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Two-player turn-based perfect-information games, surreal numbers, impartial games and Sprague-Grundy theory, partizan games

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A question about a theorem in ONAG by Conway

Does anyone here know about Conway's On numbers and games? Because I can't figure out what he does here on p18. It feels a bit like he's using the statement we want to prove I will type the proof belo …
Wouter Zandsteeg's user avatar