src/HOL/Analysis/Brouwer_Fixpoint.thy
changeset 64911 f0e07600de47
parent 64791 05a2b3b20664
child 65585 a043de9ad41e
equal deleted inserted replaced
64910:6108dddad9f0 64911:f0e07600de47
  2570             using segsub by (auto simp add: rel_frontier_def)
  2570             using segsub by (auto simp add: rel_frontier_def)
  2571         qed
  2571         qed
  2572         moreover have False if "1 < dd (x - a)"
  2572         moreover have False if "1 < dd (x - a)"
  2573           using x that dd2 [of "x - a" 1] \<open>x \<noteq> a\<close> closure_affine_hull
  2573           using x that dd2 [of "x - a" 1] \<open>x \<noteq> a\<close> closure_affine_hull
  2574           by (auto simp: rel_frontier_def)
  2574           by (auto simp: rel_frontier_def)
  2575         ultimately have "dd (x - a) = 1" --\<open>similar to another proof above\<close>
  2575         ultimately have "dd (x - a) = 1" \<comment>\<open>similar to another proof above\<close>
  2576           by fastforce
  2576           by fastforce
  2577         with that show ?thesis
  2577         with that show ?thesis
  2578           by (simp add: rel_frontier_def)
  2578           by (simp add: rel_frontier_def)
  2579       qed
  2579       qed
  2580     qed
  2580     qed