src/HOL/Library/Tree_Real.thy
changeset 70350 571ae57313a4
parent 69593 3dda49e08b9d
child 72566 831f17da1aab
equal deleted inserted replaced
70349:697450fd25c1 70350:571ae57313a4
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    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)
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