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 i. (exists pfp_gap_empty. pfp_gap_empty + S (i) = (0)) -> falseConstructive proof overview
Generated structural guide
There is no natural index below zero; empty list and permutation contracts are genuinely vacuous.
The unchanged tactic script uses 1 declared prerequisite and contains 6 exact native proof lines.
Alpha v34 checked-use · first admitted v28 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
le_zero 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.