PD0002

Lt(a,b)

Witness-defined 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

S a ≤ b

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

Hygienic expanded first-order definition 
exists h. h + S 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

Sum(b,c,l,z)SignedZeroWindow(F,k,l)

Checked theorems using this definition

DU0002 · dirichlet_kronecker_delta_table_one_valueDU0005 · dirichlet_constant_one_table_appendDU0006 · dirichlet_kronecker_delta_table_appendDU0007 · dirichlet_constant_one_table_existsDU0008 · dirichlet_kronecker_delta_table_existsDU000D · dirichlet_delta_right_entry_before_inputDU000E · dirichlet_delta_right_last_entry