PD0003

Dvd(d,n)

The natural number d divides n.

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

∃ 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)IsGCD(g,a,b)DirichletEntry(F,G,n,d,z)DivisorFactorPair(m,n,d,a,b)

Checked theorems using this definition

MX000C · coprime_divisor_gcd_productMX000F · coprime_divisor_factor_pair_existsMX0011 · coprime_divisor_factor_pair_exists_uniqueMX0012 · coprime_divisor_factor_pair_cofactorsMX004E · dirichlet_convolution_entry_nonzero_supportMX0051 · dirichlet_coprime_grid_nonzero_coordinatesMX0054 · dirichlet_coprime_grid_support_covering