src/HOL/List.thy
changeset 46151 913ea585efdc
parent 46149 54ca5b2775a8
child 46156 f58b7f9d3920
equal deleted inserted replaced
46150:d6cafcc012ec 46151:913ea585efdc
  5214 lemma in_set_member (* FIXME delete candidate *):
  5214 lemma in_set_member (* FIXME delete candidate *):
  5215   "x \<in> set xs \<longleftrightarrow> member xs x"
  5215   "x \<in> set xs \<longleftrightarrow> member xs x"
  5216   by (simp add: member_def)
  5216   by (simp add: member_def)
  5217 
  5217 
  5218 definition list_all :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> bool" where
  5218 definition list_all :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> bool" where
  5219   [code_abbrev]: list_all_iff: "list_all P xs \<longleftrightarrow> Ball (set xs) P"
  5219   list_all_iff [code_abbrev]: "list_all P xs \<longleftrightarrow> Ball (set xs) P"
  5220 
  5220 
  5221 definition list_ex :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> bool" where
  5221 definition list_ex :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> bool" where
  5222   [code_abbrev]: list_ex_iff: "list_ex P xs \<longleftrightarrow> Bex (set xs) P"
  5222   list_ex_iff [code_abbrev]: "list_ex P xs \<longleftrightarrow> Bex (set xs) P"
  5223 
  5223 
  5224 definition list_ex1 :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> bool" where
  5224 definition list_ex1 :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> bool" where
  5225   list_ex1_iff [code_abbrev]: "list_ex1 P xs \<longleftrightarrow> (\<exists>! x. x \<in> set xs \<and> P x)"
  5225   list_ex1_iff [code_abbrev]: "list_ex1 P xs \<longleftrightarrow> (\<exists>! x. x \<in> set xs \<and> P x)"
  5226 
  5226 
  5227 text {*
  5227 text {*