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### Definitions File

### Template File

### Check 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

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

theory Check imports Submission begin lemma pl0: "pl2 t 0 = pl t" by (rule Submission.pl0) end

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