Open:
-/Coq/Sets/Powerset_facts/Sets_as_an_algebra/Union_commutative.con
+/Coq/Sets/Powerset_facts/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
+alias U /Coq/Sets/Ensembles/Ensembles/U.var
+alias V /Coq/Sets/Powerset_facts/Sets_as_an_algebra/U.var
+alias Ensemble /Coq/Sets/Ensembles/Ensemble.con
+alias Union /Coq/Sets/Ensembles/Union.ind#1/1
+alias Included /Coq/Sets/Ensembles/Included.con
+alias and /Coq/Init/Logic/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))
+!C:Ensemble{U:=V}.!D:Ensemble{U:=V}.
+ (Included{U:=V} (Union{U:=V} C D) (Union{U:=V} D C))