src/HOL/Probability/ex/Measure_Not_CCC.thy
changeset 61808 fc1556774cfe
parent 61424 c3658c18b7bc
child 62390 842917225d56
equal deleted inserted replaced
61807:965769fe2b63 61808:fc1556774cfe
   148     using pair_COCOUNT[of "SIGMA j:UNIV. {j}" POW] by auto
   148     using pair_COCOUNT[of "SIGMA j:UNIV. {j}" POW] by auto
   149   have X_single: "\<And>x. x \<notin> J \<Longrightarrow> X = {x}"
   149   have X_single: "\<And>x. x \<notin> J \<Longrightarrow> X = {x}"
   150     using eq[unfolded set_eq_iff] by force
   150     using eq[unfolded set_eq_iff] by force
   151   
   151   
   152   have "uncountable (UNIV - J)"
   152   have "uncountable (UNIV - J)"
   153     using `countable J` uncountable_UNIV_real uncountable_minus_countable by blast
   153     using \<open>countable J\<close> uncountable_UNIV_real uncountable_minus_countable by blast
   154   then have "infinite (UNIV - J)"
   154   then have "infinite (UNIV - J)"
   155     by (auto intro: countable_finite)
   155     by (auto intro: countable_finite)
   156   then have "\<exists>A. finite A \<and> card A = 2 \<and> A \<subseteq> UNIV - J"
   156   then have "\<exists>A. finite A \<and> card A = 2 \<and> A \<subseteq> UNIV - J"
   157     by (rule infinite_arbitrarily_large)
   157     by (rule infinite_arbitrarily_large)
   158   then obtain i j where ij: "i \<in> UNIV - J" "j \<in> UNIV - J" "i \<noteq> j"
   158   then obtain i j where ij: "i \<in> UNIV - J" "j \<in> UNIV - J" "i \<noteq> j"