equal
deleted
inserted
replaced
1865 obtain sb where sb: "sb \<in> S" "B \<inter> sb \<noteq> {}" |
1865 obtain sb where sb: "sb \<in> S" "B \<inter> sb \<noteq> {}" |
1866 using Blap by auto |
1866 using Blap by auto |
1867 obtain x where x: "\<And>s. s \<in> S \<Longrightarrow> x \<in> s" |
1867 obtain x where x: "\<And>s. s \<in> S \<Longrightarrow> x \<in> s" |
1868 using ne by auto |
1868 using ne by auto |
1869 then have "x \<in> \<Union>S" |
1869 then have "x \<in> \<Union>S" |
1870 using `sa \<in> S` by blast |
1870 using \<open>sa \<in> S\<close> by blast |
1871 then have "x \<in> A \<or> x \<in> B" |
1871 then have "x \<in> A \<or> x \<in> B" |
1872 using cover by auto |
1872 using cover by auto |
1873 then show False |
1873 then show False |
1874 using cs [unfolded connected_def] |
1874 using cs [unfolded connected_def] |
1875 by (metis A B IntI Sup_upper sa sb disjs x cover empty_iff subset_trans) |
1875 by (metis A B IntI Sup_upper sa sb disjs x cover empty_iff subset_trans) |