PD0005

Coprime(a,b)

Public research checkpoint, not admitted to Alpha or Stable. Alpha v30 remains 3222 checked-use theorems; Stable remains 432. The on-demand Alpha Lean service does not yet expose these checkpoint theorems; their independently checked literal bundles and unchanged sources are available below.

Every common divisor of a and b is one.

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

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

FP0024 · prime_field_nonzero_coprime