(* Collect lemmas that are missing from the Coq stdlib and describe the Ensemble-operations as boolean algebra. Associativity, idempotence, commutativity, complements, distributivity, … *)
From Coq.Sets Require Export Powerset_facts.
From ZornsLemma Require Export EnsemblesImplicit EnsemblesTactics.

Lemma Complement_Union {X : Type} (U V : Ensemble X) :
Complement (Union U V) = Intersection (Complement U) (Complement V).