_lookup (x) - 0080
specialize dirichlet_convolution_prefix_lookup (1) - 0081
specialize dirichlet_convolution_prefix_lookup (x2) - 0082
apply dirichlet_convolution_prefix_lookup - 0083
exact hc_right_witness_left - 0084
specialize le_refl (1) - 0085
apply le_refl - 0086
exact hd_witness_witness_right_left - 0087
rewrite hv at hp - 0088
rewrite hv at hp - 0089
exact hp - 0090
intro hp - 0091
have hm : exists M. (exists dst_positive_code_one_base_table dst_positive_scale_one_base_table dst_negative_code_one_base_table dst_negative_scale_one_base_table. (((M) = (((((dst_positive_code_one_base_table) + (dst_positive_scale_one_base_table)) * S ((dst_positive_code_one_base_table) + (dst_positive_scale_one_base_table)) + ((dst_positive_scale_one_base_table) + (dst_positive_scale_one_base_table))) + (((dst_negative_code_one_base_table) + (dst_negative_scale_one_base_table)) * S ((dst_negative_code_one_base_table) + (dst_negative_scale_one_base_table)) + ((dst_negative_scale_one_base_table) + (dst_negative_scale_one_base_table)))) * S ((((dst_positive_code_one_base_table) + (dst_positive_scale_one_base_table)) * S ((dst_positive_code_one_base_table) + (dst_positive_scale_one_base_table)) + ((dst_positive_scale_one_base_table) + (dst_positive_scale_one_base_table))) + (((dst_negative_code_one_base_table) + (dst_negative_scale_one_base_table)) * S ((dst_negative_code_one_base_table) + (dst_negative_scale_one_base_table)) + ((dst_negative_scale_one_base_table) + (dst_negative_scale_one_base_table)))) + ((((dst_negative_code_one_base_table) + (dst_negative_scale_one_base_table)) * S ((dst_negative_code_one_base_table) + (dst_negative_scale_one_base_table)) + ((dst_negative_scale_one_base_table) + (dst_negative_scale_one_base_table))) + (((dst_negative_code_one_base_table) + (dst_negative_scale_one_base_table)) * S ((dst_negative_code_one_base_table) + (dst_negative_scale_one_base_table)) + ((dst_negative_scale_one_base_table) + (dst_negative_scale_one_base_table)))))) /\ (forall dst_index_one_base_table. (exists pvs_le_gap_one_base_tabledomain. pvs_le_gap_one_base_tabledomain + (dst_index_one_base_table) = (0)) -> exists dst_positive_one_base_table dst_negative_one_base_table dst_value_one_base_table. ((((exists ff_h_pvs_one_base_tableentrypositive. ff_h_pvs_one_base_tableentrypositive + S (dst_positive_one_base_table) = S ((S (dst_index_one_base_table)) * dst_positive_scale_one_base_table)) /\ exists ff_q_pvs_one_base_tableentrypositive. dst_positive_code_one_base_table = ff_q_pvs_one_base_tableentrypositive * S ((S (dst_index_one_base_table)) * dst_positive_scale_one_base_table) + (dst_positive_one_base_table))) /\ (((((exists ff_h_pvs_one_base_tableentrynegative. ff_h_pvs_one_base_tableentrynegative + S (dst_negative_one_base_table) = S ((S (dst_index_one_base_table)) * dst_negative_scale_one_base_table)) /\ exists ff_q_pvs_one_base_tableentrynegative. dst_negative_code_one_base_table = ff_q_pvs_one_base_tableentrynegative * S ((S (dst_index_one_base_table)) * dst_negative_scale_one_base_table) + (dst_negative_one_base_table))) /\ (exists ge_balance_positive_one_base_tableentryvalue ge_balance_negative_one_base_tableentryvalue. (((((dst_value_one_base_table) = 2 * (ge_balance_positive_one_base_tableentryvalue) /\ (ge_balance_negative_one_base_tableentryvalue) = 0) \/ exists ge_signed_half_one_base_tableentryvaluedecode. (((dst_value_one_base_table) = 2 * ge_signed_half_one_base_tableentryvaluedecode + 1 /\ (ge_balance_positive_one_base_tableentryvalue) = 0) /\ (ge_balance_negative_one_base_tableentryvalue) = S ge_signed_half_one_base_tableentryvaluedecode))) /\ ((dst_positive_one_base_table) + ge_balance_negative_one_base_tableentryvalue = (dst_negative_one_base_table) + ge_balance_positive_one_base_tableentryvalue))))))))) /\ (exists dst_positive_code_one_base_entry dst_positive_scale_one_base_entry dst_negative_code_one_base_entry dst_negative_scale_one_base_entry dst_positive_one_base_entry dst_negative_one_base_entry. (((M) = (((((dst_positive_code_one_base_entry) + (dst_positive_scale_one_base_entry)) * S ((dst_positive_code_one_base_entry) + (dst_positive_scale_one_base_entry)) + ((dst_positive_scale_one_base_entry) + (dst_positive_scale_one_base_entry))) + (((dst_negative_code_one_base_entry) + (dst_negative_scale_one_base_entry)) * S ((dst_negative_code_one_base_entry) + (dst_negative_scale_one_base_entry)) + ((dst_negative_scale_one_base_entry) + (dst_negative_scale_one_base_entry)))) * S ((((dst_positive_code_one_base_entry) + (dst_positive_scale_one_base_entry)) * S ((dst_positive_code_one_base_entry) + (dst_positive_scale_one_base_entry)) + ((dst_positive_scale_one_base_entry) + (dst_positive_scale_one_base_entry))) + (((dst_negative_code_one_base_entry) + (dst_negative_scale_one_base_entry)) * S ((dst_negative_code_one_base_entry) + (dst_negative_scale_one_base_entry)) + ((dst_negative_scale_one_base_entry) + (dst_negative_scale_one_base_entry)))) + ((((dst_negative_code_one_base_entry) + (dst_negative_scale_one_base_entry)) * S ((dst_negative_code_one_base_entry) + (dst_negative_scale_one_base_entry)) + ((dst_negative_scale_one_base_entry) + (dst_negative_scale_one_base_entry))) + (((dst_negative_code_one_base_entry) + (dst_negative_scale_one_base_entry)) * S ((dst_negative_code_one_base_entry) + (dst_negative_scale_one_base_entry)) + ((dst_negative_scale_one_base_entry) + (dst_negative_scale_one_base_entry)))))) /\ (((((exists ff_h_pvs_one_base_entrypositive. ff_h_pvs_one_base_entrypositive + S (dst_positive_one_base_entry) = S ((S (0)) * dst_positive_scale_one_base_entry)) /\ exists ff_q_pvs_one_base_entrypositive. dst_positive_code_one_base_entry = ff_q_pvs_one_base_entrypositive * S ((S (0)) * dst_positive_scale_one_base_entry) + (dst_positive_one_base_entry))) /\ (((((exists ff_h_pvs_one_base_entrynegative. ff_h_pvs_one_base_entrynegative + S (dst_negative_one_base_entry) = S ((S (0)) * dst_negative_scale_one_base_entry)) /\ exists ff_q_pvs_one_base_entrynegative. dst_negative_code_one_base_entry = ff_q_pvs_one_base_entrynegative * S ((S (0)) * dst_negative_scale_one_base_entry) + (dst_negative_one_base_entry))) /\ (exists ge_balance_positive_one_base_entryvalue ge_balance_negative_one_base_entryvalue. (((((0) = 2 * (ge_balance_positive_one_base_entryvalue) /\ (ge_balance_negative_one_base_entryvalue) = 0) \/ exists ge_signed_half_one_base_entryvaluedecode. (((0) = 2 * ge_signed_half_one_base_entryvaluedecode + 1 /\ (ge_balance_positive_one_base_entryvalue) = 0) /\ (ge_balance_negative_one_base_entryvalue) = S ge_signed_half_one_base_entryvaluedecode))) /\ ((dst_positive_one_base_entry) + ge_balance_negative_one_base_entryvalue = (dst_negative_one_base_entry) + ge_balance_positive_one_base_entryvalue))))))))) - 0092
specialize arithmetic_signed_table_singleton (0) - 0093
apply arithmetic_signed_table_singleton - 0094
cases hm - 0095
cases hm_witness - 0096
have hprefix : ((exists dst_positive_code_one_base_prefixtable dst_positive_scale_one_base_prefixtable dst_negative_code_one_base_prefixtable dst_negative_scale_one_base_prefixtable. (((x) = (((((dst_positive_code_one_base_prefixtable) + (dst_positive_scale_one_base_prefixtable)) * S ((dst_positive_code_one_base_prefixtable) + (dst_positive_scale_one_base_prefixtable)) + ((dst_positive_scale_one_base_prefixtable) + (dst_positive_scale_one_base_prefixtable))) + (((dst_negative_code_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)) * S ((dst_negative_code_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)) + ((dst_negative_scale_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)))) * S ((((dst_positive_code_one_base_prefixtable) + (dst_positive_scale_one_base_prefixtable)) * S ((dst_positive_code_one_base_prefixtable) + (dst_positive_scale_one_base_prefixtable)) + ((dst_positive_scale_one_base_prefixtable) + (dst_positive_scale_one_base_prefixtable))) + (((dst_negative_code_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)) * S ((dst_negative_code_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)) + ((dst_negative_scale_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)))) + ((((dst_negative_code_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)) * S ((dst_negative_code_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)) + ((dst_negative_scale_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable))) + (((dst_negative_code_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)) * S ((dst_negative_code_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)) + ((dst_negative_scale_one_base_prefixtable) + (dst_negative_scale_one_base_prefixtable)))))) /\ (forall dst_index_one_base_prefixtable. (exists pvs_le_gap_one_base_prefixtabledomain. pvs_le_gap_one_base_prefixtabledomain + (dst_index_one_base_prefixtable) = (0)) -> exists dst_positive_one_base_prefixtable dst_negative_one_base_prefixtable dst_value_one_base_prefixtable. ((((exists ff_h_pvs_one_base_prefixtableentrypositive. ff_h_pvs_one_base_prefixtableentrypositive + S (dst_positive_one_base_prefixtable) = S ((S (dst_index_one_base_prefixtable)) * dst_positive_scale_one_base_prefixtable)) /\ exists ff_q_pvs_one_base_prefixtableentrypositive. dst_positive_code_one_base_prefixtable = ff_q_pvs_one_base_prefixtableentrypositive * S ((S (dst_index_one_base_prefixtable)) * dst_positive_scale_one_base_prefixtable) + (dst_positive_one_base_prefixtable))) /\ (((((exists ff_h_pvs_one_base_prefixtableentrynegative. ff_h_pvs_one_base_prefixtableentrynegative + S (dst_negative_one_base_prefixtable) = S ((S (dst_index_one_base_prefixtable)) * dst_negative_scale_one_base_prefixtable)) /\ exists ff_q_pvs_one_base_prefixtableentrynegative. dst_negative_code_one_base_prefixtable = ff_q_pvs_one_base_prefixtableentrynegative * S ((S (dst_index_one_base_prefixtable)) * dst_negative_scale_one_base_prefixtable) + (dst_negative_one_base_prefixtable))) /\ (exists ge_balance_positive_one_base_prefixtableentryvalue ge_balance_negative_one_base_prefixtableentryvalue. (((((dst_value_one_base_prefixtable) = 2 * (ge_balance_positive_one_base_prefixtableentryvalue) /\ (ge_balance_negative_one_base_prefixtableentryvalue) = 0) \/ exists ge_signed_half_one_base_prefixtableentryvaluedecode. (((dst_value_one_base_prefixtable) = 2 * ge_signed_half_one_base_prefixtableentryvaluedecode + 1 /\ (ge_balance_positive_one_base_prefixtableentryvalue) = 0) /\ (ge_balance_negative_one_base_prefixtableentryvalue) = S ge_signed_half_one_base_prefixtableentryvaluedecode))) /\ ((dst_positive_one_base_prefixtable) + ge_balance_negative_one_base_prefixtableentryvalue = (dst_negative_one_base_prefixtable) + ge_balance_positive_one_base_prefixtableentryvalue))))))))) /\ (forall dc_index_one_base_prefix dc_value_one_base_prefix. (exists pvs_le_gap_one_base_prefixdomain. pvs_le_gap_one_base_prefixdomain + (dc_index_one_base_prefix) = (0)) -> (exists dst_positive_code_one_base_prefixlookup dst_positive_scale_one_base_prefixlookup dst_negative_code_one_base_prefixlookup dst_negative_scale_one_base_prefixlookup dst_positive_one_base_prefixlookup dst_negative_one_base_prefixlookup. (((x) = (((((dst_positive_code_one_base_prefixlookup) + (dst_positive_scale_one_base_prefixlookup)) * S ((dst_positive_code_one_base_prefixlookup) + (dst_positive_scale_one_base_prefixlookup)) + ((dst_positive_scale_one_base_prefixlookup) + (dst_positive_scale_one_base_prefixlookup))) + (((dst_negative_code_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)) * S ((dst_negative_code_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)) + ((dst_negative_scale_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)))) * S ((((dst_positive_code_one_base_prefixlookup) + (dst_positive_scale_one_base_prefixlookup)) * S ((dst_positive_code_one_base_prefixlookup) + (dst_positive_scale_one_base_prefixlookup)) + ((dst_positive_scale_one_base_prefixlookup) + (dst_positive_scale_one_base_prefixlookup))) + (((dst_negative_code_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)) * S ((dst_negative_code_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)) + ((dst_negative_scale_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)))) + ((((dst_negative_code_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)) * S ((dst_negative_code_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)) + ((dst_negative_scale_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup))) + (((dst_negative_code_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)) * S ((dst_negative_code_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)) + ((dst_negative_scale_one_base_prefixlookup) + (dst_negative_scale_one_base_prefixlookup)))))) /\ (((((exists ff_h_pvs_one_base_prefixlookuppositive. ff_h_pvs_one_base_prefixlookuppositive + S (dst_positive_one_base_prefixlookup) = S ((S (dc_index_one_base_prefix)) * dst_positive_scale_one_base_prefixlookup)) /\ exists ff_q_pvs_one_base_prefixlookuppositive. dst_positive_code_one_base_prefixlookup = ff_q_pvs_one_base_prefixlookuppositive * S ((S (dc_index_one_base_prefix)) * dst_positive_scale_one_base_prefixlookup) + (dst_positive_one_base_prefixlookup))) /\ (((((exists ff_h_pvs_one_base_prefixlookupnegative. ff_h_pvs_one_base_prefixlookupnegative + S (dst_negative_one_base_prefixlookup) = S ((S (dc_index_one_base_prefix)) * dst_negative_scale_one_base_prefixlookup)) /\ exists ff_q_pvs_one_base_prefixlookupnegative. dst_negative_code_one_base_prefixlookup = ff_q_pvs_one_base_prefixlookupnegative * S ((S (dc_index_one_base_prefix)) * dst_negative_scale_one_base_prefixlookup) + (dst_negative_one_base_prefixlookup))) /\ (exists ge_balance_positive_one_base_prefixlookupvalue ge_balance_negative_one_base_prefixlookupvalue. (((((dc_value_one_base_prefix) = 2 * (ge_balance_positive_one_base_prefixlookupvalue) /\ (ge_balance_negative_one_base_prefixlookupvalue) = 0) \/ exists ge_signed_half_one_base_prefixlookupvaluedecode. (((dc_value_one_base_prefix) = 2 * ge_signed_half_one_base_prefixlookupvaluedecode + 1 /\ (ge_balance_positive_one_base_prefixlookupvalue) = 0) /\ (ge_balance_negative_one_base_prefixlookupvalue) = S ge_signed_half_one_base_prefixlookupvaluedecode))) /\ ((dst_positive_one_base_prefixlookup) + ge_balance_negative_one_base_prefixlookupvalue = (dst_negative_one_base_prefixlookup) + ge_balance_positive_one_base_prefixlookupvalue))))))))) -> ((((~((dc_index_one_base_prefix)=0)) /\ (exists dc_quotient_one_base_prefixentry dc_left_one_base_prefixentry dc_right_one_base_prefixentry. (((1)=(dc_index_one_base_prefix)*dc_quotient_one_base_prefixentry) /\ (((exists dst_positive_code_one_base_prefixentryleft dst_positive_scale_one_base_prefixentryleft dst_negative_code_one_base_prefixentryleft dst_negative_scale_one_base_prefixentryleft dst_positive_one_base_prefixentryleft dst_negative_one_base_prefixentryleft. (((F) = (((((dst_positive_code_one_base_prefixentryleft) + (dst_positive_scale_one_base_prefixentryleft)) * S ((dst_positive_code_one_base_prefixentryleft) + (dst_positive_scale_one_base_prefixentryleft)) + ((dst_positive_scale_one_base_prefixentryleft) + (dst_positive_scale_one_base_prefixentryleft))) + (((dst_negative_code_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)) * S ((dst_negative_code_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)) + ((dst_negative_scale_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)))) * S ((((dst_positive_code_one_base_prefixentryleft) + (dst_positive_scale_one_base_prefixentryleft)) * S ((dst_positive_code_one_base_prefixentryleft) + (dst_positive_scale_one_base_prefixentryleft)) + ((dst_positive_scale_one_base_prefixentryleft) + (dst_positive_scale_one_base_prefixentryleft))) + (((dst_negative_code_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)) * S ((dst_negative_code_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)) + ((dst_negative_scale_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)))) + ((((dst_negative_code_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)) * S ((dst_negative_code_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)) + ((dst_negative_scale_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft))) + (((dst_negative_code_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)) * S ((dst_negative_code_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)) + ((dst_negative_scale_one_base_prefixentryleft) + (dst_negative_scale_one_base_prefixentryleft)))))) /\ (((((exists ff_h_pvs_one_base_prefixentryleftpositive. ff_h_pvs_one_base_prefixentryleftpositive + S (dst_positive_one_base_prefixentryleft) = S ((S (dc_index_one_base_prefix)) * dst_positive_scale_one_base_prefixentryleft)) /\ exists ff_q_pvs_one_base_prefixentryleftpositive. dst_positive_code_one_base_prefixentryleft = ff_q_pvs_one_base_prefixentryleftpositive * S ((S (dc_index_one_base_prefix)) * dst_positive_scale_one_base_prefixentryleft) + (dst_positive_one_base_prefixentryleft))) /\ (((((exists ff_h_pvs_one_base_prefixentryleftnegative. ff_h_pvs_one_base_prefixentryleftnegative + S (dst_negative_one_base_prefixentryleft) = S ((S (dc_index_one_base_prefix)) * dst_negative_scale_one_base_prefixentryleft)) /\ exists ff_q_pvs_one_base_prefixentryleftnegative. dst_negative_code_one_base_prefixentryleft = ff_q_pvs_one_base_prefixentryleftnegative * S ((S (dc_index_one_base_prefix)) * dst_negative_scale_one_base_prefixentryleft) + (dst_negative_one_base_prefixentryleft))) /\ (exists ge_balance_positive_one_base_prefixentryleftvalue ge_balance_negative_one_base_prefixentryleftvalue. (((((dc_left_one_base_prefixentry) = 2 * (ge_balance_positive_one_base_prefixentryleftvalue) /\ (ge_balance_negative_one_base_prefixentryleftvalue) = 0) \/ exists ge_signed_half_one_base_prefixentryleftvaluedecode. (((dc_left_one_base_prefixentry) = 2 * ge_signed_half_one_base_prefixentryleftvaluedecode + 1 /\ (ge_balance_positive_one_base_prefixentryleftvalue) = 0) /\ (ge_balance_negative_one_base_prefixentryleftvalue) = S ge_signed_half_one_base_prefixentryleftvaluedecode))) /\ ((dst_positive_one_base_prefixentryleft) + ge_balance_negative_one_base_prefixentryleftvalue = (dst_negative_one_base_prefixentryleft) + ge_balance_positive_one_base_prefixentryleftvalue))))))))) /\ (((exists dst_positive_code_one_base_prefixentryright dst_positive_scale_one_base_prefixentryright dst_negative_code_one_base_prefixentryright dst_negative_scale_one_base_prefixentryright dst_positive_one_base_prefixentryright dst_negative_one_base_prefixentryright. (((G) = (((((dst_positive_code_one_base_prefixentryright) + (dst_positive_scale_one_base_prefixentryright)) * S ((dst_positive_code_one_base_prefixentryright) + (dst_positive_scale_one_base_prefixentryright)) + ((dst_positive_scale_one_base_prefixentryright) + (dst_positive_scale_one_base_prefixentryright))) + (((dst_negative_code_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)) * S ((dst_negative_code_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)) + ((dst_negative_scale_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)))) * S ((((dst_positive_code_one_base_prefixentryright) + (dst_positive_scale_one_base_prefixentryright)) * S ((dst_positive_code_one_base_prefixentryright) + (dst_positive_scale_one_base_prefixentryright)) + ((dst_positive_scale_one_base_prefixentryright) + (dst_positive_scale_one_base_prefixentryright))) + (((dst_negative_code_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)) * S ((dst_negative_code_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)) + ((dst_negative_scale_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)))) + ((((dst_negative_code_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)) * S ((dst_negative_code_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)) + ((dst_negative_scale_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright))) + (((dst_negative_code_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)) * S ((dst_negative_code_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)) + ((dst_negative_scale_one_base_prefixentryright) + (dst_negative_scale_one_base_prefixentryright)))))) /\ (((((exists ff_h_pvs_one_base_prefixentryrightpositive. ff_h_pvs_one_base_prefixentryrightpositive + S (dst_positive_one_base_prefixentryright) = S ((S (dc_quotient_one_base_prefixentry)) * dst_positive_scale_one_base_prefixentryright)) /\ exists ff_q_pvs_one_base_prefixentryrightpositive. dst_positive_code_one_base_prefixentryright = ff_q_pvs_one_base_prefixentryrightpositive * S ((S (dc_quotient_one_base_prefixentry)) * dst_positive_scale_one_base_prefixentryright) + (dst_positive_one_base_prefixentryright))) /\ (((((exists ff_h_pvs_one_base_prefixentryrightnegative. ff_h_pvs_one_base_prefixentryrightnegative + S (dst_negative_one_base_prefixentryright) = S ((S (dc_quotient_one_base_prefixentry)) * dst_negative_scale_one_base_prefixentryright)) /\ exists ff_q_pvs_one_base_prefixentryrightnegative. dst_negative_code_one_base_prefixentryright = ff_q_pvs_one_base_prefixentryrightnegative * S ((S (dc_quotient_one_base_prefixentry)) * dst_negative_scale_one_base_prefixentryright) + (dst_negative_one_base_prefixentryright))) /\ (exists ge_balance_positive_one_base_prefixentryrightvalue ge_balance_negative_one_base_prefixentryrightvalue. (((((dc_right_one_base_prefixentry) = 2 * (ge_balance_positive_one_base_prefixentryrightvalue) /\ (ge_balance_negative_one_base_prefixentryrightvalue) = 0) \/ exists ge_signed_half_one_base_prefixentryrightvaluedecode. (((dc_right_one_base_prefixentry) = 2 * ge_signed_half_one_base_prefixentryrightvaluedecode + 1 /\ (ge_balance_positive_one_base_prefixentryrightvalue) = 0) /\ (ge_balance_negative_one_base_prefixentryrightvalue) = S ge_signed_half_one_base_prefixentryrightvaluedecode))) /\ ((dst_positive_one_base_prefixentryright) + ge_balance_negative_one_base_prefixentryrightvalue = (dst_negative_one_base_prefixentryright) + ge_balance_positive_one_base_prefixentryrightvalue))))))))) /\ (exists sto_ap_one_base_prefixentryproduct sto_an_one_base_prefixentryproduct sto_bp_one_base_prefixentryproduct sto_bn_one_base_prefixentryproduct sto_cp_one_base_prefixentryproduct sto_cn_one_base_prefixentryproduct. (((((dc_left_one_base_prefixentry) = 2 * (sto_ap_one_base_prefixentryproduct) /\ (sto_an_one_base_prefixentryproduct) = 0) \/ exists ge_signed_half_one_base_prefixentryproductleft. (((dc_left_one_base_prefixentry) = 2 * ge_signed_half_one_base_prefixentryproductleft + 1 /\ (sto_ap_one_base_prefixentryproduct) = 0) /\ (sto_an_one_base_prefixentryproduct) = S ge_signed_half_one_base_prefixentryproductleft))) /\ ((((((dc_right_one_base_prefixentry) = 2 * (sto_bp_one_base_prefixentryproduct) /\ (sto_bn_one_base_prefixentryproduct) = 0) \/ exists ge_signed_half_one_base_prefixentryproductright. (((dc_right_one_base_prefixentry) = 2 * ge_signed_half_one_base_prefixentryproductright + 1 /\ (sto_bp_one_base_prefixentryproduct) = 0) /\ (sto_bn_one_base_prefixentryproduct) = S ge_signed_half_one_base_prefixentryproductright))) /\ ((((((dc_value_one_base_prefix) = 2 * (sto_cp_one_base_prefixentryproduct) /\ (sto_cn_one_base_prefixentryproduct) = 0) \/ exists ge_signed_half_one_base_prefixentryproductoutput. (((dc_value_one_base_prefix) = 2 * ge_signed_half_one_base_prefixentryproductoutput + 1 /\ (sto_cp_one_base_prefixentryproduct) = 0) /\ (sto_cn_one_base_prefixentryproduct) = S ge_signed_half_one_base_prefixentryproductoutput))) /\ ((sto_ap_one_base_prefixentryproduct * sto_bp_one_base_prefixentryproduct + sto_an_one_base_prefixentryproduct * sto_bn_one_base_prefixentryproduct) + sto_cn_one_base_prefixentryproduct = (sto_ap_one_base_prefixentryproduct * sto_bn_one_base_prefixentryproduct + sto_an_one_base_prefixentryproduct * sto_bp_one_base_prefixentryproduct) + sto_cp_one_base_prefixentryproduct))))))))))))))) \/ ((((dc_index_one_base_prefix)=0 \/ ~(exists pvs_factor_one_base_prefixentrynondivisor. (1) = (dc_index_one_base_prefix) * pvs_factor_one_base_prefixentrynondivisor)) /\ ((dc_value_one_base_prefix)=0)))))) - 0097
specialize dirichlet_convolution_prefix_zero_constructor (F) - 0098
specialize dirichlet_convolution_prefix_zero_constructor (G) - 0099
specialize dirichlet_convolution_prefix_zero_constructor (1) - 0100
specialize dirichlet_convolution_prefix_zero_constructor (x) - 0101
apply dirichlet_convolution_prefix_zero_constructor - 0102
exact hm_witness_left - 0103
exact hm_witness_right - 0104
specialize dirichlet_convolution_prefix_last_step (F) - 0105
specialize dirichlet_convolution_prefix_last_step (G) - 0106
specialize dirichlet_convolution_prefix_last_step (0) - 0107
specialize dirichlet_convolution_prefix_last_step (x) - 0108
specialize dirichlet_convolution_prefix_last_step (0) - 0109
specialize dirichlet_convolution_prefix_last_step (a) - 0110
specialize dirichlet_convolution_prefix_last_step (b) - 0111
specialize dirichlet_convolution_prefix_last_step (z) - 0112
specialize dirichlet_convolution_prefix_last_step (z) - 0113
apply dirichlet_convolution_prefix_last_step - 0114
exact hprefix - 0115
specialize dirichlet_convolution_zero_prefix_sum (F) - 0116
specialize dirichlet_convolution_zero_prefix_sum (G) - 0117
specialize dirichlet_convolution_zero_prefix_sum (1) - 0118
specialize dirichlet_convolution_zero_prefix_sum (x) - 0119
apply dirichlet_convolution_zero_prefix_sum - 0120
exact hprefix - 0121
exact ha - 0122
exact hb - 0123
exact hp - 0124
specialize signed_add_zero_left (z) - 0125
apply signed_add_zero_left