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 original first-admission records.
Exact expanded first-order arithmetic statement
forall b c d e k l i p q. k=l -> (((((exists ff_h_pfp_swap_length_sourceoldi. ff_h_pfp_swap_length_sourceoldi + S (p) = S ((S (i)) * c)) /\ exists ff_q_pfp_swap_length_sourceoldi. b = ff_q_pfp_swap_length_sourceoldi * S ((S (i)) * c) + (p))) /\ (((((exists ff_h_pfp_swap_length_sourceoldlast. ff_h_pfp_swap_length_sourceoldlast + S (q) = S ((S (k)) * c)) /\ exists ff_q_pfp_swap_length_sourceoldlast. b = ff_q_pfp_swap_length_sourceoldlast * S ((S (k)) * c) + (q))) /\ (((((exists ff_h_pfp_swap_length_sourcenewi. ff_h_pfp_swap_length_sourcenewi + S (q) = S ((S (i)) * e)) /\ exists ff_q_pfp_swap_length_sourcenewi. d = ff_q_pfp_swap_length_sourcenewi * S ((S (i)) * e) + (q))) /\ (((((exists ff_h_pfp_swap_length_sourcenewlast. ff_h_pfp_swap_length_sourcenewlast + S (p) = S ((S (k)) * e)) /\ exists ff_q_pfp_swap_length_sourcenewlast. d = ff_q_pfp_swap_length_sourcenewlast * S ((S (k)) * e) + (p))) /\ (forall pfp_j_swap_length_source pfp_a_swap_length_source. (exists pfp_gap_swap_length_sourcebound. pfp_gap_swap_length_sourcebound + S (pfp_j_swap_length_source) = (S (k))) -> ~(pfp_j_swap_length_source = i) -> ~(pfp_j_swap_length_source = k) -> (((exists ff_h_pfp_swap_length_sourceold. ff_h_pfp_swap_length_sourceold + S (pfp_a_swap_length_source) = S ((S (pfp_j_swap_length_source)) * c)) /\ exists ff_q_pfp_swap_length_sourceold. b = ff_q_pfp_swap_length_sourceold * S ((S (pfp_j_swap_length_source)) * c) + (pfp_a_swap_length_source))) -> (((exists ff_h_pfp_swap_length_sourcenew. ff_h_pfp_swap_length_sourcenew + S (pfp_a_swap_length_source) = S ((S (pfp_j_swap_length_source)) * e)) /\ exists ff_q_pfp_swap_length_sourcenew. d = ff_q_pfp_swap_length_sourcenew * S ((S (pfp_j_swap_length_source)) * e) + (pfp_a_swap_length_source)))))))))))) -> (((((exists ff_h_pfp_swap_length_targetoldi. ff_h_pfp_swap_length_targetoldi + S (p) = S ((S (i)) * c)) /\ exists ff_q_pfp_swap_length_targetoldi. b = ff_q_pfp_swap_length_targetoldi * S ((S (i)) * c) + (p))) /\ (((((exists ff_h_pfp_swap_length_targetoldlast. ff_h_pfp_swap_length_targetoldlast + S (q) = S ((S (l)) * c)) /\ exists ff_q_pfp_swap_length_targetoldlast. b = ff_q_pfp_swap_length_targetoldlast * S ((S (l)) * c) + (q))) /\ (((((exists ff_h_pfp_swap_length_targetnewi. ff_h_pfp_swap_length_targetnewi + S (q) = S ((S (i)) * e)) /\ exists ff_q_pfp_swap_length_targetnewi. d = ff_q_pfp_swap_length_targetnewi * S ((S (i)) * e) + (q))) /\ (((((exists ff_h_pfp_swap_length_targetnewlast. ff_h_pfp_swap_length_targetnewlast + S (p) = S ((S (l)) * e)) /\ exists ff_q_pfp_swap_length_targetnewlast. d = ff_q_pfp_swap_length_targetnewlast * S ((S (l)) * e) + (p))) /\ (forall pfp_j_swap_length_target pfp_a_swap_length_target. (exists pfp_gap_swap_length_targetbound. pfp_gap_swap_length_targetbound + S (pfp_j_swap_length_target) = (S (l))) -> ~(pfp_j_swap_length_target = i) -> ~(pfp_j_swap_length_target = l) -> (((exists ff_h_pfp_swap_length_targetold. ff_h_pfp_swap_length_targetold + S (pfp_a_swap_length_target) = S ((S (pfp_j_swap_length_target)) * c)) /\ exists ff_q_pfp_swap_length_targetold. b = ff_q_pfp_swap_length_targetold * S ((S (pfp_j_swap_length_target)) * c) + (pfp_a_swap_length_target))) -> (((exists ff_h_pfp_swap_length_targetnew. ff_h_pfp_swap_length_targetnew + S (pfp_a_swap_length_target) = S ((S (pfp_j_swap_length_target)) * e)) /\ exists ff_q_pfp_swap_length_targetnew. d = ff_q_pfp_swap_length_targetnew * S ((S (pfp_j_swap_length_target)) * e) + (pfp_a_swap_length_target))))))))))))Constructive proof overview
Generated structural guide
Equality of lengths transports all actual last-entry indices and the finite preservation bound of a witnessed swap.
The unchanged tactic script uses 0 declared prerequisites and contains 18 exact native proof lines.
Alpha v34 checked-use · first admitted v30 · 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 assumptionsL1–10
02Fix variables and assumptionsL11–11
Work with arbitrary variables or the premises of the current implication.
- L11
intro h
03Calculate and transport equalitiesL12–17
04Use earlier factsL18–18
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L18
exact h