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.

Theorem Image_set_continuous' : forall (A:Ensemble U) (f:U -> V) (X:Ensemble V), Approximant V (Im U V A f) X -> exists Y : _, Approximant U A Y /\ Im U V Y f = X.