Instead of computing the sequence
for
we can just as well compute the sequence
where we omit the old values:
(In both cases we also include the initial set of states for the entry program point, they can be represented as special incoming edges.)
Lemma: Function
is monotonic and
Proof:
Monotonicity follows from the monotonicity of
, which follows from properties of
,
. By induction we then obtain
for all
. From there by induction it follows
for all
.
End of proof.