for P being Instruction-Sequence of SCMPDS
for s being 0 -started State of SCMPDS
for I being halt-free shiftable Program of
for a being Int_position
for i being Integer
for n being Nat
for X being set st s . (DataLoc ((s . a),i)) > 0 & not DataLoc ((s . a),i) in X & n > 0 & a <> DataLoc ((s . a),i) & ( for t being 0 -started State of SCMPDS
for Q being Instruction-Sequence of SCMPDS st ( for x being Int_position st x in X holds
t . x = s . x ) & t . a = s . a holds
( (IExec (I,Q,t)) . a = t . a & (IExec (I,Q,t)) . (DataLoc ((s . a),i)) = t . (DataLoc ((s . a),i)) & I is_closed_on t,Q & I is_halting_on t,Q & ( for y being Int_position st y in X holds
(IExec (I,Q,t)) . y = t . y ) ) ) holds
IExec ((for-down (a,i,n,I)),P,s) = IExec ((for-down (a,i,n,I)),P,(Initialize (IExec ((I ';' (AddTo (a,i,(- n)))),P,s))))