src/HOL/Infinite_Set.thy
changeset 14565 c6dc17aab88a
parent 14485 ea2707645af8
child 14766 c0401da7726d
equal deleted inserted replaced
14564:3667b4616e9a 14565:c6dc17aab88a
   357 
   357 
   358 syntax (xsymbols)
   358 syntax (xsymbols)
   359   "MOST " :: "[idts, bool] \<Rightarrow> bool"       ("(3\<forall>\<^sub>\<infinity>_./ _)" [0,10] 10)
   359   "MOST " :: "[idts, bool] \<Rightarrow> bool"       ("(3\<forall>\<^sub>\<infinity>_./ _)" [0,10] 10)
   360   "INF "    :: "[idts, bool] \<Rightarrow> bool"     ("(3\<exists>\<^sub>\<infinity>_./ _)" [0,10] 10)
   360   "INF "    :: "[idts, bool] \<Rightarrow> bool"     ("(3\<exists>\<^sub>\<infinity>_./ _)" [0,10] 10)
   361 
   361 
       
   362 syntax (HTML output)
       
   363   "MOST " :: "[idts, bool] \<Rightarrow> bool"       ("(3\<forall>\<^sub>\<infinity>_./ _)" [0,10] 10)
       
   364   "INF "    :: "[idts, bool] \<Rightarrow> bool"     ("(3\<exists>\<^sub>\<infinity>_./ _)" [0,10] 10)
       
   365 
   362 lemma INF_EX:
   366 lemma INF_EX:
   363   "(\<exists>\<^sub>\<infinity>x. P x) \<Longrightarrow> (\<exists>x. P x)"
   367   "(\<exists>\<^sub>\<infinity>x. P x) \<Longrightarrow> (\<exists>x. P x)"
   364 proof (unfold INF_def, rule ccontr)
   368 proof (unfold INF_def, rule ccontr)
   365   assume inf: "infinite {x. P x}"
   369   assume inf: "infinite {x. P x}"
   366     and notP: "\<not>(\<exists>x. P x)"
   370     and notP: "\<not>(\<exists>x. P x)"