The Mutilated Checkerboard in Set Theory

Abstract
An 8 by 8 checkerboard with two diagonally opposite squares removed cannot be covered by dominoes each of which covers two rectilinearly adjacent squares. present a set theory description of the proposition and an informal proof that the covering is impossible. While no present system that I know of will accept either formal description or the proof, I claim that both should be admitted in any heavy duty set theory.
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