src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy
changeset 61284 2314c2f62eb1
parent 61245 b77bf45efe21
child 61306 9dd394c866fc
equal deleted inserted replaced
61282:3e578ddef85d 61284:2314c2f62eb1
  6595         fix e :: real
  6595         fix e :: real
  6596         assume "e > 0"
  6596         assume "e > 0"
  6597         then have "\<exists>N::nat. inverse (real (N + 1)) < e"
  6597         then have "\<exists>N::nat. inverse (real (N + 1)) < e"
  6598           using real_arch_inv[of e]
  6598           using real_arch_inv[of e]
  6599           apply (auto simp add: Suc_pred')
  6599           apply (auto simp add: Suc_pred')
  6600           apply (rule_tac x="n - 1" in exI)
  6600           apply (metis Suc_pred' real_of_nat_Suc)
  6601           apply auto
       
  6602           done
  6601           done
  6603         then obtain N :: nat where "inverse (real (N + 1)) < e"
  6602         then obtain N :: nat where "inverse (real (N + 1)) < e"
  6604           by auto
  6603           by auto
  6605         then have "\<forall>n\<ge>N. inverse (real n + 1) < e"
  6604         then have "\<forall>n\<ge>N. inverse (real n + 1) < e"
  6606           apply auto
  6605           apply auto