ND0019

EuclideanHalving(b,r)

The exact constructive two-step Euclidean descent inequality r+r<b.

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_lt_ec_advanced_halving. ff_lt_ec_advanced_halving + S (r + r) = b

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

Direct definition dependencies

Definitions depending on this notation

none

Checked theorems using this definition