src/HOL/Library/Tree.thy
changeset 69115 919a1b23c192
parent 68999 2af022252782
child 69117 3d3e87835ae8
equal deleted inserted replaced
69114:163626ddaa19 69115:919a1b23c192
   349 proof (cases "complete t")
   349 proof (cases "complete t")
   350   case True
   350   case True
   351   have "(2::nat) ^ height t \<le> 2 ^ height t'"
   351   have "(2::nat) ^ height t \<le> 2 ^ height t'"
   352   proof -
   352   proof -
   353     have "2 ^ height t = size1 t"
   353     have "2 ^ height t = size1 t"
   354       using True by (simp add: complete_iff_height size1_if_complete)
   354       using True by (simp add: size1_if_complete)
   355     also have "\<dots> \<le> size1 t'" using assms(2) by(simp add: size1_size)
   355     also have "\<dots> \<le> size1 t'" using assms(2) by(simp add: size1_size)
   356     also have "\<dots> \<le> 2 ^ height t'" by (rule size1_height)
   356     also have "\<dots> \<le> 2 ^ height t'" by (rule size1_height)
   357     finally show ?thesis .
   357     finally show ?thesis .
   358   qed
   358   qed
   359   thus ?thesis by (simp)
   359   thus ?thesis by (simp)