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 p ab ac rb rc. forall pfs_index_negate_empty. (exists pfa_gap_negate_emptyindex. pfa_gap_negate_emptyindex + S (pfs_index_negate_empty) = (0)) -> exists pfs_source_negate_empty pfs_result_negate_empty. ((((exists ff_h_pfp_negate_emptysource. ff_h_pfp_negate_emptysource + S (pfs_source_negate_empty) = S ((S (pfs_index_negate_empty)) * ac)) /\ exists ff_q_pfp_negate_emptysource. ab = ff_q_pfp_negate_emptysource * S ((S (pfs_index_negate_empty)) * ac) + (pfs_source_negate_empty))) /\ (((((exists ff_h_pfp_negate_emptyresult. ff_h_pfp_negate_emptyresult + S (pfs_result_negate_empty) = S ((S (pfs_index_negate_empty)) * rc)) /\ exists ff_q_pfp_negate_emptyresult. rb = ff_q_pfp_negate_emptyresult * S ((S (pfs_index_negate_empty)) * rc) + (pfs_result_negate_empty))) /\ ((((exists pfa_gap_negate_emptyoperationadditionleft. pfa_gap_negate_emptyoperationadditionleft + S (pfs_source_negate_empty) = (p)) /\ (((exists pfa_gap_negate_emptyoperationadditionright. pfa_gap_negate_emptyoperationadditionright + S (pfs_result_negate_empty) = (p)) /\ ((((exists pfa_gap_negate_emptyoperationadditionresultbound. pfa_gap_negate_emptyoperationadditionresultbound + S (0) = (p)) /\ ((exists pfa_offset_left_negate_emptyoperationadditionresultcongruence pfa_offset_right_negate_emptyoperationadditionresultcongruence. ((pfs_source_negate_empty) + (pfs_result_negate_empty)) + (p) * pfa_offset_left_negate_emptyoperationadditionresultcongruence = (0) + (p) * pfa_offset_right_negate_emptyoperationadditionresultcongruence)))))))))))))Constructive proof overview
Generated structural guide
Every pair of empty coefficient prefixes satisfies the operation, including modulus zero and arbitrary encodings.
The unchanged tactic script uses 2 declared prerequisites and contains 14 exact native proof lines.
Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
lt_not_le Stable theorem; checked-use authorized zero_le Stable theorem; checked-use authorizedDirect 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 assumptionsL1–7
02Separate the logical casesL8–8
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L8
exfalso