theorem Th39:
for
p being
Instruction-Sequence of
SCM+FSA for
s being
State of
SCM+FSA for
a being
read-write Int-Location for
Ig being
good really-closed MacroInstruction of
SCM+FSA st
s . (intloc 0) = 1 &
ProperBodyWhile>0 a,
Ig,
s,
p &
WithVariantWhile>0 a,
Ig,
s,
p holds
for
i,
j being
Nat st
i <> j &
i <= ExitsAtWhile>0 (
a,
Ig,
p,
s) &
j <= ExitsAtWhile>0 (
a,
Ig,
p,
s) holds
(
(StepWhile>0 (a,Ig,p,s)) . i <> (StepWhile>0 (a,Ig,p,s)) . j &
DataPart ((StepWhile>0 (a,Ig,p,s)) . i) <> DataPart ((StepWhile>0 (a,Ig,p,s)) . j) )