helm/gTopLevel/esempi/sets.cic

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