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.

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

Definitions depending on this notation

none

Checked theorems using this definition