src/HOL/Analysis/Cauchy_Integral_Theorem.thy
changeset 67443 3abf6a722518
parent 67399 eab6ce8368fa
child 67613 ce654b0e6d69
equal deleted inserted replaced
67442:f075640b8868 67443:3abf6a722518
  6149   have fh': "f holomorphic_on cball z ((r + dist w z) / 2)"
  6149   have fh': "f holomorphic_on cball z ((r + dist w z) / 2)"
  6150      apply (rule holomorphic_on_subset [OF holf])
  6150      apply (rule holomorphic_on_subset [OF holf])
  6151      apply (clarsimp simp del: divide_const_simps)
  6151      apply (clarsimp simp del: divide_const_simps)
  6152      apply (metis add.commute dist_commute le_less_trans mem_ball real_gt_half_sum w)
  6152      apply (metis add.commute dist_commute le_less_trans mem_ball real_gt_half_sum w)
  6153      done
  6153      done
  6154   \<comment>\<open>Replacing @{term r} and the original (weak) premises\<close>
  6154   \<comment> \<open>Replacing @{term r} and the original (weak) premises\<close>
  6155   obtain r where "0 < r" and holfc: "f holomorphic_on cball z r" and w: "w \<in> ball z r"
  6155   obtain r where "0 < r" and holfc: "f holomorphic_on cball z r" and w: "w \<in> ball z r"
  6156     apply (rule that [of "(r + dist w z) / 2"])
  6156     apply (rule that [of "(r + dist w z) / 2"])
  6157       apply (simp_all add: fh')
  6157       apply (simp_all add: fh')
  6158      apply (metis add_0_iff ball_eq_empty dist_nz dist_self empty_iff not_less pos_add_strict w)
  6158      apply (metis add_0_iff ball_eq_empty dist_nz dist_self empty_iff not_less pos_add_strict w)
  6159     apply (metis add_less_cancel_right dist_commute mem_ball mult_2_right w)
  6159     apply (metis add_less_cancel_right dist_commute mem_ball mult_2_right w)