English
There is a canonical bijection between the sum of left moves x.LeftMoves ⊕ y.LeftMoves and the left moves of the sum (x+y).LeftMoves; i.e., x.LeftMoves ⊕ y.LeftMoves ≃ (x+y).LeftMoves.
Русский
Существует каноническое биекция между суммой левых ходов x.LeftMoves ⊕ y.LeftMoves и левачими ходами суммы (x+y).LeftMoves; то есть x.LeftMoves ⊕ y.LeftMoves ≃ (x+y).LeftMoves.
LaTeX
$$$ x.LeftMoves \oplus y.LeftMoves \cong (x+y).LeftMoves $$$
Lean4
/-- Converts a left move for `x` or `y` into a left move for `x + y` and vice versa.
Even though these types are the same (not definitionally so), this is the preferred way to convert
between them. -/
def toLeftMovesAdd {x y : PGame} : x.LeftMoves ⊕ y.LeftMoves ≃ (x + y).LeftMoves :=
Equiv.cast (leftMoves_add x y).symm
