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Kleiner Gauß

Little Carl Friedrich told Isabelle about a neat formula, she wonders whether it is correct.
Can you help?

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Definitions File

theory Defs
  imports Main
begin
  
fun sumupto :: "nat \<Rightarrow> nat" where
 "sumupto 0 = 0"
| "sumupto (Suc n) = (Suc n) + sumupto n"

  
end

Template File

theory Submission
  imports Defs
begin
  
lemma kleiner_gauss: "sumupto n = n * (n+1) div 2"
  sorry
  
  
end

Check File

theory Check
  imports Submission
begin
 
lemma "sumupto n = n * (n+1) div 2"
by (rule Submission.kleiner_gauss)

end

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