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 Pigeonhole_ter : forall (A:Ensemble U) (f:U -> V) (n:nat), injective U V f -> Finite V (Im U V A f) -> Finite U A.