(********* existence definitions **********************)
Definition DOESNT_EXIST (P : Ens -> Prop) := forall A : Ens, ~ P A.
Definition EXISTS (P : Ens -> Prop) := ~ DOESNT_EXIST P.
(********* the axiom of choice, applied to the whole Ens *******)
Parameter CHOICE : forall P : Ens -> Prop, Ens.

Axiom CHOICE_pr : forall (P : Ens -> Prop) (h : EXISTS P), P (CHOICE P).
Parameter EmptySet : Ens.