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
∀ ics_index_secondwave. ∀ ics_value0_secondwave. ∀ ics_value1_secondwave. Lt(ics_index_secondwave,l) → BetaAt(ab,ac,ics_index_secondwave,ics_value0_secondwave) → BetaAt(db,dc,ics_index_secondwave,ics_value1_secondwave) → ics_value0_secondwave = ics_value1_secondwaveOnly definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall ics_index_secondwave ics_value0_secondwave ics_value1_secondwave. (exists ics_gap_secondwave_bound. ics_gap_secondwave_bound + S (ics_index_secondwave) = (l)) -> (((exists fs_h_ics_secondwave_at0. fs_h_ics_secondwave_at0 + S (ics_value0_secondwave) = S ((S (ics_index_secondwave)) * ac)) /\ exists fs_q_ics_secondwave_at0. ab = fs_q_ics_secondwave_at0 * S ((S (ics_index_secondwave)) * ac) + (ics_value0_secondwave))) -> (((exists fs_h_ics_secondwave_at1. fs_h_ics_secondwave_at1 + S (ics_value1_secondwave) = S ((S (ics_index_secondwave)) * dc)) /\ exists fs_q_ics_secondwave_at1. db = fs_q_ics_secondwave_at1 * S ((S (ics_index_secondwave)) * dc) + (ics_value1_secondwave))) -> ics_value0_secondwave = ics_value1_secondwaveThe 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