{ obj := fun X => BddDistLat.of ↑X.toDistLat, map := fun {X Y} f => BddDistLat.ofHom (FinBddDistLat.Hom.hom f),
        map_id := FinBddDistLat.hasForgetToBddDistLat._proof_1,
        map_comp := @FinBddDistLat.hasForgetToBddDistLat._proof_2 }.comp
    (CategoryTheory.forget BddDistLat) =
  CategoryTheory.forget FinBddDistLat