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 p. (~((p) = 1) /\ forall pvs_left_square_nonunit_prime pvs_right_square_nonunit_prime. (p) = pvs_left_square_nonunit_prime * pvs_right_square_nonunit_prime -> pvs_left_square_nonunit_prime = 1 \/ pvs_right_square_nonunit_prime = 1) -> ~(p * p = 1)Constructive proof overview
Generated structural guide
The square of a genuine prime is never the unit.
The unchanged tactic script uses 1 declared prerequisite and contains 10 exact native proof lines.
Alpha v34 checked-use · first admitted v29 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
divisor_one 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 assumptionsL1–3
02Separate the logical casesL4–4
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L4
cases hp
03Use earlier factsL5–7
04Construct an explicit witnessL8–8
Supply the displayed value, then prove that it has the required property.
- L8
exists p
05Calculate and transport equalitiesL9–9
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L9
symm
06Use earlier factsL10–10
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L10
exact heq