PD0003

Dvd(d,n)

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.

The natural number d divides n.

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

Definition in prerequisite notation

∃ k. n = d · k

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

Hygienic expanded first-order definition 
exists k. n = d * k

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

Direct definition dependencies

none — first-order arithmetic only

Definitions depending on this notation

Coprime(a,b)

Checked theorems using this definition

none directly; see definition consumers