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
(((b = 0) /\ (((exists ff_gap_binary_advanced_square. ff_gap_binary_advanced_square + S (r) = m) /\ (exists ff_left_binary_advanced_square_congruence ff_right_binary_advanced_square_congruence. (u * u) + m * ff_left_binary_advanced_square_congruence = (r) + m * ff_right_binary_advanced_square_congruence)))) \/ ((b = 1) /\ (((exists ff_gap_binary_advanced_multiply. ff_gap_binary_advanced_multiply + S (r) = m) /\ (exists ff_left_binary_advanced_multiply_congruence ff_right_binary_advanced_multiply_congruence. ((u * u) * a) + m * ff_left_binary_advanced_multiply_congruence = (r) + m * ff_right_binary_advanced_multiply_congruence)))))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
Checked theorems using this definition
none directly; see definition consumers
Separate complete second-wave branches: Full T13 proof · Alpha v27.