∀ (X : Type u_1) (κ : Cardinal.{u_1}) (A : HasCardinalLT.Set X κ) (x y : (HasCardinalLT.Set.functor X κ).obj A),
  (HasCardinalLT.Set.cocone X κ).ι.app A x = (HasCardinalLT.Set.cocone X κ).ι.app A y →
    ∃ k f, (HasCardinalLT.Set.functor X κ).map f x = (HasCardinalLT.Set.functor X κ).map f y