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 d. ~(exists pvs_factor_omit_guard. (n) = (d) * pvs_factor_omit_guard) -> ((((~((d)=0)) /\ (exists dm_quotient_omit_result. (((n)=(d)*dm_quotient_omit_result) /\ (exists dst_positive_code_omit_resultinput dst_positive_scale_omit_resultinput dst_negative_code_omit_resultinput dst_negative_scale_omit_resultinput dst_positive_omit_resultinput dst_negative_omit_resultinput. (((F) = (((((dst_positive_code_omit_resultinput) + (dst_positive_scale_omit_resultinput)) * S ((dst_positive_code_omit_resultinput) + (dst_positive_scale_omit_resultinput)) + ((dst_positive_scale_omit_resultinput) + (dst_positive_scale_omit_resultinput))) + (((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) * S ((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) + ((dst_negative_scale_omit_resultinput) + (dst_negative_scale_omit_resultinput)))) * S ((((dst_positive_code_omit_resultinput) + (dst_positive_scale_omit_resultinput)) * S ((dst_positive_code_omit_resultinput) + (dst_positive_scale_omit_resultinput)) + ((dst_positive_scale_omit_resultinput) + (dst_positive_scale_omit_resultinput))) + (((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) * S ((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) + ((dst_negative_scale_omit_resultinput) + (dst_negative_scale_omit_resultinput)))) + ((((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) * S ((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) + ((dst_negative_scale_omit_resultinput) + (dst_negative_scale_omit_resultinput))) + (((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) * S ((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) + ((dst_negative_scale_omit_resultinput) + (dst_negative_scale_omit_resultinput)))))) /\ (((((exists ff_h_pvs_omit_resultinputpositive. ff_h_pvs_omit_resultinputpositive + S (dst_positive_omit_resultinput) = S ((S (d)) * dst_positive_scale_omit_resultinput)) /\ exists ff_q_pvs_omit_resultinputpositive. dst_positive_code_omit_resultinput = ff_q_pvs_omit_resultinputpositive * S ((S (d)) * dst_positive_scale_omit_resultinput) + (dst_positive_omit_resultinput))) /\ (((((exists ff_h_pvs_omit_resultinputnegative. ff_h_pvs_omit_resultinputnegative + S (dst_negative_omit_resultinput) = S ((S (d)) * dst_negative_scale_omit_resultinput)) /\ exists ff_q_pvs_omit_resultinputnegative. dst_negative_code_omit_resultinput = ff_q_pvs_omit_resultinputnegative * S ((S (d)) * dst_negative_scale_omit_resultinput) + (dst_negative_omit_resultinput))) /\ (exists ge_balance_positive_omit_resultinputvalue ge_balance_negative_omit_resultinputvalue. (((((0) = 2 * (ge_balance_positive_omit_resultinputvalue) /\ (ge_balance_negative_omit_resultinputvalue) = 0) \/ exists ge_signed_half_omit_resultinputvaluedecode. (((0) = 2 * ge_signed_half_omit_resultinputvaluedecode + 1 /\ (ge_balance_positive_omit_resultinputvalue) = 0) /\ (ge_balance_negative_omit_resultinputvalue) = S ge_signed_half_omit_resultinputvaluedecode))) /\ ((dst_positive_omit_resultinput) + ge_balance_negative_omit_resultinputvalue = (dst_negative_omit_resultinput) + ge_balance_positive_omit_resultinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_omit_resultnondivisor. (n) = (d) * pvs_factor_omit_resultnondivisor)) /\ ((0)=0))))Constructive proof overview
Generated structural guide
A proved nondivisor contributes zero independently of every signed input value.
The unchanged tactic script uses 0 declared prerequisites and contains 9 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.
01Fix variables and assumptionsL1–4
02Separate the logical casesL5–7
03Use earlier factsL8–8
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L8
exact hd
04Calculate and transport equalitiesL9–9
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L9
refl