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 approximant_can_be_any_size : forall A X:Ensemble U, ~ Finite U A -> forall n:nat, exists Y : _, cardinal U Y n /\ Approximant U A Y.