src/HOL/Topological_Spaces.thy
changeset 61342 b98cd131e2b5
parent 61306 9dd394c866fc
child 61426 d53db136e8fd
equal deleted inserted replaced
61341:e60c7d0bb4b1 61342:b98cd131e2b5
  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)