24 \item \emph {$\Rightarrow $}, \bold{5} |
24 \item \emph {$\Rightarrow $}, \bold{5} |
25 \item \ttlbr, \bold{209} |
25 \item \ttlbr, \bold{209} |
26 \item \ttrbr, \bold{209} |
26 \item \ttrbr, \bold{209} |
27 \item \texttt {\%}, \bold{209} |
27 \item \texttt {\%}, \bold{209} |
28 \item \texttt {;}, \bold{7} |
28 \item \texttt {;}, \bold{7} |
29 \item \isa {()} (constant), 24 |
29 \item \isa {()} (constant), \hyperpage{24} |
30 \item \isa {+} (tactical), 99 |
30 \item \isa {+} (tactical), \hyperpage{99} |
31 \item \isa {<*lex*>}, \see{lexicographic product}{1} |
31 \item \isa {<*lex*>}, \see{lexicographic product}{1} |
32 \item \isa {?} (tactical), 99 |
32 \item \isa {?} (tactical), \hyperpage{99} |
33 \item \texttt{|} (tactical), 99 |
33 \item \texttt{|} (tactical), \hyperpage{99} |
34 |
34 |
35 \indexspace |
35 \indexspace |
36 |
36 |
37 \item \isa {0} (constant), 22, 23, 150 |
37 \item \isa {0} (constant), \hyperpage{22, 23}, \hyperpage{150} |
38 \item \isa {1} (constant), 23, 150, 151 |
38 \item \isa {1} (constant), \hyperpage{23}, \hyperpage{150, 151} |
39 |
39 |
40 \indexspace |
40 \indexspace |
41 |
41 |
42 \item abandoning a proof, \bold{13} |
42 \item abandoning a proof, \bold{13} |
43 \item abandoning a theory, \bold{16} |
43 \item abandoning a theory, \bold{16} |
44 \item \isa {abs} (constant), 153 |
44 \item \isa {abs} (constant), \hyperpage{153} |
45 \item \texttt {abs}, \bold{209} |
45 \item \texttt {abs}, \bold{209} |
46 \item absolute value, 153 |
46 \item absolute value, \hyperpage{153} |
47 \item \isa {add} (modifier), 29 |
47 \item \isa {add} (modifier), \hyperpage{29} |
48 \item \isa {add_ac} (theorems), 152 |
48 \item \isa {add_ac} (theorems), \hyperpage{152} |
49 \item \isa {add_assoc} (theorem), \bold{152} |
49 \item \isa {add_assoc} (theorem), \bold{152} |
50 \item \isa {add_commute} (theorem), \bold{152} |
50 \item \isa {add_commute} (theorem), \bold{152} |
51 \item \isa {add_mult_distrib} (theorem), \bold{151} |
51 \item \isa {add_mult_distrib} (theorem), \bold{151} |
52 \item \texttt {ALL}, \bold{209} |
52 \item \texttt {ALL}, \bold{209} |
53 \item \isa {All} (constant), 109 |
53 \item \isa {All} (constant), \hyperpage{109} |
54 \item \isa {allE} (theorem), \bold{81} |
54 \item \isa {allE} (theorem), \bold{81} |
55 \item \isa {allI} (theorem), \bold{80} |
55 \item \isa {allI} (theorem), \bold{80} |
56 \item antiquotation, \bold{61} |
56 \item antiquotation, \bold{61} |
57 \item append function, 10--14 |
57 \item append function, 10--14 |
58 \item \isacommand {apply} (command), 15 |
58 \item \isacommand {apply} (command), \hyperpage{15} |
59 \item \isa {arg_cong} (theorem), \bold{96} |
59 \item \isa {arg_cong} (theorem), \bold{96} |
60 \item \isa {arith} (method), 23, 149 |
60 \item \isa {arith} (method), \hyperpage{23}, \hyperpage{149} |
61 \item arithmetic operations |
61 \item arithmetic operations |
62 \subitem for \protect\isa{nat}, 23 |
62 \subitem for \protect\isa{nat}, \hyperpage{23} |
63 \item \textsc {ascii} symbols, \bold{209} |
63 \item \textsc {ascii} symbols, \bold{209} |
64 \item Aspinall, David, viii |
64 \item Aspinall, David, \hyperpage{viii} |
65 \item associative-commutative function, 176 |
65 \item associative-commutative function, \hyperpage{176} |
66 \item \isa {assumption} (method), 69 |
66 \item \isa {assumption} (method), \hyperpage{69} |
67 \item assumptions |
67 \item assumptions |
68 \subitem of subgoal, 12 |
68 \subitem of subgoal, \hyperpage{12} |
69 \subitem renaming, 82--83 |
69 \subitem renaming, 82--83 |
70 \subitem reusing, 83 |
70 \subitem reusing, 83 |
71 \item \isa {auto} (method), 38, 92 |
71 \item \isa {auto} (method), \hyperpage{38}, \hyperpage{92} |
72 \item \isa {axclass}, 164--170 |
72 \item \isa {axclass}, 164--170 |
73 \item axiom of choice, 86 |
73 \item axiom of choice, \hyperpage{86} |
74 \item axiomatic type classes, 164--170 |
74 \item axiomatic type classes, 164--170 |
75 |
75 |
76 \indexspace |
76 \indexspace |
77 |
77 |
78 \item \isacommand {back} (command), 78 |
78 \item \isacommand {back} (command), \hyperpage{78} |
79 \item \isa {Ball} (constant), 109 |
79 \item \isa {Ball} (constant), \hyperpage{109} |
80 \item \isa {ballI} (theorem), \bold{108} |
80 \item \isa {ballI} (theorem), \bold{108} |
81 \item \isa {best} (method), 92 |
81 \item \isa {best} (method), \hyperpage{92} |
82 \item \isa {Bex} (constant), 109 |
82 \item \isa {Bex} (constant), \hyperpage{109} |
83 \item \isa {bexE} (theorem), \bold{108} |
83 \item \isa {bexE} (theorem), \bold{108} |
84 \item \isa {bexI} (theorem), \bold{108} |
84 \item \isa {bexI} (theorem), \bold{108} |
85 \item \isa {bij_def} (theorem), \bold{110} |
85 \item \isa {bij_def} (theorem), \bold{110} |
86 \item bijections, 110 |
86 \item bijections, \hyperpage{110} |
87 \item binary trees, 18 |
87 \item binary trees, \hyperpage{18} |
88 \item binomial coefficients, 109 |
88 \item binomial coefficients, \hyperpage{109} |
89 \item bisimulations, 116 |
89 \item bisimulations, \hyperpage{116} |
90 \item \isa {blast} (method), 89--90, 92 |
90 \item \isa {blast} (method), 89--90, \hyperpage{92} |
91 \item \isa {bool} (type), 4, 5 |
91 \item \isa {bool} (type), \hyperpage{4, 5} |
92 \item boolean expressions example, 20--22 |
92 \item boolean expressions example, 20--22 |
93 \item \isa {bspec} (theorem), \bold{108} |
93 \item \isa {bspec} (theorem), \bold{108} |
94 \item \isacommand{by} (command), 73 |
94 \item \isacommand{by} (command), 73 |
95 |
95 |
96 \indexspace |
96 \indexspace |
97 |
97 |
98 \item \isa {card} (constant), 109 |
98 \item \isa {card} (constant), \hyperpage{109} |
99 \item \isa {card_Pow} (theorem), \bold{109} |
99 \item \isa {card_Pow} (theorem), \bold{109} |
100 \item \isa {card_Un_Int} (theorem), \bold{109} |
100 \item \isa {card_Un_Int} (theorem), \bold{109} |
101 \item cardinality, 109 |
101 \item cardinality, \hyperpage{109} |
102 \item \isa {case} (symbol), 32, 33 |
102 \item \isa {case} (symbol), \hyperpage{32, 33} |
103 \item \isa {case} expressions, 5, 6, 18 |
103 \item \isa {case} expressions, \hyperpage{5, 6}, \hyperpage{18} |
104 \item case distinctions, 19 |
104 \item case distinctions, \hyperpage{19} |
105 \item case splits, \bold{31} |
105 \item case splits, \bold{31} |
106 \item \isa {case_tac} (method), 19, 101, 157 |
106 \item \isa {case_tac} (method), \hyperpage{19}, \hyperpage{101}, |
107 \item \isa {cases} (method), 162 |
107 \hyperpage{157} |
108 \item \isacommand {chapter} (command), 59 |
108 \item \isa {cases} (method), \hyperpage{162} |
109 \item \isa {clarify} (method), 91, 92 |
109 \item \isacommand {chapter} (command), \hyperpage{59} |
110 \item \isa {clarsimp} (method), 91, 92 |
110 \item \isa {clarify} (method), \hyperpage{91, 92} |
|
111 \item \isa {clarsimp} (method), \hyperpage{91, 92} |
111 \item \isa {classical} (theorem), \bold{73} |
112 \item \isa {classical} (theorem), \bold{73} |
112 \item coinduction, \bold{116} |
113 \item coinduction, \bold{116} |
113 \item \isa {Collect} (constant), 109 |
114 \item \isa {Collect} (constant), \hyperpage{109} |
114 \item compiling expressions example, 36--38 |
115 \item compiling expressions example, 36--38 |
115 \item \isa {Compl_iff} (theorem), \bold{106} |
116 \item \isa {Compl_iff} (theorem), \bold{106} |
116 \item complement |
117 \item complement |
117 \subitem of a set, 105 |
118 \subitem of a set, \hyperpage{105} |
118 \item composition |
119 \item composition |
119 \subitem of functions, \bold{110} |
120 \subitem of functions, \bold{110} |
120 \subitem of relations, \bold{112} |
121 \subitem of relations, \bold{112} |
121 \item conclusion |
122 \item conclusion |
122 \subitem of subgoal, 12 |
123 \subitem of subgoal, \hyperpage{12} |
123 \item conditional expressions, \see{\isa{if} expressions}{1} |
124 \item conditional expressions, \see{\isa{if} expressions}{1} |
124 \item conditional simplification rules, 31 |
125 \item conditional simplification rules, \hyperpage{31} |
125 \item \isa {cong} (attribute), 176 |
126 \item \isa {cong} (attribute), \hyperpage{176} |
126 \item congruence rules, \bold{175} |
127 \item congruence rules, \bold{175} |
127 \item \isa {conjE} (theorem), \bold{71} |
128 \item \isa {conjE} (theorem), \bold{71} |
128 \item \isa {conjI} (theorem), \bold{68} |
129 \item \isa {conjI} (theorem), \bold{68} |
129 \item \isa {Cons} (constant), 9 |
130 \item \isa {Cons} (constant), \hyperpage{9} |
130 \item \isacommand {constdefs} (command), 25 |
131 \item \isacommand {constdefs} (command), \hyperpage{25} |
131 \item \isacommand {consts} (command), 10 |
132 \item \isacommand {consts} (command), \hyperpage{10} |
132 \item contrapositives, 73 |
133 \item contrapositives, 73 |
133 \item converse |
134 \item converse |
134 \subitem of a relation, \bold{112} |
135 \subitem of a relation, \bold{112} |
135 \item \isa {converse_iff} (theorem), \bold{112} |
136 \item \isa {converse_iff} (theorem), \bold{112} |
136 \item CTL, 121--126, 191--193 |
137 \item CTL, 121--126, 191--193 |
137 |
138 |
138 \indexspace |
139 \indexspace |
139 |
140 |
140 \item \isacommand {datatype} (command), 9, 38--43 |
141 \item \isacommand {datatype} (command), \hyperpage{9}, 38--43 |
141 \item datatypes, 17--22 |
142 \item datatypes, 17--22 |
142 \subitem and nested recursion, 40, 44 |
143 \subitem and nested recursion, \hyperpage{40}, \hyperpage{44} |
143 \subitem mutually recursive, 38 |
144 \subitem mutually recursive, \hyperpage{38} |
144 \subitem nested, 180 |
145 \subitem nested, \hyperpage{180} |
145 \item \isacommand {defer} (command), 16, 100 |
146 \item \isacommand {defer} (command), \hyperpage{16}, \hyperpage{100} |
146 \item Definitional Approach, 26 |
147 \item Definitional Approach, \hyperpage{26} |
147 \item definitions, \bold{25} |
148 \item definitions, \bold{25} |
148 \subitem unfolding, \bold{30} |
149 \subitem unfolding, \bold{30} |
149 \item \isacommand {defs} (command), 25 |
150 \item \isacommand {defs} (command), \hyperpage{25} |
150 \item \isa {del} (modifier), 29 |
151 \item \isa {del} (modifier), \hyperpage{29} |
151 \item description operators, 85--87 |
152 \item description operators, 85--87 |
152 \item descriptions |
153 \item descriptions |
153 \subitem definite, 85 |
154 \subitem definite, \hyperpage{85} |
154 \subitem indefinite, 86 |
155 \subitem indefinite, \hyperpage{86} |
155 \item \isa {dest} (attribute), 102 |
156 \item \isa {dest} (attribute), \hyperpage{102} |
156 \item destruction rules, 71 |
157 \item destruction rules, 71 |
157 \item \isa {diff_mult_distrib} (theorem), \bold{151} |
158 \item \isa {diff_mult_distrib} (theorem), \bold{151} |
158 \item difference |
159 \item difference |
159 \subitem of sets, \bold{106} |
160 \subitem of sets, \bold{106} |
160 \item \isa {disjCI} (theorem), \bold{74} |
161 \item \isa {disjCI} (theorem), \bold{74} |
161 \item \isa {disjE} (theorem), \bold{70} |
162 \item \isa {disjE} (theorem), \bold{70} |
162 \item \isa {div} (symbol), 23 |
163 \item \isa {div} (symbol), \hyperpage{23} |
163 \item divides relation, 84, 95, 101--104, 152 |
164 \item divides relation, \hyperpage{84}, \hyperpage{95}, 101--104, |
|
165 \hyperpage{152} |
164 \item division |
166 \item division |
165 \subitem by negative numbers, 153 |
167 \subitem by negative numbers, \hyperpage{153} |
166 \subitem by zero, 152 |
168 \subitem by zero, \hyperpage{152} |
167 \subitem for type \protect\isa{nat}, 151 |
169 \subitem for type \protect\isa{nat}, \hyperpage{151} |
168 \item documents, \bold{57} |
170 \item documents, \bold{57} |
169 \item domain |
171 \item domain |
170 \subitem of a relation, 112 |
172 \subitem of a relation, \hyperpage{112} |
171 \item \isa {Domain_iff} (theorem), \bold{112} |
173 \item \isa {Domain_iff} (theorem), \bold{112} |
172 \item \isacommand {done} (command), 13 |
174 \item \isacommand {done} (command), \hyperpage{13} |
173 \item \isa {drule_tac} (method), 76, 96 |
175 \item \isa {drule_tac} (method), \hyperpage{76}, \hyperpage{96} |
174 \item \isa {dvd_add} (theorem), \bold{152} |
176 \item \isa {dvd_add} (theorem), \bold{152} |
175 \item \isa {dvd_anti_sym} (theorem), \bold{152} |
177 \item \isa {dvd_anti_sym} (theorem), \bold{152} |
176 \item \isa {dvd_def} (theorem), \bold{152} |
178 \item \isa {dvd_def} (theorem), \bold{152} |
177 |
179 |
178 \indexspace |
180 \indexspace |
179 |
181 |
180 \item \isa {elim!} (attribute), 131 |
182 \item \isa {elim!} (attribute), \hyperpage{131} |
181 \item elimination rules, 69--70 |
183 \item elimination rules, 69--70 |
182 \item \isacommand {end} (command), 14 |
184 \item \isacommand {end} (command), \hyperpage{14} |
183 \item \isa {Eps} (constant), 109 |
185 \item \isa {Eps} (constant), \hyperpage{109} |
184 \item equality, 5 |
186 \item equality, \hyperpage{5} |
185 \subitem of functions, \bold{109} |
187 \subitem of functions, \bold{109} |
186 \subitem of records, 161 |
188 \subitem of records, \hyperpage{161} |
187 \subitem of sets, \bold{106} |
189 \subitem of sets, \bold{106} |
188 \item \isa {equalityE} (theorem), \bold{106} |
190 \item \isa {equalityE} (theorem), \bold{106} |
189 \item \isa {equalityI} (theorem), \bold{106} |
191 \item \isa {equalityI} (theorem), \bold{106} |
190 \item \isa {erule} (method), 70 |
192 \item \isa {erule} (method), \hyperpage{70} |
191 \item \isa {erule_tac} (method), 76 |
193 \item \isa {erule_tac} (method), \hyperpage{76} |
192 \item Euclid's algorithm, 101--104 |
194 \item Euclid's algorithm, 101--104 |
193 \item even numbers |
195 \item even numbers |
194 \subitem defining inductively, 127--131 |
196 \subitem defining inductively, 127--131 |
195 \item \texttt {EX}, \bold{209} |
197 \item \texttt {EX}, \bold{209} |
196 \item \isa {Ex} (constant), 109 |
198 \item \isa {Ex} (constant), \hyperpage{109} |
197 \item \isa {exE} (theorem), \bold{82} |
199 \item \isa {exE} (theorem), \bold{82} |
198 \item \isa {exI} (theorem), \bold{82} |
200 \item \isa {exI} (theorem), \bold{82} |
199 \item \isa {ext} (theorem), \bold{109} |
201 \item \isa {ext} (theorem), \bold{109} |
200 \item \isa {extend} (constant), 163 |
202 \item \isa {extend} (constant), \hyperpage{163} |
201 \item extensionality |
203 \item extensionality |
202 \subitem for functions, \bold{109, 110} |
204 \subitem for functions, \bold{109, 110} |
203 \subitem for records, 162 |
205 \subitem for records, \hyperpage{162} |
204 \subitem for sets, \bold{106} |
206 \subitem for sets, \bold{106} |
205 \item \ttEXU, \bold{209} |
207 \item \ttEXU, \bold{209} |
206 |
208 |
207 \indexspace |
209 \indexspace |
208 |
210 |
209 \item \isa {False} (constant), 5 |
211 \item \isa {False} (constant), \hyperpage{5} |
210 \item \isa {fast} (method), 92, 124 |
212 \item \isa {fast} (method), \hyperpage{92}, \hyperpage{124} |
211 \item Fibonacci function, 47 |
213 \item Fibonacci function, \hyperpage{47} |
212 \item \isa {fields} (constant), 163 |
214 \item \isa {fields} (constant), \hyperpage{163} |
213 \item \isa {finite} (symbol), 109 |
215 \item \isa {finite} (symbol), \hyperpage{109} |
214 \item \isa {Finites} (constant), 109 |
216 \item \isa {Finites} (constant), \hyperpage{109} |
215 \item fixed points, 116 |
217 \item fixed points, 116 |
216 \item flags, 5, 6, 33 |
218 \item flags, \hyperpage{5, 6}, \hyperpage{33} |
217 \subitem setting and resetting, 5 |
219 \subitem setting and resetting, \hyperpage{5} |
218 \item \isa {force} (method), 91, 92 |
220 \item \isa {force} (method), \hyperpage{91, 92} |
219 \item formal comments, \bold{61} |
221 \item formal comments, \bold{61} |
220 \item formal proof documents, \bold{57} |
222 \item formal proof documents, \bold{57} |
221 \item formulae, 5--6 |
223 \item formulae, 5--6 |
222 \item forward proof, 92--98 |
224 \item forward proof, 92--98 |
223 \item \isa {frule} (method), 83 |
225 \item \isa {frule} (method), 83 |
224 \item \isa {frule_tac} (method), 76 |
226 \item \isa {frule_tac} (method), \hyperpage{76} |
225 \item \isa {fst} (constant), 24 |
227 \item \isa {fst} (constant), \hyperpage{24} |
226 \item function types, 5 |
228 \item function types, \hyperpage{5} |
227 \item functions, 109--111 |
229 \item functions, 109--111 |
228 \subitem partial, 182 |
230 \subitem partial, \hyperpage{182} |
229 \subitem total, 11, 46--52 |
231 \subitem total, \hyperpage{11}, 47--52 |
230 \subitem underdefined, 183 |
232 \subitem underdefined, \hyperpage{183} |
231 |
233 |
232 \indexspace |
234 \indexspace |
233 |
235 |
234 \item \isa {gcd} (constant), 93--94, 101--104 |
236 \item \isa {gcd} (constant), 93--94, 101--104 |
235 \item generalizing for induction, 129 |
237 \item generalizing for induction, \hyperpage{129} |
236 \item generalizing induction formulae, 35 |
238 \item generalizing induction formulae, \hyperpage{35} |
237 \item Girard, Jean-Yves, \fnote{71} |
239 \item Girard, Jean-Yves, \fnote{71} |
238 \item Gordon, Mike, 3 |
240 \item Gordon, Mike, \hyperpage{3} |
239 \item grammars |
241 \item grammars |
240 \subitem defining inductively, 140--145 |
242 \subitem defining inductively, 140--145 |
241 \item ground terms example, 135--140 |
243 \item ground terms example, 135--140 |
242 |
244 |
243 \indexspace |
245 \indexspace |
244 |
246 |
245 \item \isa {hd} (constant), 17, 37 |
247 \item \isa {hd} (constant), \hyperpage{17}, \hyperpage{37} |
246 \item \isacommand {header} (command), 59 |
248 \item \isacommand {header} (command), \hyperpage{59} |
247 \item Hilbert's $\varepsilon$-operator, 86 |
249 \item Hilbert's $\varepsilon$-operator, \hyperpage{86} |
248 \item HOLCF, 43 |
250 \item HOLCF, \hyperpage{43} |
249 \item Hopcroft, J. E., 145 |
251 \item Hopcroft, J. E., \hyperpage{145} |
250 \item \isa {hypreal} (type), 155 |
252 \item \isa {hypreal} (type), \hyperpage{155} |
251 |
253 |
252 \indexspace |
254 \indexspace |
253 |
255 |
254 \item \isa {Id_def} (theorem), \bold{112} |
256 \item \isa {Id_def} (theorem), \bold{112} |
255 \item \isa {id_def} (theorem), \bold{110} |
257 \item \isa {id_def} (theorem), \bold{110} |
256 \item identifiers, \bold{6} |
258 \item identifiers, \bold{6} |
257 \subitem qualified, \bold{4} |
259 \subitem qualified, \bold{4} |
258 \item identity function, \bold{110} |
260 \item identity function, \bold{110} |
259 \item identity relation, \bold{112} |
261 \item identity relation, \bold{112} |
260 \item \isa {if} expressions, 5, 6 |
262 \item \isa {if} expressions, \hyperpage{5, 6} |
261 \subitem simplification of, 33 |
263 \subitem simplification of, \hyperpage{33} |
262 \subitem splitting of, 31, 49 |
264 \subitem splitting of, \hyperpage{31}, \hyperpage{49} |
263 \item if-and-only-if, 6 |
265 \item if-and-only-if, \hyperpage{6} |
264 \item \isa {iff} (attribute), 90, 102, 130 |
266 \item \isa {iff} (attribute), \hyperpage{90}, \hyperpage{102}, |
|
267 \hyperpage{130} |
265 \item \isa {iffD1} (theorem), \bold{94} |
268 \item \isa {iffD1} (theorem), \bold{94} |
266 \item \isa {iffD2} (theorem), \bold{94} |
269 \item \isa {iffD2} (theorem), \bold{94} |
267 \item ignored material, \bold{64} |
270 \item ignored material, \bold{64} |
268 \item image |
271 \item image |
269 \subitem under a function, \bold{111} |
272 \subitem under a function, \bold{111} |
270 \subitem under a relation, \bold{112} |
273 \subitem under a relation, \bold{112} |
271 \item \isa {image_def} (theorem), \bold{111} |
274 \item \isa {image_def} (theorem), \bold{111} |
272 \item \isa {Image_iff} (theorem), \bold{112} |
275 \item \isa {Image_iff} (theorem), \bold{112} |
273 \item \isa {impI} (theorem), \bold{72} |
276 \item \isa {impI} (theorem), \bold{72} |
274 \item implication, 72--73 |
277 \item implication, 72--73 |
275 \item \isa {ind_cases} (method), 131 |
278 \item \isa {ind_cases} (method), \hyperpage{131} |
276 \item \isa {induct_tac} (method), 12, 19, 52, 190 |
279 \item \isa {induct_tac} (method), \hyperpage{12}, \hyperpage{19}, |
|
280 \hyperpage{52}, \hyperpage{190} |
277 \item induction, 186--193 |
281 \item induction, 186--193 |
278 \subitem complete, 188 |
282 \subitem complete, \hyperpage{188} |
279 \subitem deriving new schemas, 190 |
283 \subitem deriving new schemas, \hyperpage{190} |
280 \subitem on a term, 187 |
284 \subitem on a term, \hyperpage{187} |
281 \subitem recursion, 51--52 |
285 \subitem recursion, 51--52 |
282 \subitem structural, 19 |
286 \subitem structural, \hyperpage{19} |
283 \subitem well-founded, 115 |
287 \subitem well-founded, 115 |
284 \item induction heuristics, 34--36 |
288 \item induction heuristics, 34--36 |
285 \item \isacommand {inductive} (command), 127 |
289 \item \isacommand {inductive} (command), \hyperpage{127} |
286 \item inductive definition |
290 \item inductive definition |
287 \subitem simultaneous, 141 |
291 \subitem simultaneous, \hyperpage{141} |
288 \item inductive definitions, 127--145 |
292 \item inductive definitions, 127--145 |
289 \item \isacommand {inductive\_cases} (command), 131, 139 |
293 \item \isacommand {inductive\_cases} (command), \hyperpage{131}, |
290 \item infinitely branching trees, 43 |
294 \hyperpage{139} |
291 \item infix annotations, 53 |
295 \item infinitely branching trees, \hyperpage{43} |
292 \item \isacommand{infixr} (annotation), 10 |
296 \item infix annotations, \hyperpage{53} |
|
297 \item \isacommand{infixr} (annotation), \hyperpage{10} |
293 \item \isa {inj_on_def} (theorem), \bold{110} |
298 \item \isa {inj_on_def} (theorem), \bold{110} |
294 \item injections, 110 |
299 \item injections, \hyperpage{110} |
295 \item \isa {insert} (constant), 107 |
300 \item \isa {insert} (constant), \hyperpage{107} |
296 \item \isa {insert} (method), 97--98 |
301 \item \isa {insert} (method), \hyperpage{97}, 97, \hyperpage{98} |
297 \item instance, \bold{166} |
302 \item instance, \bold{166} |
298 \item \texttt {INT}, \bold{209} |
303 \item \texttt {INT}, \bold{209} |
299 \item \texttt {Int}, \bold{209} |
304 \item \texttt {Int}, \bold{209} |
300 \item \isa {int} (type), 153--154 |
305 \item \isa {int} (type), 153--154 |
301 \item \isa {INT_iff} (theorem), \bold{108} |
306 \item \isa {INT_iff} (theorem), \bold{108} |
302 \item \isa {IntD1} (theorem), \bold{105} |
307 \item \isa {IntD1} (theorem), \bold{105} |
303 \item \isa {IntD2} (theorem), \bold{105} |
308 \item \isa {IntD2} (theorem), \bold{105} |
304 \item integers, 153--154 |
309 \item integers, 153--154 |
305 \item \isa {INTER} (constant), 109 |
310 \item \isa {INTER} (constant), \hyperpage{109} |
306 \item \texttt {Inter}, \bold{209} |
311 \item \texttt {Inter}, \bold{209} |
307 \item \isa {Inter_iff} (theorem), \bold{108} |
312 \item \isa {Inter_iff} (theorem), \bold{108} |
308 \item intersection, 105 |
313 \item intersection, \hyperpage{105} |
309 \subitem indexed, 108 |
314 \subitem indexed, \hyperpage{108} |
310 \item \isa {IntI} (theorem), \bold{105} |
315 \item \isa {IntI} (theorem), \bold{105} |
311 \item \isa {intro} (method), 74 |
316 \item \isa {intro} (method), \hyperpage{74} |
312 \item \isa {intro!} (attribute), 128 |
317 \item \isa {intro!} (attribute), \hyperpage{128} |
313 \item \isa {intro_classes} (method), 166 |
318 \item \isa {intro_classes} (method), \hyperpage{166} |
314 \item introduction rules, 68--69 |
319 \item introduction rules, 68--69 |
315 \item \isa {inv} (constant), 86 |
320 \item \isa {inv} (constant), \hyperpage{86} |
316 \item \isa {inv_image_def} (theorem), \bold{115} |
321 \item \isa {inv_image_def} (theorem), \bold{115} |
317 \item inverse |
322 \item inverse |
318 \subitem of a function, \bold{110} |
323 \subitem of a function, \bold{110} |
319 \subitem of a relation, \bold{112} |
324 \subitem of a relation, \bold{112} |
320 \item inverse image |
325 \item inverse image |
321 \subitem of a function, 111 |
326 \subitem of a function, \hyperpage{111} |
322 \subitem of a relation, 114 |
327 \subitem of a relation, \hyperpage{114} |
323 \item \isa {itrev} (constant), 34 |
328 \item \isa {itrev} (constant), \hyperpage{34} |
324 |
329 |
325 \indexspace |
330 \indexspace |
326 |
331 |
327 \item \isacommand {kill} (command), 16 |
332 \item \isacommand {kill} (command), \hyperpage{16} |
328 |
333 |
329 \indexspace |
334 \indexspace |
330 |
335 |
331 \item $\lambda$ expressions, 5 |
336 \item $\lambda$ expressions, \hyperpage{5} |
332 \item LCF, 43 |
337 \item LCF, \hyperpage{43} |
333 \item \isa {LEAST} (symbol), 23, 85 |
338 \item \isa {LEAST} (symbol), \hyperpage{23}, \hyperpage{85} |
334 \item least number operator, \see{\protect\isa{LEAST}}{85} |
339 \item least number operator, \see{\protect\isa{LEAST}}{85} |
335 \item Leibniz, Gottfried Wilhelm, 53 |
340 \item Leibniz, Gottfried Wilhelm, \hyperpage{53} |
336 \item \isacommand {lemma} (command), 13 |
341 \item \isacommand {lemma} (command), \hyperpage{13} |
337 \item \isacommand {lemmas} (command), 93, 102 |
342 \item \isacommand {lemmas} (command), \hyperpage{93}, \hyperpage{102} |
338 \item \isa {length} (symbol), 18 |
343 \item \isa {length} (symbol), \hyperpage{18} |
339 \item \isa {length_induct}, \bold{190} |
344 \item \isa {length_induct}, \bold{190} |
340 \item \isa {less_than} (constant), 114 |
345 \item \isa {less_than} (constant), \hyperpage{114} |
341 \item \isa {less_than_iff} (theorem), \bold{114} |
346 \item \isa {less_than_iff} (theorem), \bold{114} |
342 \item \isa {let} expressions, 5, 6, 31 |
347 \item \isa {let} expressions, \hyperpage{5, 6}, \hyperpage{31} |
343 \item \isa {Let_def} (theorem), 31 |
348 \item \isa {Let_def} (theorem), \hyperpage{31} |
344 \item \isa {lex_prod_def} (theorem), \bold{115} |
349 \item \isa {lex_prod_def} (theorem), \bold{115} |
345 \item lexicographic product, \bold{115}, 178 |
350 \item lexicographic product, \bold{115}, \hyperpage{178} |
346 \item {\texttt{lfp}} |
351 \item {\texttt{lfp}} |
347 \subitem applications of, \see{CTL}{116} |
352 \subitem applications of, \see{CTL}{116} |
348 \item Library, 4 |
353 \item Library, \hyperpage{4} |
349 \item linear arithmetic, 22--24, 149 |
354 \item linear arithmetic, 22--24, \hyperpage{149} |
350 \item \isa {List} (theory), 17 |
355 \item \isa {List} (theory), \hyperpage{17} |
351 \item \isa {list} (type), 5, 9, 17 |
356 \item \isa {list} (type), \hyperpage{5}, \hyperpage{9}, |
352 \item \isa {list.split} (theorem), 32 |
357 \hyperpage{17} |
|
358 \item \isa {list.split} (theorem), \hyperpage{32} |
353 \item \isa {lists_mono} (theorem), \bold{137} |
359 \item \isa {lists_mono} (theorem), \bold{137} |
354 \item Lowe, Gavin, 196--197 |
360 \item Lowe, Gavin, 196--197 |
355 |
361 |
356 \indexspace |
362 \indexspace |
357 |
363 |
358 \item \isa {Main} (theory), 4 |
364 \item \isa {Main} (theory), \hyperpage{4} |
359 \item major premise, \bold{75} |
365 \item major premise, \bold{75} |
360 \item \isa {make} (constant), 163 |
366 \item \isa {make} (constant), \hyperpage{163} |
361 \item marginal comments, \bold{61} |
367 \item marginal comments, \bold{61} |
362 \item markup commands, \bold{59} |
368 \item markup commands, \bold{59} |
363 \item \isa {max} (constant), 23, 24 |
369 \item \isa {max} (constant), \hyperpage{23, 24} |
364 \item measure functions, 47, 114 |
370 \item measure functions, \hyperpage{47}, \hyperpage{114} |
365 \item \isa {measure_def} (theorem), \bold{115} |
371 \item \isa {measure_def} (theorem), \bold{115} |
366 \item meta-logic, \bold{80} |
372 \item meta-logic, \bold{80} |
367 \item methods, \bold{16} |
373 \item methods, \bold{16} |
368 \item \isa {min} (constant), 23, 24 |
374 \item \isa {min} (constant), \hyperpage{23, 24} |
369 \item mixfix annotations, \bold{53} |
375 \item mixfix annotations, \bold{53} |
370 \item \isa {mod} (symbol), 23 |
376 \item \isa {mod} (symbol), \hyperpage{23} |
371 \item \isa {mod_div_equality} (theorem), \bold{151} |
377 \item \isa {mod_div_equality} (theorem), \bold{151} |
372 \item \isa {mod_mult_distrib} (theorem), \bold{151} |
378 \item \isa {mod_mult_distrib} (theorem), \bold{151} |
373 \item model checking example, 116--126 |
379 \item model checking example, 116--126 |
374 \item \emph{modus ponens}, 67, 72 |
380 \item \emph{modus ponens}, \hyperpage{67}, \hyperpage{72} |
375 \item \isa {mono_def} (theorem), \bold{116} |
381 \item \isa {mono_def} (theorem), \bold{116} |
376 \item monotone functions, \bold{116}, 139 |
382 \item monotone functions, \bold{116}, \hyperpage{139} |
377 \subitem and inductive definitions, 137--138 |
383 \subitem and inductive definitions, 137--138 |
378 \item \isa {more} (constant), 158, 160 |
384 \item \isa {more} (constant), \hyperpage{158}, \hyperpage{160} |
379 \item \isa {mp} (theorem), \bold{72} |
385 \item \isa {mp} (theorem), \bold{72} |
380 \item \isa {mult_ac} (theorems), 152 |
386 \item \isa {mult_ac} (theorems), \hyperpage{152} |
381 \item multiple inheritance, \bold{169} |
387 \item multiple inheritance, \bold{169} |
382 \item multiset ordering, \bold{115} |
388 \item multiset ordering, \bold{115} |
383 |
389 |
384 \indexspace |
390 \indexspace |
385 |
391 |
386 \item \isa {nat} (type), 4, 22, 151--153 |
392 \item \isa {nat} (type), \hyperpage{4}, \hyperpage{22}, 151--153 |
387 \item \isa {nat_less_induct} (theorem), 188 |
393 \item \isa {nat_less_induct} (theorem), \hyperpage{188} |
388 \item natural deduction, 67--68 |
394 \item natural deduction, 67--68 |
389 \item natural numbers, 22, 151--153 |
395 \item natural numbers, \hyperpage{22}, 151--153 |
390 \item Needham-Schroeder protocol, 195--197 |
396 \item Needham-Schroeder protocol, 195--197 |
391 \item negation, 73--75 |
397 \item negation, 73--75 |
392 \item \isa {Nil} (constant), 9 |
398 \item \isa {Nil} (constant), \hyperpage{9} |
393 \item \isa {no_asm} (modifier), 29 |
399 \item \isa {no_asm} (modifier), \hyperpage{29} |
394 \item \isa {no_asm_simp} (modifier), 30 |
400 \item \isa {no_asm_simp} (modifier), \hyperpage{30} |
395 \item \isa {no_asm_use} (modifier), 30 |
401 \item \isa {no_asm_use} (modifier), \hyperpage{30} |
396 \item \isa {no_vars} (attribute), 62 |
402 \item \isa {no_vars} (attribute), \hyperpage{62} |
397 \item non-standard reals, 155 |
403 \item non-standard reals, \hyperpage{155} |
398 \item \isa {None} (constant), \bold{24} |
404 \item \isa {None} (constant), \bold{24} |
399 \item \isa {notE} (theorem), \bold{73} |
405 \item \isa {notE} (theorem), \bold{73} |
400 \item \isa {notI} (theorem), \bold{73} |
406 \item \isa {notI} (theorem), \bold{73} |
401 \item numbers, 149--155 |
407 \item numbers, 149--155 |
402 \item numeric literals, 150 |
408 \item numeric literals, 150 |
403 \subitem for type \protect\isa{nat}, 151 |
409 \subitem for type \protect\isa{nat}, \hyperpage{151} |
404 \subitem for type \protect\isa{real}, 155 |
410 \subitem for type \protect\isa{real}, \hyperpage{155} |
405 |
411 |
406 \indexspace |
412 \indexspace |
407 |
413 |
408 \item \isa {O} (symbol), 112 |
414 \item \isa {O} (symbol), \hyperpage{112} |
409 \item \texttt {o}, \bold{209} |
415 \item \texttt {o}, \bold{209} |
410 \item \isa {o_def} (theorem), \bold{110} |
416 \item \isa {o_def} (theorem), \bold{110} |
411 \item \isa {OF} (attribute), 95--96 |
417 \item \isa {OF} (attribute), 95--96, \hyperpage{96} |
412 \item \isa {of} (attribute), 93, 96 |
418 \item \isa {of} (attribute), \hyperpage{93}, \hyperpage{96} |
413 \item \isa {only} (modifier), 29 |
419 \item \isa {only} (modifier), \hyperpage{29} |
414 \item \isacommand {oops} (command), 13 |
420 \item \isacommand {oops} (command), \hyperpage{13} |
415 \item \isa {option} (type), \bold{24} |
421 \item \isa {option} (type), \bold{24} |
416 \item ordered rewriting, \bold{176} |
422 \item ordered rewriting, \bold{176} |
417 \item overloading, 23, 165--167 |
423 \item overloading, \hyperpage{23}, 165--167 |
418 \subitem and arithmetic, 150 |
424 \subitem and arithmetic, \hyperpage{150} |
419 |
425 |
420 \indexspace |
426 \indexspace |
421 |
427 |
422 \item pairs and tuples, 24, 155--158 |
428 \item pairs and tuples, \hyperpage{24}, 155--158 |
423 \item parent theories, \bold{4} |
429 \item parent theories, \bold{4} |
424 \item pattern matching |
430 \item pattern matching |
425 \subitem and \isacommand{recdef}, 47 |
431 \subitem and \isacommand{recdef}, \hyperpage{47} |
426 \item patterns |
432 \item patterns |
427 \subitem higher-order, \bold{177} |
433 \subitem higher-order, \bold{177} |
428 \item PDL, 118--120 |
434 \item PDL, 118--120 |
429 \item \isacommand {pr} (command), 16, 100 |
435 \item \isacommand {pr} (command), \hyperpage{16}, \hyperpage{100} |
430 \item \isacommand {prefer} (command), 16, 100 |
436 \item \isacommand {prefer} (command), \hyperpage{16}, \hyperpage{100} |
431 \item prefix annotation, 55 |
437 \item prefix annotation, \hyperpage{55} |
432 \item primitive recursion, \see{recursion, primitive}{1} |
438 \item primitive recursion, \see{recursion, primitive}{1} |
433 \item \isacommand {primrec} (command), 10, 18, 38--43 |
439 \item \isacommand {primrec} (command), \hyperpage{10}, \hyperpage{18}, |
|
440 \hyperpage{41}, 38--43 |
434 \item print mode, \bold{55} |
441 \item print mode, \bold{55} |
435 \item product type, \see{pairs and tuples}{1} |
442 \item product type, \see{pairs and tuples}{1} |
436 \item Proof General, \bold{7} |
443 \item Proof General, \bold{7} |
437 \item proof state, 12 |
444 \item proof state, \hyperpage{12} |
438 \item proofs |
445 \item proofs |
439 \subitem abandoning, \bold{13} |
446 \subitem abandoning, \bold{13} |
440 \subitem examples of failing, 87--89 |
447 \subitem examples of failing, 87--89 |
441 \item protocols |
448 \item protocols |
442 \subitem security, 195--205 |
449 \subitem security, 195--205 |
443 |
450 |
444 \indexspace |
451 \indexspace |
445 |
452 |
446 \item quantifiers, 6 |
453 \item quantifiers, \hyperpage{6} |
447 \subitem and inductive definitions, 135--137 |
454 \subitem and inductive definitions, 135--137 |
448 \subitem existential, 82 |
455 \subitem existential, 82 |
449 \subitem for sets, 108 |
456 \subitem for sets, 108 |
450 \subitem instantiating, 84 |
457 \subitem instantiating, \hyperpage{84} |
451 \subitem universal, 79--82 |
458 \subitem universal, 79--82 |
452 |
459 |
453 \indexspace |
460 \indexspace |
454 |
461 |
455 \item \isa {r_into_rtrancl} (theorem), \bold{112} |
462 \item \isa {r_into_rtrancl} (theorem), \bold{112} |
456 \item \isa {r_into_trancl} (theorem), \bold{113} |
463 \item \isa {r_into_trancl} (theorem), \bold{113} |
457 \item range |
464 \item range |
458 \subitem of a function, 111 |
465 \subitem of a function, \hyperpage{111} |
459 \subitem of a relation, 112 |
466 \subitem of a relation, \hyperpage{112} |
460 \item \isa {range} (symbol), 111 |
467 \item \isa {range} (symbol), \hyperpage{111} |
461 \item \isa {Range_iff} (theorem), \bold{112} |
468 \item \isa {Range_iff} (theorem), \bold{112} |
462 \item \isa {Real} (theory), 155 |
469 \item \isa {Real} (theory), \hyperpage{155} |
463 \item \isa {real} (type), 154--155 |
470 \item \isa {real} (type), 154--155 |
464 \item real numbers, 154--155 |
471 \item real numbers, 154--155 |
465 \item \isacommand {recdef} (command), 46--52, 114, 178--186 |
472 \item \isacommand {recdef} (command), 47--52, \hyperpage{114}, |
466 \subitem and numeric literals, 150 |
473 178--186 |
467 \item \isa {recdef_cong} (attribute), 182 |
474 \subitem and numeric literals, \hyperpage{150} |
468 \item \isa {recdef_simp} (attribute), 49 |
475 \item \isa {recdef_cong} (attribute), \hyperpage{182} |
469 \item \isa {recdef_wf} (attribute), 180 |
476 \item \isa {recdef_simp} (attribute), \hyperpage{49} |
470 \item \isacommand {record} (command), 159 |
477 \item \isa {recdef_wf} (attribute), \hyperpage{180} |
|
478 \item \isacommand {record} (command), \hyperpage{159} |
471 \item records, 158--164 |
479 \item records, 158--164 |
472 \subitem extensible, 160--161 |
480 \subitem extensible, 160--161 |
473 \item recursion |
481 \item recursion |
474 \subitem guarded, 183 |
482 \subitem guarded, \hyperpage{183} |
475 \subitem primitive, 18 |
483 \subitem primitive, \hyperpage{18} |
476 \subitem well-founded, \bold{179} |
484 \subitem well-founded, \bold{179} |
477 \item recursion induction, 51--52 |
485 \item recursion induction, 51--52 |
478 \item \isacommand {redo} (command), 16 |
486 \item \isacommand {redo} (command), \hyperpage{16} |
479 \item reflexive and transitive closure, 112--114 |
487 \item reflexive and transitive closure, 112--114 |
480 \item reflexive transitive closure |
488 \item reflexive transitive closure |
481 \subitem defining inductively, 132--135 |
489 \subitem defining inductively, 132--135 |
482 \item \isa {rel_comp_def} (theorem), \bold{112} |
490 \item \isa {rel_comp_def} (theorem), \bold{112} |
483 \item relations, 111--114 |
491 \item relations, 111--114 |
484 \subitem well-founded, 114--115 |
492 \subitem well-founded, 114--115 |
485 \item \isa {rename_tac} (method), 82--83 |
493 \item \isa {rename_tac} (method), 82--83 |
486 \item \isa {rev} (constant), 10--14, 34 |
494 \item \isa {rev} (constant), \hyperpage{10}, 10--14, \hyperpage{34} |
487 \item rewrite rules, \bold{27} |
495 \item rewrite rules, \bold{27} |
488 \subitem permutative, \bold{176} |
496 \subitem permutative, \bold{176} |
489 \item rewriting, \bold{27} |
497 \item rewriting, \bold{27} |
490 \item \isa {rotate_tac} (method), 30 |
498 \item \isa {rotate_tac} (method), \hyperpage{30} |
491 \item \isa {rtrancl_refl} (theorem), \bold{112} |
499 \item \isa {rtrancl_refl} (theorem), \bold{112} |
492 \item \isa {rtrancl_trans} (theorem), \bold{112} |
500 \item \isa {rtrancl_trans} (theorem), \bold{112} |
493 \item rule induction, 128--130 |
501 \item rule induction, 128--130 |
494 \item rule inversion, 130--131, 139--140 |
502 \item rule inversion, 130--131, 139--140 |
495 \item \isa {rule_format} (attribute), 187 |
503 \item \isa {rule_format} (attribute), \hyperpage{187} |
496 \item \isa {rule_tac} (method), 76 |
504 \item \isa {rule_tac} (method), \hyperpage{76} |
497 \subitem and renaming, 83 |
505 \subitem and renaming, \hyperpage{83} |
498 |
506 |
499 \indexspace |
507 \indexspace |
500 |
508 |
501 \item \isa {safe} (method), 91, 92 |
509 \item \isa {safe} (method), \hyperpage{91, 92} |
502 \item safe rules, \bold{90} |
510 \item safe rules, \bold{90} |
503 \item \isacommand {sect} (command), 59 |
511 \item \isacommand {sect} (command), \hyperpage{59} |
504 \item \isacommand {section} (command), 59 |
512 \item \isacommand {section} (command), \hyperpage{59} |
505 \item selector |
513 \item selector |
506 \subitem record, 159 |
514 \subitem record, \hyperpage{159} |
507 \item session, \bold{58} |
515 \item session, \bold{58} |
508 \item \isa {set} (type), 5, 105 |
516 \item \isa {set} (type), \hyperpage{5}, \hyperpage{105} |
509 \item set comprehensions, 107--108 |
517 \item set comprehensions, 107--108 |
510 \item \isa {set_ext} (theorem), \bold{106} |
518 \item \isa {set_ext} (theorem), \bold{106} |
511 \item sets, 105--109 |
519 \item sets, 105--109 |
512 \subitem finite, 109 |
520 \subitem finite, \hyperpage{109} |
513 \subitem notation for finite, \bold{107} |
521 \subitem notation for finite, \bold{107} |
514 \item settings, \see{flags}{1} |
522 \item settings, \see{flags}{1} |
515 \item \isa {show_brackets} (flag), 6 |
523 \item \isa {show_brackets} (flag), \hyperpage{6} |
516 \item \isa {show_types} (flag), 5, 16 |
524 \item \isa {show_types} (flag), \hyperpage{5}, \hyperpage{16} |
517 \item \isa {simp} (attribute), 11, 28 |
525 \item \isa {simp} (attribute), \hyperpage{11}, \hyperpage{28} |
518 \item \isa {simp} (method), \bold{28} |
526 \item \isa {simp} (method), \bold{28} |
519 \item \isa {simp} del (attribute), 28 |
527 \item \isa {simp} del (attribute), \hyperpage{28} |
520 \item \isa {simp_all} (method), 29, 38 |
528 \item \isa {simp_all} (method), \hyperpage{29}, \hyperpage{38} |
521 \item simplification, 27--33, 175--178 |
529 \item simplification, 27--33, 175--178 |
522 \subitem of \isa{let}-expressions, 31 |
530 \subitem of \isa{let}-expressions, \hyperpage{31} |
523 \subitem with definitions, 30 |
531 \subitem with definitions, \hyperpage{30} |
524 \subitem with/of assumptions, 29 |
532 \subitem with/of assumptions, \hyperpage{29} |
525 \item simplification rule, 177--178 |
533 \item simplification rule, 177--178 |
526 \item simplification rules, 28 |
534 \item simplification rules, \hyperpage{28} |
527 \subitem adding and deleting, 29 |
535 \subitem adding and deleting, \hyperpage{29} |
528 \item \isa {simplified} (attribute), 93, 96 |
536 \item \isa {simplified} (attribute), \hyperpage{93}, \hyperpage{96} |
529 \item \isa {size} (constant), 17 |
537 \item \isa {size} (constant), \hyperpage{17} |
530 \item \isa {snd} (constant), 24 |
538 \item \isa {snd} (constant), \hyperpage{24} |
531 \item \isa {SOME} (symbol), 86 |
539 \item \isa {SOME} (symbol), \hyperpage{86} |
532 \item \texttt {SOME}, \bold{209} |
540 \item \texttt {SOME}, \bold{209} |
533 \item \isa {Some} (constant), \bold{24} |
541 \item \isa {Some} (constant), \bold{24} |
534 \item \isa {some_equality} (theorem), \bold{86} |
542 \item \isa {some_equality} (theorem), \bold{86} |
535 \item \isa {someI} (theorem), \bold{86} |
543 \item \isa {someI} (theorem), \bold{86} |
536 \item \isa {someI2} (theorem), \bold{86} |
544 \item \isa {someI2} (theorem), \bold{86} |
537 \item \isa {someI_ex} (theorem), \bold{87} |
545 \item \isa {someI_ex} (theorem), \bold{87} |
538 \item sorts, 170 |
546 \item sorts, \hyperpage{170} |
539 \item source comments, \bold{60} |
547 \item source comments, \bold{60} |
540 \item \isa {spec} (theorem), \bold{80} |
548 \item \isa {spec} (theorem), \bold{80} |
541 \item \isa {split} (attribute), 32 |
549 \item \isa {split} (attribute), \hyperpage{32} |
542 \item \isa {split} (constant), 156 |
550 \item \isa {split} (constant), \hyperpage{156} |
543 \item \isa {split} (method), 31, 156 |
551 \item \isa {split} (method), \hyperpage{31}, \hyperpage{156} |
544 \item \isa {split} (modifier), 32 |
552 \item \isa {split} (modifier), \hyperpage{32} |
545 \item split rule, \bold{32} |
553 \item split rule, \bold{32} |
546 \item \isa {split_if} (theorem), 32 |
554 \item \isa {split_if} (theorem), \hyperpage{32} |
547 \item \isa {split_if_asm} (theorem), 32 |
555 \item \isa {split_if_asm} (theorem), \hyperpage{32} |
548 \item \isa {ssubst} (theorem), \bold{77} |
556 \item \isa {ssubst} (theorem), \bold{77} |
549 \item structural induction, \see{induction, structural}{1} |
557 \item structural induction, \see{induction, structural}{1} |
550 \item subclasses, 164, 169 |
558 \item subclasses, \hyperpage{164}, \hyperpage{169} |
551 \item subgoal numbering, 46 |
559 \item subgoal numbering, \hyperpage{46} |
552 \item \isa {subgoal_tac} (method), 98 |
560 \item \isa {subgoal_tac} (method), \hyperpage{98} |
553 \item subgoals, 12 |
561 \item subgoals, \hyperpage{12} |
554 \item \isacommand {subsect} (command), 59 |
562 \item \isacommand {subsect} (command), \hyperpage{59} |
555 \item \isacommand {subsection} (command), 59 |
563 \item \isacommand {subsection} (command), \hyperpage{59} |
556 \item subset relation, \bold{106} |
564 \item subset relation, \bold{106} |
557 \item \isa {subsetD} (theorem), \bold{106} |
565 \item \isa {subsetD} (theorem), \bold{106} |
558 \item \isa {subsetI} (theorem), \bold{106} |
566 \item \isa {subsetI} (theorem), \bold{106} |
559 \item \isa {subst} (method), 77 |
567 \item \isa {subst} (method), \hyperpage{77} |
560 \item substitution, 77--79 |
568 \item substitution, 77--79 |
561 \item \isacommand {subsubsect} (command), 59 |
569 \item \isacommand {subsubsect} (command), \hyperpage{59} |
562 \item \isacommand {subsubsection} (command), 59 |
570 \item \isacommand {subsubsection} (command), \hyperpage{59} |
563 \item \isa {Suc} (constant), 22 |
571 \item \isa {Suc} (constant), \hyperpage{22} |
564 \item \isa {surj_def} (theorem), \bold{110} |
572 \item \isa {surj_def} (theorem), \bold{110} |
565 \item surjections, 110 |
573 \item surjections, \hyperpage{110} |
566 \item \isa {sym} (theorem), \bold{94} |
574 \item \isa {sym} (theorem), \bold{94} |
567 \item symbols, \bold{54} |
575 \item symbols, \bold{54} |
568 \item syntax, 6, 11 |
576 \item syntax, \hyperpage{6}, \hyperpage{11} |
569 \item \isacommand {syntax} (command), 55 |
577 \item \isacommand {syntax} (command), \hyperpage{55} |
570 \item syntax (command), 56 |
578 \item syntax (command), \hyperpage{56} |
571 \item syntax translations, \bold{56} |
579 \item syntax translations, \bold{56} |
572 |
580 |
573 \indexspace |
581 \indexspace |
574 |
582 |
575 \item tacticals, 99 |
583 \item tacticals, 99 |
576 \item tactics, 12 |
584 \item tactics, \hyperpage{12} |
577 \item \isacommand {term} (command), 16 |
585 \item \isacommand {term} (command), \hyperpage{16} |
578 \item term rewriting, \bold{27} |
586 \item term rewriting, \bold{27} |
579 \item termination, \see{functions, total}{1} |
587 \item termination, \see{functions, total}{1} |
580 \item terms, 5 |
588 \item terms, 5 |
581 \item text, \bold{61} |
589 \item text, \bold{61} |
582 \item text blocks, \bold{61} |
590 \item text blocks, \bold{61} |
583 \item \isa {THE} (symbol), 85 |
591 \item \isa {THE} (symbol), \hyperpage{85} |
584 \item \isa {the_equality} (theorem), \bold{85} |
592 \item \isa {the_equality} (theorem), \bold{85} |
585 \item \isa {THEN} (attribute), \bold{94}, 96, 102 |
593 \item \isa {THEN} (attribute), \bold{94}, \hyperpage{96}, |
586 \item \isacommand {theorem} (command), \bold{11}, 13 |
594 \hyperpage{102} |
|
595 \item \isacommand {theorem} (command), \bold{11}, \hyperpage{13} |
587 \item theories, 4 |
596 \item theories, 4 |
588 \subitem abandoning, \bold{16} |
597 \subitem abandoning, \bold{16} |
589 \item \isacommand {theory} (command), 16 |
598 \item \isacommand {theory} (command), \hyperpage{16} |
590 \item theory files, 4 |
599 \item theory files, \hyperpage{4} |
591 \item \isacommand {thm} (command), 16 |
600 \item \isacommand {thm} (command), \hyperpage{16} |
592 \item \isa {tl} (constant), 17 |
601 \item \isa {tl} (constant), \hyperpage{17} |
593 \item \isa {ToyList} example, 9--14 |
602 \item \isa {ToyList} example, 9--14 |
594 \item \isa {trace_simp} (flag), 33 |
603 \item \isa {trace_simp} (flag), \hyperpage{33} |
595 \item tracing the simplifier, \bold{33} |
604 \item tracing the simplifier, \bold{33} |
596 \item \isa {trancl_trans} (theorem), \bold{113} |
605 \item \isa {trancl_trans} (theorem), \bold{113} |
597 \item transition systems, 117 |
606 \item transition systems, \hyperpage{117} |
598 \item \isacommand {translations} (command), 56 |
607 \item \isacommand {translations} (command), \hyperpage{56} |
599 \item tries, 44--46 |
608 \item tries, 44--46 |
600 \item \isa {True} (constant), 5 |
609 \item \isa {True} (constant), \hyperpage{5} |
601 \item \isa {truncate} (constant), 163 |
610 \item \isa {truncate} (constant), \hyperpage{163} |
602 \item tuples, \see{pairs and tuples}{1} |
611 \item tuples, \see{pairs and tuples}{1} |
603 \item txt, \bold{61} |
612 \item txt, \bold{61} |
604 \item \isacommand {typ} (command), 16 |
613 \item \isacommand {typ} (command), \hyperpage{16} |
605 \item type constraints, \bold{6} |
614 \item type constraints, \bold{6} |
606 \item type constructors, 5 |
615 \item type constructors, \hyperpage{5} |
607 \item type inference, \bold{5} |
616 \item type inference, \bold{5} |
608 \item type synonyms, 25 |
617 \item type synonyms, \hyperpage{25} |
609 \item type variables, 5 |
618 \item type variables, \hyperpage{5} |
610 \item \isacommand {typedecl} (command), 117, 171 |
619 \item \isacommand {typedecl} (command), \hyperpage{117}, |
|
620 \hyperpage{171} |
611 \item \isacommand {typedef} (command), 171--174 |
621 \item \isacommand {typedef} (command), 171--174 |
612 \item types, 4--5 |
622 \item types, 4--5 |
613 \subitem declaring, 171 |
623 \subitem declaring, 171 |
614 \subitem defining, 171--174 |
624 \subitem defining, 171--174 |
615 \item \isacommand {types} (command), 25 |
625 \item \isacommand {types} (command), \hyperpage{25} |
616 |
626 |
617 \indexspace |
627 \indexspace |
618 |
628 |
619 \item Ullman, J. D., 145 |
629 \item Ullman, J. D., \hyperpage{145} |
620 \item \texttt {UN}, \bold{209} |
630 \item \texttt {UN}, \bold{209} |
621 \item \texttt {Un}, \bold{209} |
631 \item \texttt {Un}, \bold{209} |
622 \item \isa {UN_E} (theorem), \bold{108} |
632 \item \isa {UN_E} (theorem), \bold{108} |
623 \item \isa {UN_I} (theorem), \bold{108} |
633 \item \isa {UN_I} (theorem), \bold{108} |
624 \item \isa {UN_iff} (theorem), \bold{108} |
634 \item \isa {UN_iff} (theorem), \bold{108} |
625 \item \isa {Un_subset_iff} (theorem), \bold{106} |
635 \item \isa {Un_subset_iff} (theorem), \bold{106} |
626 \item \isacommand {undo} (command), 16 |
636 \item \isacommand {undo} (command), \hyperpage{16} |
627 \item \isa {unfold} (method), \bold{31} |
637 \item \isa {unfold} (method), \bold{31} |
628 \item unification, 76--79 |
638 \item unification, 76--79 |
629 \item \isa {UNION} (constant), 109 |
639 \item \isa {UNION} (constant), \hyperpage{109} |
630 \item \texttt {Union}, \bold{209} |
640 \item \texttt {Union}, \bold{209} |
631 \item union |
641 \item union |
632 \subitem indexed, 108 |
642 \subitem indexed, \hyperpage{108} |
633 \item \isa {Union_iff} (theorem), \bold{108} |
643 \item \isa {Union_iff} (theorem), \bold{108} |
634 \item \isa {unit} (type), 24 |
644 \item \isa {unit} (type), \hyperpage{24} |
635 \item unknowns, 7, \bold{68} |
645 \item unknowns, \hyperpage{7}, \bold{68} |
636 \item unsafe rules, \bold{90} |
646 \item unsafe rules, \bold{90} |
637 \item update |
647 \item update |
638 \subitem record, 159 |
648 \subitem record, \hyperpage{159} |
639 \item updating a function, \bold{109} |
649 \item updating a function, \bold{109} |
640 |
650 |
641 \indexspace |
651 \indexspace |
642 |
652 |
643 \item variables, 7 |
653 \item variables, 7 |
644 \subitem schematic, 7 |
654 \subitem schematic, \hyperpage{7} |
645 \subitem type, 5 |
655 \subitem type, \hyperpage{5} |
646 \item \isa {vimage_def} (theorem), \bold{111} |
656 \item \isa {vimage_def} (theorem), \bold{111} |
647 |
657 |
648 \indexspace |
658 \indexspace |
649 |
659 |
650 \item \isa {wf_induct} (theorem), \bold{115} |
660 \item \isa {wf_induct} (theorem), \bold{115} |
651 \item \isa {wf_inv_image} (theorem), \bold{115} |
661 \item \isa {wf_inv_image} (theorem), \bold{115} |
652 \item \isa {wf_less_than} (theorem), \bold{114} |
662 \item \isa {wf_less_than} (theorem), \bold{114} |
653 \item \isa {wf_lex_prod} (theorem), \bold{115} |
663 \item \isa {wf_lex_prod} (theorem), \bold{115} |
654 \item \isa {wf_measure} (theorem), \bold{115} |
664 \item \isa {wf_measure} (theorem), \bold{115} |
655 \item \isa {wf_subset} (theorem), 180 |
665 \item \isa {wf_subset} (theorem), \hyperpage{180} |
656 \item \isa {while} (constant), 185 |
666 \item \isa {while} (constant), \hyperpage{185} |
657 \item \isa {While_Combinator} (theory), 185 |
667 \item \isa {While_Combinator} (theory), \hyperpage{185} |
658 \item \isa {while_rule} (theorem), 185 |
668 \item \isa {while_rule} (theorem), \hyperpage{185} |
659 |
669 |
660 \indexspace |
670 \indexspace |
661 |
671 |
662 \item \isa {zadd_ac} (theorems), 153 |
672 \item \isa {zadd_ac} (theorems), \hyperpage{153} |
663 \item \isa {zmult_ac} (theorems), 153 |
673 \item \isa {zmult_ac} (theorems), \hyperpage{153} |
664 |
674 |
665 \end{theindex} |
675 \end{theindex} |