theorem Th39: :: SCMPDS_6:48

for P being Instruction-Sequence of SCMPDS
for s being State of SCMPDS
for I being shiftable Program of
for a being Int_position
for k1 being Integer st s . (DataLoc ((s . a),k1)) = 0 & I is_closed_on s,P & I is_halting_on s,P holds
( if=0 (a,k1,I) is_closed_on s,P & if=0 (a,k1,I) is_halting_on s,P )