src/HOL/Library/Lub_Glb.thy
changeset 69593 3dda49e08b9d
parent 68356 46d5a9f428e1
child 69597 ff784d5a5bfb
equal deleted inserted replaced
69592:a80d8ec6c998 69593:3dda49e08b9d
    43 
    43 
    44 definition ubs :: "'a set \<Rightarrow> 'a::ord set \<Rightarrow> 'a set"
    44 definition ubs :: "'a set \<Rightarrow> 'a::ord set \<Rightarrow> 'a set"
    45   where "ubs R S = Collect (isUb R S)"
    45   where "ubs R S = Collect (isUb R S)"
    46 
    46 
    47 
    47 
    48 subsection \<open>Rules about the Operators @{term leastP}, @{term ub} and @{term lub}\<close>
    48 subsection \<open>Rules about the Operators \<^term>\<open>leastP\<close>, \<^term>\<open>ub\<close> and \<^term>\<open>lub\<close>\<close>
    49 
    49 
    50 lemma leastPD1: "leastP P x \<Longrightarrow> P x"
    50 lemma leastPD1: "leastP P x \<Longrightarrow> P x"
    51   by (simp add: leastP_def)
    51   by (simp add: leastP_def)
    52 
    52 
    53 lemma leastPD2: "leastP P x \<Longrightarrow> x <=* Collect P"
    53 lemma leastPD2: "leastP P x \<Longrightarrow> x <=* Collect P"
   116 
   116 
   117 definition lbs :: "'a set \<Rightarrow> 'a::ord set \<Rightarrow> 'a set"
   117 definition lbs :: "'a set \<Rightarrow> 'a::ord set \<Rightarrow> 'a set"
   118   where "lbs R S = Collect (isLb R S)"
   118   where "lbs R S = Collect (isLb R S)"
   119 
   119 
   120 
   120 
   121 subsection \<open>Rules about the Operators @{term greatestP}, @{term isLb} and @{term isGlb}\<close>
   121 subsection \<open>Rules about the Operators \<^term>\<open>greatestP\<close>, \<^term>\<open>isLb\<close> and \<^term>\<open>isGlb\<close>\<close>
   122 
   122 
   123 lemma greatestPD1: "greatestP P x \<Longrightarrow> P x"
   123 lemma greatestPD1: "greatestP P x \<Longrightarrow> P x"
   124   by (simp add: greatestP_def)
   124   by (simp add: greatestP_def)
   125 
   125 
   126 lemma greatestPD2: "greatestP P x \<Longrightarrow> Collect P *<= x"
   126 lemma greatestPD2: "greatestP P x \<Longrightarrow> Collect P *<= x"