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), Finite V X -> Included V X (Im U V A f) -> exists n : _, (exists Y : _, (cardinal U Y n /\ Included U Y A) /\ Im U V Y f = X).