Thanks for your reply, that's clear now.
My understanding is only very elementary, but these articles offer great insight.
Number 2, utterly simple yet so inexplicably awkward. Duality seems intrinsic to all of the universe and even contributes to the complexity of the GC. That is, we're proving a condition for a multiple of 2, concerning 2 numbers, neither of which will be multiple of 2.
Thanks again