| author | wenzelm |
| Tue, 16 Oct 2007 17:07:40 +0200 | |
| changeset 25056 | 743f3603ba8b |
| parent 23504 | 2b2323124e8e |
| child 27376 | ffe9b958bada |
| permissions | -rw-r--r-- |
| paulson@10602 | 1 |
% |
| paulson@11187 | 2 |
\begin{isabellebody}%
|
| paulson@11187 | 3 |
\def\isabellecontext{Numbers}%
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| wenzelm@17056 | 4 |
% |
| wenzelm@17056 | 5 |
\isadelimtheory |
| paulson@10602 | 6 |
\isanewline |
| wenzelm@17056 | 7 |
% |
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\endisadelimtheory |
| wenzelm@17056 | 9 |
% |
| wenzelm@17056 | 10 |
\isatagtheory |
| wenzelm@17175 | 11 |
\isacommand{theory}\isamarkupfalse%
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| wenzelm@17175 | 12 |
\ Numbers\ \isakeyword{imports}\ Real\ \isakeyword{begin}%
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| wenzelm@17056 | 13 |
\endisatagtheory |
| wenzelm@17056 | 14 |
{\isafoldtheory}%
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| wenzelm@17056 | 15 |
% |
| wenzelm@17056 | 16 |
\isadelimtheory |
| paulson@10602 | 17 |
\isanewline |
| wenzelm@17056 | 18 |
% |
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\endisadelimtheory |
| wenzelm@17056 | 20 |
% |
| wenzelm@17056 | 21 |
\isadelimML |
| wenzelm@17056 | 22 |
\isanewline |
| wenzelm@17056 | 23 |
% |
| wenzelm@17056 | 24 |
\endisadelimML |
| wenzelm@17056 | 25 |
% |
| wenzelm@17056 | 26 |
\isatagML |
| wenzelm@17175 | 27 |
\isacommand{ML}\isamarkupfalse%
|
| wenzelm@17175 | 28 |
\ {\isachardoublequoteopen}Pretty{\isachardot}setmargin\ {\isadigit{6}}{\isadigit{4}}{\isachardoublequoteclose}\isanewline
|
| wenzelm@17175 | 29 |
\isacommand{ML}\isamarkupfalse%
|
| wenzelm@22649 | 30 |
\ {\isachardoublequoteopen}ThyOutput{\isachardot}indent\ {\isacharcolon}{\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}%
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| wenzelm@17056 | 31 |
\endisatagML |
| wenzelm@17056 | 32 |
{\isafoldML}%
|
| wenzelm@17056 | 33 |
% |
| wenzelm@17056 | 34 |
\isadelimML |
| wenzelm@17056 | 35 |
% |
| wenzelm@17056 | 36 |
\endisadelimML |
| wenzelm@11866 | 37 |
% |
| paulson@11187 | 38 |
\begin{isamarkuptext}%
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| paulson@10602 | 39 |
numeric literals; default simprules; can re-orient% |
| paulson@11187 | 40 |
\end{isamarkuptext}%
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| wenzelm@17175 | 41 |
\isamarkuptrue% |
| wenzelm@17175 | 42 |
\isacommand{lemma}\isamarkupfalse%
|
| wenzelm@17175 | 43 |
\ {\isachardoublequoteopen}{\isadigit{2}}\ {\isacharasterisk}\ m\ {\isacharequal}\ m\ {\isacharplus}\ m{\isachardoublequoteclose}%
|
| wenzelm@17056 | 44 |
\isadelimproof |
| wenzelm@17056 | 45 |
% |
| wenzelm@17056 | 46 |
\endisadelimproof |
| wenzelm@17056 | 47 |
% |
| wenzelm@17056 | 48 |
\isatagproof |
| wenzelm@16353 | 49 |
% |
| wenzelm@16353 | 50 |
\begin{isamarkuptxt}%
|
| wenzelm@16353 | 51 |
\begin{isabelle}%
|
| wenzelm@16353 | 52 |
\ {\isadigit{1}}{\isachardot}\ {\isacharparenleft}{\isadigit{2}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharasterisk}\ m\ {\isacharequal}\ m\ {\isacharplus}\ m%
|
| wenzelm@16353 | 53 |
\end{isabelle}%
|
| wenzelm@16353 | 54 |
\end{isamarkuptxt}%
|
| wenzelm@17175 | 55 |
\isamarkuptrue% |
| wenzelm@17175 | 56 |
\isacommand{oops}\isamarkupfalse%
|
| wenzelm@17175 | 57 |
% |
| wenzelm@17056 | 58 |
\endisatagproof |
| wenzelm@17056 | 59 |
{\isafoldproof}%
|
| wenzelm@17056 | 60 |
% |
| wenzelm@17056 | 61 |
\isadelimproof |
| wenzelm@17056 | 62 |
% |
| wenzelm@17056 | 63 |
\endisadelimproof |
| wenzelm@17056 | 64 |
\isanewline |
| paulson@15481 | 65 |
\isanewline |
| wenzelm@17175 | 66 |
\isacommand{consts}\isamarkupfalse%
|
| wenzelm@17175 | 67 |
\ h\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
|
| wenzelm@17175 | 68 |
\isacommand{recdef}\isamarkupfalse%
|
| wenzelm@17175 | 69 |
\ h\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceright}{\isachardoublequoteclose}\isanewline
|
| wenzelm@17175 | 70 |
{\isachardoublequoteopen}h\ i\ {\isacharequal}\ {\isacharparenleft}if\ i\ {\isacharequal}\ {\isadigit{3}}\ then\ {\isadigit{2}}\ else\ i{\isacharparenright}{\isachardoublequoteclose}%
|
| paulson@11187 | 71 |
\begin{isamarkuptext}%
|
| wenzelm@11708 | 72 |
\isa{h\ {\isadigit{3}}\ {\isacharequal}\ {\isadigit{2}}}
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| paulson@11187 | 73 |
\isa{h\ i\ {\isacharequal}\ i}%
|
| paulson@11187 | 74 |
\end{isamarkuptext}%
|
| wenzelm@11866 | 75 |
\isamarkuptrue% |
| paulson@10878 | 76 |
% |
| paulson@11187 | 77 |
\begin{isamarkuptext}%
|
| paulson@11187 | 78 |
\begin{isabelle}%
|
| paulson@14387 | 79 |
Numeral{\isadigit{0}}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}%
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| paulson@11187 | 80 |
\end{isabelle}
|
| paulson@11174 | 81 |
\rulename{numeral_0_eq_0}
|
| paulson@11187 | 82 |
|
| paulson@11187 | 83 |
\begin{isabelle}%
|
| paulson@14387 | 84 |
Numeral{\isadigit{1}}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{1}}{\isasymColon}{\isacharprime}a{\isacharparenright}%
|
| paulson@10602 | 85 |
\end{isabelle}
|
| paulson@11187 | 86 |
\rulename{numeral_1_eq_1}
|
| paulson@10602 | 87 |
|
| paulson@11187 | 88 |
\begin{isabelle}%
|
| wenzelm@11708 | 89 |
{\isadigit{2}}\ {\isacharplus}\ n\ {\isacharequal}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}%
|
| paulson@10602 | 90 |
\end{isabelle}
|
| paulson@11187 | 91 |
\rulename{add_2_eq_Suc}
|
| paulson@10602 | 92 |
|
| paulson@11187 | 93 |
\begin{isabelle}%
|
| wenzelm@11708 | 94 |
n\ {\isacharplus}\ {\isadigit{2}}\ {\isacharequal}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}%
|
| paulson@10602 | 95 |
\end{isabelle}
|
| paulson@11187 | 96 |
\rulename{add_2_eq_Suc'}
|
| paulson@10602 | 97 |
|
| paulson@11187 | 98 |
\begin{isabelle}%
|
| paulson@14270 | 99 |
a\ {\isacharplus}\ b\ {\isacharplus}\ c\ {\isacharequal}\ a\ {\isacharplus}\ {\isacharparenleft}b\ {\isacharplus}\ c{\isacharparenright}%
|
| paulson@10602 | 100 |
\end{isabelle}
|
| paulson@11187 | 101 |
\rulename{add_assoc}
|
| paulson@10602 | 102 |
|
| paulson@11187 | 103 |
\begin{isabelle}%
|
| paulson@14270 | 104 |
a\ {\isacharplus}\ b\ {\isacharequal}\ b\ {\isacharplus}\ a%
|
| paulson@10602 | 105 |
\end{isabelle}
|
| paulson@11187 | 106 |
\rulename{add_commute}
|
| paulson@10602 | 107 |
|
| paulson@11187 | 108 |
\begin{isabelle}%
|
| paulson@14270 | 109 |
a\ {\isacharplus}\ {\isacharparenleft}b\ {\isacharplus}\ c{\isacharparenright}\ {\isacharequal}\ b\ {\isacharplus}\ {\isacharparenleft}a\ {\isacharplus}\ c{\isacharparenright}%
|
| paulson@10602 | 110 |
\end{isabelle}
|
| paulson@11174 | 111 |
\rulename{add_left_commute}
|
| paulson@10602 | 112 |
|
| paulson@10602 | 113 |
these form add_ac; similarly there is mult_ac% |
| paulson@11187 | 114 |
\end{isamarkuptext}%
|
| wenzelm@17175 | 115 |
\isamarkuptrue% |
| wenzelm@17175 | 116 |
\isacommand{lemma}\isamarkupfalse%
|
| wenzelm@17175 | 117 |
\ {\isachardoublequoteopen}Suc{\isacharparenleft}i\ {\isacharplus}\ j{\isacharasterisk}l{\isacharasterisk}k\ {\isacharplus}\ m{\isacharasterisk}n{\isacharparenright}\ {\isacharequal}\ f\ {\isacharparenleft}n{\isacharasterisk}m\ {\isacharplus}\ i\ {\isacharplus}\ k{\isacharasterisk}j{\isacharasterisk}l{\isacharparenright}{\isachardoublequoteclose}%
|
| wenzelm@17056 | 118 |
\isadelimproof |
| wenzelm@17056 | 119 |
% |
| wenzelm@17056 | 120 |
\endisadelimproof |
| wenzelm@17056 | 121 |
% |
| wenzelm@17056 | 122 |
\isatagproof |
| wenzelm@16353 | 123 |
% |
| wenzelm@16353 | 124 |
\begin{isamarkuptxt}%
|
| wenzelm@16353 | 125 |
\begin{isabelle}%
|
| wenzelm@16353 | 126 |
\ {\isadigit{1}}{\isachardot}\ Suc\ {\isacharparenleft}i\ {\isacharplus}\ j\ {\isacharasterisk}\ l\ {\isacharasterisk}\ k\ {\isacharplus}\ m\ {\isacharasterisk}\ n{\isacharparenright}\ {\isacharequal}\ f\ {\isacharparenleft}n\ {\isacharasterisk}\ m\ {\isacharplus}\ i\ {\isacharplus}\ k\ {\isacharasterisk}\ j\ {\isacharasterisk}\ l{\isacharparenright}%
|
| wenzelm@16353 | 127 |
\end{isabelle}%
|
| wenzelm@16353 | 128 |
\end{isamarkuptxt}%
|
| wenzelm@17175 | 129 |
\isamarkuptrue% |
| wenzelm@17175 | 130 |
\isacommand{apply}\isamarkupfalse%
|
| wenzelm@17175 | 131 |
\ {\isacharparenleft}simp\ add{\isacharcolon}\ add{\isacharunderscore}ac\ mult{\isacharunderscore}ac{\isacharparenright}%
|
| wenzelm@16353 | 132 |
\begin{isamarkuptxt}%
|
| wenzelm@16353 | 133 |
\begin{isabelle}%
|
| wenzelm@16353 | 134 |
\ {\isadigit{1}}{\isachardot}\ Suc\ {\isacharparenleft}i\ {\isacharplus}\ {\isacharparenleft}m\ {\isacharasterisk}\ n\ {\isacharplus}\ j\ {\isacharasterisk}\ {\isacharparenleft}k\ {\isacharasterisk}\ l{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
|
| wenzelm@16353 | 135 |
\isaindent{\ {\isadigit{1}}{\isachardot}\ }f\ {\isacharparenleft}i\ {\isacharplus}\ {\isacharparenleft}m\ {\isacharasterisk}\ n\ {\isacharplus}\ j\ {\isacharasterisk}\ {\isacharparenleft}k\ {\isacharasterisk}\ l{\isacharparenright}{\isacharparenright}{\isacharparenright}%
|
| wenzelm@16353 | 136 |
\end{isabelle}%
|
| wenzelm@16353 | 137 |
\end{isamarkuptxt}%
|
| wenzelm@17175 | 138 |
\isamarkuptrue% |
| wenzelm@17175 | 139 |
\isacommand{oops}\isamarkupfalse%
|
| wenzelm@17175 | 140 |
% |
| wenzelm@17056 | 141 |
\endisatagproof |
| wenzelm@17056 | 142 |
{\isafoldproof}%
|
| wenzelm@17056 | 143 |
% |
| wenzelm@17056 | 144 |
\isadelimproof |
| wenzelm@17056 | 145 |
% |
| wenzelm@17056 | 146 |
\endisadelimproof |
| wenzelm@11866 | 147 |
% |
| paulson@11187 | 148 |
\begin{isamarkuptext}%
|
| paulson@11187 | 149 |
\begin{isabelle}%
|
| paulson@11187 | 150 |
m\ {\isasymle}\ n\ {\isasymLongrightarrow}\ m\ div\ k\ {\isasymle}\ n\ div\ k%
|
| paulson@11174 | 151 |
\end{isabelle}
|
| paulson@11187 | 152 |
\rulename{div_le_mono}
|
| paulson@10602 | 153 |
|
| paulson@11187 | 154 |
\begin{isabelle}%
|
| paulson@11187 | 155 |
{\isacharparenleft}m\ {\isacharminus}\ n{\isacharparenright}\ {\isacharasterisk}\ k\ {\isacharequal}\ m\ {\isacharasterisk}\ k\ {\isacharminus}\ n\ {\isacharasterisk}\ k%
|
| paulson@10602 | 156 |
\end{isabelle}
|
| paulson@11187 | 157 |
\rulename{diff_mult_distrib}
|
| paulson@10602 | 158 |
|
| paulson@11187 | 159 |
\begin{isabelle}%
|
| paulson@11187 | 160 |
m\ mod\ n\ {\isacharasterisk}\ k\ {\isacharequal}\ m\ {\isacharasterisk}\ k\ mod\ {\isacharparenleft}n\ {\isacharasterisk}\ k{\isacharparenright}%
|
| paulson@10602 | 161 |
\end{isabelle}
|
| paulson@11187 | 162 |
\rulename{mod_mult_distrib}
|
| paulson@10602 | 163 |
|
| paulson@11187 | 164 |
\begin{isabelle}%
|
| paulson@11187 | 165 |
P\ {\isacharparenleft}a\ {\isacharminus}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenleft}a\ {\isacharless}\ b\ {\isasymlongrightarrow}\ P\ {\isadigit{0}}{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}d{\isachardot}\ a\ {\isacharequal}\ b\ {\isacharplus}\ d\ {\isasymlongrightarrow}\ P\ d{\isacharparenright}{\isacharparenright}%
|
| paulson@10602 | 166 |
\end{isabelle}
|
| paulson@11187 | 167 |
\rulename{nat_diff_split}%
|
| paulson@11187 | 168 |
\end{isamarkuptext}%
|
| wenzelm@17175 | 169 |
\isamarkuptrue% |
| wenzelm@17175 | 170 |
\isacommand{lemma}\isamarkupfalse%
|
| wenzelm@17175 | 171 |
\ {\isachardoublequoteopen}{\isacharparenleft}n\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharequal}\ n\ {\isacharasterisk}\ n\ {\isacharminus}\ {\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isachardoublequoteclose}\isanewline
|
| wenzelm@17056 | 172 |
% |
| wenzelm@17056 | 173 |
\isadelimproof |
| wenzelm@17056 | 174 |
% |
| wenzelm@17056 | 175 |
\endisadelimproof |
| wenzelm@17056 | 176 |
% |
| wenzelm@17056 | 177 |
\isatagproof |
| wenzelm@17175 | 178 |
\isacommand{apply}\isamarkupfalse%
|
| wenzelm@17175 | 179 |
\ {\isacharparenleft}clarsimp\ split{\isacharcolon}\ nat{\isacharunderscore}diff{\isacharunderscore}split\ iff\ del{\isacharcolon}\ less{\isacharunderscore}Suc{\isadigit{0}}{\isacharparenright}\isanewline
|
| wenzelm@16353 | 180 |
\ % |
| wenzelm@16353 | 181 |
\isamarkupcmt{\begin{isabelle}%
|
| wenzelm@16353 | 182 |
\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}d{\isachardot}\ {\isasymlbrakk}n\ {\isacharless}\ Suc\ {\isadigit{0}}{\isacharsemicolon}\ n\ {\isacharasterisk}\ n\ {\isacharequal}\ Suc\ d{\isasymrbrakk}\ {\isasymLongrightarrow}\ d\ {\isacharequal}\ {\isadigit{0}}%
|
| wenzelm@16353 | 183 |
\end{isabelle}%
|
| wenzelm@16353 | 184 |
} |
| wenzelm@16353 | 185 |
\isanewline |
| wenzelm@17175 | 186 |
\isacommand{apply}\isamarkupfalse%
|
| wenzelm@17175 | 187 |
\ {\isacharparenleft}subgoal{\isacharunderscore}tac\ {\isachardoublequoteopen}n{\isacharequal}{\isadigit{0}}{\isachardoublequoteclose}{\isacharcomma}\ force{\isacharcomma}\ arith{\isacharparenright}\isanewline
|
| wenzelm@17175 | 188 |
\isacommand{done}\isamarkupfalse%
|
| wenzelm@17175 | 189 |
% |
| wenzelm@17056 | 190 |
\endisatagproof |
| wenzelm@17056 | 191 |
{\isafoldproof}%
|
| wenzelm@17056 | 192 |
% |
| wenzelm@17056 | 193 |
\isadelimproof |
| wenzelm@17056 | 194 |
\isanewline |
| wenzelm@17056 | 195 |
% |
| wenzelm@17056 | 196 |
\endisadelimproof |
| paulson@12156 | 197 |
\isanewline |
| paulson@12156 | 198 |
\isanewline |
| wenzelm@17175 | 199 |
\isacommand{lemma}\isamarkupfalse%
|
| wenzelm@17175 | 200 |
\ {\isachardoublequoteopen}{\isacharparenleft}n\ {\isacharminus}\ {\isadigit{2}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ n\ {\isacharasterisk}\ n\ {\isacharminus}\ {\isacharparenleft}{\isadigit{4}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isachardoublequoteclose}\isanewline
|
| wenzelm@17056 | 201 |
% |
| wenzelm@17056 | 202 |
\isadelimproof |
| wenzelm@17056 | 203 |
% |
| wenzelm@17056 | 204 |
\endisadelimproof |
| wenzelm@17056 | 205 |
% |
| wenzelm@17056 | 206 |
\isatagproof |
| wenzelm@17175 | 207 |
\isacommand{apply}\isamarkupfalse%
|
| wenzelm@17175 | 208 |
\ {\isacharparenleft}simp\ split{\isacharcolon}\ nat{\isacharunderscore}diff{\isacharunderscore}split{\isacharcomma}\ clarify{\isacharparenright}\isanewline
|
| wenzelm@16353 | 209 |
\ % |
| wenzelm@16353 | 210 |
\isamarkupcmt{\begin{isabelle}%
|
| wenzelm@16353 | 211 |
\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}d{\isachardot}\ {\isasymlbrakk}n\ {\isacharless}\ {\isadigit{2}}{\isacharsemicolon}\ n\ {\isacharasterisk}\ n\ {\isacharequal}\ {\isadigit{4}}\ {\isacharplus}\ d{\isasymrbrakk}\ {\isasymLongrightarrow}\ d\ {\isacharequal}\ {\isadigit{0}}%
|
| wenzelm@16353 | 212 |
\end{isabelle}%
|
| wenzelm@16353 | 213 |
} |
| wenzelm@16353 | 214 |
\isanewline |
| wenzelm@17175 | 215 |
\isacommand{apply}\isamarkupfalse%
|
| wenzelm@17175 | 216 |
\ {\isacharparenleft}subgoal{\isacharunderscore}tac\ {\isachardoublequoteopen}n{\isacharequal}{\isadigit{0}}\ {\isacharbar}\ n{\isacharequal}{\isadigit{1}}{\isachardoublequoteclose}{\isacharcomma}\ force{\isacharcomma}\ arith{\isacharparenright}\isanewline
|
| wenzelm@17175 | 217 |
\isacommand{done}\isamarkupfalse%
|
| wenzelm@17175 | 218 |
% |
| wenzelm@17056 | 219 |
\endisatagproof |
| wenzelm@17056 | 220 |
{\isafoldproof}%
|
| wenzelm@17056 | 221 |
% |
| wenzelm@17056 | 222 |
\isadelimproof |
| wenzelm@17056 | 223 |
% |
| wenzelm@17056 | 224 |
\endisadelimproof |
| wenzelm@11866 | 225 |
% |
| paulson@11187 | 226 |
\begin{isamarkuptext}%
|
| paulson@11187 | 227 |
\begin{isabelle}%
|
| paulson@11187 | 228 |
m\ mod\ n\ {\isacharequal}\ {\isacharparenleft}if\ m\ {\isacharless}\ n\ then\ m\ else\ {\isacharparenleft}m\ {\isacharminus}\ n{\isacharparenright}\ mod\ n{\isacharparenright}%
|
| paulson@11187 | 229 |
\end{isabelle}
|
| paulson@11187 | 230 |
\rulename{mod_if}
|
| paulson@10602 | 231 |
|
| paulson@11187 | 232 |
\begin{isabelle}%
|
| paulson@11187 | 233 |
m\ div\ n\ {\isacharasterisk}\ n\ {\isacharplus}\ m\ mod\ n\ {\isacharequal}\ m%
|
| paulson@10602 | 234 |
\end{isabelle}
|
| paulson@11187 | 235 |
\rulename{mod_div_equality}
|
| paulson@10602 | 236 |
|
| paulson@11187 | 237 |
|
| paulson@11187 | 238 |
\begin{isabelle}%
|
| paulson@11187 | 239 |
a\ {\isacharasterisk}\ b\ div\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ div\ c{\isacharparenright}\ {\isacharplus}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ div\ c%
|
| paulson@10602 | 240 |
\end{isabelle}
|
| paulson@11187 | 241 |
\rulename{div_mult1_eq}
|
| paulson@11187 | 242 |
|
| paulson@11187 | 243 |
\begin{isabelle}%
|
| paulson@11187 | 244 |
a\ {\isacharasterisk}\ b\ mod\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ mod\ c%
|
| paulson@10602 | 245 |
\end{isabelle}
|
| paulson@11187 | 246 |
\rulename{mod_mult1_eq}
|
| paulson@10602 | 247 |
|
| paulson@11187 | 248 |
\begin{isabelle}%
|
| paulson@11187 | 249 |
a\ div\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ a\ div\ b\ div\ c%
|
| paulson@10602 | 250 |
\end{isabelle}
|
| paulson@11187 | 251 |
\rulename{div_mult2_eq}
|
| paulson@10602 | 252 |
|
| paulson@11187 | 253 |
\begin{isabelle}%
|
| paulson@11187 | 254 |
a\ mod\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ b\ {\isacharasterisk}\ {\isacharparenleft}a\ div\ b\ mod\ c{\isacharparenright}\ {\isacharplus}\ a\ mod\ b%
|
| paulson@11187 | 255 |
\end{isabelle}
|
| paulson@11187 | 256 |
\rulename{mod_mult2_eq}
|
| paulson@10602 | 257 |
|
| paulson@11187 | 258 |
\begin{isabelle}%
|
| paulson@11187 | 259 |
{\isadigit{0}}\ {\isacharless}\ c\ {\isasymLongrightarrow}\ c\ {\isacharasterisk}\ a\ div\ {\isacharparenleft}c\ {\isacharasterisk}\ b{\isacharparenright}\ {\isacharequal}\ a\ div\ b%
|
| paulson@10602 | 260 |
\end{isabelle}
|
| paulson@11187 | 261 |
\rulename{div_mult_mult1}
|
| paulson@10602 | 262 |
|
| paulson@11187 | 263 |
\begin{isabelle}%
|
| paulson@11187 | 264 |
a\ div\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}%
|
| paulson@10602 | 265 |
\end{isabelle}
|
| paulson@11187 | 266 |
\rulename{DIVISION_BY_ZERO_DIV}
|
| paulson@10602 | 267 |
|
| paulson@11187 | 268 |
\begin{isabelle}%
|
| paulson@11187 | 269 |
a\ mod\ {\isadigit{0}}\ {\isacharequal}\ a%
|
| paulson@10602 | 270 |
\end{isabelle}
|
| paulson@11187 | 271 |
\rulename{DIVISION_BY_ZERO_MOD}
|
| paulson@10602 | 272 |
|
| paulson@11187 | 273 |
\begin{isabelle}%
|
| paulson@11187 | 274 |
{\isasymlbrakk}m\ dvd\ n{\isacharsemicolon}\ n\ dvd\ m{\isasymrbrakk}\ {\isasymLongrightarrow}\ m\ {\isacharequal}\ n%
|
| paulson@10602 | 275 |
\end{isabelle}
|
| paulson@11187 | 276 |
\rulename{dvd_anti_sym}
|
| paulson@10602 | 277 |
|
| paulson@11187 | 278 |
\begin{isabelle}%
|
| paulson@11187 | 279 |
{\isasymlbrakk}k\ dvd\ m{\isacharsemicolon}\ k\ dvd\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ k\ dvd\ m\ {\isacharplus}\ n%
|
| paulson@10602 | 280 |
\end{isabelle}
|
| paulson@11174 | 281 |
\rulename{dvd_add}
|
| paulson@10602 | 282 |
|
| paulson@10602 | 283 |
For the integers, I'd list a few theorems that somehow involve negative |
| paulson@13758 | 284 |
numbers.% |
| paulson@13758 | 285 |
\end{isamarkuptext}%
|
| paulson@13758 | 286 |
\isamarkuptrue% |
| paulson@13758 | 287 |
% |
| paulson@13758 | 288 |
\begin{isamarkuptext}%
|
| paulson@10602 | 289 |
Division, remainder of negatives |
| paulson@10602 | 290 |
|
| paulson@10602 | 291 |
|
| paulson@11187 | 292 |
\begin{isabelle}%
|
| paulson@11870 | 293 |
{\isadigit{0}}\ {\isacharless}\ b\ {\isasymLongrightarrow}\ {\isadigit{0}}\ {\isasymle}\ a\ mod\ b%
|
| paulson@11187 | 294 |
\end{isabelle}
|
| paulson@11174 | 295 |
\rulename{pos_mod_sign}
|
| paulson@11187 | 296 |
|
| paulson@11187 | 297 |
\begin{isabelle}%
|
| paulson@11870 | 298 |
{\isadigit{0}}\ {\isacharless}\ b\ {\isasymLongrightarrow}\ a\ mod\ b\ {\isacharless}\ b%
|
| paulson@10602 | 299 |
\end{isabelle}
|
| paulson@11187 | 300 |
\rulename{pos_mod_bound}
|
| paulson@10602 | 301 |
|
| paulson@11187 | 302 |
\begin{isabelle}%
|
| paulson@11870 | 303 |
b\ {\isacharless}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ a\ mod\ b\ {\isasymle}\ {\isadigit{0}}%
|
| paulson@10602 | 304 |
\end{isabelle}
|
| paulson@11187 | 305 |
\rulename{neg_mod_sign}
|
| paulson@10602 | 306 |
|
| paulson@11187 | 307 |
\begin{isabelle}%
|
| paulson@11870 | 308 |
b\ {\isacharless}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ b\ {\isacharless}\ a\ mod\ b%
|
| paulson@10602 | 309 |
\end{isabelle}
|
| paulson@11187 | 310 |
\rulename{neg_mod_bound}
|
| paulson@10602 | 311 |
|
| paulson@11187 | 312 |
\begin{isabelle}%
|
| paulson@11187 | 313 |
{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ div\ c\ {\isacharequal}\ a\ div\ c\ {\isacharplus}\ b\ div\ c\ {\isacharplus}\ {\isacharparenleft}a\ mod\ c\ {\isacharplus}\ b\ mod\ c{\isacharparenright}\ div\ c%
|
| paulson@10602 | 314 |
\end{isabelle}
|
| paulson@11187 | 315 |
\rulename{zdiv_zadd1_eq}
|
| paulson@10602 | 316 |
|
| paulson@11187 | 317 |
\begin{isabelle}%
|
| paulson@11187 | 318 |
{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ mod\ c\ {\isacharequal}\ {\isacharparenleft}a\ mod\ c\ {\isacharplus}\ b\ mod\ c{\isacharparenright}\ mod\ c%
|
| paulson@10602 | 319 |
\end{isabelle}
|
| paulson@11187 | 320 |
\rulename{zmod_zadd1_eq}
|
| paulson@10602 | 321 |
|
| paulson@11187 | 322 |
\begin{isabelle}%
|
| paulson@11187 | 323 |
a\ {\isacharasterisk}\ b\ div\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ div\ c{\isacharparenright}\ {\isacharplus}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ div\ c%
|
| paulson@10602 | 324 |
\end{isabelle}
|
| paulson@11187 | 325 |
\rulename{zdiv_zmult1_eq}
|
| paulson@10602 | 326 |
|
| paulson@11187 | 327 |
\begin{isabelle}%
|
| paulson@11187 | 328 |
a\ {\isacharasterisk}\ b\ mod\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ mod\ c%
|
| paulson@10602 | 329 |
\end{isabelle}
|
| paulson@11187 | 330 |
\rulename{zmod_zmult1_eq}
|
| paulson@10602 | 331 |
|
| paulson@11187 | 332 |
\begin{isabelle}%
|
| paulson@11870 | 333 |
{\isadigit{0}}\ {\isacharless}\ c\ {\isasymLongrightarrow}\ a\ div\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ a\ div\ b\ div\ c%
|
| paulson@10602 | 334 |
\end{isabelle}
|
| paulson@11187 | 335 |
\rulename{zdiv_zmult2_eq}
|
| paulson@10602 | 336 |
|
| paulson@11187 | 337 |
\begin{isabelle}%
|
| paulson@11870 | 338 |
{\isadigit{0}}\ {\isacharless}\ c\ {\isasymLongrightarrow}\ a\ mod\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ b\ {\isacharasterisk}\ {\isacharparenleft}a\ div\ b\ mod\ c{\isacharparenright}\ {\isacharplus}\ a\ mod\ b%
|
| paulson@10602 | 339 |
\end{isabelle}
|
| paulson@14400 | 340 |
\rulename{zmod_zmult2_eq}%
|
| paulson@11187 | 341 |
\end{isamarkuptext}%
|
| wenzelm@17175 | 342 |
\isamarkuptrue% |
| wenzelm@17175 | 343 |
\isacommand{lemma}\isamarkupfalse%
|
| wenzelm@17175 | 344 |
\ {\isachardoublequoteopen}abs\ {\isacharparenleft}x{\isacharplus}y{\isacharparenright}\ {\isasymle}\ abs\ x\ {\isacharplus}\ abs\ {\isacharparenleft}y\ {\isacharcolon}{\isacharcolon}\ int{\isacharparenright}{\isachardoublequoteclose}\isanewline
|
| wenzelm@17056 | 345 |
% |
| wenzelm@17056 | 346 |
\isadelimproof |
| wenzelm@17056 | 347 |
% |
| wenzelm@17056 | 348 |
\endisadelimproof |
| wenzelm@17056 | 349 |
% |
| wenzelm@17056 | 350 |
\isatagproof |
| wenzelm@17175 | 351 |
\isacommand{by}\isamarkupfalse%
|
| wenzelm@17175 | 352 |
\ arith% |
| wenzelm@17056 | 353 |
\endisatagproof |
| wenzelm@17056 | 354 |
{\isafoldproof}%
|
| wenzelm@17056 | 355 |
% |
| wenzelm@17056 | 356 |
\isadelimproof |
| wenzelm@17056 | 357 |
\isanewline |
| wenzelm@17056 | 358 |
% |
| wenzelm@17056 | 359 |
\endisadelimproof |
| paulson@15481 | 360 |
\isanewline |
| wenzelm@17175 | 361 |
\isacommand{lemma}\isamarkupfalse%
|
| wenzelm@17175 | 362 |
\ {\isachardoublequoteopen}abs\ {\isacharparenleft}{\isadigit{2}}{\isacharasterisk}x{\isacharparenright}\ {\isacharequal}\ {\isadigit{2}}\ {\isacharasterisk}\ abs\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ int{\isacharparenright}{\isachardoublequoteclose}\isanewline
|
| wenzelm@17056 | 363 |
% |
| wenzelm@17056 | 364 |
\isadelimproof |
| wenzelm@17056 | 365 |
% |
| wenzelm@17056 | 366 |
\endisadelimproof |
| wenzelm@17056 | 367 |
% |
| wenzelm@17056 | 368 |
\isatagproof |
| wenzelm@17175 | 369 |
\isacommand{by}\isamarkupfalse%
|
| wenzelm@17175 | 370 |
\ {\isacharparenleft}simp\ add{\isacharcolon}\ abs{\isacharunderscore}if{\isacharparenright}%
|
| wenzelm@17056 | 371 |
\endisatagproof |
| wenzelm@17056 | 372 |
{\isafoldproof}%
|
| wenzelm@17056 | 373 |
% |
| wenzelm@17056 | 374 |
\isadelimproof |
| wenzelm@17056 | 375 |
% |
| wenzelm@17056 | 376 |
\endisadelimproof |
| wenzelm@11866 | 377 |
% |
| paulson@11187 | 378 |
\begin{isamarkuptext}%
|
| paulson@13758 | 379 |
Induction rules for the Integers |
| paulson@13758 | 380 |
|
| paulson@13758 | 381 |
\begin{isabelle}%
|
| paulson@13758 | 382 |
{\isasymlbrakk}k\ {\isasymle}\ i{\isacharsemicolon}\ P\ k{\isacharsemicolon}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}k\ {\isasymle}\ i{\isacharsemicolon}\ P\ i{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ i%
|
| paulson@13758 | 383 |
\end{isabelle}
|
| paulson@13758 | 384 |
\rulename{int_ge_induct}
|
| paulson@13758 | 385 |
|
| paulson@13758 | 386 |
\begin{isabelle}%
|
| paulson@13758 | 387 |
{\isasymlbrakk}k\ {\isacharless}\ i{\isacharsemicolon}\ P\ {\isacharparenleft}k\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isacharsemicolon}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}k\ {\isacharless}\ i{\isacharsemicolon}\ P\ i{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ i%
|
| paulson@13758 | 388 |
\end{isabelle}
|
| paulson@13758 | 389 |
\rulename{int_gr_induct}
|
| paulson@13758 | 390 |
|
| paulson@13758 | 391 |
\begin{isabelle}%
|
| paulson@13758 | 392 |
{\isasymlbrakk}i\ {\isasymle}\ k{\isacharsemicolon}\ P\ k{\isacharsemicolon}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}i\ {\isasymle}\ k{\isacharsemicolon}\ P\ i{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}i\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ i%
|
| paulson@13758 | 393 |
\end{isabelle}
|
| paulson@13758 | 394 |
\rulename{int_le_induct}
|
| paulson@13758 | 395 |
|
| paulson@13758 | 396 |
\begin{isabelle}%
|
| paulson@13758 | 397 |
{\isasymlbrakk}i\ {\isacharless}\ k{\isacharsemicolon}\ P\ {\isacharparenleft}k\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}{\isacharsemicolon}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}i\ {\isacharless}\ k{\isacharsemicolon}\ P\ i{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}i\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ i%
|
| paulson@13758 | 398 |
\end{isabelle}
|
| paulson@13758 | 399 |
\rulename{int_less_induct}%
|
| paulson@13758 | 400 |
\end{isamarkuptext}%
|
| paulson@13758 | 401 |
\isamarkuptrue% |
| paulson@13758 | 402 |
% |
| paulson@13758 | 403 |
\begin{isamarkuptext}%
|
| paulson@14400 | 404 |
FIELDS |
| wenzelm@10776 | 405 |
|
| paulson@11187 | 406 |
\begin{isabelle}%
|
| wenzelm@25056 | 407 |
x\ {\isacharless}\ y\ {\isasymLongrightarrow}\ {\isasymexists}z{\isachargreater}x{\isachardot}\ z\ {\isacharless}\ y%
|
| wenzelm@10776 | 408 |
\end{isabelle}
|
| paulson@14295 | 409 |
\rulename{dense}
|
| paulson@11174 | 410 |
|
| paulson@11187 | 411 |
\begin{isabelle}%
|
| paulson@14288 | 412 |
a\ {\isacharasterisk}\ {\isacharparenleft}b\ {\isacharslash}\ c{\isacharparenright}\ {\isacharequal}\ a\ {\isacharasterisk}\ b\ {\isacharslash}\ c%
|
| paulson@11174 | 413 |
\end{isabelle}
|
| paulson@14288 | 414 |
\rulename{times_divide_eq_right}
|
| wenzelm@10776 | 415 |
|
| paulson@11187 | 416 |
\begin{isabelle}%
|
| paulson@14288 | 417 |
b\ {\isacharslash}\ c\ {\isacharasterisk}\ a\ {\isacharequal}\ b\ {\isacharasterisk}\ a\ {\isacharslash}\ c%
|
| wenzelm@10776 | 418 |
\end{isabelle}
|
| paulson@14288 | 419 |
\rulename{times_divide_eq_left}
|
| wenzelm@10776 | 420 |
|
| paulson@11187 | 421 |
\begin{isabelle}%
|
| paulson@14288 | 422 |
a\ {\isacharslash}\ {\isacharparenleft}b\ {\isacharslash}\ c{\isacharparenright}\ {\isacharequal}\ a\ {\isacharasterisk}\ c\ {\isacharslash}\ b%
|
| wenzelm@10776 | 423 |
\end{isabelle}
|
| paulson@14288 | 424 |
\rulename{divide_divide_eq_right}
|
| wenzelm@10776 | 425 |
|
| paulson@11187 | 426 |
\begin{isabelle}%
|
| paulson@14288 | 427 |
a\ {\isacharslash}\ b\ {\isacharslash}\ c\ {\isacharequal}\ a\ {\isacharslash}\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}%
|
| wenzelm@10776 | 428 |
\end{isabelle}
|
| paulson@14288 | 429 |
\rulename{divide_divide_eq_left}
|
| wenzelm@10776 | 430 |
|
| paulson@11187 | 431 |
\begin{isabelle}%
|
| paulson@14295 | 432 |
{\isacharminus}\ {\isacharparenleft}a\ {\isacharslash}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharminus}\ a\ {\isacharslash}\ b%
|
| wenzelm@10776 | 433 |
\end{isabelle}
|
| paulson@14295 | 434 |
\rulename{minus_divide_left}
|
| wenzelm@10776 | 435 |
|
| paulson@11187 | 436 |
\begin{isabelle}%
|
| paulson@14295 | 437 |
{\isacharminus}\ {\isacharparenleft}a\ {\isacharslash}\ b{\isacharparenright}\ {\isacharequal}\ a\ {\isacharslash}\ {\isacharminus}\ b%
|
| wenzelm@10776 | 438 |
\end{isabelle}
|
| paulson@14295 | 439 |
\rulename{minus_divide_right}
|
| wenzelm@10776 | 440 |
|
| wenzelm@10776 | 441 |
This last NOT a simprule |
| wenzelm@10776 | 442 |
|
| paulson@11187 | 443 |
\begin{isabelle}%
|
| paulson@14295 | 444 |
{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharslash}\ c\ {\isacharequal}\ a\ {\isacharslash}\ c\ {\isacharplus}\ b\ {\isacharslash}\ c%
|
| nipkow@10790 | 445 |
\end{isabelle}
|
| paulson@14295 | 446 |
\rulename{add_divide_distrib}%
|
| paulson@11187 | 447 |
\end{isamarkuptext}%
|
| wenzelm@17175 | 448 |
\isamarkuptrue% |
| wenzelm@17175 | 449 |
\isacommand{lemma}\isamarkupfalse%
|
| wenzelm@17175 | 450 |
\ {\isachardoublequoteopen}{\isadigit{3}}{\isacharslash}{\isadigit{4}}\ {\isacharless}\ {\isacharparenleft}{\isadigit{7}}{\isacharslash}{\isadigit{8}}\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isachardoublequoteclose}\isanewline
|
| wenzelm@17056 | 451 |
% |
| wenzelm@17056 | 452 |
\isadelimproof |
| wenzelm@17056 | 453 |
% |
| wenzelm@17056 | 454 |
\endisadelimproof |
| wenzelm@17056 | 455 |
% |
| wenzelm@17056 | 456 |
\isatagproof |
| wenzelm@17175 | 457 |
\isacommand{by}\isamarkupfalse%
|
| wenzelm@17175 | 458 |
\ simp% |
| wenzelm@17056 | 459 |
\endisatagproof |
| wenzelm@17056 | 460 |
{\isafoldproof}%
|
| wenzelm@17056 | 461 |
% |
| wenzelm@17056 | 462 |
\isadelimproof |
| wenzelm@17056 | 463 |
\ \isanewline |
| wenzelm@17056 | 464 |
% |
| wenzelm@17056 | 465 |
\endisadelimproof |
| paulson@11174 | 466 |
\isanewline |
| wenzelm@17175 | 467 |
\isacommand{lemma}\isamarkupfalse%
|
| wenzelm@17175 | 468 |
\ {\isachardoublequoteopen}P\ {\isacharparenleft}{\isacharparenleft}{\isadigit{3}}{\isacharslash}{\isadigit{4}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}{\isacharslash}{\isadigit{1}}{\isadigit{5}}\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
|
| wenzelm@17056 | 469 |
\isadelimproof |
| wenzelm@17056 | 470 |
% |
| wenzelm@17056 | 471 |
\endisadelimproof |
| wenzelm@17056 | 472 |
% |
| wenzelm@17056 | 473 |
\isatagproof |
| wenzelm@16353 | 474 |
% |
| wenzelm@16353 | 475 |
\begin{isamarkuptxt}%
|
| wenzelm@16353 | 476 |
\begin{isabelle}%
|
| wenzelm@16353 | 477 |
\ {\isadigit{1}}{\isachardot}\ P\ {\isacharparenleft}{\isadigit{3}}\ {\isacharslash}\ {\isadigit{4}}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}\ {\isacharslash}\ {\isadigit{1}}{\isadigit{5}}{\isacharparenright}{\isacharparenright}%
|
| wenzelm@16353 | 478 |
\end{isabelle}%
|
| wenzelm@16353 | 479 |
\end{isamarkuptxt}%
|
| wenzelm@17175 | 480 |
\isamarkuptrue% |
| wenzelm@17175 | 481 |
\isacommand{apply}\isamarkupfalse%
|
| wenzelm@17175 | 482 |
\ simp% |
| wenzelm@16353 | 483 |
\begin{isamarkuptxt}%
|
| wenzelm@16353 | 484 |
\begin{isabelle}%
|
| wenzelm@16353 | 485 |
\ {\isadigit{1}}{\isachardot}\ P\ {\isacharparenleft}{\isadigit{2}}\ {\isacharslash}\ {\isadigit{5}}{\isacharparenright}%
|
| wenzelm@16353 | 486 |
\end{isabelle}%
|
| wenzelm@16353 | 487 |
\end{isamarkuptxt}%
|
| wenzelm@17175 | 488 |
\isamarkuptrue% |
| wenzelm@17175 | 489 |
\isacommand{oops}\isamarkupfalse%
|
| wenzelm@17175 | 490 |
% |
| wenzelm@17056 | 491 |
\endisatagproof |
| wenzelm@17056 | 492 |
{\isafoldproof}%
|
| wenzelm@17056 | 493 |
% |
| wenzelm@17056 | 494 |
\isadelimproof |
| wenzelm@17056 | 495 |
% |
| wenzelm@17056 | 496 |
\endisadelimproof |
| wenzelm@17056 | 497 |
\isanewline |
| paulson@15481 | 498 |
\isanewline |
| wenzelm@17175 | 499 |
\isacommand{lemma}\isamarkupfalse%
|
| wenzelm@17175 | 500 |
\ {\isachardoublequoteopen}{\isacharparenleft}{\isadigit{3}}{\isacharslash}{\isadigit{4}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}{\isacharslash}{\isadigit{1}}{\isadigit{5}}{\isacharparenright}\ {\isacharless}\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isachardoublequoteclose}%
|
| wenzelm@17056 | 501 |
\isadelimproof |
| wenzelm@17056 | 502 |
% |
| wenzelm@17056 | 503 |
\endisadelimproof |
| wenzelm@17056 | 504 |
% |
| wenzelm@17056 | 505 |
\isatagproof |
| wenzelm@16353 | 506 |
% |
| wenzelm@16353 | 507 |
\begin{isamarkuptxt}%
|
| wenzelm@16353 | 508 |
\begin{isabelle}%
|
| wenzelm@16353 | 509 |
\ {\isadigit{1}}{\isachardot}\ {\isadigit{3}}\ {\isacharslash}\ {\isadigit{4}}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}\ {\isacharslash}\ {\isadigit{1}}{\isadigit{5}}{\isacharparenright}\ {\isacharless}\ x%
|
| wenzelm@16353 | 510 |
\end{isabelle}%
|
| wenzelm@16353 | 511 |
\end{isamarkuptxt}%
|
| wenzelm@17175 | 512 |
\isamarkuptrue% |
| wenzelm@17175 | 513 |
\isacommand{apply}\isamarkupfalse%
|
| wenzelm@17175 | 514 |
\ simp% |
| wenzelm@16353 | 515 |
\begin{isamarkuptxt}%
|
| wenzelm@16353 | 516 |
\begin{isabelle}%
|
| wenzelm@16353 | 517 |
\ {\isadigit{1}}{\isachardot}\ {\isadigit{2}}\ {\isacharless}\ x\ {\isacharasterisk}\ {\isadigit{5}}%
|
| wenzelm@16353 | 518 |
\end{isabelle}%
|
| wenzelm@16353 | 519 |
\end{isamarkuptxt}%
|
| wenzelm@17175 | 520 |
\isamarkuptrue% |
| wenzelm@17175 | 521 |
\isacommand{oops}\isamarkupfalse%
|
| wenzelm@17175 | 522 |
% |
| wenzelm@17056 | 523 |
\endisatagproof |
| wenzelm@17056 | 524 |
{\isafoldproof}%
|
| wenzelm@17056 | 525 |
% |
| wenzelm@17056 | 526 |
\isadelimproof |
| wenzelm@17056 | 527 |
% |
| wenzelm@17056 | 528 |
\endisadelimproof |
| paulson@14400 | 529 |
% |
| paulson@14400 | 530 |
\begin{isamarkuptext}%
|
| paulson@14400 | 531 |
Ring and Field |
| paulson@14400 | 532 |
|
| paulson@14400 | 533 |
Requires a field, or else an ordered ring |
| paulson@14400 | 534 |
|
| paulson@14400 | 535 |
\begin{isabelle}%
|
| paulson@14400 | 536 |
{\isacharparenleft}a\ {\isacharasterisk}\ b\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isasymor}\ b\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}{\isacharparenright}%
|
| paulson@14400 | 537 |
\end{isabelle}
|
| paulson@14400 | 538 |
\rulename{mult_eq_0_iff}
|
| paulson@14400 | 539 |
|
| paulson@14400 | 540 |
\begin{isabelle}%
|
| paulson@14400 | 541 |
{\isacharparenleft}a\ {\isacharasterisk}\ c\ {\isacharequal}\ b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}c\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isasymor}\ a\ {\isacharequal}\ b{\isacharparenright}%
|
| paulson@14400 | 542 |
\end{isabelle}
|
| paulson@14400 | 543 |
\rulename{mult_cancel_right}
|
| paulson@14400 | 544 |
|
| paulson@14400 | 545 |
\begin{isabelle}%
|
| paulson@23504 | 546 |
{\isacharparenleft}c\ {\isacharasterisk}\ a\ {\isacharequal}\ c\ {\isacharasterisk}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}c\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isasymor}\ a\ {\isacharequal}\ b{\isacharparenright}%
|
| paulson@14400 | 547 |
\end{isabelle}
|
| paulson@23504 | 548 |
\rulename{mult_cancel_left}%
|
| paulson@14400 | 549 |
\end{isamarkuptext}%
|
| wenzelm@17175 | 550 |
\isamarkuptrue% |
| wenzelm@17056 | 551 |
% |
| wenzelm@17056 | 552 |
\isadelimML |
| wenzelm@17056 | 553 |
% |
| wenzelm@17056 | 554 |
\endisadelimML |
| wenzelm@17056 | 555 |
% |
| wenzelm@17056 | 556 |
\isatagML |
| wenzelm@17175 | 557 |
\isacommand{ML}\isamarkupfalse%
|
| wenzelm@17181 | 558 |
{\isacharverbatimopen}set\ show{\isacharunderscore}sorts{\isacharverbatimclose}%
|
| wenzelm@17056 | 559 |
\endisatagML |
| wenzelm@17056 | 560 |
{\isafoldML}%
|
| wenzelm@17056 | 561 |
% |
| wenzelm@17056 | 562 |
\isadelimML |
| wenzelm@17056 | 563 |
% |
| wenzelm@17056 | 564 |
\endisadelimML |
| paulson@14400 | 565 |
% |
| paulson@14400 | 566 |
\begin{isamarkuptext}%
|
| paulson@14400 | 567 |
effect of show sorts on the above |
| paulson@14400 | 568 |
|
| paulson@14400 | 569 |
\begin{isabelle}%
|
| paulson@23504 | 570 |
{\isacharparenleft}{\isacharparenleft}c{\isasymColon}{\isacharprime}a{\isasymColon}ring{\isacharunderscore}no{\isacharunderscore}zero{\isacharunderscore}divisors{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}a{\isasymColon}{\isacharprime}a{\isasymColon}ring{\isacharunderscore}no{\isacharunderscore}zero{\isacharunderscore}divisors{\isacharparenright}\ {\isacharequal}\isanewline
|
| paulson@23504 | 571 |
\isaindent{{\isacharparenleft}}c\ {\isacharasterisk}\ {\isacharparenleft}b{\isasymColon}{\isacharprime}a{\isasymColon}ring{\isacharunderscore}no{\isacharunderscore}zero{\isacharunderscore}divisors{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
|
| paulson@23504 | 572 |
{\isacharparenleft}c\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isasymColon}ring{\isacharunderscore}no{\isacharunderscore}zero{\isacharunderscore}divisors{\isacharparenright}\ {\isasymor}\ a\ {\isacharequal}\ b{\isacharparenright}%
|
| paulson@14400 | 573 |
\end{isabelle}
|
| paulson@23504 | 574 |
\rulename{mult_cancel_left}%
|
| paulson@14400 | 575 |
\end{isamarkuptext}%
|
| wenzelm@17175 | 576 |
\isamarkuptrue% |
| wenzelm@17056 | 577 |
% |
| wenzelm@17056 | 578 |
\isadelimML |
| wenzelm@17056 | 579 |
% |
| wenzelm@17056 | 580 |
\endisadelimML |
| wenzelm@17056 | 581 |
% |
| wenzelm@17056 | 582 |
\isatagML |
| wenzelm@17175 | 583 |
\isacommand{ML}\isamarkupfalse%
|
| wenzelm@17181 | 584 |
{\isacharverbatimopen}reset\ show{\isacharunderscore}sorts{\isacharverbatimclose}%
|
| wenzelm@17056 | 585 |
\endisatagML |
| wenzelm@17056 | 586 |
{\isafoldML}%
|
| wenzelm@17056 | 587 |
% |
| wenzelm@17056 | 588 |
\isadelimML |
| wenzelm@17056 | 589 |
% |
| wenzelm@17056 | 590 |
\endisadelimML |
| paulson@14400 | 591 |
% |
| paulson@14400 | 592 |
\begin{isamarkuptext}%
|
| paulson@14400 | 593 |
absolute value |
| paulson@14400 | 594 |
|
| paulson@14400 | 595 |
\begin{isabelle}%
|
| paulson@14400 | 596 |
{\isasymbar}a\ {\isacharasterisk}\ b{\isasymbar}\ {\isacharequal}\ {\isasymbar}a{\isasymbar}\ {\isacharasterisk}\ {\isasymbar}b{\isasymbar}%
|
| paulson@14400 | 597 |
\end{isabelle}
|
| paulson@14400 | 598 |
\rulename{abs_mult}
|
| paulson@14400 | 599 |
|
| paulson@14400 | 600 |
\begin{isabelle}%
|
| paulson@14400 | 601 |
{\isacharparenleft}{\isasymbar}a{\isasymbar}\ {\isasymle}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a\ {\isasymle}\ b\ {\isasymand}\ {\isacharminus}\ a\ {\isasymle}\ b{\isacharparenright}%
|
| paulson@14400 | 602 |
\end{isabelle}
|
| paulson@14400 | 603 |
\rulename{abs_le_iff}
|
| paulson@14400 | 604 |
|
| paulson@14400 | 605 |
\begin{isabelle}%
|
| paulson@14400 | 606 |
{\isasymbar}a\ {\isacharplus}\ b{\isasymbar}\ {\isasymle}\ {\isasymbar}a{\isasymbar}\ {\isacharplus}\ {\isasymbar}b{\isasymbar}%
|
| paulson@14400 | 607 |
\end{isabelle}
|
| paulson@14400 | 608 |
\rulename{abs_triangle_ineq}
|
| paulson@14400 | 609 |
|
| paulson@14400 | 610 |
\begin{isabelle}%
|
| paulson@14400 | 611 |
a\ {\isacharcircum}\ {\isacharparenleft}m\ {\isacharplus}\ n{\isacharparenright}\ {\isacharequal}\ a\ {\isacharcircum}\ m\ {\isacharasterisk}\ a\ {\isacharcircum}\ n%
|
| paulson@14400 | 612 |
\end{isabelle}
|
| paulson@14400 | 613 |
\rulename{power_add}
|
| paulson@14400 | 614 |
|
| paulson@14400 | 615 |
\begin{isabelle}%
|
| paulson@14400 | 616 |
a\ {\isacharcircum}\ {\isacharparenleft}m\ {\isacharasterisk}\ n{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a\ {\isacharcircum}\ m{\isacharparenright}\ {\isacharcircum}\ n%
|
| paulson@14400 | 617 |
\end{isabelle}
|
| paulson@14400 | 618 |
\rulename{power_mult}
|
| paulson@14400 | 619 |
|
| paulson@14400 | 620 |
\begin{isabelle}%
|
| paulson@14400 | 621 |
{\isasymbar}a\ {\isacharcircum}\ n{\isasymbar}\ {\isacharequal}\ {\isasymbar}a{\isasymbar}\ {\isacharcircum}\ n%
|
| paulson@14400 | 622 |
\end{isabelle}
|
| paulson@14400 | 623 |
\rulename{power_abs}%
|
| paulson@14400 | 624 |
\end{isamarkuptext}%
|
| wenzelm@17175 | 625 |
\isamarkuptrue% |
| wenzelm@17056 | 626 |
% |
| wenzelm@17056 | 627 |
\isadelimtheory |
| wenzelm@17056 | 628 |
% |
| wenzelm@17056 | 629 |
\endisadelimtheory |
| wenzelm@17056 | 630 |
% |
| wenzelm@17056 | 631 |
\isatagtheory |
| wenzelm@17175 | 632 |
\isacommand{end}\isamarkupfalse%
|
| wenzelm@17175 | 633 |
% |
| wenzelm@17056 | 634 |
\endisatagtheory |
| wenzelm@17056 | 635 |
{\isafoldtheory}%
|
| wenzelm@17056 | 636 |
% |
| wenzelm@17056 | 637 |
\isadelimtheory |
| wenzelm@17056 | 638 |
% |
| wenzelm@17056 | 639 |
\endisadelimtheory |
| wenzelm@17056 | 640 |
\isanewline |
| paulson@11187 | 641 |
\end{isabellebody}%
|
| paulson@10602 | 642 |
%%% Local Variables: |
| paulson@10602 | 643 |
%%% mode: latex |
| paulson@10602 | 644 |
%%% TeX-master: "root" |
| paulson@10602 | 645 |
%%% End: |