∀ (xl xr : Type u_1) (xL : xl → SetTheory.PGame) (xR : xr → SetTheory.PGame) (yl yr : Type u_1)
  (yL : yl → SetTheory.PGame) (yR : yr → SetTheory.PGame) (i : xl) (j : yl),
  (invImage (fun x => PSigma.casesOn x fun x y => (x, y)) Prod.instWellFoundedRelation).1 ⟨xL i, yL j⟩
    ⟨SetTheory.PGame.mk xl xr xL xR, SetTheory.PGame.mk yl yr yL yR⟩