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
∃ ee_real_square_lowerlayer. ∃ ee_imag_square_lowerlayer. SignedDifferenceSquare(ap,an,ee_real_square_lowerlayer) ∧ (SignedDifferenceSquare(bp,bn,ee_imag_square_lowerlayer) ∧ n = ee_real_square_lowerlayer + 3 · ee_imag_square_lowerlayer)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists ee_real_square_lowerlayer ee_imag_square_lowerlayer. (((((ap) * (ap))) + (((an) * (an)))) = ((ee_real_square_lowerlayer) + (((((ap) * (an))) + (((an) * (ap))))))) /\ ((((((bp) * (bp))) + (((bn) * (bn)))) = ((ee_imag_square_lowerlayer) + (((((bp) * (bn))) + (((bn) * (bp))))))) /\ (n) = ee_real_square_lowerlayer + 3 * ee_imag_square_lowerlayer)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
none