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. Exact original first-admission records.

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

CRTPrefixGcdCongruences(b,c,l,m,u,v)CRTPrefixLCM(b,c,l,M)CRTPrefixSolution(r,s,b,c,l,x)CRTNormalizedPrefixSolution(r,s,b,c,l,x,M)CRTPairwiseCompatiblePrefix(r,s,b,c,l)CRTPositiveModuliPrefix(b,c,l)

Checked theorems using this definition

FC000C · crt_pairwise_compatible_prefix_induces_gcd_congruencesFC000D · crt_pairwise_compatible_prefix_implies_merge_compatibleFC000F · crt_pairwise_compatible_prefix_canonical_exists_uniqueFC0010 · crt_canonical_prefix_solution_implies_normalizedFC0012 · crt_prefix_solution_normalized_existsFC0015 · crt_pairwise_compatible_prefix_merge_iffFC0018 · crt_positive_normalized_prefix_iff_canonical