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_positive_lowerlayer. ∃ ge_real_negative_lowerlayer. ∃ ge_imaginary_positive_lowerlayer. ∃ ge_imaginary_negative_lowerlayer. ZPairDecode(z,ge_real_positive_lowerlayer,ge_real_negative_lowerlayer,ge_imaginary_positive_lowerlayer,ge_imaginary_negative_lowerlayer)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists ge_real_positive_lowerlayer ge_real_negative_lowerlayer ge_imaginary_positive_lowerlayer ge_imaginary_negative_lowerlayer. (exists ge_real_code_lowerlayerdecode ge_imaginary_code_lowerlayerdecode. (((z) = ((ge_real_code_lowerlayerdecode) + (ge_imaginary_code_lowerlayerdecode)) * S ((ge_real_code_lowerlayerdecode) + (ge_imaginary_code_lowerlayerdecode)) + ((ge_imaginary_code_lowerlayerdecode) + (ge_imaginary_code_lowerlayerdecode))) /\ (((((ge_real_code_lowerlayerdecode) = 2 * (ge_real_positive_lowerlayer) /\ (ge_real_negative_lowerlayer) = 0) \/ exists ge_signed_half_ge_lowerlayerdecode_real. (((ge_real_code_lowerlayerdecode) = 2 * ge_signed_half_ge_lowerlayerdecode_real + 1 /\ (ge_real_positive_lowerlayer) = 0) /\ (ge_real_negative_lowerlayer) = S ge_signed_half_ge_lowerlayerdecode_real))) /\ ((((ge_imaginary_code_lowerlayerdecode) = 2 * (ge_imaginary_positive_lowerlayer) /\ (ge_imaginary_negative_lowerlayer) = 0) \/ exists ge_signed_half_ge_lowerlayerdecode_imaginary. (((ge_imaginary_code_lowerlayerdecode) = 2 * ge_signed_half_ge_lowerlayerdecode_imaginary + 1 /\ (ge_imaginary_positive_lowerlayer) = 0) /\ (ge_imaginary_negative_lowerlayer) = S ge_signed_half_ge_lowerlayerdecode_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
none