| author | Walther Neuper <neuper@ist.tugraz.at> |
| Thu, 12 Aug 2010 15:03:34 +0200 | |
| branch | isac-from-Isabelle2009-2 |
| changeset 37913 | 20e3616b2d9c |
| parent 27015 | f8537d69f514 |
| permissions | -rw-r--r-- |
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(*<*) |
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theory Plus imports Main begin |
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(*>*) |
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text{*\noindent Define the following addition function *}
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primrec add :: "nat \<Rightarrow> nat \<Rightarrow> nat" where |
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"add m 0 = m" | |
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"add m (Suc n) = add (Suc m) n" |
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text{*\noindent and prove*}
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(*<*) |
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lemma [simp]: "!m. add m n = m+n" |
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apply(induct_tac n) |
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by(auto) |
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(*>*) |
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lemma "add m n = m+n" |
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(*<*) |
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by(simp) |
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end |
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(*>*) |