src/HOL/Complete_Lattices.thy
changeset 52141 eff000cab70f
parent 51540 eea5c4ca4a0e
child 52729 412c9e0381a1
equal deleted inserted replaced
52140:88a69da5d3fa 52141:eff000cab70f
   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