equal
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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 |