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
∃ sbz_xp_lowerlayer. ∃ sbz_xn_lowerlayer. ∃ sbz_yp_lowerlayer. ∃ sbz_yn_lowerlayer. SignedDecode(u,sbz_xp_lowerlayer,sbz_xn_lowerlayer) ∧ (SignedDecode(v,sbz_yp_lowerlayer,sbz_yn_lowerlayer) ∧ a · sbz_xp_lowerlayer + b · sbz_yp_lowerlayer = g + (a · sbz_xn_lowerlayer + b · sbz_yn_lowerlayer))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists sbz_xp_lowerlayer sbz_xn_lowerlayer sbz_yp_lowerlayer sbz_yn_lowerlayer. (((u = 2 * sbz_xp_lowerlayer /\ sbz_xn_lowerlayer = 0) \/ exists sd_half_lowerlayer_x. ((u = 2 * sd_half_lowerlayer_x + 1 /\ sbz_xp_lowerlayer = 0) /\ sbz_xn_lowerlayer = S sd_half_lowerlayer_x)) /\ (((v = 2 * sbz_yp_lowerlayer /\ sbz_yn_lowerlayer = 0) \/ exists sd_half_lowerlayer_y. ((v = 2 * sd_half_lowerlayer_y + 1 /\ sbz_yp_lowerlayer = 0) /\ sbz_yn_lowerlayer = S sd_half_lowerlayer_y)) /\ a * sbz_xp_lowerlayer + b * sbz_yp_lowerlayer = g + (a * sbz_xn_lowerlayer + b * sbz_yn_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