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1 Open:
2 /Coq/Sets/Powerset_facts/Sets_as_an_algebra/Union_commutative.con
3
4 We prove the conjunction again:
5
6 alias Ensemble /Coq/Sets/Ensembles/Ensembles/Ensemble.con
7 alias Union    /Coq/Sets/Ensembles/Ensembles/Union.ind#1/1
8 alias Included /Coq/Sets/Ensembles/Ensembles/Included.con
9 alias and      /Coq/Init/Logic/Conjunction/and.ind#1/1
10
11 The two parts of the conjunction can be proved in the same way. So we
12 can make a Cut:
13
14 !V:Set.!C:(Ensemble V).!D:(Ensemble V).(Included V (Union V C D)
15 (Union V D C))