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theory Defs imports Main begin fun sumto :: "(nat \<Rightarrow> nat) \<Rightarrow> nat \<Rightarrow> nat" where "sumto f 0 = 0" | "sumto f (Suc n) = sumto f n + f(Suc n)" end
theory Template imports Defs begin lemma split_lists: "\<exists>ys zs. length ys = length xs div n \<and> xs=ys@zs" sorry lemma sum_ident: "sumto (\<lambda>i. i* 2 ^ i) n = n * 2 ^ (n + 1) - (2 ^ (n + 1) - 2)" sorry end
theory Check imports Template begin lemma split_lists: "\<exists>ys zs. length ys = length xs div n \<and> xs=ys@zs" by(rule split_lists) lemma sum_ident: "sumto (\<lambda>i. i* 2 ^ i) n = n * 2 ^ (n + 1) - (2 ^ (n + 1) - 2)" by(rule sum_ident) end