theorem Th8: :: SCMFSA_9:27

for P being Instruction-Sequence of SCM+FSA
for I being really-closed MacroInstruction of SCM+FSA
for a being read-write Int-Location
for s being State of SCM+FSA st ( for k being Nat holds I is_halting_on (StepWhile=0 (a,I,P,s)) . k,P +* (while=0 (a,I)) ) & ex f being Function of (product (the_Values_of SCM+FSA)),NAT st
for k being Nat holds
( ( f . ((StepWhile=0 (a,I,P,s)) . (k + 1)) < f . ((StepWhile=0 (a,I,P,s)) . k) or f . ((StepWhile=0 (a,I,P,s)) . k) = 0 ) & ( f . ((StepWhile=0 (a,I,P,s)) . k) = 0 implies ((StepWhile=0 (a,I,P,s)) . k) . a <> 0 ) & ( ((StepWhile=0 (a,I,P,s)) . k) . a <> 0 implies f . ((StepWhile=0 (a,I,P,s)) . k) = 0 ) ) holds
while=0 (a,I) is_halting_on s,P