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

DivRem(n,d,q,r)Product(b,c,l,z)Repeat(b,c,a,l)

Checked theorems using this definition

CG0003 · linear_congruence_reduced_representative_existsCG0004 · linear_congruence_progression_bound_iffCG0005 · linear_congruence_bounded_residue_parametrizedCG0007 · linear_congruence_bounded_solutions_parametrizedCG0008 · linear_congruence_exact_bounded_enumeration_existsCG000B · linear_congruence_modulus_one_bounded_iff_zero