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 z. ((((x) * (x) + (y) * (y) = (z) * (z)) /\ (forall pff_divisor_pairwise_source. (exists pff_left_pairwise_source. (x) = pff_divisor_pairwise_source * pff_left_pairwise_source) -> (exists pff_right_pairwise_source. (y) = pff_divisor_pairwise_source * pff_right_pairwise_source) -> pff_divisor_pairwise_source = 1))) -> (exists a. x = 2 * a) -> (exists b. y = 2 * b) -> falseConstructive proof overview
Generated structural guide
The two legs of a primitive Pythagorean triple cannot both have even witnesses.
The unchanged tactic script uses 1 declared prerequisite and contains 13 exact native proof lines.
dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged
Proof neighborhood
Direct dependencies
prime_two 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.