Basic definitions about impartial (pre-)games #
We will define an impartial game, one in which left and right can make exactly the same moves. Our definition differs slightly by saying that the game is always equivalent to its negative, no matter what moves are played. This allows for games such as poker-nim to be classified as impartial.
@[irreducible]
The definition for an impartial game, defined using Conway induction.
Equations
Instances For
instance
SetTheory.PGame.Impartial.moveRight_impartial
{G : PGame}
[h : G.Impartial]
(j : G.RightMoves)
:
@[irreducible]
theorem
SetTheory.PGame.Impartial.impartial_congr
{G H : PGame}
(e : G.Relabelling H)
[G.Impartial]
: