src/HOL/Data_Structures/RBT_Set.thy
changeset 67118 ccab07d1196c
parent 66088 c9c9438cfc0f
child 67963 9541f2c5ce8d
equal deleted inserted replaced
67117:19f627407264 67118:ccab07d1196c
   301     using rbt_height_bheight[OF assms] by (simp)
   301     using rbt_height_bheight[OF assms] by (simp)
   302   also have "\<dots> \<le> size1 t" using assms
   302   also have "\<dots> \<le> size1 t" using assms
   303     by (simp add: powr_realpow bheight_size_bound rbt_def)
   303     by (simp add: powr_realpow bheight_size_bound rbt_def)
   304   finally have "2 powr (height t / 2) \<le> size1 t" .
   304   finally have "2 powr (height t / 2) \<le> size1 t" .
   305   hence "height t / 2 \<le> log 2 (size1 t)"
   305   hence "height t / 2 \<le> log 2 (size1 t)"
   306     by(simp add: le_log_iff size1_def del: Int.divide_le_eq_numeral1(1))
   306     by (simp add: le_log_iff size1_def del: divide_le_eq_numeral1(1))
   307   thus ?thesis by simp
   307   thus ?thesis by simp
   308 qed
   308 qed
   309 
   309 
   310 end
   310 end