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
z = 2 · p ∧ n = 0 ∨ (∃ x. z = 2 · x + 1 ∧ p = 0 ∧ n = S x)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
(z = 2 * p /\ n = 0) \/ exists sd_half_lowerlayer. ((z = 2 * sd_half_lowerlayer + 1 /\ p = 0) /\ n = S sd_half_lowerlayer)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