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
p · p + n · n = s + (p · n + n · p)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
((((p) * (p))) + (((n) * (n)))) = ((s) + (((((p) * (n))) + (((n) * (p))))))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