Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
A genuine divisor mask has S n entries, indexed zero through n, and forces its zeroth entry to zero regardless of F(0). Möbius values remain positive-domain only. This family constructs divisor sums and Möbius tables; cancellation and the full G007 endpoint are separately proved later in the same release.
Exact theorem in conservative defined notation
∀ F. ∀ n. ∀ l. ∀ k. ∀ M. DivisorMask(F,n,l,M) → Le(k,l) → DivisorMask(F,n,k,M)
Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Original expanded first-order statement
forall F n l k M. (((exists dst_positive_code_restrict_masktable dst_positive_scale_restrict_masktable dst_negative_code_restrict_masktable dst_negative_scale_restrict_masktable. (((M) = (((((dst_positive_code_restrict_masktable) + (dst_positive_scale_restrict_masktable)) * S ((dst_positive_code_restrict_masktable) + (dst_positive_scale_restrict_masktable)) + ((dst_positive_scale_restrict_masktable) + (dst_positive_scale_restrict_masktable))) + (((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) * S ((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) + ((dst_negative_scale_restrict_masktable) + (dst_negative_scale_restrict_masktable)))) * S ((((dst_positive_code_restrict_masktable) + (dst_positive_scale_restrict_masktable)) * S ((dst_positive_code_restrict_masktable) + (dst_positive_scale_restrict_masktable)) + ((dst_positive_scale_restrict_masktable) + (dst_positive_scale_restrict_masktable))) + (((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) * S ((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) + ((dst_negative_scale_restrict_masktable) + (dst_negative_scale_restrict_masktable)))) + ((((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) * S ((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) + ((dst_negative_scale_restrict_masktable) + (dst_negative_scale_restrict_masktable))) + (((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) * S ((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) + ((dst_negative_scale_restrict_masktable) + (dst_negative_scale_restrict_masktable)))))) /\ (forall dst_index_restrict_masktable. (exists pvs_le_gap_restrict_masktabledomain. pvs_le_gap_restrict_masktabledomain + (dst_index_restrict_masktable) = (l)) -> exists dst_positive_restrict_masktable dst_negative_restrict_masktable dst_value_restrict_masktable. ((((exists ff_h_pvs_restrict_masktableentrypositive. ff_h_pvs_restrict_masktableentrypositive + S (dst_positive_restrict_masktable) = S ((S (dst_index_restrict_masktable)) * dst_positive_scale_restrict_masktable)) /\ exists ff_q_pvs_restrict_masktableentrypositive. dst_positive_code_restrict_masktable = ff_q_pvs_restrict_masktableentrypositive * S ((S (dst_index_restrict_masktable)) * dst_positive_scale_restrict_masktable) + (dst_positive_restrict_masktable))) /\ (((((exists ff_h_pvs_restrict_masktableentrynegative. ff_h_pvs_restrict_masktableentrynegative + S (dst_negative_restrict_masktable) = S ((S (dst_index_restrict_masktable)) * dst_negative_scale_restrict_masktable)) /\ exists ff_q_pvs_restrict_masktableentrynegative. dst_negative_code_restrict_masktable = ff_q_pvs_restrict_masktableentrynegative * S ((S (dst_index_restrict_masktable)) * dst_negative_scale_restrict_masktable) + (dst_negative_restrict_masktable))) /\ (exists ge_balance_positive_restrict_masktableentryvalue ge_balance_negative_restrict_masktableentryvalue. (((((dst_value_restrict_masktable) = 2 * (ge_balance_positive_restrict_masktableentryvalue) /\ (ge_balance_negative_restrict_masktableentryvalue) = 0) \/ exists ge_signed_half_restrict_masktableentryvaluedecode. (((dst_value_restrict_masktable) = 2 * ge_signed_half_restrict_masktableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_masktableentryvalue) = 0) /\ (ge_balance_negative_restrict_masktableentryvalue) = S ge_signed_half_restrict_masktableentryvaluedecode))) /\ ((dst_positive_restrict_masktable) + ge_balance_negative_restrict_masktableentryvalue = (dst_negative_restrict_masktable) + ge_balance_positive_restrict_masktableentryvalue))))))))) /\ (forall dm_index_restrict_mask dm_value_restrict_mask. (exists pvs_le_gap_restrict_maskdomain. pvs_le_gap_restrict_maskdomain + (dm_index_restrict_mask) = (l)) -> (exists dst_positive_code_restrict_masklookup dst_positive_scale_restrict_masklookup dst_negative_code_restrict_masklookup dst_negative_scale_restrict_masklookup dst_positive_restrict_masklookup dst_negative_restrict_masklookup. (((M) = (((((dst_positive_code_restrict_masklookup) + (dst_positive_scale_restrict_masklookup)) * S ((dst_positive_code_restrict_masklookup) + (dst_positive_scale_restrict_masklookup)) + ((dst_positive_scale_restrict_masklookup) + (dst_positive_scale_restrict_masklookup))) + (((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) * S ((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) + ((dst_negative_scale_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)))) * S ((((dst_positive_code_restrict_masklookup) + (dst_positive_scale_restrict_masklookup)) * S ((dst_positive_code_restrict_masklookup) + (dst_positive_scale_restrict_masklookup)) + ((dst_positive_scale_restrict_masklookup) + (dst_positive_scale_restrict_masklookup))) + (((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) * S ((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) + ((dst_negative_scale_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)))) + ((((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) * S ((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) + ((dst_negative_scale_restrict_masklookup) + (dst_negative_scale_restrict_masklookup))) + (((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) * S ((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) + ((dst_negative_scale_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)))))) /\ (((((exists ff_h_pvs_restrict_masklookuppositive. ff_h_pvs_restrict_masklookuppositive + S (dst_positive_restrict_masklookup) = S ((S (dm_index_restrict_mask)) * dst_positive_scale_restrict_masklookup)) /\ exists ff_q_pvs_restrict_masklookuppositive. dst_positive_code_restrict_masklookup = ff_q_pvs_restrict_masklookuppositive * S ((S (dm_index_restrict_mask)) * dst_positive_scale_restrict_masklookup) + (dst_positive_restrict_masklookup))) /\ (((((exists ff_h_pvs_restrict_masklookupnegative. ff_h_pvs_restrict_masklookupnegative + S (dst_negative_restrict_masklookup) = S ((S (dm_index_restrict_mask)) * dst_negative_scale_restrict_masklookup)) /\ exists ff_q_pvs_restrict_masklookupnegative. dst_negative_code_restrict_masklookup = ff_q_pvs_restrict_masklookupnegative * S ((S (dm_index_restrict_mask)) * dst_negative_scale_restrict_masklookup) + (dst_negative_restrict_masklookup))) /\ (exists ge_balance_positive_restrict_masklookupvalue ge_balance_negative_restrict_masklookupvalue. (((((dm_value_restrict_mask) = 2 * (ge_balance_positive_restrict_masklookupvalue) /\ (ge_balance_negative_restrict_masklookupvalue) = 0) \/ exists ge_signed_half_restrict_masklookupvaluedecode. (((dm_value_restrict_mask) = 2 * ge_signed_half_restrict_masklookupvaluedecode + 1 /\ (ge_balance_positive_restrict_masklookupvalue) = 0) /\ (ge_balance_negative_restrict_masklookupvalue) = S ge_signed_half_restrict_masklookupvaluedecode))) /\ ((dst_positive_restrict_masklookup) + ge_balance_negative_restrict_masklookupvalue = (dst_negative_restrict_masklookup) + ge_balance_positive_restrict_masklookupvalue))))))))) -> ((((~((dm_index_restrict_mask)=0)) /\ (exists dm_quotient_restrict_maskentry. (((n)=(dm_index_restrict_mask)*dm_quotient_restrict_maskentry) /\ (exists dst_positive_code_restrict_maskentryinput dst_positive_scale_restrict_maskentryinput dst_negative_code_restrict_maskentryinput dst_negative_scale_restrict_maskentryinput dst_positive_restrict_maskentryinput dst_negative_restrict_maskentryinput. (((F) = (((((dst_positive_code_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput)) * S ((dst_positive_code_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput)) + ((dst_positive_scale_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput))) + (((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) * S ((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) + ((dst_negative_scale_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)))) * S ((((dst_positive_code_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput)) * S ((dst_positive_code_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput)) + ((dst_positive_scale_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput))) + (((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) * S ((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) + ((dst_negative_scale_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)))) + ((((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) * S ((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) + ((dst_negative_scale_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput))) + (((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) * S ((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) + ((dst_negative_scale_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)))))) /\ (((((exists ff_h_pvs_restrict_maskentryinputpositive. ff_h_pvs_restrict_maskentryinputpositive + S (dst_positive_restrict_maskentryinput) = S ((S (dm_index_restrict_mask)) * dst_positive_scale_restrict_maskentryinput)) /\ exists ff_q_pvs_restrict_maskentryinputpositive. dst_positive_code_restrict_maskentryinput = ff_q_pvs_restrict_maskentryinputpositive * S ((S (dm_index_restrict_mask)) * dst_positive_scale_restrict_maskentryinput) + (dst_positive_restrict_maskentryinput))) /\ (((((exists ff_h_pvs_restrict_maskentryinputnegative. ff_h_pvs_restrict_maskentryinputnegative + S (dst_negative_restrict_maskentryinput) = S ((S (dm_index_restrict_mask)) * dst_negative_scale_restrict_maskentryinput)) /\ exists ff_q_pvs_restrict_maskentryinputnegative. dst_negative_code_restrict_maskentryinput = ff_q_pvs_restrict_maskentryinputnegative * S ((S (dm_index_restrict_mask)) * dst_negative_scale_restrict_maskentryinput) + (dst_negative_restrict_maskentryinput))) /\ (exists ge_balance_positive_restrict_maskentryinputvalue ge_balance_negative_restrict_maskentryinputvalue. (((((dm_value_restrict_mask) = 2 * (ge_balance_positive_restrict_maskentryinputvalue) /\ (ge_balance_negative_restrict_maskentryinputvalue) = 0) \/ exists ge_signed_half_restrict_maskentryinputvaluedecode. (((dm_value_restrict_mask) = 2 * ge_signed_half_restrict_maskentryinputvaluedecode + 1 /\ (ge_balance_positive_restrict_maskentryinputvalue) = 0) /\ (ge_balance_negative_restrict_maskentryinputvalue) = S ge_signed_half_restrict_maskentryinputvaluedecode))) /\ ((dst_positive_restrict_maskentryinput) + ge_balance_negative_restrict_maskentryinputvalue = (dst_negative_restrict_maskentryinput) + ge_balance_positive_restrict_maskentryinputvalue))))))))))))) \/ ((((dm_index_restrict_mask)=0 \/ ~(exists pvs_factor_restrict_maskentrynondivisor. (n) = (dm_index_restrict_mask) * pvs_factor_restrict_maskentrynondivisor)) /\ ((dm_value_restrict_mask)=0))))))) -> (exists pvs_le_gap_restrict_bound. pvs_le_gap_restrict_bound + (k) = (l)) -> (((exists dst_positive_code_restrict_resulttable dst_positive_scale_restrict_resulttable dst_negative_code_restrict_resulttable dst_negative_scale_restrict_resulttable. (((M) = (((((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) * S ((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) + ((dst_positive_scale_restrict_resulttable) + (dst_positive_scale_restrict_resulttable))) + (((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)))) * S ((((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) * S ((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) + ((dst_positive_scale_restrict_resulttable) + (dst_positive_scale_restrict_resulttable))) + (((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)))) + ((((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable))) + (((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)))))) /\ (forall dst_index_restrict_resulttable. (exists pvs_le_gap_restrict_resulttabledomain. pvs_le_gap_restrict_resulttabledomain + (dst_index_restrict_resulttable) = (k)) -> exists dst_positive_restrict_resulttable dst_negative_restrict_resulttable dst_value_restrict_resulttable. ((((exists ff_h_pvs_restrict_resulttableentrypositive. ff_h_pvs_restrict_resulttableentrypositive + S (dst_positive_restrict_resulttable) = S ((S (dst_index_restrict_resulttable)) * dst_positive_scale_restrict_resulttable)) /\ exists ff_q_pvs_restrict_resulttableentrypositive. dst_positive_code_restrict_resulttable = ff_q_pvs_restrict_resulttableentrypositive * S ((S (dst_index_restrict_resulttable)) * dst_positive_scale_restrict_resulttable) + (dst_positive_restrict_resulttable))) /\ (((((exists ff_h_pvs_restrict_resulttableentrynegative. ff_h_pvs_restrict_resulttableentrynegative + S (dst_negative_restrict_resulttable) = S ((S (dst_index_restrict_resulttable)) * dst_negative_scale_restrict_resulttable)) /\ exists ff_q_pvs_restrict_resulttableentrynegative. dst_negative_code_restrict_resulttable = ff_q_pvs_restrict_resulttableentrynegative * S ((S (dst_index_restrict_resulttable)) * dst_negative_scale_restrict_resulttable) + (dst_negative_restrict_resulttable))) /\ (exists ge_balance_positive_restrict_resulttableentryvalue ge_balance_negative_restrict_resulttableentryvalue. (((((dst_value_restrict_resulttable) = 2 * (ge_balance_positive_restrict_resulttableentryvalue) /\ (ge_balance_negative_restrict_resulttableentryvalue) = 0) \/ exists ge_signed_half_restrict_resulttableentryvaluedecode. (((dst_value_restrict_resulttable) = 2 * ge_signed_half_restrict_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_resulttableentryvalue) = 0) /\ (ge_balance_negative_restrict_resulttableentryvalue) = S ge_signed_half_restrict_resulttableentryvaluedecode))) /\ ((dst_positive_restrict_resulttable) + ge_balance_negative_restrict_resulttableentryvalue = (dst_negative_restrict_resulttable) + ge_balance_positive_restrict_resulttableentryvalue))))))))) /\ (forall dm_index_restrict_result dm_value_restrict_result. (exists pvs_le_gap_restrict_resultdomain. pvs_le_gap_restrict_resultdomain + (dm_index_restrict_result) = (k)) -> (exists dst_positive_code_restrict_resultlookup dst_positive_scale_restrict_resultlookup dst_negative_code_restrict_resultlookup dst_negative_scale_restrict_resultlookup dst_positive_restrict_resultlookup dst_negative_restrict_resultlookup. (((M) = (((((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) * S ((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) + ((dst_positive_scale_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup))) + (((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)))) * S ((((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) * S ((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) + ((dst_positive_scale_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup))) + (((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)))) + ((((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup))) + (((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)))))) /\ (((((exists ff_h_pvs_restrict_resultlookuppositive. ff_h_pvs_restrict_resultlookuppositive + S (dst_positive_restrict_resultlookup) = S ((S (dm_index_restrict_result)) * dst_positive_scale_restrict_resultlookup)) /\ exists ff_q_pvs_restrict_resultlookuppositive. dst_positive_code_restrict_resultlookup = ff_q_pvs_restrict_resultlookuppositive * S ((S (dm_index_restrict_result)) * dst_positive_scale_restrict_resultlookup) + (dst_positive_restrict_resultlookup))) /\ (((((exists ff_h_pvs_restrict_resultlookupnegative. ff_h_pvs_restrict_resultlookupnegative + S (dst_negative_restrict_resultlookup) = S ((S (dm_index_restrict_result)) * dst_negative_scale_restrict_resultlookup)) /\ exists ff_q_pvs_restrict_resultlookupnegative. dst_negative_code_restrict_resultlookup = ff_q_pvs_restrict_resultlookupnegative * S ((S (dm_index_restrict_result)) * dst_negative_scale_restrict_resultlookup) + (dst_negative_restrict_resultlookup))) /\ (exists ge_balance_positive_restrict_resultlookupvalue ge_balance_negative_restrict_resultlookupvalue. (((((dm_value_restrict_result) = 2 * (ge_balance_positive_restrict_resultlookupvalue) /\ (ge_balance_negative_restrict_resultlookupvalue) = 0) \/ exists ge_signed_half_restrict_resultlookupvaluedecode. (((dm_value_restrict_result) = 2 * ge_signed_half_restrict_resultlookupvaluedecode + 1 /\ (ge_balance_positive_restrict_resultlookupvalue) = 0) /\ (ge_balance_negative_restrict_resultlookupvalue) = S ge_signed_half_restrict_resultlookupvaluedecode))) /\ ((dst_positive_restrict_resultlookup) + ge_balance_negative_restrict_resultlookupvalue = (dst_negative_restrict_resultlookup) + ge_balance_positive_restrict_resultlookupvalue))))))))) -> ((((~((dm_index_restrict_result)=0)) /\ (exists dm_quotient_restrict_resultentry. (((n)=(dm_index_restrict_result)*dm_quotient_restrict_resultentry) /\ (exists dst_positive_code_restrict_resultentryinput dst_positive_scale_restrict_resultentryinput dst_negative_code_restrict_resultentryinput dst_negative_scale_restrict_resultentryinput dst_positive_restrict_resultentryinput dst_negative_restrict_resultentryinput. (((F) = (((((dst_positive_code_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput)) * S ((dst_positive_code_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput)) + ((dst_positive_scale_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput))) + (((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) * S ((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) + ((dst_negative_scale_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)))) * S ((((dst_positive_code_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput)) * S ((dst_positive_code_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput)) + ((dst_positive_scale_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput))) + (((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) * S ((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) + ((dst_negative_scale_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)))) + ((((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) * S ((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) + ((dst_negative_scale_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput))) + (((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) * S ((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) + ((dst_negative_scale_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)))))) /\ (((((exists ff_h_pvs_restrict_resultentryinputpositive. ff_h_pvs_restrict_resultentryinputpositive + S (dst_positive_restrict_resultentryinput) = S ((S (dm_index_restrict_result)) * dst_positive_scale_restrict_resultentryinput)) /\ exists ff_q_pvs_restrict_resultentryinputpositive. dst_positive_code_restrict_resultentryinput = ff_q_pvs_restrict_resultentryinputpositive * S ((S (dm_index_restrict_result)) * dst_positive_scale_restrict_resultentryinput) + (dst_positive_restrict_resultentryinput))) /\ (((((exists ff_h_pvs_restrict_resultentryinputnegative. ff_h_pvs_restrict_resultentryinputnegative + S (dst_negative_restrict_resultentryinput) = S ((S (dm_index_restrict_result)) * dst_negative_scale_restrict_resultentryinput)) /\ exists ff_q_pvs_restrict_resultentryinputnegative. dst_negative_code_restrict_resultentryinput = ff_q_pvs_restrict_resultentryinputnegative * S ((S (dm_index_restrict_result)) * dst_negative_scale_restrict_resultentryinput) + (dst_negative_restrict_resultentryinput))) /\ (exists ge_balance_positive_restrict_resultentryinputvalue ge_balance_negative_restrict_resultentryinputvalue. (((((dm_value_restrict_result) = 2 * (ge_balance_positive_restrict_resultentryinputvalue) /\ (ge_balance_negative_restrict_resultentryinputvalue) = 0) \/ exists ge_signed_half_restrict_resultentryinputvaluedecode. (((dm_value_restrict_result) = 2 * ge_signed_half_restrict_resultentryinputvaluedecode + 1 /\ (ge_balance_positive_restrict_resultentryinputvalue) = 0) /\ (ge_balance_negative_restrict_resultentryinputvalue) = S ge_signed_half_restrict_resultentryinputvaluedecode))) /\ ((dst_positive_restrict_resultentryinput) + ge_balance_negative_restrict_resultentryinputvalue = (dst_negative_restrict_resultentryinput) + ge_balance_positive_restrict_resultentryinputvalue))))))))))))) \/ ((((dm_index_restrict_result)=0 \/ ~(exists pvs_factor_restrict_resultentrynondivisor. (n) = (dm_index_restrict_result) * pvs_factor_restrict_resultentrynondivisor)) /\ ((dm_value_restrict_result)=0)))))))Complete tactic proof in conservative notation
All 29 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay script.
Read the argument
Proof checkpoints
29 script commands · 5 reading checkpoints · 0 local claims
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.
01Fix variables and assumptionsL1–7
02Separate the logical casesL8–9
03Use earlier factsL10–15
04Fix variables and assumptionsL16–19
05Use earlier factsL20–29
Original defined command ledger · 29 lines
- 0001
intro F - 0002
intro n - 0003
intro l - 0004
intro k - 0005
intro M - 0006
intro hm - 0007
intro hkl - 0008
cases hm - 0009
split - 0010
specialize divisor_signed_table_restrict (l) - 0011
specialize divisor_signed_table_restrict (k) - 0012
specialize divisor_signed_table_restrict (M) - 0013
apply divisor_signed_table_restrict - 0014
exact hm_left - 0015
exact hkl - 0016
intro d - 0017
intro z - 0018
intro hd - 0019
intro hz - 0020
specialize hm_right (d) - 0021
specialize hm_right (z) - 0022
apply hm_right - 0023
specialize le_trans (d) - 0024
specialize le_trans (k) - 0025
specialize le_trans (l) - 0026
apply le_trans - 0027
exact hd - 0028
exact hkl - 0029
exact hz