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
BetaAt(h,e,i,((a + r) · S (a + r) + (r + r) + (((u + t) · S (u + t) + (t + t) + q) · S ((u + t) · S (u + t) + (t + t) + q) + (q + q))) · S ((a + r) · S (a + r) + (r + r) + (((u + t) · S (u + t) + (t + t) + q) · S ((u + t) · S (u + t) + (t + t) + q) + (q + q))) + (((u + t) · S (u + t) + (t + t) + q) · S ((u + t) · S (u + t) + (t + t) + q) + (q + q) + (((u + t) · S (u + t) + (t + t) + q) · S ((u + t) · S (u + t) + (t + t) + q) + (q + q))))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
((exists ff_h_cor_secondwave. ff_h_cor_secondwave + S (((((a) + (r)) * S ((a) + (r)) + ((r) + (r))) + (((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) * S ((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) + ((q) + (q)))) * S ((((a) + (r)) * S ((a) + (r)) + ((r) + (r))) + (((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) * S ((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) + ((q) + (q)))) + ((((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) * S ((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) + ((q) + (q))) + (((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) * S ((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) + ((q) + (q))))) = S ((S (i)) * e)) /\ exists ff_q_cor_secondwave. h = ff_q_cor_secondwave * S ((S (i)) * e) + (((((a) + (r)) * S ((a) + (r)) + ((r) + (r))) + (((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) * S ((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) + ((q) + (q)))) * S ((((a) + (r)) * S ((a) + (r)) + ((r) + (r))) + (((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) * S ((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) + ((q) + (q)))) + ((((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) * S ((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) + ((q) + (q))) + (((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) * S ((((u) + (t)) * S ((u) + (t)) + ((t) + (t))) + (q)) + ((q) + (q))))))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.