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.
Inputs are genuine canonical signed-pair codes, not arbitrary naturals. Products start at the actual Gaussian identity, whose code is six. The factor list uses the proved prime-divisor property; irreducibility alone is not silently renamed primality. Uniqueness supplies equal lengths, a bounded bijection, and an actual unit at each match, including repeated factors. Units have empty factorizations and zero is excluded. Sorted primary representatives, Gaussian prime classification, and Eisenstein factorization are separate targets.
Exact theorem in conservative defined notation
∀ ap. ∀ an. ∀ bp. ∀ bn. ∀ cp. ∀ cn. ∀ dp. ∀ dn. ap · cp + an · cn + (bp · dn + bn · dp) + (cp · an + cn · ap + (dp · bp + dn · bn)) = cp · ap + cn · an + (dp · bn + dn · bp) + (ap · cn + an · cp + (bp · dp + bn · dn)) ∧ ap · dp + an · dn + (bp · cp + bn · cn) + (cp · bn + cn · bp + (dp · an + dn · ap)) = cp · bp + cn · bn + (dp · ap + dn · an) + (ap · dn + an · dp + (bp · cn + bn · cp))Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Complete tactic proof in conservative notation
All 11 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay script.
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 assumptionsL1–8
02Separate the logical casesL9–9
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L9
split