(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(* This contribution was updated for Coq V5.10 by the COQ workgroup.        *)
(* January 1995                                                             *)
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(*                                   ps.v                                   *)
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Section The_power_set_partial_order.
Variable U : Type.
Inductive Power_set (A : Ensemble U) : Ensemble (Ensemble U) :=
Definition_of_Power_set :
forall X : Ensemble U,
Included U X A -> In (Ensemble U) (Power_set A) X.
Hint Resolve Definition_of_Power_set.
(* Consider a set A, and its powerset P  *)
Variable A : Ensemble U.

Theorem Empty_set_minimal :
forall X : Ensemble U, Included U (Empty_set U) X.