ND0178

NaturalAbsDifference(p,n,D)

The actual nonnegative absolute difference |p−n|, witnessed by one of the two natural balance equations.

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. Exact original first-admission records.

Definition in prerequisite notation

p = n + D ∨ n = p + D

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

Hygienic expanded first-order definition 
((p) = (n) + (D)) \/ ((n) = (p) + (D))

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

RationalApproximationError(a,b,rp,rn,t,E)BestApproximationSecondKind(a,b,u,v)SignedBestApproximationSecondKind(a,b,u,v)

Checked theorems using this definition

BA0009 · cf_approximation_identity_current_absolute_errorBA000F · cf_approximation_opposite_errors_linear_absoluteBA0018 · cf_approximation_signed_basis_normalizationBA0026 · cf_approximation_derived_invariant_best_signedBA0027 · cf_approximation_natural_error_as_signed