X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2FgTopLevel%2Fesempi%2Fsets.cic;h=5bd913e725896f432fcc81580636a19b7ebd6229;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=156e231a23669c30f6a0b5e1fdacbd458ddcc99f;hpb=fde1a6daa3aaa72c5c7536f4d2c65a3873b1c1bc;p=helm.git diff --git a/helm/gTopLevel/esempi/sets.cic b/helm/gTopLevel/esempi/sets.cic index 156e231a2..5bd913e72 100644 --- a/helm/gTopLevel/esempi/sets.cic +++ b/helm/gTopLevel/esempi/sets.cic @@ -1,15 +1,17 @@ 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))