ND0121 — IntegerVectorZero(ab,ac,db,dc,l)

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_secondwave

Only 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_secondwave

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.

Direct definition dependencies

BetaAt(b,c,i,x)Lt(a,b)

Definitions depending on this notation

JordanTupleEnumeration(k,n,B,C,D,E,j)JordanTupleListed(b,c,k,B,C,D,E,j)JordanTupleScan(k,n,c,limit,B,C,D,E,j)JordanTupleRepresentatives(k,n,c,T)

Checked theorems using this definition