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 x y d. (exists olte_gap_strict_difference. olte_gap_strict_difference + S (y) = (x)) -> x = y + d -> ~(d = 0)Constructive proof overview
Generated structural guide
A witnessed strictly positive natural difference is nonzero.
The unchanged tactic script uses 1 declared prerequisite and contains 15 exact native proof lines.
Alpha v34 checked-use · first admitted v29 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
lt_irrefl_expanded 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.
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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.