Inductive Approximant (A X:Ensemble U) : Prop :=
    Defn_of_Approximant : Finite U X -> Included U X A -> Approximant A X.Inductive Approximant (A X:Ensemble U) : Prop :=
    Defn_of_Approximant : Finite U X -> Included U X A -> Approximant A X.

Lemma make_new_approximant : forall A X:Ensemble U, ~ Finite U A -> Approximant U A X -> Inhabited U (Setminus U A X).