theorem Th21: :: SCMPDS_7:23

for s being State of SCMPDS
for P being Instruction-Sequence of SCMPDS
for I, J being Program of st I is_halting_on s,P & J is_closed_on IExec (I,P,(Initialize s)),P & J is_halting_on IExec (I,P,(Initialize s)),P holds
( J is_closed_on Comput ((P +* (stop I)),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s)))),P +* (stop I) & J is_halting_on Comput ((P +* (stop I)),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s)))),P +* (stop I) )