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.

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

none

Checked theorems using this definition

JT000B · jordan_primitive_tuple_coprime_product