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Path Length

This is the task corresponding to exercise 1. Path Length.

Resources

Definitions File

```theory Defs
imports "HOL-Library.Tree"
begin

declare [[names_short]]

fun pl :: "'a tree \<Rightarrow> nat" where
"pl Leaf = 0" |
"pl (Node l x r) = pl l + size1 l + pl r + size1 r"

fun pl2 :: "'a tree \<Rightarrow> nat \<Rightarrow> nat" where
"pl2 Leaf n = n" |
"pl2 (Node l x r) n = pl2 l (n+1) + pl2 r (n+1)"

end```

Template File

```theory Submission
imports Defs
begin

lemma pl2_pl: "pl2 t n = pl t + a * n"
oops

lemma pl0: "pl2 t 0 = pl t"
sorry

end```

Check File

```theory Check
imports Submission
begin

lemma pl0: "pl2 t 0 = pl t"
by (rule Submission.pl0)

end```

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