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
∃ sa_lp_lowerlayer. ∃ sa_ln_lowerlayer. ∃ sa_rp_lowerlayer. ∃ sa_rn_lowerlayer. ∃ sa_op_lowerlayer. ∃ sa_on_lowerlayer. SignedDecode(a,sa_lp_lowerlayer,sa_ln_lowerlayer) ∧ (SignedDecode(b,sa_rp_lowerlayer,sa_rn_lowerlayer) ∧ (SignedDecode(c,sa_op_lowerlayer,sa_on_lowerlayer) ∧ sa_lp_lowerlayer + sa_rp_lowerlayer + sa_on_lowerlayer = sa_ln_lowerlayer + sa_rn_lowerlayer + sa_op_lowerlayer))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists sa_lp_lowerlayer sa_ln_lowerlayer sa_rp_lowerlayer sa_rn_lowerlayer sa_op_lowerlayer sa_on_lowerlayer. (((a = 2 * sa_lp_lowerlayer /\ sa_ln_lowerlayer = 0) \/ exists sd_half_lowerlayer_left. ((a = 2 * sd_half_lowerlayer_left + 1 /\ sa_lp_lowerlayer = 0) /\ sa_ln_lowerlayer = S sd_half_lowerlayer_left)) /\ (((b = 2 * sa_rp_lowerlayer /\ sa_rn_lowerlayer = 0) \/ exists sd_half_lowerlayer_right. ((b = 2 * sd_half_lowerlayer_right + 1 /\ sa_rp_lowerlayer = 0) /\ sa_rn_lowerlayer = S sd_half_lowerlayer_right)) /\ (((c = 2 * sa_op_lowerlayer /\ sa_on_lowerlayer = 0) \/ exists sd_half_lowerlayer_output. ((c = 2 * sd_half_lowerlayer_output + 1 /\ sa_op_lowerlayer = 0) /\ sa_on_lowerlayer = S sd_half_lowerlayer_output)) /\ (sa_lp_lowerlayer + sa_rp_lowerlayer) + sa_on_lowerlayer = (sa_ln_lowerlayer + sa_rn_lowerlayer) + sa_op_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
Checked theorems using this definition
none directly; see definition consumers