(* End of proof of lem_Comp_eq_OComp                                       *)

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(* Difference symetrique de deux ensembles                                 *)
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Definition Delta (a b : E) := union (Comp a b) (Comp b a).

(* Specifications: *)
Lemma lem_inter_commut : forall a b : E, inter a b = inter b a.
Lemma lem_inter_assoc : forall a b c : E, inter (inter a b) c = inter a (inter b c).
Lemma lem_union_commut : forall a b : E, union a b = union b a.
Lemma lem_union_assoc : forall a b c : E, union (union a b) c = union a (union b c).
Lemma lem_inter_dist : forall a b c : E, inter a (union b c) = union (inter a b) (inter a c).
Lemma lem_union_dist : forall a b c : E, union a (inter b c) = inter (union a b) (union a c).
Lemma lem_reunion_vide : reunion Vide = Vide.
Lemma lem_union_vide : forall a : E, union a Vide = a.
Lemma lem_inter_vide : forall a : E, inter a Vide = Vide.
Lemma lem_vide_is_inc : forall a : E, inc Vide a.