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feat(set_theory/game/pgame): Add remark on relabelings (#13732)
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vihdzp committed May 6, 2022
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Expand Up @@ -601,6 +601,8 @@ end
`relabelling x y` says that `x` and `y` are really the same game, just dressed up differently.
Specifically, there is a bijection between the moves for Left in `x` and in `y`, and similarly
for Right, and under these bijections we inductively have `relabelling`s for the consequent games.
In ZFC, relabellings would indeed be the same games.
-/
inductive relabelling : pgame.{u} → pgame.{u} → Type (u+1)
| mk : Π {x y : pgame} (L : x.left_moves ≃ y.left_moves) (R : x.right_moves ≃ y.right_moves),
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