PD0001

Le(a,b)

Witness-defined non-strict order on natural numbers.

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

a ≤ b

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

Hygienic expanded first-order definition 
exists h. h + a = b

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

ConvergentErrorInvariant(a,b,u,U,v,V)BestApproximationSecondKind(a,b,u,v)SignedBestApproximationSecondKind(a,b,u,v)

Checked theorems using this definition

BA001D · cf_approximation_positive_coefficient_boundBA0023 · cf_approximation_subtractive_error_lower_boundBA0024 · cf_approximation_unimodular_best_approximationBA0025 · cf_approximation_alternating_identity_best_approximationBA0026 · cf_approximation_derived_invariant_best_signedBA003B · cf_convergent_matrix_extend_preserved_prefixBA003F · cf_convergent_every_valid_matrix_prefix_existsBA0040 · cf_convergent_actual_prefix_index_bound