src/HOL/Enum.thy
changeset 45141 b2eb87bd541b
parent 45140 339a8b3c4791
child 45144 3f4742ce4629
     1.1 --- a/src/HOL/Enum.thy	Thu Oct 13 23:27:46 2011 +0200
     1.2 +++ b/src/HOL/Enum.thy	Thu Oct 13 23:35:15 2011 +0200
     1.3 @@ -759,11 +759,10 @@
     1.4  qed
     1.5  
     1.6  
     1.7 -subsection {* An executable card operator on finite types *}
     1.8 +subsection {* Transitive closure on relations over finite types *}
     1.9  
    1.10 -lemma [code]:
    1.11 -  "card R = length (filter R enum)"
    1.12 -  by (simp add: distinct_length_filter [OF enum_distinct] enum_UNIV Collect_def)
    1.13 +lemma [code]: "trancl (R :: (('a :: enum) \<times> 'a) set) = ntrancl (length (filter R enum) - 1) R"
    1.14 +  by (simp add: finite_trancl_ntranl distinct_length_filter [OF enum_distinct] enum_UNIV Collect_def)
    1.15  
    1.16  
    1.17  subsection {* Closing up *}