equal
deleted
inserted
replaced
17 |
17 |
18 lemma min_height_size1_log: "min_height t \<le> log 2 (size1 t)" |
18 lemma min_height_size1_log: "min_height t \<le> log 2 (size1 t)" |
19 by (simp add: le_log2_of_power min_height_size1) |
19 by (simp add: le_log2_of_power min_height_size1) |
20 |
20 |
21 lemma size1_log_if_complete: "complete t \<Longrightarrow> height t = log 2 (size1 t)" |
21 lemma size1_log_if_complete: "complete t \<Longrightarrow> height t = log 2 (size1 t)" |
22 by (simp add: log2_of_power_eq size1_if_complete) |
22 by (simp add: size1_if_complete) |
23 |
23 |
24 lemma min_height_size1_log_if_incomplete: |
24 lemma min_height_size1_log_if_incomplete: |
25 "\<not> complete t \<Longrightarrow> min_height t < log 2 (size1 t)" |
25 "\<not> complete t \<Longrightarrow> min_height t < log 2 (size1 t)" |
26 by (simp add: less_log2_of_power min_height_size1_if_incomplete) |
26 by (simp add: less_log2_of_power min_height_size1_if_incomplete) |
27 |
27 |