theorem :: SCMISORT:15

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 ex f being Function of (product (the_Values_of SCM+FSA)),NAT st
for k being Nat holds
( ( f . ((StepWhile>0 (a,P,s,I)) . k) <> 0 implies ( f . ((StepWhile>0 (a,P,s,I)) . (k + 1)) < f . ((StepWhile>0 (a,P,s,I)) . k) & I is_halting_onInit (StepWhile>0 (a,P,s,I)) . k,P +* (while>0 (a,I)) ) ) & ((StepWhile>0 (a,P,s,I)) . (k + 1)) . (intloc 0) = 1 & ( f . ((StepWhile>0 (a,P,s,I)) . k) = 0 implies ((StepWhile>0 (a,P,s,I)) . k) . a <= 0 ) & ( ((StepWhile>0 (a,P,s,I)) . k) . a <= 0 implies f . ((StepWhile>0 (a,P,s,I)) . k) = 0 ) ) holds
while>0 (a,I) is_halting_onInit s,P