theorem Th5: :: SCPQSORT:5

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, x, y being Int_position
for i, c being Integer st s . x >= c + (s . (DataLoc ((s . a),i))) & ( for t being 0 -started State of SCMPDS
for Q being Instruction-Sequence of SCMPDS st t . x >= c + (t . (DataLoc ((s . a),i))) & t . y = s . y & t . a = s . a & t . (DataLoc ((s . a),i)) > 0 holds
( (IExec (I,Q,t)) . a = t . a & I is_closed_on t,Q & I is_halting_on t,Q & (IExec (I,Q,t)) . (DataLoc ((s . a),i)) < t . (DataLoc ((s . a),i)) & (IExec (I,Q,t)) . x >= c + ((IExec (I,Q,t)) . (DataLoc ((s . a),i))) & (IExec (I,Q,t)) . y = t . y ) ) holds
( while>0 (a,i,I) is_closed_on s,P & while>0 (a,i,I) is_halting_on s,P & ( s . (DataLoc ((s . a),i)) > 0 implies IExec ((while>0 (a,i,I)),P,s) = IExec ((while>0 (a,i,I)),P,(Initialize (IExec (I,P,s)))) ) )