∀ (G : SetTheory.PGame),
  SetTheory.PGame.ImpartialAux✝ G =
    (G ≈ -G ∧
      (∀ (i : G.LeftMoves), SetTheory.PGame.ImpartialAux✝¹ (G.moveLeft i)) ∧
        ∀ (j : G.RightMoves), SetTheory.PGame.ImpartialAux✝² (G.moveRight j))