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.

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

ArithTable(N,F)DirichletPrefix(F,G,n,l,M)DirichletTable(N,F,G,H)DivisorMask(F,n,l,M)ArithPositiveEqual(F,G,N)SignedZeroWindow(F,k,l)ConstantOneTable(N,U)KroneckerDeltaTable(N,E)

Checked theorems using this definition

DU0001 · dirichlet_constant_one_table_valueDU0003 · dirichlet_kronecker_delta_table_other_valueDU0005 · dirichlet_constant_one_table_appendDU0006 · dirichlet_kronecker_delta_table_appendDU000D · dirichlet_delta_right_entry_before_inputDU000E · dirichlet_delta_right_last_entryDU000F · dirichlet_delta_right_sum_valueDU0010 · dirichlet_delta_right_sumDU0014 · dirichlet_constant_one_entry_to_divisor_maskDU0015 · dirichlet_constant_one_entry_from_divisor_maskDU0016 · dirichlet_constant_one_prefix_to_divisor_maskDU0017 · dirichlet_constant_one_prefix_from_divisor_maskDU0018 · dirichlet_constant_one_sum_iffDU0019 · dirichlet_constant_one_realizes_divisor_sum