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src/HOL/Transitive_Closure.thy
changeset 14361 ad2f5da643b4
parent 14337 e13731554e50
child 14398 c5c47703f763
equal deleted inserted replaced
14360:e654599b114e 14361:ad2f5da643b4 
    37   "_reflcl" :: "('a \<times> 'a) set => ('a \<times> 'a) set"    ("(_^=)" [1000] 999)
 
    37   "_reflcl" :: "('a \<times> 'a) set => ('a \<times> 'a) set"    ("(_^=)" [1000] 999)
 
    38 translations
 
    38 translations
 
    39   "r^=" == "r \<union> Id"
 
    39   "r^=" == "r \<union> Id"
 
    40 
    40 
    41 syntax (xsymbols)
 
    41 syntax (xsymbols)
 
    42   rtrancl :: "('a \<times> 'a) set => ('a \<times> 'a) set"    ("(_\\<^sup>*)" [1000] 999)
 
    42   rtrancl :: "('a \<times> 'a) set => ('a \<times> 'a) set"    ("(_\<^sup>*)" [1000] 999)
 
    43   trancl :: "('a \<times> 'a) set => ('a \<times> 'a) set"    ("(_\\<^sup>+)" [1000] 999)
 
    43   trancl :: "('a \<times> 'a) set => ('a \<times> 'a) set"    ("(_\<^sup>+)" [1000] 999)
 
    44   "_reflcl" :: "('a \<times> 'a) set => ('a \<times> 'a) set"    ("(_\\<^sup>=)" [1000] 999)
 
    44   "_reflcl" :: "('a \<times> 'a) set => ('a \<times> 'a) set"    ("(_\<^sup>=)" [1000] 999)
 
    45 
    45 
    46 
    46 
    47 subsection {* Reflexive-transitive closure *}
 
    47 subsection {* Reflexive-transitive closure *}
 
    48 
    48 
    49 lemma r_into_rtrancl [intro]: "!!p. p \<in> r ==> p \<in> r^*"
 
    49 lemma r_into_rtrancl [intro]: "!!p. p \<in> r ==> p \<in> r^*"
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