ND0045

EuclidThreeNumber(c,n)

The subtraction-free Euclidean number n=4d+3 with positive common multiple c=S d.

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_predecessor_ptmf_milestone. (c = S ff_predecessor_ptmf_milestone /\ n = 4 * ff_predecessor_ptmf_milestone + 3)

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

none directly; see definition consumers