src/HOL/Nominal/Nominal.thy
changeset 19869 eba1b9e7c458
parent 19858 d319e39a2e0e
child 19972 89c5afe4139a
equal deleted inserted replaced
19868:e93ffc043dfd 19869:eba1b9e7c458
   696   hence inf2: "infinite (UNIV-{a})" by (rule infinite_remove)
   696   hence inf2: "infinite (UNIV-{a})" by (rule infinite_remove)
   697   have "(UNIV-{a}) \<noteq> ({}::'x set)" 
   697   have "(UNIV-{a}) \<noteq> ({}::'x set)" 
   698   proof (rule_tac ccontr, drule_tac notnotD)
   698   proof (rule_tac ccontr, drule_tac notnotD)
   699     assume "UNIV-{a} = ({}::'x set)"
   699     assume "UNIV-{a} = ({}::'x set)"
   700     with inf2 have "infinite ({}::'x set)" by simp
   700     with inf2 have "infinite ({}::'x set)" by simp
   701     then show "False" by (auto intro: infinite_nonempty)
   701     then show "False" by auto
   702   qed
   702   qed
   703   hence "\<exists>(b::'x). b\<in>(UNIV-{a})" by blast
   703   hence "\<exists>(b::'x). b\<in>(UNIV-{a})" by blast
   704   then obtain b::"'x" where mem2: "b\<in>(UNIV-{a})" by blast
   704   then obtain b::"'x" where mem2: "b\<in>(UNIV-{a})" by blast
   705   from mem2 have "a\<noteq>b" by blast
   705   from mem2 have "a\<noteq>b" by blast
   706   then show "\<exists>(b::'x). a\<noteq>b" by blast
   706   then show "\<exists>(b::'x). a\<noteq>b" by blast