ND0317

DivisorFactorPair(m,n,d,a,b)

Actual positive a,b divide m,n respectively and d=a*b. Coprimality of m,n, coordinate bounds, gcd recovery, existence and uniqueness are separate hypotheses or proved consequences, not clauses of this relation.

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

¬a = 0 ∧ (¬b = 0 ∧ (Dvd(a,m) ∧ (Dvd(b,n) ∧ d = a · b)))

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

Hygienic expanded first-order definition 
((~(((a))=0)) /\ (((~(((b))=0)) /\ (((exists pvs_factor_g009_definitionleft. ((m)) = ((a)) * pvs_factor_g009_definitionleft) /\ (((exists pvs_factor_g009_definitionright. ((n)) = ((b)) * pvs_factor_g009_definitionright) /\ (((d))=((a))*((b))))))))))

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

DirichletDivisorGridWitness(F,G,m,n,i,z,d,e,a,b)

Checked theorems using this definition

MX000D · coprime_divisor_factor_pair_coordinatesMX000E · coprime_divisor_factor_pair_uniqueMX000F · coprime_divisor_factor_pair_existsMX0010 · coprime_divisor_factor_pair_boundsMX0011 · coprime_divisor_factor_pair_exists_uniqueMX0012 · coprime_divisor_factor_pair_cofactorsMX0013 · divisor_factor_pair_quotient_productMX004F · dirichlet_multiplicative_pair_factorizationMX0050 · dirichlet_multiplicative_pair_entryMX0053 · dirichlet_coprime_grid_support_injectiveMX0054 · dirichlet_coprime_grid_support_covering