Prove that it is possible, from any starting KBNK position, to accomplish the mate by manoeuvering to arrive at key positions from a well-known method or strategy whilst the losing king actively tries to avoid reaching the key positions that would lead to mate within 50 moves. In terms of the players' goals:
Winning player's goal: reach the key positions and still have moves to mate within 50
Losing player's goal: avoid getting mated within 50
Given a starting KBNK position, there exist paths through the tree of variations satisfying the winning player's goal with optimal play by the losing player. Is this satisfied for ALL legal KBNK positions using that particular strategem only?
How would one go about attempting to prove this using KBNK tablebases?