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

Product(b,c,l,z)Repeat(b,c,a,l)PrimeExponentPrefixGCD(b,c,l,g)InjectivePrefix(b,c,l)PrimeExponentEntries(n,pb,pc,eb,ec,vb,vc,l)PrimeDivisorSupport(n,pb,pc,l)AllPrime(b,c,l)

Checked theorems using this definition

SK0009 · bounded_prime_square_divisor_searchSK000A · squarefree_or_prime_square_divisorSK000B · squarefree_decomposition_bounded_existsSK0019 · prime_valuation_divisible_power_root_boundedSK001B · prime_exponent_common_divisor_dropSK001C · prime_exponent_common_divisor_successorSK001D · prime_exponent_common_divisor_factorSK0023 · prime_valuation_support_exponent_gcd_nonzeroSK0024 · prime_exponent_entry_has_prime_valuationSK0025 · prime_support_common_divisor_implies_all_valuationsSK0026 · prime_support_all_valuations_implies_common_divisorSK002A · perfect_power_root_table_prefix_appendSK002C · perfect_power_root_table_prefix_existsSK002D · perfect_power_root_table_exists