∀ {F : CategoryTheory.Functor LightProfiniteᵒᵖ (Type u_1)}
  (hF :
    (S : LightProfinite) →
      CategoryTheory.Limits.IsColimit (F.mapCocone (CategoryTheory.Limits.coconeRightOpOfCone S.asLimitCone)))
  {X Y : LightProfiniteᵒᵖ} (x : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((LightCondensed.lanPresheaf F).map x)
      (match Y with
        | Opposite.op S => LightCondensed.lanPresheafIso (hF S)).hom =
    CategoryTheory.CategoryStruct.comp
      (match X with
        | Opposite.op S => LightCondensed.lanPresheafIso (hF S)).hom
      (F.map x)