Definition Naturals := REPLACEMENT Element_of_NN.

(* Specifications: *)
Theorem Naturals_pr1 : forall X : Ens, Element_of_NN X -> IN X Naturals.
Theorem Naturals_pr2 : forall X : Ens, IN X Naturals -> Element_of_NN X.
Theorem Zero_in_Naturals : IN Zero Naturals.
Theorem Nexts_in_Naturals : forall (A : Ens) (h : IN A Naturals), IN (Next A) Naturals.
Theorem Contains_NN_Naturals : Contains_NN Naturals.