author | Christian Urban <christian dot urban at kcl dot ac dot uk> |
Tue, 03 Dec 2013 03:20:42 +0000 | |
changeset 146 | 6f884231ca57 |
parent 90 | d1d07f05325a |
child 152 | 0c62ec6dc691 |
permissions | -rw-r--r-- |
88
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
1 |
\documentclass[dvipsnames,14pt,t]{beamer} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
2 |
\usepackage{proof} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
3 |
\usepackage{beamerthemeplainculight} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
4 |
\usepackage[T1]{fontenc} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
5 |
\usepackage[latin1]{inputenc} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
6 |
\usepackage{mathpartir} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
7 |
\usepackage{isabelle} |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
8 |
\usepackage{isabellesym} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
9 |
\usepackage[absolute,overlay]{textpos} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
10 |
\usepackage{ifthen} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
11 |
\usepackage{tikz} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
12 |
\usepackage{courier} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
13 |
\usepackage{listings} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
14 |
\usetikzlibrary{arrows} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
15 |
\usetikzlibrary{positioning} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
16 |
\usetikzlibrary{calc} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
17 |
\usepackage{graphicx} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
18 |
\usetikzlibrary{shapes} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
19 |
\usetikzlibrary{shadows} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
20 |
\usetikzlibrary{plotmarks} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
21 |
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
22 |
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
23 |
\isabellestyle{rm} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
24 |
\renewcommand{\isastyle}{\rm}% |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
25 |
\renewcommand{\isastyleminor}{\rm}% |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
26 |
\renewcommand{\isastylescript}{\footnotesize\rm\slshape}% |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
27 |
\renewcommand{\isatagproof}{} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
28 |
\renewcommand{\endisatagproof}{} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
29 |
\renewcommand{\isamarkupcmt}[1]{#1} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
30 |
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
31 |
% Isabelle characters |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
32 |
\renewcommand{\isacharunderscore}{\_} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
33 |
\renewcommand{\isacharbar}{\isamath{\mid}} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
34 |
\renewcommand{\isasymiota}{} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
35 |
\renewcommand{\isacharbraceleft}{\{} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
36 |
\renewcommand{\isacharbraceright}{\}} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
37 |
\renewcommand{\isacharless}{$\langle$} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
38 |
\renewcommand{\isachargreater}{$\rangle$} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
39 |
\renewcommand{\isasymsharp}{\isamath{\#}} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
40 |
\renewcommand{\isasymdots}{\isamath{...}} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
41 |
\renewcommand{\isasymbullet}{\act} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
42 |
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
43 |
% beamer stuff |
146
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
90
diff
changeset
|
44 |
\renewcommand{\slidecaption}{APP 09, King's College London, 3 December 2013} |
88
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
45 |
\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
46 |
\newcommand{\bl}[1]{\textcolor{blue}{#1}} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
47 |
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
48 |
\begin{document} |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
49 |
|
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
50 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
51 |
\mode<presentation>{ |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
52 |
\begin{frame}<1>[t] |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
53 |
\frametitle{% |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
54 |
\begin{tabular}{@ {}c@ {}} |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
55 |
\\ |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
56 |
\LARGE Access Control and \\[-3mm] |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
57 |
\LARGE Privacy Policies (10)\\[-6mm] |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
58 |
\end{tabular}}\bigskip\bigskip\bigskip |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
59 |
|
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
60 |
%\begin{center} |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
61 |
%\includegraphics[scale=1.3]{pics/barrier.jpg} |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
62 |
%\end{center} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
63 |
|
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
64 |
\normalsize |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
65 |
\begin{center} |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
66 |
\begin{tabular}{ll} |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
67 |
Email: & christian.urban at kcl.ac.uk\\ |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
68 |
Of$\!$fice: & S1.27 (1st floor Strand Building)\\ |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
69 |
Slides: & KEATS (also homework is there)\\ |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
70 |
\end{tabular} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
71 |
\end{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
72 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
73 |
\end{frame}} |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
74 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
75 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
76 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
77 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
78 |
\mode<presentation>{ |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
79 |
\begin{frame}[c] |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
80 |
\frametitle{Revision: Proofs} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
81 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
82 |
\begin{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
83 |
\includegraphics[scale=0.4]{pics/river-stones.jpg} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
84 |
\end{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
85 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
86 |
\begin{textblock}{5}(11.7,5) |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
87 |
goal |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
88 |
\end{textblock} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
89 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
90 |
\begin{textblock}{5}(11.7,14) |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
91 |
start |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
92 |
\end{textblock} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
93 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
94 |
\begin{textblock}{5}(0,7) |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
95 |
\begin{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
96 |
\bl{\infer[\small\textcolor{black}{\text{axiom}}]{\quad\vdash\quad}{}}\\[8mm] |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
97 |
\bl{\infer{\vdash}{\quad\vdash\quad}}\\[8mm] |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
98 |
\bl{\infer{\vdash}{\quad\vdash\qquad\vdash\quad}} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
99 |
\end{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
100 |
\end{textblock} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
101 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
102 |
\end{frame}} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
103 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
104 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
105 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
106 |
\mode<presentation>{ |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
107 |
\begin{frame}[c] |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
108 |
\frametitle{Proof Example Proof} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
109 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
110 |
\begin{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
111 |
\bl{\infer{P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash Q\;\text{says}\;F_2 \wedge P\;\text{says}\;F_1} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
112 |
{\raisebox{2mm}{\text{\LARGE $?$}}}} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
113 |
\end{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
114 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
115 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
116 |
\end{frame}} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
117 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
118 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
119 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
120 |
\mode<presentation>{ |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
121 |
\begin{frame}[c] |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
122 |
\frametitle{Proof Example Proof} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
123 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
124 |
\begin{tabular}{@{\hspace{-6mm}}l} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
125 |
\begin{minipage}{1.1\textwidth} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
126 |
We have (by axiom) |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
127 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
128 |
\begin{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
129 |
\begin{tabular}{@{}ll@{}} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
130 |
(1) & \bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2$} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
131 |
\end{tabular} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
132 |
\end{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
133 |
|
89
be35ff24cccc
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
88
diff
changeset
|
134 |
From (1) we get |
88
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
135 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
136 |
\begin{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
137 |
\begin{tabular}{@{}ll@{}} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
138 |
(2) & \bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash P\;\text{says}\;F_1$}\\ |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
139 |
(3) & \bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash Q\;\text{says}\;F_2$}\\ |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
140 |
\end{tabular} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
141 |
\end{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
142 |
|
89
be35ff24cccc
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
88
diff
changeset
|
143 |
From (3) and (2) we get |
88
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
144 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
145 |
\begin{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
146 |
\begin{tabular}{@{}ll@{}} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
147 |
\bl{$P\;\text{says}\;F_1 \wedge Q\;\text{says}\;F_2 \vdash Q\;\text{says}\;F_2 \wedge P\;\text{says}\;F_1$} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
148 |
\end{tabular} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
149 |
\end{center} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
150 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
151 |
Done. |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
152 |
\end{minipage} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
153 |
\end{tabular} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
154 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
155 |
\end{frame}} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
156 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
157 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
158 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
159 |
\end{document} |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
160 |
|
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
161 |
%%% Local Variables: |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
162 |
%%% mode: latex |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
163 |
%%% TeX-master: t |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
164 |
%%% End: |
a30f60a08939
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
165 |