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
∃ ge_real_square_lowerlayer. ∃ ge_imaginary_square_lowerlayer. SignedDifferenceSquare(ap,an,ge_real_square_lowerlayer) ∧ (SignedDifferenceSquare(bp,bn,ge_imaginary_square_lowerlayer) ∧ N = ge_real_square_lowerlayer + ge_imaginary_square_lowerlayer)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists ge_real_square_lowerlayer ge_imaginary_square_lowerlayer. ((((((ap) * (ap))) + (((an) * (an)))) = ((ge_real_square_lowerlayer) + (((((ap) * (an))) + (((an) * (ap))))))) /\ ((((((bp) * (bp))) + (((bn) * (bn)))) = ((ge_imaginary_square_lowerlayer) + (((((bp) * (bn))) + (((bn) * (bp))))))) /\ ((N) = ge_real_square_lowerlayer + ge_imaginary_square_lowerlayer)))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.