| author | nipkow |
| Fri, 05 Jul 2002 17:48:05 +0200 | |
| changeset 13305 | f88d0c363582 |
| child 16417 | 9bc16273c2d4 |
| permissions | -rw-r--r-- |
| nipkow@13305 | 1 |
(*<*) |
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theory Plus = Main: |
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(*>*) |
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text{*\noindent Define the following addition function *}
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consts plus :: "nat \<Rightarrow> nat \<Rightarrow> nat" |
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primrec |
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"plus m 0 = m" |
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"plus m (Suc n) = plus (Suc m) n" |
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text{*\noindent and prove*}
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(*<*) |
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lemma [simp]: "!m. plus 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 "plus m n = m+n" |
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(*<*) |
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by(simp) |
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end |
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(*>*) |