Not.. neither... either

Question

the "not.. neither.." issue is pretty common, but I cannot seem to wrap my mind around the following particular case.

I have the sentence:

Then, in lines 6–9 of the algorithm, we add edges to E (if not existing in E
and, thus, neither in E')), such that.. bla bla.

I want to state that if the edges do not belong to the set of edges E, then they will not belong to the set of edges E' either. It is a consequence.

I suppose a correct way to say it would be:

Then, in lines 6–9 of the algorithm, we add edges to E (if not existing in E 
and, thus, not existing in E' either)), such that.. bla bla.

But I want to keep it as short as possible.

Any help is appreciated.

Answer 1

Then, in lines 6–9 of the algorithm, we add edges to E (if not existing in E and thus neither in E'), such that...

and

Then, in lines 6–9 of the algorithm, we add edges to E (if not existing in E and thus not in E' either), such that...

and

Then, in lines 6–9 of the algorithm, we add edges to E (if not existing in E and thus not in E'), such that...

are all correct. For brevity, we may use the last.