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author | nipkow |

Wed, 10 Jul 2002 07:20:02 +0200 | |

changeset 13329 | 53c4ec15cae0 |

parent 13328 | 703de709a64b |

child 13330 | c9e9b6add754 |

*** empty log message ***

doc-src/TutorialI/IsarOverview/Isar/Logic.thy | file | annotate | diff | comparison | revisions | |

doc-src/TutorialI/IsarOverview/Isar/document/root.tex | file | annotate | diff | comparison | revisions |

--- a/doc-src/TutorialI/IsarOverview/Isar/Logic.thy Tue Jul 09 23:05:26 2002 +0200 +++ b/doc-src/TutorialI/IsarOverview/Isar/Logic.thy Wed Jul 10 07:20:02 2002 +0200 @@ -33,13 +33,13 @@ Text starting with ``--'' is a comment. Note that propositions in \isakeyword{assume} may but need not be -separated by \isakeyword{and} whose purpose is to structure the -assumptions into possibly named blocks, for example +separated by \isakeyword{and}, whose purpose is to structure the +assumptions into possibly named blocks. For example in \begin{center} \isakeyword{assume} @{text"A:"} $A_1$ $A_2$ \isakeyword{and} @{text"B:"} $A_3$ \isakeyword{and} $A_4$ \end{center} -Here label @{text A} refers to the list of propositions $A_1$ $A_2$ and +label @{text A} refers to the list of propositions $A_1$ $A_2$ and label @{text B} to $A_3$. *} @@ -246,13 +246,15 @@ qed qed text{*\noindent Apart from demonstrating the strangeness of classical -arguments by contradiction, this example also introduces three new constructs: -\begin{itemize} -\item \isakeyword{next} deals with multiple subgoals. When showing -@{term"A \<and> B"} we need to show both @{term A} and @{term B}. Each subgoal -is proved separately, in \emph{any} order. The individual proofs are -separated by \isakeyword{next}. -\end{itemize} +arguments by contradiction, this example also introduces two new +abbrebviations: +\begin{center} +\begin{tabular}{lcl} +\isakeyword{hence} &=& \isakeyword{then} \isakeyword{have} \\ +\isakeyword{with}~\emph{facts} &=& +\isakeyword{from}~\emph{facts} \isakeyword{and} @{text this} +\end{tabular} +\end{center} *} subsection{*Avoiding duplication*} @@ -269,7 +271,13 @@ text{*\noindent The \isakeyword{proof} always works on the conclusion, @{prop"B \<and> A"} in our case, thus selecting $\land$-introduction. Hence we must show @{prop B} and @{prop A}; both are proved by -$\land$-elimination. +$\land$-elimination and the proofs are separated by \isakeyword{next}: +\begin{description} +\item[\isakeyword{next}] deals with multiple subgoals. For example, +when showing @{term"A \<and> B"} we need to show both @{term A} and @{term +B}. Each subgoal is proved separately, in \emph{any} order. The +individual proofs are separated by \isakeyword{next}. +\end{description} This is all very well as long as formulae are small. Let us now look at some devices to avoid repeating (possibly large) formulae. A very general method @@ -384,9 +392,8 @@ \isakeyword{fix} and \isakeyword{assume} together with a soundness proof of the elimination involved. -Here is a proof of a well known tautology which employs another useful -abbreviation: \isakeyword{hence} abbreviates \isakeyword{from}~@{text -this}~\isakeyword{have}. Figure out which rule is used where! *} +Here is a proof of a well known tautology. +Figure out which rule is used where! *} lemma assumes ex: "\<exists>x. \<forall>y. P x y" shows "\<forall>y. \<exists>x. P x y" proof @@ -418,7 +425,7 @@ qed qed text{*\noindent -For a start, the example demonstrates three new language elements: +For a start, the example demonstrates two new constructs: \begin{itemize} \item \isakeyword{let} introduces an abbreviation for a term, in our case the witness for the claim, because the term occurs multiple times in the proof. @@ -426,11 +433,6 @@ implicit what the two cases are: it is merely expected that the two subproofs prove @{prop"P \<Longrightarrow> Q"} and @{prop"\<not>P \<Longrightarrow> Q"} for suitable @{term P} and @{term Q}. -\item \isakeyword{with} is an abbreviation: -\begin{center} -\isakeyword{with}~\emph{facts} \quad = \quad -\isakeyword{from}~\emph{facts} \isakeyword{and} @{text this} -\end{center} \end{itemize} If you wonder how to \isakeyword{obtain} @{term y}: via the predefined elimination rule @{thm rangeE[no_vars]}. @@ -699,4 +701,20 @@ see very clearly how things fit together and permit ourselves the obvious forward step @{text"IH[OF B]"}. *} +consts rot :: "'a list \<Rightarrow> 'a list" +recdef rot "measure length" +"rot [] = []" +"rot [x] = [x]" +"rot (x#y#zs) = y # rot(x#zs)" + +lemma "length(rot xs) = length xs" (is "?P xs") +proof (induct xs rule: rot.induct) + show "?P []" by simp +next + fix x show "?P [x]" by simp +next + fix x y zs assume "?P (x#zs)" + thus "?P (x#y#zs)" by simp +qed + (*<*)end(*>*)

--- a/doc-src/TutorialI/IsarOverview/Isar/document/root.tex Tue Jul 09 23:05:26 2002 +0200 +++ b/doc-src/TutorialI/IsarOverview/Isar/document/root.tex Wed Jul 10 07:20:02 2002 +0200 @@ -32,8 +32,8 @@ %%% End: \paragraph{Acknowledgment} -I am deeply indebted to Markus Wenzel for conceiving Isar and for -commenting on this document. +I am deeply indebted to Markus Wenzel for conceiving Isar. Stefan Berghofer +and Markus Wenzel commented on this document. \begingroup \bibliographystyle{plain} \small\raggedright\frenchspacing