H> Infinite articulation of the sequence into antidiagonalisation is the H> illegal operation, its obvisously not indicative of incompleteness as H> has been demonstrated.
Sez who? We DO have some RULES about which operations are legal and which are not. Just because a set (or list) is infinite does not mean it cannot be operated on, member-wise.
Suppose you had an infinite list of all 1's. The member-wise complement of that list is a list of all 0's. Are you saying that just because the list is infinite, we can't ever finish complementing all of it, therefore we can't produce a list of all 0's?
If the list of an infinite number of 1's was legitimate to begin with, then surely the list of all 0's is too. Therefore, if the infinitely long diagonal was legitimate to begin with, the anti- diagonal is, too.
I don't see how you can have a problem with infinitely many "anti"-flips or compelements when you DIDN'T have any problem with infinitely many flips-in-the-first-place. Complementing a flip is no harder, no easier, and no more "illegal" than making a flip in the first place.