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.
For n>1 the exponent gcd and a real beta table classify and witness all positive root degrees. The unit n=1 has a separate uniform certificate for every positive degree. Zero is excluded. NaturalSquarefreeDecomposition is deliberately distinct from the unrelated polynomial definition.
Exact theorem in conservative defined notation
∀ p. Prime(p) → ¬p · p = 1Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Complete tactic proof in conservative notation
All 10 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 assumptionsL1–3
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