equal
deleted
inserted
replaced
749 |
749 |
750 abbreviation Inter :: "'a set set \<Rightarrow> 'a set" where |
750 abbreviation Inter :: "'a set set \<Rightarrow> 'a set" where |
751 "Inter S \<equiv> \<Sqinter>S" |
751 "Inter S \<equiv> \<Sqinter>S" |
752 |
752 |
753 notation (xsymbols) |
753 notation (xsymbols) |
754 Inter ("\<Inter>_" [90] 90) |
754 Inter ("\<Inter>_" [900] 900) |
755 |
755 |
756 lemma Inter_eq: |
756 lemma Inter_eq: |
757 "\<Inter>A = {x. \<forall>B \<in> A. x \<in> B}" |
757 "\<Inter>A = {x. \<forall>B \<in> A. x \<in> B}" |
758 proof (rule set_eqI) |
758 proof (rule set_eqI) |
759 fix x |
759 fix x |
932 |
932 |
933 abbreviation Union :: "'a set set \<Rightarrow> 'a set" where |
933 abbreviation Union :: "'a set set \<Rightarrow> 'a set" where |
934 "Union S \<equiv> \<Squnion>S" |
934 "Union S \<equiv> \<Squnion>S" |
935 |
935 |
936 notation (xsymbols) |
936 notation (xsymbols) |
937 Union ("\<Union>_" [90] 90) |
937 Union ("\<Union>_" [900] 900) |
938 |
938 |
939 lemma Union_eq: |
939 lemma Union_eq: |
940 "\<Union>A = {x. \<exists>B \<in> A. x \<in> B}" |
940 "\<Union>A = {x. \<exists>B \<in> A. x \<in> B}" |
941 proof (rule set_eqI) |
941 proof (rule set_eqI) |
942 fix x |
942 fix x |