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
(((~(p = 1) /\ forall frm_prime_left_bpc_explorer_prime frm_prime_right_bpc_explorer_prime. p = frm_prime_left_bpc_explorer_prime * frm_prime_right_bpc_explorer_prime -> frm_prime_left_bpc_explorer_prime = 1 \/ frm_prime_right_bpc_explorer_prime = 1)) /\ ((exists bcf_lt_gap_bpc_explorer_lower. bcf_lt_gap_bpc_explorer_lower + S (n) = p) /\ (exists bcf_lt_gap_bpc_explorer_upper. bcf_lt_gap_bpc_explorer_upper + S (p) = n + n)))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.