equal
deleted
inserted
replaced
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" |