ND0021

BinaryModulus(m)

The exact constructive nontrivial-modulus guard 1<m.

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.

Hygienic expanded first-order definition

exists ff_modulus_gap_binary_advanced. ff_modulus_gap_binary_advanced + S 1 = m

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.

Direct definition dependencies

Lt(a,b)

Definitions depending on this notation

none

Checked theorems using this definition

BD0013 · binary_modular_exponent_coded_execution_power_correctBD0014 · binary_modular_exponent_coded_execution_existsBD0015 · binary_modular_exponent_coded_execution_result_functionalBD0016 · binary_modular_exponent_coded_execution_exists_uniqueBD0018 · binary_modular_execution_logarithmic_bound

Separate complete second-wave branches: Full T13 proof · Alpha v27.