(***************************************)
(**********     Doubletons  ************)
(***************************************)

Definition Doubleton (X Y : Ens) := union (Singleton X) (Singleton Y).Definition doubleton_th1_Out : IN X D :=
  union_th1 (Singleton X) (Singleton Y) X iXsX.

Theorem Doubleton_th1 : forall X Y : Ens, IN X (Doubleton X Y).