author | paulson |
Mon, 22 Oct 2001 12:01:35 +0200 | |
changeset 11870 | 181bd2050cf4 |
parent 11866 | fbd097aec213 |
child 12156 | d2758965362e |
permissions | -rw-r--r-- |
10602 | 1 |
% |
11187 | 2 |
\begin{isabellebody}% |
3 |
\def\isabellecontext{Numbers}% |
|
10602 | 4 |
\isanewline |
11187 | 5 |
\isacommand{theory}\ Numbers\ {\isacharequal}\ Real{\isacharcolon}\isanewline |
10602 | 6 |
\isanewline |
11866 | 7 |
\isamarkupfalse% |
11187 | 8 |
\isacommand{ML}\ {\isachardoublequote}Pretty{\isachardot}setmargin\ {\isadigit{6}}{\isadigit{4}}{\isachardoublequote}\isanewline |
11866 | 9 |
\isamarkupfalse% |
10 |
\isacommand{ML}\ {\isachardoublequote}IsarOutput{\isachardot}indent\ {\isacharcolon}{\isacharequal}\ {\isadigit{0}}{\isachardoublequote}\isamarkupfalse% |
|
11 |
% |
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11187 | 12 |
\begin{isamarkuptext}% |
10602 | 13 |
numeric literals; default simprules; can re-orient% |
11187 | 14 |
\end{isamarkuptext}% |
11866 | 15 |
\isamarkuptrue% |
16 |
\isacommand{lemma}\ {\isachardoublequote}{\isadigit{2}}\ {\isacharasterisk}\ m\ {\isacharequal}\ m\ {\isacharplus}\ m{\isachardoublequote}\isamarkupfalse% |
|
17 |
% |
|
11187 | 18 |
\begin{isamarkuptxt}% |
19 |
\begin{isabelle}% |
|
11708 | 20 |
\ {\isadigit{1}}{\isachardot}\ {\isacharparenleft}{\isadigit{2}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharasterisk}\ m\ {\isacharequal}\ m\ {\isacharplus}\ m% |
11187 | 21 |
\end{isabelle}% |
22 |
\end{isamarkuptxt}% |
|
11866 | 23 |
\isamarkuptrue% |
10878 | 24 |
\isacommand{oops}\isanewline |
10602 | 25 |
\isanewline |
11866 | 26 |
\isamarkupfalse% |
11187 | 27 |
\isacommand{consts}\ h\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}nat\ {\isasymRightarrow}\ nat{\isachardoublequote}\isanewline |
11866 | 28 |
\isamarkupfalse% |
11187 | 29 |
\isacommand{recdef}\ h\ {\isachardoublequote}{\isacharbraceleft}{\isacharbraceright}{\isachardoublequote}\isanewline |
11866 | 30 |
{\isachardoublequote}h\ i\ {\isacharequal}\ {\isacharparenleft}if\ i\ {\isacharequal}\ {\isadigit{3}}\ then\ {\isadigit{2}}\ else\ i{\isacharparenright}{\isachardoublequote}\isamarkupfalse% |
31 |
% |
|
11187 | 32 |
\begin{isamarkuptext}% |
11708 | 33 |
\isa{h\ {\isadigit{3}}\ {\isacharequal}\ {\isadigit{2}}} |
11187 | 34 |
\isa{h\ i\ {\isacharequal}\ i}% |
35 |
\end{isamarkuptext}% |
|
11866 | 36 |
\isamarkuptrue% |
10878 | 37 |
% |
11187 | 38 |
\begin{isamarkuptext}% |
39 |
\begin{isabelle}% |
|
11708 | 40 |
Numeral{\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}% |
11187 | 41 |
\end{isabelle} |
11174 | 42 |
\rulename{numeral_0_eq_0} |
10602 | 43 |
|
11187 | 44 |
\begin{isabelle}% |
11708 | 45 |
Numeral{\isadigit{1}}\ {\isacharequal}\ {\isadigit{1}}% |
10602 | 46 |
\end{isabelle} |
11187 | 47 |
\rulename{numeral_1_eq_1} |
11174 | 48 |
|
11187 | 49 |
\begin{isabelle}% |
11708 | 50 |
{\isadigit{2}}\ {\isacharplus}\ n\ {\isacharequal}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}% |
11187 | 51 |
\end{isabelle} |
10602 | 52 |
\rulename{add_2_eq_Suc} |
11187 | 53 |
|
54 |
\begin{isabelle}% |
|
11708 | 55 |
n\ {\isacharplus}\ {\isadigit{2}}\ {\isacharequal}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}% |
10602 | 56 |
\end{isabelle} |
11174 | 57 |
\rulename{add_2_eq_Suc'} |
58 |
||
11187 | 59 |
\begin{isabelle}% |
60 |
m\ {\isacharplus}\ n\ {\isacharplus}\ k\ {\isacharequal}\ m\ {\isacharplus}\ {\isacharparenleft}n\ {\isacharplus}\ k{\isacharparenright}% |
|
11174 | 61 |
\end{isabelle} |
11187 | 62 |
\rulename{add_assoc} |
10602 | 63 |
|
11187 | 64 |
\begin{isabelle}% |
65 |
m\ {\isacharplus}\ n\ {\isacharequal}\ n\ {\isacharplus}\ m% |
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11174 | 66 |
\end{isabelle} |
11187 | 67 |
\rulename{add_commute} |
10602 | 68 |
|
11187 | 69 |
\begin{isabelle}% |
70 |
x\ {\isacharplus}\ {\isacharparenleft}y\ {\isacharplus}\ z{\isacharparenright}\ {\isacharequal}\ y\ {\isacharplus}\ {\isacharparenleft}x\ {\isacharplus}\ z{\isacharparenright}% |
|
71 |
\end{isabelle} |
|
11174 | 72 |
\rulename{add_left_commute} |
10602 | 73 |
|
74 |
these form add_ac; similarly there is mult_ac% |
|
11187 | 75 |
\end{isamarkuptext}% |
11866 | 76 |
\isamarkuptrue% |
77 |
\isacommand{lemma}\ {\isachardoublequote}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}{\isachardoublequote}\isamarkupfalse% |
|
78 |
% |
|
11187 | 79 |
\begin{isamarkuptxt}% |
80 |
\begin{isabelle}% |
|
81 |
\ {\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}% |
|
82 |
\end{isabelle}% |
|
83 |
\end{isamarkuptxt}% |
|
11866 | 84 |
\isamarkuptrue% |
85 |
\isacommand{apply}\ {\isacharparenleft}simp\ add{\isacharcolon}\ add{\isacharunderscore}ac\ mult{\isacharunderscore}ac{\isacharparenright}\isamarkupfalse% |
|
86 |
% |
|
11187 | 87 |
\begin{isamarkuptxt}% |
88 |
\begin{isabelle}% |
|
89 |
\ {\isadigit{1}}{\isachardot}\ Suc\ {\isacharparenleft}i\ {\isacharplus}\ {\isacharparenleft}m\ {\isacharasterisk}\ n\ {\isacharplus}\ j\ {\isacharasterisk}\ {\isacharparenleft}k\ {\isacharasterisk}\ l{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline |
|
90 |
\isaindent{\ {\isadigit{1}}{\isachardot}\ }f\ {\isacharparenleft}i\ {\isacharplus}\ {\isacharparenleft}m\ {\isacharasterisk}\ n\ {\isacharplus}\ j\ {\isacharasterisk}\ {\isacharparenleft}k\ {\isacharasterisk}\ l{\isacharparenright}{\isacharparenright}{\isacharparenright}% |
|
91 |
\end{isabelle}% |
|
92 |
\end{isamarkuptxt}% |
|
11866 | 93 |
\isamarkuptrue% |
94 |
\isacommand{oops}\isamarkupfalse% |
|
95 |
% |
|
11187 | 96 |
\begin{isamarkuptext}% |
97 |
\begin{isabelle}% |
|
98 |
{\isasymlbrakk}i\ {\isasymle}\ j{\isacharsemicolon}\ k\ {\isasymle}\ l{\isasymrbrakk}\ {\isasymLongrightarrow}\ i\ {\isacharasterisk}\ k\ {\isasymle}\ j\ {\isacharasterisk}\ l% |
|
10602 | 99 |
\end{isabelle} |
100 |
\rulename{mult_le_mono} |
|
101 |
||
11187 | 102 |
\begin{isabelle}% |
103 |
{\isasymlbrakk}i\ {\isacharless}\ j{\isacharsemicolon}\ {\isadigit{0}}\ {\isacharless}\ k{\isasymrbrakk}\ {\isasymLongrightarrow}\ i\ {\isacharasterisk}\ k\ {\isacharless}\ j\ {\isacharasterisk}\ k% |
|
104 |
\end{isabelle} |
|
10602 | 105 |
\rulename{mult_less_mono1} |
106 |
||
11187 | 107 |
\begin{isabelle}% |
108 |
m\ {\isasymle}\ n\ {\isasymLongrightarrow}\ m\ div\ k\ {\isasymle}\ n\ div\ k% |
|
109 |
\end{isabelle} |
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11174 | 110 |
\rulename{div_le_mono} |
10602 | 111 |
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11187 | 112 |
\begin{isabelle}% |
113 |
{\isacharparenleft}m\ {\isacharplus}\ n{\isacharparenright}\ {\isacharasterisk}\ k\ {\isacharequal}\ m\ {\isacharasterisk}\ k\ {\isacharplus}\ n\ {\isacharasterisk}\ k% |
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114 |
\end{isabelle} |
|
11174 | 115 |
\rulename{add_mult_distrib} |
10602 | 116 |
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11187 | 117 |
\begin{isabelle}% |
118 |
{\isacharparenleft}m\ {\isacharminus}\ n{\isacharparenright}\ {\isacharasterisk}\ k\ {\isacharequal}\ m\ {\isacharasterisk}\ k\ {\isacharminus}\ n\ {\isacharasterisk}\ k% |
|
119 |
\end{isabelle} |
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11174 | 120 |
\rulename{diff_mult_distrib} |
10602 | 121 |
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11187 | 122 |
\begin{isabelle}% |
123 |
m\ mod\ n\ {\isacharasterisk}\ k\ {\isacharequal}\ m\ {\isacharasterisk}\ k\ mod\ {\isacharparenleft}n\ {\isacharasterisk}\ k{\isacharparenright}% |
|
124 |
\end{isabelle} |
|
11174 | 125 |
\rulename{mod_mult_distrib} |
10602 | 126 |
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11187 | 127 |
\begin{isabelle}% |
128 |
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}% |
|
10602 | 129 |
\end{isabelle} |
11187 | 130 |
\rulename{nat_diff_split}% |
131 |
\end{isamarkuptext}% |
|
11866 | 132 |
\isamarkuptrue% |
11708 | 133 |
\isacommand{lemma}\ {\isachardoublequote}{\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}{\isachardoublequote}\isanewline |
11866 | 134 |
\isamarkupfalse% |
11480 | 135 |
\isacommand{apply}\ {\isacharparenleft}clarsimp\ split{\isacharcolon}\ nat{\isacharunderscore}diff{\isacharunderscore}split{\isacharparenright}\isanewline |
136 |
\ % |
|
137 |
\isamarkupcmt{\begin{isabelle}% |
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11708 | 138 |
\ {\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}}% |
11480 | 139 |
\end{isabelle}% |
140 |
} |
|
141 |
\isanewline |
|
11866 | 142 |
\isamarkupfalse% |
11480 | 143 |
\isacommand{apply}\ {\isacharparenleft}subgoal{\isacharunderscore}tac\ {\isachardoublequote}n{\isacharequal}{\isadigit{0}}\ {\isacharbar}\ n{\isacharequal}{\isadigit{1}}{\isachardoublequote}{\isacharcomma}\ force{\isacharcomma}\ arith{\isacharparenright}\isanewline |
11866 | 144 |
\isamarkupfalse% |
145 |
\isacommand{done}\isamarkupfalse% |
|
146 |
% |
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11187 | 147 |
\begin{isamarkuptext}% |
148 |
\begin{isabelle}% |
|
149 |
m\ mod\ n\ {\isacharequal}\ {\isacharparenleft}if\ m\ {\isacharless}\ n\ then\ m\ else\ {\isacharparenleft}m\ {\isacharminus}\ n{\isacharparenright}\ mod\ n{\isacharparenright}% |
|
150 |
\end{isabelle} |
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11174 | 151 |
\rulename{mod_if} |
11187 | 152 |
|
153 |
\begin{isabelle}% |
|
154 |
m\ div\ n\ {\isacharasterisk}\ n\ {\isacharplus}\ m\ mod\ n\ {\isacharequal}\ m% |
|
10602 | 155 |
\end{isabelle} |
11174 | 156 |
\rulename{mod_div_equality} |
10602 | 157 |
|
158 |
||
11187 | 159 |
\begin{isabelle}% |
160 |
a\ {\isacharasterisk}\ b\ div\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ div\ c{\isacharparenright}\ {\isacharplus}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ div\ c% |
|
161 |
\end{isabelle} |
|
11174 | 162 |
\rulename{div_mult1_eq} |
10602 | 163 |
|
11187 | 164 |
\begin{isabelle}% |
165 |
a\ {\isacharasterisk}\ b\ mod\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ mod\ c% |
|
166 |
\end{isabelle} |
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11174 | 167 |
\rulename{mod_mult1_eq} |
10602 | 168 |
|
11187 | 169 |
\begin{isabelle}% |
170 |
a\ div\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ a\ div\ b\ div\ c% |
|
171 |
\end{isabelle} |
|
11174 | 172 |
\rulename{div_mult2_eq} |
10602 | 173 |
|
11187 | 174 |
\begin{isabelle}% |
175 |
a\ mod\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ b\ {\isacharasterisk}\ {\isacharparenleft}a\ div\ b\ mod\ c{\isacharparenright}\ {\isacharplus}\ a\ mod\ b% |
|
176 |
\end{isabelle} |
|
11174 | 177 |
\rulename{mod_mult2_eq} |
10602 | 178 |
|
11187 | 179 |
\begin{isabelle}% |
180 |
{\isadigit{0}}\ {\isacharless}\ c\ {\isasymLongrightarrow}\ c\ {\isacharasterisk}\ a\ div\ {\isacharparenleft}c\ {\isacharasterisk}\ b{\isacharparenright}\ {\isacharequal}\ a\ div\ b% |
|
181 |
\end{isabelle} |
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11174 | 182 |
\rulename{div_mult_mult1} |
10602 | 183 |
|
11187 | 184 |
\begin{isabelle}% |
185 |
a\ div\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}% |
|
186 |
\end{isabelle} |
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11174 | 187 |
\rulename{DIVISION_BY_ZERO_DIV} |
10602 | 188 |
|
11187 | 189 |
\begin{isabelle}% |
190 |
a\ mod\ {\isadigit{0}}\ {\isacharequal}\ a% |
|
191 |
\end{isabelle} |
|
11174 | 192 |
\rulename{DIVISION_BY_ZERO_MOD} |
10602 | 193 |
|
11187 | 194 |
\begin{isabelle}% |
195 |
{\isasymlbrakk}m\ dvd\ n{\isacharsemicolon}\ n\ dvd\ m{\isasymrbrakk}\ {\isasymLongrightarrow}\ m\ {\isacharequal}\ n% |
|
196 |
\end{isabelle} |
|
11174 | 197 |
\rulename{dvd_anti_sym} |
10602 | 198 |
|
11187 | 199 |
\begin{isabelle}% |
200 |
{\isasymlbrakk}k\ dvd\ m{\isacharsemicolon}\ k\ dvd\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ k\ dvd\ m\ {\isacharplus}\ n% |
|
201 |
\end{isabelle} |
|
11174 | 202 |
\rulename{dvd_add} |
10602 | 203 |
|
204 |
For the integers, I'd list a few theorems that somehow involve negative |
|
205 |
numbers. |
|
206 |
||
207 |
Division, remainder of negatives |
|
208 |
||
209 |
||
11187 | 210 |
\begin{isabelle}% |
11870
181bd2050cf4
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paulson
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11866
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211 |
{\isadigit{0}}\ {\isacharless}\ b\ {\isasymLongrightarrow}\ {\isadigit{0}}\ {\isasymle}\ a\ mod\ b% |
11187 | 212 |
\end{isabelle} |
11174 | 213 |
\rulename{pos_mod_sign} |
10602 | 214 |
|
11187 | 215 |
\begin{isabelle}% |
11870
181bd2050cf4
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paulson
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11866
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216 |
{\isadigit{0}}\ {\isacharless}\ b\ {\isasymLongrightarrow}\ a\ mod\ b\ {\isacharless}\ b% |
11174 | 217 |
\end{isabelle} |
11187 | 218 |
\rulename{pos_mod_bound} |
10602 | 219 |
|
11187 | 220 |
\begin{isabelle}% |
11870
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221 |
b\ {\isacharless}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ a\ mod\ b\ {\isasymle}\ {\isadigit{0}}% |
11174 | 222 |
\end{isabelle} |
11187 | 223 |
\rulename{neg_mod_sign} |
10602 | 224 |
|
11187 | 225 |
\begin{isabelle}% |
11870
181bd2050cf4
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paulson
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11866
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226 |
b\ {\isacharless}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ b\ {\isacharless}\ a\ mod\ b% |
11187 | 227 |
\end{isabelle} |
11174 | 228 |
\rulename{neg_mod_bound} |
10602 | 229 |
|
11187 | 230 |
\begin{isabelle}% |
231 |
{\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% |
|
11174 | 232 |
\end{isabelle} |
11187 | 233 |
\rulename{zdiv_zadd1_eq} |
10602 | 234 |
|
11187 | 235 |
\begin{isabelle}% |
236 |
{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ mod\ c\ {\isacharequal}\ {\isacharparenleft}a\ mod\ c\ {\isacharplus}\ b\ mod\ c{\isacharparenright}\ mod\ c% |
|
237 |
\end{isabelle} |
|
10602 | 238 |
\rulename{zmod_zadd1_eq} |
239 |
||
11187 | 240 |
\begin{isabelle}% |
241 |
a\ {\isacharasterisk}\ b\ div\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ div\ c{\isacharparenright}\ {\isacharplus}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ div\ c% |
|
10602 | 242 |
\end{isabelle} |
11187 | 243 |
\rulename{zdiv_zmult1_eq} |
10602 | 244 |
|
11187 | 245 |
\begin{isabelle}% |
246 |
a\ {\isacharasterisk}\ b\ mod\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ mod\ c% |
|
247 |
\end{isabelle} |
|
10602 | 248 |
\rulename{zmod_zmult1_eq} |
249 |
||
11187 | 250 |
\begin{isabelle}% |
11870
181bd2050cf4
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paulson
parents:
11866
diff
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|
251 |
{\isadigit{0}}\ {\isacharless}\ c\ {\isasymLongrightarrow}\ a\ div\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ a\ div\ b\ div\ c% |
11174 | 252 |
\end{isabelle} |
11187 | 253 |
\rulename{zdiv_zmult2_eq} |
10602 | 254 |
|
11187 | 255 |
\begin{isabelle}% |
11870
181bd2050cf4
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paulson
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11866
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256 |
{\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% |
11187 | 257 |
\end{isabelle} |
11174 | 258 |
\rulename{zmod_zmult2_eq} |
11187 | 259 |
|
260 |
\begin{isabelle}% |
|
261 |
{\isasymbar}x\ {\isacharasterisk}\ y{\isasymbar}\ {\isacharequal}\ {\isasymbar}x{\isasymbar}\ {\isacharasterisk}\ {\isasymbar}y{\isasymbar}% |
|
10602 | 262 |
\end{isabelle} |
11187 | 263 |
\rulename{abs_mult}% |
264 |
\end{isamarkuptext}% |
|
11866 | 265 |
\isamarkuptrue% |
11187 | 266 |
\isacommand{lemma}\ {\isachardoublequote}abs\ {\isacharparenleft}x{\isacharplus}y{\isacharparenright}\ {\isasymle}\ abs\ x\ {\isacharplus}\ abs\ {\isacharparenleft}y\ {\isacharcolon}{\isacharcolon}\ int{\isacharparenright}{\isachardoublequote}\isanewline |
11866 | 267 |
\isamarkupfalse% |
11174 | 268 |
\isacommand{by}\ arith\isanewline |
269 |
\isanewline |
|
11866 | 270 |
\isamarkupfalse% |
11708 | 271 |
\isacommand{lemma}\ {\isachardoublequote}abs\ {\isacharparenleft}{\isadigit{2}}{\isacharasterisk}x{\isacharparenright}\ {\isacharequal}\ {\isadigit{2}}\ {\isacharasterisk}\ abs\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ int{\isacharparenright}{\isachardoublequote}\isanewline |
11866 | 272 |
\isamarkupfalse% |
273 |
\isacommand{by}\ {\isacharparenleft}simp\ add{\isacharcolon}\ zabs{\isacharunderscore}def{\isacharparenright}\isamarkupfalse% |
|
274 |
% |
|
11187 | 275 |
\begin{isamarkuptext}% |
10776 | 276 |
REALS |
277 |
||
11187 | 278 |
\begin{isabelle}% |
279 |
{\isasymbar}r{\isasymbar}\ {\isacharcircum}\ n\ {\isacharequal}\ {\isasymbar}r\ {\isacharcircum}\ n{\isasymbar}% |
|
280 |
\end{isabelle} |
|
11174 | 281 |
\rulename{realpow_abs} |
10776 | 282 |
|
11187 | 283 |
\begin{isabelle}% |
284 |
x\ {\isacharless}\ y\ {\isasymLongrightarrow}\ {\isasymexists}r{\isachardot}\ x\ {\isacharless}\ r\ {\isasymand}\ r\ {\isacharless}\ y% |
|
285 |
\end{isabelle} |
|
11174 | 286 |
\rulename{real_dense} |
10776 | 287 |
|
11187 | 288 |
\begin{isabelle}% |
289 |
{\isasymbar}r{\isasymbar}\ {\isacharcircum}\ n\ {\isacharequal}\ {\isasymbar}r\ {\isacharcircum}\ n{\isasymbar}% |
|
290 |
\end{isabelle} |
|
11174 | 291 |
\rulename{realpow_abs} |
10776 | 292 |
|
11187 | 293 |
\begin{isabelle}% |
294 |
x\ {\isacharasterisk}\ {\isacharparenleft}y\ {\isacharslash}\ z{\isacharparenright}\ {\isacharequal}\ x\ {\isacharasterisk}\ y\ {\isacharslash}\ z% |
|
295 |
\end{isabelle} |
|
11174 | 296 |
\rulename{real_times_divide1_eq} |
10776 | 297 |
|
11187 | 298 |
\begin{isabelle}% |
299 |
y\ {\isacharslash}\ z\ {\isacharasterisk}\ x\ {\isacharequal}\ y\ {\isacharasterisk}\ x\ {\isacharslash}\ z% |
|
300 |
\end{isabelle} |
|
11174 | 301 |
\rulename{real_times_divide2_eq} |
10776 | 302 |
|
11187 | 303 |
\begin{isabelle}% |
304 |
x\ {\isacharslash}\ {\isacharparenleft}y\ {\isacharslash}\ z{\isacharparenright}\ {\isacharequal}\ x\ {\isacharasterisk}\ z\ {\isacharslash}\ y% |
|
305 |
\end{isabelle} |
|
11174 | 306 |
\rulename{real_divide_divide1_eq} |
10776 | 307 |
|
11187 | 308 |
\begin{isabelle}% |
309 |
x\ {\isacharslash}\ y\ {\isacharslash}\ z\ {\isacharequal}\ x\ {\isacharslash}\ {\isacharparenleft}y\ {\isacharasterisk}\ z{\isacharparenright}% |
|
310 |
\end{isabelle} |
|
11174 | 311 |
\rulename{real_divide_divide2_eq} |
10776 | 312 |
|
11187 | 313 |
\begin{isabelle}% |
314 |
{\isacharminus}\ x\ {\isacharslash}\ y\ {\isacharequal}\ {\isacharminus}\ {\isacharparenleft}x\ {\isacharslash}\ y{\isacharparenright}% |
|
315 |
\end{isabelle} |
|
11174 | 316 |
\rulename{real_minus_divide_eq} |
10776 | 317 |
|
11187 | 318 |
\begin{isabelle}% |
319 |
x\ {\isacharslash}\ {\isacharminus}\ y\ {\isacharequal}\ {\isacharminus}\ {\isacharparenleft}x\ {\isacharslash}\ y{\isacharparenright}% |
|
320 |
\end{isabelle} |
|
11174 | 321 |
\rulename{real_divide_minus_eq} |
10776 | 322 |
|
323 |
This last NOT a simprule |
|
324 |
||
11187 | 325 |
\begin{isabelle}% |
326 |
{\isacharparenleft}x\ {\isacharplus}\ y{\isacharparenright}\ {\isacharslash}\ z\ {\isacharequal}\ x\ {\isacharslash}\ z\ {\isacharplus}\ y\ {\isacharslash}\ z% |
|
11174 | 327 |
\end{isabelle} |
11187 | 328 |
\rulename{real_add_divide_distrib}% |
329 |
\end{isamarkuptext}% |
|
11866 | 330 |
\isamarkuptrue% |
11708 | 331 |
\isacommand{lemma}\ {\isachardoublequote}{\isadigit{3}}{\isacharslash}{\isadigit{4}}\ {\isacharless}\ {\isacharparenleft}{\isadigit{7}}{\isacharslash}{\isadigit{8}}\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isachardoublequote}\isanewline |
11866 | 332 |
\isamarkupfalse% |
11187 | 333 |
\isacommand{by}\ simp\ \isanewline |
11174 | 334 |
\isanewline |
11866 | 335 |
\isamarkupfalse% |
336 |
\isacommand{lemma}\ {\isachardoublequote}P\ {\isacharparenleft}{\isacharparenleft}{\isadigit{3}}{\isacharslash}{\isadigit{4}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}{\isacharslash}{\isadigit{1}}{\isadigit{5}}\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isamarkupfalse% |
|
337 |
% |
|
11187 | 338 |
\begin{isamarkuptxt}% |
339 |
\begin{isabelle}% |
|
11708 | 340 |
\ {\isadigit{1}}{\isachardot}\ P\ {\isacharparenleft}{\isadigit{3}}\ {\isacharslash}\ {\isadigit{4}}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}\ {\isacharslash}\ {\isadigit{1}}{\isadigit{5}}{\isacharparenright}{\isacharparenright}% |
11187 | 341 |
\end{isabelle}% |
342 |
\end{isamarkuptxt}% |
|
11866 | 343 |
\isamarkuptrue% |
344 |
\isacommand{apply}\ simp\isamarkupfalse% |
|
345 |
% |
|
11187 | 346 |
\begin{isamarkuptxt}% |
347 |
\begin{isabelle}% |
|
11708 | 348 |
\ {\isadigit{1}}{\isachardot}\ P\ {\isacharparenleft}{\isadigit{2}}\ {\isacharslash}\ {\isadigit{5}}{\isacharparenright}% |
11187 | 349 |
\end{isabelle}% |
350 |
\end{isamarkuptxt}% |
|
11866 | 351 |
\isamarkuptrue% |
11174 | 352 |
\isacommand{oops}\isanewline |
353 |
\isanewline |
|
11866 | 354 |
\isamarkupfalse% |
355 |
\isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}{\isadigit{3}}{\isacharslash}{\isadigit{4}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}{\isacharslash}{\isadigit{1}}{\isadigit{5}}{\isacharparenright}\ {\isacharless}\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isachardoublequote}\isamarkupfalse% |
|
356 |
% |
|
11187 | 357 |
\begin{isamarkuptxt}% |
358 |
\begin{isabelle}% |
|
11708 | 359 |
\ {\isadigit{1}}{\isachardot}\ {\isadigit{3}}\ {\isacharslash}\ {\isadigit{4}}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}\ {\isacharslash}\ {\isadigit{1}}{\isadigit{5}}{\isacharparenright}\ {\isacharless}\ x% |
11187 | 360 |
\end{isabelle}% |
361 |
\end{isamarkuptxt}% |
|
11866 | 362 |
\isamarkuptrue% |
363 |
\isacommand{apply}\ simp\isamarkupfalse% |
|
364 |
% |
|
11187 | 365 |
\begin{isamarkuptxt}% |
366 |
\begin{isabelle}% |
|
11708 | 367 |
\ {\isadigit{1}}{\isachardot}\ {\isadigit{2}}\ {\isacharless}\ x\ {\isacharasterisk}\ {\isadigit{5}}% |
11187 | 368 |
\end{isabelle}% |
369 |
\end{isamarkuptxt}% |
|
11866 | 370 |
\isamarkuptrue% |
11187 | 371 |
\isacommand{oops}\isanewline |
372 |
\isanewline |
|
11866 | 373 |
\isamarkupfalse% |
11708 | 374 |
\isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}{\isadigit{3}}{\isacharslash}{\isadigit{4}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{1}}{\isadigit{0}}{\isacharcircum}{\isadigit{1}}{\isadigit{5}}{\isacharparenright}\ {\isacharless}\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isachardoublequote}\isanewline |
11866 | 375 |
\isamarkupfalse% |
11187 | 376 |
\isacommand{apply}\ simp\ \isanewline |
11866 | 377 |
\isamarkupfalse% |
11174 | 378 |
\isacommand{oops}\isanewline |
379 |
\isanewline |
|
380 |
\isanewline |
|
381 |
\isanewline |
|
11866 | 382 |
\isamarkupfalse% |
10602 | 383 |
\isacommand{end}\isanewline |
11866 | 384 |
\isamarkupfalse% |
11187 | 385 |
\end{isabellebody}% |
10602 | 386 |
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