∀ {J : Type u_1} (f : J → ωCPO) (j : J)
  (x :
    OmegaCompletePartialOrder.Chain
      { carrier := (j : J) → (f j).carrier, str := instOmegaCompletePartialOrderForall }.carrier),
  (Pi.evalOrderHom j).toFun (OmegaCompletePartialOrder.ωSup x) =
    (Pi.evalOrderHom j).toFun (OmegaCompletePartialOrder.ωSup x)