ND0123

IntegerVectorNegate(ab,ac,db,dc,pb,pc,nb,nc,l)

The target equals the vector obtained by swapping the two source components, in integer-difference equality.

Conservative notation; not a theorem, primitive, or axiom.

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

IntegerVectorEqual(db,dc,ab,ac,pb,pc,nb,nc,l)

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 ics_value2_secondwave ics_value3_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)) * dc)) /\ exists fs_q_ics_secondwave_at0. db = fs_q_ics_secondwave_at0 * S ((S (ics_index_secondwave)) * dc) + (ics_value0_secondwave))) -> (((exists fs_h_ics_secondwave_at1. fs_h_ics_secondwave_at1 + S (ics_value1_secondwave) = S ((S (ics_index_secondwave)) * ac)) /\ exists fs_q_ics_secondwave_at1. ab = fs_q_ics_secondwave_at1 * S ((S (ics_index_secondwave)) * ac) + (ics_value1_secondwave))) -> (((exists fs_h_ics_secondwave_at2. fs_h_ics_secondwave_at2 + S (ics_value2_secondwave) = S ((S (ics_index_secondwave)) * pc)) /\ exists fs_q_ics_secondwave_at2. pb = fs_q_ics_secondwave_at2 * S ((S (ics_index_secondwave)) * pc) + (ics_value2_secondwave))) -> (((exists fs_h_ics_secondwave_at3. fs_h_ics_secondwave_at3 + S (ics_value3_secondwave) = S ((S (ics_index_secondwave)) * nc)) /\ exists fs_q_ics_secondwave_at3. nb = fs_q_ics_secondwave_at3 * S ((S (ics_index_secondwave)) * nc) + (ics_value3_secondwave))) -> ics_value0_secondwave + ics_value3_secondwave = ics_value2_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

Definitions depending on this notation

none

Checked theorems using this definition

none directly; see definition consumers