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theory Defs imports Main begin fun sumupto :: "nat \<Rightarrow> nat" where "sumupto 0 = 0" | "sumupto (Suc n) = (Suc n) + sumupto n" end
theory Submission imports Defs begin lemma kleiner_gauss: "sumupto n = n * (n+1) div 2" sorry end
theory Check imports Submission begin lemma "sumupto n = n * (n+1) div 2" by (rule Submission.kleiner_gauss) end