equal
deleted
inserted
replaced
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) |