Open: /Coq/Sets/Powerset_facts/Sets_as_an_algebra/Union_commutative.con We prove the conjunction again: alias Ensemble /Coq/Sets/Ensembles/Ensembles/Ensemble.con alias Union /Coq/Sets/Ensembles/Ensembles/Union.ind#1/1 alias Included /Coq/Sets/Ensembles/Ensembles/Included.con alias and /Coq/Init/Logic/Conjunction/and.ind#1/1 The two parts of the conjunction can be proved in the same way. So we can make a Cut: !V:Set.!C:(Ensemble V).!D:(Ensemble V).(Included V (Union V C D) (Union V D C))