src/HOL/Types_To_Sets/Examples/T2_Spaces.thy
changeset 68428 46beee72fb66
parent 67399 eab6ce8368fa
child 69530 fc0da2166cda
equal deleted inserted replaced
68427:f75d765a281f 68428:46beee72fb66
   118 lemmas dictionary_second_step =  internalized_sort[unoverload "open :: 'a set \<Rightarrow> bool"]
   118 lemmas dictionary_second_step =  internalized_sort[unoverload "open :: 'a set \<Rightarrow> bool"]
   119 text\<open>The theorem with internalized type classes and compiled out operations is the starting point
   119 text\<open>The theorem with internalized type classes and compiled out operations is the starting point
   120      for the original relativization algorithm.\<close>
   120      for the original relativization algorithm.\<close>
   121 thm dictionary_second_step
   121 thm dictionary_second_step
   122 
   122 
       
   123 text \<open>Alternative construction using \<open>unoverload_type\<close>
       
   124   (This does not require fiddling with \<open>Sign.add_const_constraint\<close>).\<close>
       
   125 lemmas dictionary_second_step' = dictionary_first_step[unoverload_type 'a]
   123 
   126 
   124 text\<open>This is the set-based variant of the theorem compact_imp_closed.\<close>
   127 text\<open>This is the set-based variant of the theorem compact_imp_closed.\<close>
   125 lemma compact_imp_closed_set_based:
   128 lemma compact_imp_closed_set_based:
   126   assumes "(A::'a set) \<noteq> {}"
   129   assumes "(A::'a set) \<noteq> {}"
   127   shows "\<forall>open. t2_space_on_with A open \<longrightarrow> (\<forall>S\<subseteq>A. compact_on_with A open S \<longrightarrow>
   130   shows "\<forall>open. t2_space_on_with A open \<longrightarrow> (\<forall>S\<subseteq>A. compact_on_with A open S \<longrightarrow>