theorem Th8: :: SFMASTR2:12

for s being State of SCM+FSA
for p being Instruction-Sequence of SCM+FSA
for a being Int-Location
for k being Nat
for J being really-closed good MacroInstruction of SCM+FSA st ((StepTimes (a,J,p,s)) . k) . (intloc 0) = 1 & J is_halting_on (StepTimes (a,J,p,s)) . k,p +* (times* (a,J)) holds
( ((StepTimes (a,J,p,s)) . (k + 1)) . (intloc 0) = 1 & ( ((StepTimes (a,J,p,s)) . k) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) > 0 implies ((StepTimes (a,J,p,s)) . (k + 1)) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = (((StepTimes (a,J,p,s)) . k) . (1 -stRWNotIn ({a} \/ (UsedILoc J)))) - 1 ) )