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 approximants_grow' : forall A X:Ensemble U, ~ Finite U A -> forall n:nat, cardinal U X n -> Approximant U A X -> exists Y : _, cardinal U Y (S n) /\ Approximant U A Y.