∀ {X Y : BddDistLat} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((BddDistLat.dual.comp BddDistLat.dual).map f)
      ((fun X => BddDistLat.Iso.mk (OrderIso.dualDual ↑X.toDistLat)) Y).hom =
    CategoryTheory.CategoryStruct.comp ((fun X => BddDistLat.Iso.mk (OrderIso.dualDual ↑X.toDistLat)) X).hom
      ((CategoryTheory.Functor.id BddDistLat).map f)