for P being Instruction-Sequence of SCMPDS
for s being State of SCMPDS
for I being Program of SCMPDS
for J being parahalting shiftable Program of SCMPDS st I is_closed_on s,P & I is_halting_on s,P holds
( I ';' J is_closed_on s,P & I ';' J is_halting_on s,P )