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theory Reverse
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79495
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imports Define_Time_Function
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begin
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79969
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time_fun append
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time_fun rev
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lemma T_append: "T_append xs ys = length xs + 1"
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by(induction xs) auto
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lemma T_rev: "T_rev xs \<le> (length xs + 1)^2"
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by(induction xs) (auto simp: T_append power2_eq_square)
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fun itrev :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a list" where
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"itrev [] ys = ys" |
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"itrev (x#xs) ys = itrev xs (x # ys)"
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lemma itrev: "itrev xs ys = rev xs @ ys"
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by(induction xs arbitrary: ys) auto
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lemma itrev_Nil: "itrev xs [] = rev xs"
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by(simp add: itrev)
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time_fun itrev
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lemma T_itrev: "T_itrev xs ys = length xs + 1"
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by(induction xs arbitrary: ys) auto
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end |