PD0004 · conservative definition

Prime

p is nonunit and every factorization of p has a unit factor.

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.

Readable signature

Prime(p)

Exact expansion

~(p = 1) /\ forall a b. p = a * b -> a = 1 \/ b = 1

This node is conservative notation, not a theorem, axiom, predicate constant, or kernel rule. Its expansion remains in the unchanged first-order language.

Definition neighborhood

Depends on conservative definitions

none

Used by conservative definitions

none

All transitive conservative prerequisites

none

Used by theorem statements or local proof propositions

KU000C kummer_binomial_carry_bit_count KU000D prime_power_valuation_zero_iff_not_divides KU000E kummer_carry_free_iff_not_divides

Grand-campaign planning vocabulary

Locate Prime in the global campaign vocabulary →

Reviewed Prime corresponds to blueprint Prime with checked argument positions [0].

The global atlas describes planning vocabulary and does not itself certify a definition or theorem. The reviewed expansion and conservative dependency DAG on this page are the actual family-local reading definitions.