src/HOL/Analysis/Convex_Euclidean_Space.thy
changeset 67155 9e5b05d54f9d
parent 67135 1a94352812f4
child 67399 eab6ce8368fa
equal deleted inserted replaced
67154:c7def8f836d0 67155:9e5b05d54f9d
  7260       by (simp add: d_def DIM_positive)
  7260       by (simp add: d_def DIM_positive)
  7261     show "convex hull c \<subseteq> cball x e"
  7261     show "convex hull c \<subseteq> cball x e"
  7262       unfolding 2
  7262       unfolding 2
  7263       apply clarsimp
  7263       apply clarsimp
  7264       apply (subst euclidean_dist_l2)
  7264       apply (subst euclidean_dist_l2)
  7265       apply (rule order_trans [OF setL2_le_sum])
  7265       apply (rule order_trans [OF L2_set_le_sum])
  7266       apply (rule zero_le_dist)
  7266       apply (rule zero_le_dist)
  7267       unfolding e'
  7267       unfolding e'
  7268       apply (rule sum_mono)
  7268       apply (rule sum_mono)
  7269       apply simp
  7269       apply simp
  7270       done
  7270       done