|
1 \begin{theindex} |
|
2 |
|
3 \item {\tt\#*} symbol, 45 |
|
4 \item {\tt\#+} symbol, 45 |
|
5 \item {\tt\#-} symbol, 45 |
|
6 \item {\tt\&} symbol, 5 |
|
7 \item {\tt *} symbol, 25 |
|
8 \item {\tt +} symbol, 41 |
|
9 \item {\tt -} symbol, 24 |
|
10 \item {\tt -->} symbol, 5 |
|
11 \item {\tt ->} symbol, 25 |
|
12 \item {\tt -``} symbol, 24 |
|
13 \item {\tt :} symbol, 24 |
|
14 \item {\tt <->} symbol, 5 |
|
15 \item {\tt <=} symbol, 24 |
|
16 \item {\tt =} symbol, 5 |
|
17 \item {\tt `} symbol, 24 |
|
18 \item {\tt ``} symbol, 24 |
|
19 \item {\tt |} symbol, 5 |
|
20 |
|
21 \indexspace |
|
22 |
|
23 \item {\tt 0} constant, 24 |
|
24 |
|
25 \indexspace |
|
26 |
|
27 \item {\tt add_0} theorem, 45 |
|
28 \item {\tt add_mult_dist} theorem, 45 |
|
29 \item {\tt add_succ} theorem, 45 |
|
30 \item {\tt ALL} symbol, 5, 25 |
|
31 \item {\tt All} constant, 5 |
|
32 \item {\tt all_dupE} theorem, 3, 7 |
|
33 \item {\tt all_impE} theorem, 7 |
|
34 \item {\tt allE} theorem, 3, 7 |
|
35 \item {\tt allI} theorem, 6 |
|
36 \item {\tt and_def} theorem, 41 |
|
37 \item {\tt apply_def} theorem, 29 |
|
38 \item {\tt apply_equality} theorem, 38, 39, 69 |
|
39 \item {\tt apply_equality2} theorem, 38 |
|
40 \item {\tt apply_iff} theorem, 38 |
|
41 \item {\tt apply_Pair} theorem, 38, 69 |
|
42 \item {\tt apply_type} theorem, 38 |
|
43 \item {\tt Arith} theory, 42 |
|
44 \item assumptions |
|
45 \subitem contradictory, 14 |
|
46 |
|
47 \indexspace |
|
48 |
|
49 \item {\tt Ball} constant, 24, 27 |
|
50 \item {\tt ball_cong} theorem, 31, 32 |
|
51 \item {\tt Ball_def} theorem, 28 |
|
52 \item {\tt ballE} theorem, 31, 32 |
|
53 \item {\tt ballI} theorem, 31 |
|
54 \item {\tt beta} theorem, 38, 39 |
|
55 \item {\tt Bex} constant, 24, 27 |
|
56 \item {\tt bex_cong} theorem, 31, 32 |
|
57 \item {\tt Bex_def} theorem, 28 |
|
58 \item {\tt bexCI} theorem, 31 |
|
59 \item {\tt bexE} theorem, 31 |
|
60 \item {\tt bexI} theorem, 31 |
|
61 \item {\tt bij} constant, 44 |
|
62 \item {\tt bij_converse_bij} theorem, 44 |
|
63 \item {\tt bij_def} theorem, 44 |
|
64 \item {\tt bij_disjoint_Un} theorem, 44 |
|
65 \item {\tt Blast_tac}, 15, 67, 68 |
|
66 \item {\tt blast_tac}, 16, 17, 19 |
|
67 \item {\tt bnd_mono_def} theorem, 43 |
|
68 \item {\tt Bool} theory, 39 |
|
69 \item {\tt bool_0I} theorem, 41 |
|
70 \item {\tt bool_1I} theorem, 41 |
|
71 \item {\tt bool_def} theorem, 41 |
|
72 \item {\tt boolE} theorem, 41 |
|
73 \item {\tt bspec} theorem, 31 |
|
74 |
|
75 \indexspace |
|
76 |
|
77 \item {\tt case} constant, 41 |
|
78 \item {\tt case_def} theorem, 41 |
|
79 \item {\tt case_Inl} theorem, 41 |
|
80 \item {\tt case_Inr} theorem, 41 |
|
81 \item {\tt coinduct} theorem, 43 |
|
82 \item {\tt coinductive}, 57--62 |
|
83 \item {\tt Collect} constant, 24, 25, 30 |
|
84 \item {\tt Collect_def} theorem, 28 |
|
85 \item {\tt Collect_subset} theorem, 35 |
|
86 \item {\tt CollectD1} theorem, 32, 33 |
|
87 \item {\tt CollectD2} theorem, 32, 33 |
|
88 \item {\tt CollectE} theorem, 32, 33 |
|
89 \item {\tt CollectI} theorem, 33 |
|
90 \item {\tt comp_assoc} theorem, 44 |
|
91 \item {\tt comp_bij} theorem, 44 |
|
92 \item {\tt comp_def} theorem, 44 |
|
93 \item {\tt comp_func} theorem, 44 |
|
94 \item {\tt comp_func_apply} theorem, 44 |
|
95 \item {\tt comp_inj} theorem, 44 |
|
96 \item {\tt comp_surj} theorem, 44 |
|
97 \item {\tt comp_type} theorem, 44 |
|
98 \item {\tt cond_0} theorem, 41 |
|
99 \item {\tt cond_1} theorem, 41 |
|
100 \item {\tt cond_def} theorem, 41 |
|
101 \item congruence rules, 32 |
|
102 \item {\tt conj_cong}, 4 |
|
103 \item {\tt conj_impE} theorem, 7, 8 |
|
104 \item {\tt conjE} theorem, 7 |
|
105 \item {\tt conjI} theorem, 6 |
|
106 \item {\tt conjunct1} theorem, 6 |
|
107 \item {\tt conjunct2} theorem, 6 |
|
108 \item {\tt cons} constant, 23, 24 |
|
109 \item {\tt cons_def} theorem, 29 |
|
110 \item {\tt Cons_iff} theorem, 47 |
|
111 \item {\tt consCI} theorem, 34 |
|
112 \item {\tt consE} theorem, 34 |
|
113 \item {\tt ConsI} theorem, 47 |
|
114 \item {\tt consI1} theorem, 34 |
|
115 \item {\tt consI2} theorem, 34 |
|
116 \item {\tt converse} constant, 24, 37 |
|
117 \item {\tt converse_def} theorem, 29 |
|
118 \item {\tt cut_facts_tac}, 17 |
|
119 |
|
120 \indexspace |
|
121 |
|
122 \item {\tt datatype}, 48--55 |
|
123 \item {\tt Diff_cancel} theorem, 40 |
|
124 \item {\tt Diff_contains} theorem, 35 |
|
125 \item {\tt Diff_def} theorem, 28 |
|
126 \item {\tt Diff_disjoint} theorem, 40 |
|
127 \item {\tt Diff_Int} theorem, 40 |
|
128 \item {\tt Diff_partition} theorem, 40 |
|
129 \item {\tt Diff_subset} theorem, 35 |
|
130 \item {\tt Diff_Un} theorem, 40 |
|
131 \item {\tt DiffD1} theorem, 34 |
|
132 \item {\tt DiffD2} theorem, 34 |
|
133 \item {\tt DiffE} theorem, 34 |
|
134 \item {\tt DiffI} theorem, 34 |
|
135 \item {\tt disj_impE} theorem, 7, 8, 12 |
|
136 \item {\tt disjCI} theorem, 9 |
|
137 \item {\tt disjE} theorem, 6 |
|
138 \item {\tt disjI1} theorem, 6 |
|
139 \item {\tt disjI2} theorem, 6 |
|
140 \item {\tt div} symbol, 45 |
|
141 \item {\tt div_def} theorem, 45 |
|
142 \item {\tt domain} constant, 24, 37 |
|
143 \item {\tt domain_def} theorem, 29 |
|
144 \item {\tt domain_of_fun} theorem, 38 |
|
145 \item {\tt domain_subset} theorem, 37 |
|
146 \item {\tt domain_type} theorem, 38 |
|
147 \item {\tt domainE} theorem, 37 |
|
148 \item {\tt domainI} theorem, 37 |
|
149 \item {\tt double_complement} theorem, 40 |
|
150 \item {\tt dresolve_tac}, 66 |
|
151 |
|
152 \indexspace |
|
153 |
|
154 \item {\tt empty_subsetI} theorem, 31 |
|
155 \item {\tt emptyE} theorem, 31 |
|
156 \item {\tt eq_mp_tac}, \bold{8} |
|
157 \item {\tt equalityD1} theorem, 31 |
|
158 \item {\tt equalityD2} theorem, 31 |
|
159 \item {\tt equalityE} theorem, 31 |
|
160 \item {\tt equalityI} theorem, 31, 65 |
|
161 \item {\tt equals0D} theorem, 31 |
|
162 \item {\tt equals0I} theorem, 31 |
|
163 \item {\tt eresolve_tac}, 14 |
|
164 \item {\tt eta} theorem, 38, 39 |
|
165 \item {\tt EX} symbol, 5, 25 |
|
166 \item {\tt Ex} constant, 5 |
|
167 \item {\tt EX!} symbol, 5 |
|
168 \item {\tt ex/Term} theory, 49 |
|
169 \item {\tt Ex1} constant, 5 |
|
170 \item {\tt ex1_def} theorem, 6 |
|
171 \item {\tt ex1E} theorem, 7 |
|
172 \item {\tt ex1I} theorem, 7 |
|
173 \item {\tt ex_impE} theorem, 7 |
|
174 \item {\tt exCI} theorem, 9, 13 |
|
175 \item {\tt excluded_middle} theorem, 9 |
|
176 \item {\tt exE} theorem, 6 |
|
177 \item {\tt exhaust_tac}, \bold{51} |
|
178 \item {\tt exI} theorem, 6 |
|
179 \item {\tt extension} theorem, 28 |
|
180 |
|
181 \indexspace |
|
182 |
|
183 \item {\tt False} constant, 5 |
|
184 \item {\tt FalseE} theorem, 6 |
|
185 \item {\tt field} constant, 24 |
|
186 \item {\tt field_def} theorem, 29 |
|
187 \item {\tt field_subset} theorem, 37 |
|
188 \item {\tt fieldCI} theorem, 37 |
|
189 \item {\tt fieldE} theorem, 37 |
|
190 \item {\tt fieldI1} theorem, 37 |
|
191 \item {\tt fieldI2} theorem, 37 |
|
192 \item {\tt Fin.consI} theorem, 46 |
|
193 \item {\tt Fin.emptyI} theorem, 46 |
|
194 \item {\tt Fin_induct} theorem, 46 |
|
195 \item {\tt Fin_mono} theorem, 46 |
|
196 \item {\tt Fin_subset} theorem, 46 |
|
197 \item {\tt Fin_UnI} theorem, 46 |
|
198 \item {\tt Fin_UnionI} theorem, 46 |
|
199 \item first-order logic, 3--21 |
|
200 \item {\tt Fixedpt} theory, 42 |
|
201 \item {\tt flat} constant, 47 |
|
202 \item {\tt FOL} theory, 3, 9 |
|
203 \item {\tt FOL_cs}, \bold{9}, 48 |
|
204 \item {\tt FOL_ss}, \bold{4}, 46 |
|
205 \item {\tt foundation} theorem, 28 |
|
206 \item {\tt fst} constant, 24, 30 |
|
207 \item {\tt fst_conv} theorem, 36 |
|
208 \item {\tt fst_def} theorem, 29 |
|
209 \item {\tt fun_disjoint_apply1} theorem, 38, 69 |
|
210 \item {\tt fun_disjoint_apply2} theorem, 38 |
|
211 \item {\tt fun_disjoint_Un} theorem, 38, 70 |
|
212 \item {\tt fun_empty} theorem, 38 |
|
213 \item {\tt fun_extension} theorem, 38, 39 |
|
214 \item {\tt fun_is_rel} theorem, 38 |
|
215 \item {\tt fun_single} theorem, 38 |
|
216 \item function applications |
|
217 \subitem in \ZF, 24 |
|
218 |
|
219 \indexspace |
|
220 |
|
221 \item {\tt gfp_def} theorem, 43 |
|
222 \item {\tt gfp_least} theorem, 43 |
|
223 \item {\tt gfp_mono} theorem, 43 |
|
224 \item {\tt gfp_subset} theorem, 43 |
|
225 \item {\tt gfp_Tarski} theorem, 43 |
|
226 \item {\tt gfp_upperbound} theorem, 43 |
|
227 \item {\tt Goalw}, 16, 17 |
|
228 |
|
229 \indexspace |
|
230 |
|
231 \item {\tt hyp_subst_tac}, 4 |
|
232 |
|
233 \indexspace |
|
234 |
|
235 \item {\textit {i}} type, 23 |
|
236 \item {\tt id} constant, 44 |
|
237 \item {\tt id_def} theorem, 44 |
|
238 \item {\tt if} constant, 24 |
|
239 \item {\tt if_def} theorem, 16, 28 |
|
240 \item {\tt if_not_P} theorem, 34 |
|
241 \item {\tt if_P} theorem, 34 |
|
242 \item {\tt ifE} theorem, 17 |
|
243 \item {\tt iff_def} theorem, 6 |
|
244 \item {\tt iff_impE} theorem, 7 |
|
245 \item {\tt iffCE} theorem, 9 |
|
246 \item {\tt iffD1} theorem, 7 |
|
247 \item {\tt iffD2} theorem, 7 |
|
248 \item {\tt iffE} theorem, 7 |
|
249 \item {\tt iffI} theorem, 7, 17 |
|
250 \item {\tt ifI} theorem, 17 |
|
251 \item {\tt IFOL} theory, 3 |
|
252 \item {\tt IFOL_ss}, \bold{4} |
|
253 \item {\tt image_def} theorem, 29 |
|
254 \item {\tt imageE} theorem, 37 |
|
255 \item {\tt imageI} theorem, 37 |
|
256 \item {\tt imp_impE} theorem, 7, 12 |
|
257 \item {\tt impCE} theorem, 9 |
|
258 \item {\tt impE} theorem, 7, 8 |
|
259 \item {\tt impI} theorem, 6 |
|
260 \item {\tt in} symbol, 26 |
|
261 \item {\tt induct} theorem, 43 |
|
262 \item {\tt induct_tac}, \bold{51} |
|
263 \item {\tt inductive}, 57--62 |
|
264 \item {\tt Inf} constant, 24, 30 |
|
265 \item {\tt infinity} theorem, 29 |
|
266 \item {\tt inj} constant, 44 |
|
267 \item {\tt inj_converse_inj} theorem, 44 |
|
268 \item {\tt inj_def} theorem, 44 |
|
269 \item {\tt Inl} constant, 41 |
|
270 \item {\tt Inl_def} theorem, 41 |
|
271 \item {\tt Inl_inject} theorem, 41 |
|
272 \item {\tt Inl_neq_Inr} theorem, 41 |
|
273 \item {\tt Inr} constant, 41 |
|
274 \item {\tt Inr_def} theorem, 41 |
|
275 \item {\tt Inr_inject} theorem, 41 |
|
276 \item {\tt INT} symbol, 25, 27 |
|
277 \item {\tt Int} symbol, 24 |
|
278 \item {\tt Int_absorb} theorem, 40 |
|
279 \item {\tt Int_assoc} theorem, 40 |
|
280 \item {\tt Int_commute} theorem, 40 |
|
281 \item {\tt Int_def} theorem, 28 |
|
282 \item {\tt INT_E} theorem, 33 |
|
283 \item {\tt Int_greatest} theorem, 35, 65, 66 |
|
284 \item {\tt INT_I} theorem, 33 |
|
285 \item {\tt Int_lower1} theorem, 35, 65 |
|
286 \item {\tt Int_lower2} theorem, 35, 65 |
|
287 \item {\tt Int_Un_distrib} theorem, 40 |
|
288 \item {\tt Int_Union_RepFun} theorem, 40 |
|
289 \item {\tt IntD1} theorem, 34 |
|
290 \item {\tt IntD2} theorem, 34 |
|
291 \item {\tt IntE} theorem, 34, 66 |
|
292 \item {\tt Inter} constant, 24 |
|
293 \item {\tt Inter_def} theorem, 28 |
|
294 \item {\tt Inter_greatest} theorem, 35 |
|
295 \item {\tt Inter_lower} theorem, 35 |
|
296 \item {\tt Inter_Un_distrib} theorem, 40 |
|
297 \item {\tt InterD} theorem, 33 |
|
298 \item {\tt InterE} theorem, 33 |
|
299 \item {\tt InterI} theorem, 32, 33 |
|
300 \item {\tt IntI} theorem, 34 |
|
301 \item {\tt IntPr.best_tac}, \bold{9} |
|
302 \item {\tt IntPr.fast_tac}, \bold{8}, 11 |
|
303 \item {\tt IntPr.inst_step_tac}, \bold{8} |
|
304 \item {\tt IntPr.safe_step_tac}, \bold{8} |
|
305 \item {\tt IntPr.safe_tac}, \bold{8} |
|
306 \item {\tt IntPr.step_tac}, \bold{8} |
|
307 |
|
308 \indexspace |
|
309 |
|
310 \item {\tt lam} symbol, 25, 27 |
|
311 \item {\tt lam_def} theorem, 29 |
|
312 \item {\tt lam_type} theorem, 38 |
|
313 \item {\tt Lambda} constant, 24, 27 |
|
314 \item $\lambda$-abstractions |
|
315 \subitem in \ZF, 25 |
|
316 \item {\tt lamE} theorem, 38, 39 |
|
317 \item {\tt lamI} theorem, 38, 39 |
|
318 \item {\tt le_cs}, \bold{48} |
|
319 \item {\tt left_comp_id} theorem, 44 |
|
320 \item {\tt left_comp_inverse} theorem, 44 |
|
321 \item {\tt left_inverse} theorem, 44 |
|
322 \item {\tt length} constant, 47 |
|
323 \item {\tt Let} constant, 23, 24 |
|
324 \item {\tt let} symbol, 26 |
|
325 \item {\tt Let_def} theorem, 23, 28 |
|
326 \item {\tt lfp_def} theorem, 43 |
|
327 \item {\tt lfp_greatest} theorem, 43 |
|
328 \item {\tt lfp_lowerbound} theorem, 43 |
|
329 \item {\tt lfp_mono} theorem, 43 |
|
330 \item {\tt lfp_subset} theorem, 43 |
|
331 \item {\tt lfp_Tarski} theorem, 43 |
|
332 \item {\tt list} constant, 47 |
|
333 \item {\tt List.induct} theorem, 47 |
|
334 \item {\tt list_case} constant, 47 |
|
335 \item {\tt list_mono} theorem, 47 |
|
336 \item {\tt logic} class, 3 |
|
337 |
|
338 \indexspace |
|
339 |
|
340 \item {\tt map} constant, 47 |
|
341 \item {\tt map_app_distrib} theorem, 47 |
|
342 \item {\tt map_compose} theorem, 47 |
|
343 \item {\tt map_flat} theorem, 47 |
|
344 \item {\tt map_ident} theorem, 47 |
|
345 \item {\tt map_type} theorem, 47 |
|
346 \item {\tt mem_asym} theorem, 34, 35 |
|
347 \item {\tt mem_irrefl} theorem, 34 |
|
348 \item {\tt mk_cases}, 54, 61 |
|
349 \item {\tt mod} symbol, 45 |
|
350 \item {\tt mod_def} theorem, 45 |
|
351 \item {\tt mod_quo_equality} theorem, 45 |
|
352 \item {\tt mp} theorem, 6 |
|
353 \item {\tt mp_tac}, \bold{8} |
|
354 \item {\tt mult_0} theorem, 45 |
|
355 \item {\tt mult_assoc} theorem, 45 |
|
356 \item {\tt mult_commute} theorem, 45 |
|
357 \item {\tt mult_succ} theorem, 45 |
|
358 \item {\tt mult_type} theorem, 45 |
|
359 |
|
360 \indexspace |
|
361 |
|
362 \item {\tt Nat} theory, 42 |
|
363 \item {\tt nat} constant, 45 |
|
364 \item {\tt nat_0I} theorem, 45 |
|
365 \item {\tt nat_case} constant, 45 |
|
366 \item {\tt nat_case_0} theorem, 45 |
|
367 \item {\tt nat_case_def} theorem, 45 |
|
368 \item {\tt nat_case_succ} theorem, 45 |
|
369 \item {\tt nat_def} theorem, 45 |
|
370 \item {\tt nat_induct} theorem, 45 |
|
371 \item {\tt nat_succI} theorem, 45 |
|
372 \item {\tt Nil_Cons_iff} theorem, 47 |
|
373 \item {\tt NilI} theorem, 47 |
|
374 \item {\tt Not} constant, 5 |
|
375 \item {\tt not_def} theorem, 6, 41 |
|
376 \item {\tt not_impE} theorem, 7 |
|
377 \item {\tt notE} theorem, 7, 8 |
|
378 \item {\tt notI} theorem, 7 |
|
379 \item {\tt notnotD} theorem, 9 |
|
380 |
|
381 \indexspace |
|
382 |
|
383 \item {\tt O} symbol, 44 |
|
384 \item {\textit {o}} type, 3 |
|
385 \item {\tt or_def} theorem, 41 |
|
386 |
|
387 \indexspace |
|
388 |
|
389 \item {\tt Pair} constant, 24, 25 |
|
390 \item {\tt Pair_def} theorem, 29 |
|
391 \item {\tt Pair_inject} theorem, 36 |
|
392 \item {\tt Pair_inject1} theorem, 36 |
|
393 \item {\tt Pair_inject2} theorem, 36 |
|
394 \item {\tt Pair_neq_0} theorem, 36 |
|
395 \item {\tt pairing} theorem, 33 |
|
396 \item {\tt Perm} theory, 42 |
|
397 \item {\tt Pi} constant, 24, 27, 39 |
|
398 \item {\tt Pi_def} theorem, 29 |
|
399 \item {\tt Pi_type} theorem, 38, 39 |
|
400 \item {\tt Pow} constant, 24 |
|
401 \item {\tt Pow_iff} theorem, 28 |
|
402 \item {\tt Pow_mono} theorem, 65 |
|
403 \item {\tt PowD} theorem, 31, 66 |
|
404 \item {\tt PowI} theorem, 31, 66 |
|
405 \item {\tt primrec}, 55--57 |
|
406 \item {\tt PrimReplace} constant, 24, 30 |
|
407 \item priorities, 1 |
|
408 \item {\tt PROD} symbol, 25, 27 |
|
409 \item {\tt prop_cs}, \bold{9} |
|
410 |
|
411 \indexspace |
|
412 |
|
413 \item {\tt qcase_def} theorem, 42 |
|
414 \item {\tt qconverse} constant, 39 |
|
415 \item {\tt qconverse_def} theorem, 42 |
|
416 \item {\tt qed_spec_mp}, 54 |
|
417 \item {\tt qfsplit_def} theorem, 42 |
|
418 \item {\tt QInl_def} theorem, 42 |
|
419 \item {\tt QInr_def} theorem, 42 |
|
420 \item {\tt QPair} theory, 39 |
|
421 \item {\tt QPair_def} theorem, 42 |
|
422 \item {\tt QSigma} constant, 39 |
|
423 \item {\tt QSigma_def} theorem, 42 |
|
424 \item {\tt qsplit} constant, 39 |
|
425 \item {\tt qsplit_def} theorem, 42 |
|
426 \item {\tt qsum_def} theorem, 42 |
|
427 \item {\tt QUniv} theory, 46 |
|
428 |
|
429 \indexspace |
|
430 |
|
431 \item {\tt range} constant, 24 |
|
432 \item {\tt range_def} theorem, 29 |
|
433 \item {\tt range_of_fun} theorem, 38, 39 |
|
434 \item {\tt range_subset} theorem, 37 |
|
435 \item {\tt range_type} theorem, 38 |
|
436 \item {\tt rangeE} theorem, 37 |
|
437 \item {\tt rangeI} theorem, 37 |
|
438 \item {\tt rank} constant, 62 |
|
439 \item recursion |
|
440 \subitem primitive, 57 |
|
441 \item recursive functions, \see{recursion}{55} |
|
442 \item {\tt refl} theorem, 6 |
|
443 \item {\tt RepFun} constant, 24, 27, 30, 32 |
|
444 \item {\tt RepFun_def} theorem, 28 |
|
445 \item {\tt RepFunE} theorem, 33 |
|
446 \item {\tt RepFunI} theorem, 33 |
|
447 \item {\tt Replace} constant, 24, 25, 30, 32 |
|
448 \item {\tt Replace_def} theorem, 28 |
|
449 \item {\tt ReplaceE} theorem, 33 |
|
450 \item {\tt ReplaceI} theorem, 33 |
|
451 \item {\tt replacement} theorem, 28 |
|
452 \item {\tt restrict} constant, 24, 30 |
|
453 \item {\tt restrict} theorem, 38 |
|
454 \item {\tt restrict_bij} theorem, 44 |
|
455 \item {\tt restrict_def} theorem, 29 |
|
456 \item {\tt restrict_type} theorem, 38 |
|
457 \item {\tt rev} constant, 47 |
|
458 \item {\tt rew_tac}, 17 |
|
459 \item {\tt rewrite_rule}, 17 |
|
460 \item {\tt right_comp_id} theorem, 44 |
|
461 \item {\tt right_comp_inverse} theorem, 44 |
|
462 \item {\tt right_inverse} theorem, 44 |
|
463 |
|
464 \indexspace |
|
465 |
|
466 \item {\tt separation} theorem, 33 |
|
467 \item set theory, 22--70 |
|
468 \item {\tt Sigma} constant, 24, 27, 30, 36 |
|
469 \item {\tt Sigma_def} theorem, 29 |
|
470 \item {\tt SigmaE} theorem, 36 |
|
471 \item {\tt SigmaE2} theorem, 36 |
|
472 \item {\tt SigmaI} theorem, 36 |
|
473 \item simplification |
|
474 \subitem of conjunctions, 4 |
|
475 \item {\tt singletonE} theorem, 34 |
|
476 \item {\tt singletonI} theorem, 34 |
|
477 \item {\tt snd} constant, 24, 30 |
|
478 \item {\tt snd_conv} theorem, 36 |
|
479 \item {\tt snd_def} theorem, 29 |
|
480 \item {\tt spec} theorem, 6 |
|
481 \item {\tt split} constant, 24, 30 |
|
482 \item {\tt split} theorem, 36 |
|
483 \item {\tt split_def} theorem, 29 |
|
484 \item {\tt ssubst} theorem, 7 |
|
485 \item {\tt Step_tac}, 20 |
|
486 \item {\tt step_tac}, 21 |
|
487 \item {\tt subset_def} theorem, 28 |
|
488 \item {\tt subset_refl} theorem, 31 |
|
489 \item {\tt subset_trans} theorem, 31 |
|
490 \item {\tt subsetCE} theorem, 31 |
|
491 \item {\tt subsetD} theorem, 31, 68 |
|
492 \item {\tt subsetI} theorem, 31, 66, 67 |
|
493 \item {\tt subst} theorem, 6 |
|
494 \item {\tt succ} constant, 24, 30 |
|
495 \item {\tt succ_def} theorem, 29 |
|
496 \item {\tt succ_inject} theorem, 34 |
|
497 \item {\tt succ_neq_0} theorem, 34 |
|
498 \item {\tt succCI} theorem, 34 |
|
499 \item {\tt succE} theorem, 34 |
|
500 \item {\tt succI1} theorem, 34 |
|
501 \item {\tt succI2} theorem, 34 |
|
502 \item {\tt SUM} symbol, 25, 27 |
|
503 \item {\tt Sum} theory, 39 |
|
504 \item {\tt sum_def} theorem, 41 |
|
505 \item {\tt sum_InlI} theorem, 41 |
|
506 \item {\tt sum_InrI} theorem, 41 |
|
507 \item {\tt SUM_Int_distrib1} theorem, 40 |
|
508 \item {\tt SUM_Int_distrib2} theorem, 40 |
|
509 \item {\tt SUM_Un_distrib1} theorem, 40 |
|
510 \item {\tt SUM_Un_distrib2} theorem, 40 |
|
511 \item {\tt sumE2} theorem, 41 |
|
512 \item {\tt surj} constant, 44 |
|
513 \item {\tt surj_def} theorem, 44 |
|
514 \item {\tt swap} theorem, 9 |
|
515 \item {\tt swap_res_tac}, 14 |
|
516 \item {\tt sym} theorem, 7 |
|
517 |
|
518 \indexspace |
|
519 |
|
520 \item {\tt term} class, 3 |
|
521 \item {\tt THE} symbol, 25, 27, 35 |
|
522 \item {\tt The} constant, 24, 27, 30 |
|
523 \item {\tt the_def} theorem, 28 |
|
524 \item {\tt the_equality} theorem, 34, 35 |
|
525 \item {\tt theI} theorem, 34, 35 |
|
526 \item {\tt trace_induct}, \bold{59} |
|
527 \item {\tt trans} theorem, 7 |
|
528 \item {\tt True} constant, 5 |
|
529 \item {\tt True_def} theorem, 6 |
|
530 \item {\tt TrueI} theorem, 7 |
|
531 \item {\tt Trueprop} constant, 5 |
|
532 |
|
533 \indexspace |
|
534 |
|
535 \item {\tt UN} symbol, 25, 27 |
|
536 \item {\tt Un} symbol, 24 |
|
537 \item {\tt Un_absorb} theorem, 40 |
|
538 \item {\tt Un_assoc} theorem, 40 |
|
539 \item {\tt Un_commute} theorem, 40 |
|
540 \item {\tt Un_def} theorem, 28 |
|
541 \item {\tt UN_E} theorem, 33 |
|
542 \item {\tt UN_I} theorem, 33 |
|
543 \item {\tt Un_Int_distrib} theorem, 40 |
|
544 \item {\tt Un_Inter_RepFun} theorem, 40 |
|
545 \item {\tt Un_least} theorem, 35 |
|
546 \item {\tt Un_upper1} theorem, 35 |
|
547 \item {\tt Un_upper2} theorem, 35 |
|
548 \item {\tt UnCI} theorem, 32, 34 |
|
549 \item {\tt UnE} theorem, 34 |
|
550 \item {\tt UnI1} theorem, 32, 34, 69 |
|
551 \item {\tt UnI2} theorem, 32, 34 |
|
552 \item {\tt Union} constant, 24 |
|
553 \item {\tt Union_iff} theorem, 28 |
|
554 \item {\tt Union_least} theorem, 35 |
|
555 \item {\tt Union_Un_distrib} theorem, 40 |
|
556 \item {\tt Union_upper} theorem, 35 |
|
557 \item {\tt UnionE} theorem, 33, 67 |
|
558 \item {\tt UnionI} theorem, 33, 67 |
|
559 \item {\tt Univ} theory, 42 |
|
560 \item {\tt Upair} constant, 23, 24, 30 |
|
561 \item {\tt Upair_def} theorem, 28 |
|
562 \item {\tt UpairE} theorem, 33 |
|
563 \item {\tt UpairI1} theorem, 33 |
|
564 \item {\tt UpairI2} theorem, 33 |
|
565 |
|
566 \indexspace |
|
567 |
|
568 \item {\tt vimage_def} theorem, 29 |
|
569 \item {\tt vimageE} theorem, 37 |
|
570 \item {\tt vimageI} theorem, 37 |
|
571 |
|
572 \indexspace |
|
573 |
|
574 \item {\tt xor_def} theorem, 41 |
|
575 |
|
576 \indexspace |
|
577 |
|
578 \item {\tt ZF} theory, 22 |
|
579 \item {\tt ZF_cs}, \bold{48} |
|
580 \item {\tt ZF_ss}, \bold{46} |
|
581 |
|
582 \end{theindex} |