PD0005

Coprime(a,b)

Every common divisor of a and b is one.

Conservative notation; not a theorem, primitive, or axiom.

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.

Definition in prerequisite notation

∀ d. Dvd(d,a) → Dvd(d,b) → d = 1

Only definitions earlier in this acyclic notation graph are used here.

Hygienic expanded first-order definition 
forall d. (exists x. a = d * x) -> (exists y. b = d * y) -> d = 1

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.

Direct definition dependencies

Dvd(d,n)

Definitions depending on this notation

SimpleHornerRoot(b,c,a,l,m,p)

Checked theorems using this definition

HL0002 · hensel_coprime_mod_transportHL0008 · hensel_canonical_horner_lift_exists_uniqueHL0009 · beta_horner_simple_canonical_representativeHL000A · beta_horner_simple_root_hensel_lift_exists_uniqueHL000D · beta_horner_simple_root_at_congruent_pointHL0010 · beta_horner_prime_power_hensel_lift_exists_uniqueHL0011 · beta_horner_simple_lift_preserves_simplicityHL0012 · beta_horner_hensel_iterated_exists_uniqueHL0013 · beta_horner_prime_power_iterated_lifts_exists_uniqueHL001A · hensel_signed_blend_unit_coprimeHL001F · beta_signed_horner_hensel_iterated_exists_uniqueHL0025 · hensel_prime_blended_nonzero_derivative_is_unit