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_code_lowerlayer. ∃ ge_imaginary_code_lowerlayer. z = (ge_real_code_lowerlayer + ge_imaginary_code_lowerlayer) · S (ge_real_code_lowerlayer + ge_imaginary_code_lowerlayer) + (ge_imaginary_code_lowerlayer + ge_imaginary_code_lowerlayer) ∧ (SignedDecode(ge_real_code_lowerlayer,ap,an) ∧ SignedDecode(ge_imaginary_code_lowerlayer,bp,bn))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists ge_real_code_lowerlayer ge_imaginary_code_lowerlayer. (((z) = ((ge_real_code_lowerlayer) + (ge_imaginary_code_lowerlayer)) * S ((ge_real_code_lowerlayer) + (ge_imaginary_code_lowerlayer)) + ((ge_imaginary_code_lowerlayer) + (ge_imaginary_code_lowerlayer))) /\ (((((ge_real_code_lowerlayer) = 2 * (ap) /\ (an) = 0) \/ exists ge_signed_half_ge_lowerlayer_real. (((ge_real_code_lowerlayer) = 2 * ge_signed_half_ge_lowerlayer_real + 1 /\ (ap) = 0) /\ (an) = S ge_signed_half_ge_lowerlayer_real))) /\ ((((ge_imaginary_code_lowerlayer) = 2 * (bp) /\ (bn) = 0) \/ exists ge_signed_half_ge_lowerlayer_imaginary. (((ge_imaginary_code_lowerlayer) = 2 * ge_signed_half_ge_lowerlayer_imaginary + 1 /\ (bp) = 0) /\ (bn) = S ge_signed_half_ge_lowerlayer_imaginary)))))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