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src/Doc/Tutorial/Misc/prime_def.thy
author paulson <lp15@cam.ac.uk>
Fri, 06 Jun 2025 16:18:44 +0100
changeset 82689 817f97d8cd26
parent 69597 ff784d5a5bfb
permissions -rw-r--r--
New lemmas for floor/ceiling/round, plus tidying
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(*<*)
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theory prime_def imports Main begin
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consts prime :: "nat \<Rightarrow> bool"
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(*>*)
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text\<open>
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\begin{warn}
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A common mistake when writing definitions is to introduce extra free
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variables on the right-hand side.  Consider the following, flawed definition
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(where \<open>dvd\<close> means ``divides''):
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@{term[display,quotes]"prime(p) \<equiv> 1 < p \<and> (m dvd p \<longrightarrow> (m=1 \<or> m=p))"}
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\par\noindent\hangindent=0pt
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Isabelle rejects this ``definition'' because of the extra \<^term>\<open>m\<close> on the
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right-hand side, which would introduce an inconsistency (why?).
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The correct version is
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@{term[display,quotes]"prime(p) \<equiv> 1 < p \<and> (\<forall>m. m dvd p \<longrightarrow> (m=1 \<or> m=p))"}
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\end{warn}
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\<close>
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(*<*)
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end
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(*>*)
isabelle