PD0005

Coprime(a,b)

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

Dvd(d,n)

Definitions depending on this notation

none

Checked theorems using this definition

JT000B · jordan_primitive_tuple_coprime_productJT002C · jordan_crt_tuple_existsJT0032 · jordan_canonical_crt_tuple_existsJT0033 · jordan_primitive_crt_tuple_existsJT003A · jordan_tuple_congruence_coprime_productJT003C · jordan_canonical_crt_tuple_uniqueJT0040 · jordan_rectangle_crt_appendJT0041 · jordan_rectangle_crt_successorJT0042 · jordan_rectangle_crt_existsJT0047 · jordan_rectangle_crt_coversJT0048 · jordan_rectangle_crt_enumerationJT0049 · jordan_product_enumeration_existsJT004A · jordan_totient_coprime_productJT004B · jordan_totient_multiplicativity_existsJT0056 · jordan_totient_multiplicativity_unique_counts