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 n. ((((~((0)=0)) /\ (exists dm_quotient_zero_entry. (((n)=(0)*dm_quotient_zero_entry) /\ (exists dst_positive_code_zero_entryinput dst_positive_scale_zero_entryinput dst_negative_code_zero_entryinput dst_negative_scale_zero_entryinput dst_positive_zero_entryinput dst_negative_zero_entryinput. (((F) = (((((dst_positive_code_zero_entryinput) + (dst_positive_scale_zero_entryinput)) * S ((dst_positive_code_zero_entryinput) + (dst_positive_scale_zero_entryinput)) + ((dst_positive_scale_zero_entryinput) + (dst_positive_scale_zero_entryinput))) + (((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) * S ((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) + ((dst_negative_scale_zero_entryinput) + (dst_negative_scale_zero_entryinput)))) * S ((((dst_positive_code_zero_entryinput) + (dst_positive_scale_zero_entryinput)) * S ((dst_positive_code_zero_entryinput) + (dst_positive_scale_zero_entryinput)) + ((dst_positive_scale_zero_entryinput) + (dst_positive_scale_zero_entryinput))) + (((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) * S ((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) + ((dst_negative_scale_zero_entryinput) + (dst_negative_scale_zero_entryinput)))) + ((((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) * S ((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) + ((dst_negative_scale_zero_entryinput) + (dst_negative_scale_zero_entryinput))) + (((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) * S ((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) + ((dst_negative_scale_zero_entryinput) + (dst_negative_scale_zero_entryinput)))))) /\ (((((exists ff_h_pvs_zero_entryinputpositive. ff_h_pvs_zero_entryinputpositive + S (dst_positive_zero_entryinput) = S ((S (0)) * dst_positive_scale_zero_entryinput)) /\ exists ff_q_pvs_zero_entryinputpositive. dst_positive_code_zero_entryinput = ff_q_pvs_zero_entryinputpositive * S ((S (0)) * dst_positive_scale_zero_entryinput) + (dst_positive_zero_entryinput))) /\ (((((exists ff_h_pvs_zero_entryinputnegative. ff_h_pvs_zero_entryinputnegative + S (dst_negative_zero_entryinput) = S ((S (0)) * dst_negative_scale_zero_entryinput)) /\ exists ff_q_pvs_zero_entryinputnegative. dst_negative_code_zero_entryinput = ff_q_pvs_zero_entryinputnegative * S ((S (0)) * dst_negative_scale_zero_entryinput) + (dst_negative_zero_entryinput))) /\ (exists ge_balance_positive_zero_entryinputvalue ge_balance_negative_zero_entryinputvalue. (((((0) = 2 * (ge_balance_positive_zero_entryinputvalue) /\ (ge_balance_negative_zero_entryinputvalue) = 0) \/ exists ge_signed_half_zero_entryinputvaluedecode. (((0) = 2 * ge_signed_half_zero_entryinputvaluedecode + 1 /\ (ge_balance_positive_zero_entryinputvalue) = 0) /\ (ge_balance_negative_zero_entryinputvalue) = S ge_signed_half_zero_entryinputvaluedecode))) /\ ((dst_positive_zero_entryinput) + ge_balance_negative_zero_entryinputvalue = (dst_negative_zero_entryinput) + ge_balance_positive_zero_entryinputvalue))))))))))))) \/ ((((0)=0 \/ ~(exists pvs_factor_zero_entrynondivisor. (n) = (0) * pvs_factor_zero_entrynondivisor)) /\ ((0)=0))))Constructive proof overview
Generated structural guide
Index zero is masked to canonical zero for every input table and n, without inspecting or restricting F(0).
The unchanged tactic script uses 0 declared prerequisites and contains 7 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct 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.