author | oheimb |
Wed, 18 Dec 1996 13:32:29 +0100 | |
changeset 2439 | e73cb5924261 |
parent 2421 | a07181dd2118 |
permissions | -rw-r--r-- |
1461 | 1 |
(* Title: HOLCF/Dnat.ML |
1274 | 2 |
ID: $Id$ |
1461 | 3 |
Author: Franz Regensburger |
1274 | 4 |
Copyright 1993 Technische Universitaet Muenchen |
5 |
||
6 |
Lemmas for dnat.thy |
|
7 |
*) |
|
8 |
||
9 |
open Dnat; |
|
10 |
||
11 |
(* ------------------------------------------------------------------------*) |
|
12 |
(* The isomorphisms dnat_rep_iso and dnat_abs_iso are strict *) |
|
13 |
(* ------------------------------------------------------------------------*) |
|
14 |
||
15 |
val dnat_iso_strict = dnat_rep_iso RS (dnat_abs_iso RS |
|
1461 | 16 |
(allI RSN (2,allI RS iso_strict))); |
1274 | 17 |
|
18 |
val dnat_rews = [dnat_iso_strict RS conjunct1, |
|
1461 | 19 |
dnat_iso_strict RS conjunct2]; |
1274 | 20 |
|
21 |
(* ------------------------------------------------------------------------*) |
|
22 |
(* Properties of dnat_copy *) |
|
23 |
(* ------------------------------------------------------------------------*) |
|
24 |
||
25 |
fun prover defs thm = prove_goalw Dnat.thy defs thm |
|
26 |
(fn prems => |
|
1461 | 27 |
[ |
28 |
(cut_facts_tac prems 1), |
|
29 |
(asm_simp_tac (!simpset addsimps |
|
30 |
(dnat_rews @ [dnat_abs_iso,dnat_rep_iso])) 1) |
|
31 |
]); |
|
1274 | 32 |
|
33 |
val dnat_copy = |
|
1461 | 34 |
[ |
35 |
prover [dnat_copy_def] "dnat_copy`f`UU=UU", |
|
36 |
prover [dnat_copy_def,dzero_def] "dnat_copy`f`dzero= dzero", |
|
37 |
prover [dnat_copy_def,dsucc_def] |
|
38 |
"n~=UU ==> dnat_copy`f`(dsucc`n) = dsucc`(f`n)" |
|
39 |
]; |
|
1274 | 40 |
|
41 |
val dnat_rews = dnat_copy @ dnat_rews; |
|
42 |
||
43 |
(* ------------------------------------------------------------------------*) |
|
44 |
(* Exhaustion and elimination for dnat *) |
|
45 |
(* ------------------------------------------------------------------------*) |
|
46 |
||
47 |
qed_goalw "Exh_dnat" Dnat.thy [dsucc_def,dzero_def] |
|
1461 | 48 |
"n = UU | n = dzero | (? x . x~=UU & n = dsucc`x)" |
1274 | 49 |
(fn prems => |
1461 | 50 |
[ |
51 |
(Simp_tac 1), |
|
52 |
(rtac (dnat_rep_iso RS subst) 1), |
|
53 |
(res_inst_tac [("p","dnat_rep`n")] ssumE 1), |
|
54 |
(rtac disjI1 1), |
|
55 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
56 |
(rtac (disjI1 RS disjI2) 1), |
|
57 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
58 |
(res_inst_tac [("p","x")] oneE 1), |
|
59 |
(contr_tac 1), |
|
60 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
61 |
(rtac (disjI2 RS disjI2) 1), |
|
62 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
63 |
(fast_tac HOL_cs 1) |
|
64 |
]); |
|
1274 | 65 |
|
66 |
qed_goal "dnatE" Dnat.thy |
|
67 |
"[| n=UU ==> Q; n=dzero ==> Q; !!x.[|n=dsucc`x;x~=UU|]==>Q|]==>Q" |
|
68 |
(fn prems => |
|
1461 | 69 |
[ |
70 |
(rtac (Exh_dnat RS disjE) 1), |
|
71 |
(eresolve_tac prems 1), |
|
72 |
(etac disjE 1), |
|
73 |
(eresolve_tac prems 1), |
|
74 |
(REPEAT (etac exE 1)), |
|
75 |
(resolve_tac prems 1), |
|
76 |
(fast_tac HOL_cs 1), |
|
77 |
(fast_tac HOL_cs 1) |
|
78 |
]); |
|
1274 | 79 |
|
80 |
(* ------------------------------------------------------------------------*) |
|
81 |
(* Properties of dnat_when *) |
|
82 |
(* ------------------------------------------------------------------------*) |
|
83 |
||
84 |
fun prover defs thm = prove_goalw Dnat.thy defs thm |
|
85 |
(fn prems => |
|
1461 | 86 |
[ |
87 |
(cut_facts_tac prems 1), |
|
88 |
(asm_simp_tac (!simpset addsimps |
|
89 |
(dnat_rews @ [dnat_abs_iso,dnat_rep_iso])) 1) |
|
90 |
]); |
|
1274 | 91 |
|
92 |
||
93 |
val dnat_when = [ |
|
1461 | 94 |
prover [dnat_when_def] "dnat_when`c`f`UU=UU", |
95 |
prover [dnat_when_def,dzero_def] "dnat_when`c`f`dzero=c", |
|
96 |
prover [dnat_when_def,dsucc_def] |
|
97 |
"n~=UU ==> dnat_when`c`f`(dsucc`n)=f`n" |
|
98 |
]; |
|
1274 | 99 |
|
100 |
val dnat_rews = dnat_when @ dnat_rews; |
|
101 |
||
102 |
(* ------------------------------------------------------------------------*) |
|
103 |
(* Rewrites for discriminators and selectors *) |
|
104 |
(* ------------------------------------------------------------------------*) |
|
105 |
||
106 |
fun prover defs thm = prove_goalw Dnat.thy defs thm |
|
107 |
(fn prems => |
|
1461 | 108 |
[ |
109 |
(simp_tac (!simpset addsimps dnat_rews) 1) |
|
110 |
]); |
|
1274 | 111 |
|
112 |
val dnat_discsel = [ |
|
1461 | 113 |
prover [is_dzero_def] "is_dzero`UU=UU", |
114 |
prover [is_dsucc_def] "is_dsucc`UU=UU", |
|
115 |
prover [dpred_def] "dpred`UU=UU" |
|
116 |
]; |
|
1274 | 117 |
|
118 |
||
119 |
fun prover defs thm = prove_goalw Dnat.thy defs thm |
|
120 |
(fn prems => |
|
1461 | 121 |
[ |
122 |
(cut_facts_tac prems 1), |
|
123 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1) |
|
124 |
]); |
|
1274 | 125 |
|
126 |
val dnat_discsel = [ |
|
1461 | 127 |
prover [is_dzero_def] "is_dzero`dzero=TT", |
128 |
prover [is_dzero_def] "n~=UU ==>is_dzero`(dsucc`n)=FF", |
|
129 |
prover [is_dsucc_def] "is_dsucc`dzero=FF", |
|
130 |
prover [is_dsucc_def] "n~=UU ==> is_dsucc`(dsucc`n)=TT", |
|
131 |
prover [dpred_def] "dpred`dzero=UU", |
|
132 |
prover [dpred_def] "n~=UU ==> dpred`(dsucc`n)=n" |
|
133 |
] @ dnat_discsel; |
|
1274 | 134 |
|
135 |
val dnat_rews = dnat_discsel @ dnat_rews; |
|
136 |
||
137 |
(* ------------------------------------------------------------------------*) |
|
138 |
(* Definedness and strictness *) |
|
139 |
(* ------------------------------------------------------------------------*) |
|
140 |
||
141 |
fun prover contr thm = prove_goal Dnat.thy thm |
|
142 |
(fn prems => |
|
1461 | 143 |
[ |
2439 | 144 |
(res_inst_tac [("P1",contr)] classical2 1), |
1461 | 145 |
(simp_tac (!simpset addsimps dnat_rews) 1), |
146 |
(dtac sym 1), |
|
147 |
(Asm_simp_tac 1), |
|
148 |
(simp_tac (!simpset addsimps (prems @ dnat_rews)) 1) |
|
149 |
]); |
|
1274 | 150 |
|
151 |
val dnat_constrdef = [ |
|
1461 | 152 |
prover "is_dzero`UU ~= UU" "dzero~=UU", |
153 |
prover "is_dsucc`UU ~= UU" "n~=UU ==> dsucc`n~=UU" |
|
154 |
]; |
|
1274 | 155 |
|
156 |
||
157 |
fun prover defs thm = prove_goalw Dnat.thy defs thm |
|
158 |
(fn prems => |
|
1461 | 159 |
[ |
160 |
(simp_tac (!simpset addsimps dnat_rews) 1) |
|
161 |
]); |
|
1274 | 162 |
|
163 |
val dnat_constrdef = [ |
|
1461 | 164 |
prover [dsucc_def] "dsucc`UU=UU" |
165 |
] @ dnat_constrdef; |
|
1274 | 166 |
|
167 |
val dnat_rews = dnat_constrdef @ dnat_rews; |
|
168 |
||
169 |
||
170 |
(* ------------------------------------------------------------------------*) |
|
171 |
(* Distinctness wrt. << and = *) |
|
172 |
(* ------------------------------------------------------------------------*) |
|
173 |
||
174 |
val temp = prove_goal Dnat.thy "~dzero << dsucc`n" |
|
175 |
(fn prems => |
|
1461 | 176 |
[ |
2439 | 177 |
(res_inst_tac [("P1","TT << FF")] classical2 1), |
1461 | 178 |
(resolve_tac dist_less_tr 1), |
2421 | 179 |
(dres_inst_tac [("fo","is_dzero")] monofun_cfun_arg 1), |
1461 | 180 |
(etac box_less 1), |
181 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
1675 | 182 |
(case_tac "n=UU" 1), |
1461 | 183 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
184 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1) |
|
185 |
]); |
|
1274 | 186 |
|
187 |
val dnat_dist_less = [temp]; |
|
188 |
||
189 |
val temp = prove_goal Dnat.thy "n~=UU ==> ~dsucc`n << dzero" |
|
190 |
(fn prems => |
|
1461 | 191 |
[ |
192 |
(cut_facts_tac prems 1), |
|
2439 | 193 |
(res_inst_tac [("P1","TT << FF")] classical2 1), |
1461 | 194 |
(resolve_tac dist_less_tr 1), |
2421 | 195 |
(dres_inst_tac [("fo","is_dsucc")] monofun_cfun_arg 1), |
1461 | 196 |
(etac box_less 1), |
197 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
198 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1) |
|
199 |
]); |
|
1274 | 200 |
|
201 |
val dnat_dist_less = temp::dnat_dist_less; |
|
202 |
||
203 |
val temp = prove_goal Dnat.thy "dzero ~= dsucc`n" |
|
204 |
(fn prems => |
|
1461 | 205 |
[ |
1675 | 206 |
(case_tac "n=UU" 1), |
1461 | 207 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
2439 | 208 |
(res_inst_tac [("P1","TT = FF")] classical2 1), |
1461 | 209 |
(resolve_tac dist_eq_tr 1), |
210 |
(dres_inst_tac [("f","is_dzero")] cfun_arg_cong 1), |
|
211 |
(etac box_equals 1), |
|
212 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
213 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1) |
|
214 |
]); |
|
1274 | 215 |
|
216 |
val dnat_dist_eq = [temp, temp RS not_sym]; |
|
217 |
||
218 |
val dnat_rews = dnat_dist_less @ dnat_dist_eq @ dnat_rews; |
|
219 |
||
220 |
(* ------------------------------------------------------------------------*) |
|
221 |
(* Invertibility *) |
|
222 |
(* ------------------------------------------------------------------------*) |
|
223 |
||
224 |
val dnat_invert = |
|
1461 | 225 |
[ |
1274 | 226 |
prove_goal Dnat.thy |
227 |
"[|x1~=UU; y1~=UU; dsucc`x1 << dsucc`y1 |] ==> x1<< y1" |
|
228 |
(fn prems => |
|
1461 | 229 |
[ |
230 |
(cut_facts_tac prems 1), |
|
2421 | 231 |
(dres_inst_tac [("fo","dnat_when`c`(LAM x.x)")] monofun_cfun_arg 1), |
1461 | 232 |
(etac box_less 1), |
233 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
234 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1) |
|
235 |
]) |
|
236 |
]; |
|
1274 | 237 |
|
238 |
(* ------------------------------------------------------------------------*) |
|
239 |
(* Injectivity *) |
|
240 |
(* ------------------------------------------------------------------------*) |
|
241 |
||
242 |
val dnat_inject = |
|
1461 | 243 |
[ |
1274 | 244 |
prove_goal Dnat.thy |
245 |
"[|x1~=UU; y1~=UU; dsucc`x1 = dsucc`y1 |] ==> x1= y1" |
|
246 |
(fn prems => |
|
1461 | 247 |
[ |
248 |
(cut_facts_tac prems 1), |
|
249 |
(dres_inst_tac [("f","dnat_when`c`(LAM x.x)")] cfun_arg_cong 1), |
|
250 |
(etac box_equals 1), |
|
251 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
252 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1) |
|
253 |
]) |
|
254 |
]; |
|
1274 | 255 |
|
256 |
(* ------------------------------------------------------------------------*) |
|
257 |
(* definedness for discriminators and selectors *) |
|
258 |
(* ------------------------------------------------------------------------*) |
|
259 |
||
260 |
||
261 |
fun prover thm = prove_goal Dnat.thy thm |
|
262 |
(fn prems => |
|
1461 | 263 |
[ |
264 |
(cut_facts_tac prems 1), |
|
265 |
(rtac dnatE 1), |
|
266 |
(contr_tac 1), |
|
267 |
(REPEAT (asm_simp_tac (!simpset addsimps dnat_rews) 1)) |
|
268 |
]); |
|
1274 | 269 |
|
270 |
val dnat_discsel_def = |
|
1461 | 271 |
[ |
272 |
prover "n~=UU ==> is_dzero`n ~= UU", |
|
273 |
prover "n~=UU ==> is_dsucc`n ~= UU" |
|
274 |
]; |
|
1274 | 275 |
|
276 |
val dnat_rews = dnat_discsel_def @ dnat_rews; |
|
277 |
||
278 |
||
279 |
(* ------------------------------------------------------------------------*) |
|
280 |
(* Properties dnat_take *) |
|
281 |
(* ------------------------------------------------------------------------*) |
|
282 |
val temp = prove_goalw Dnat.thy [dnat_take_def] "dnat_take n`UU = UU" |
|
283 |
(fn prems => |
|
1461 | 284 |
[ |
285 |
(res_inst_tac [("n","n")] natE 1), |
|
286 |
(Asm_simp_tac 1), |
|
287 |
(Asm_simp_tac 1), |
|
288 |
(simp_tac (!simpset addsimps dnat_rews) 1) |
|
289 |
]); |
|
1274 | 290 |
|
291 |
val dnat_take = [temp]; |
|
292 |
||
293 |
val temp = prove_goalw Dnat.thy [dnat_take_def] "dnat_take 0`xs = UU" |
|
294 |
(fn prems => |
|
1461 | 295 |
[ |
296 |
(Asm_simp_tac 1) |
|
297 |
]); |
|
1274 | 298 |
|
299 |
val dnat_take = temp::dnat_take; |
|
300 |
||
301 |
val temp = prove_goalw Dnat.thy [dnat_take_def] |
|
1461 | 302 |
"dnat_take (Suc n)`dzero=dzero" |
1274 | 303 |
(fn prems => |
1461 | 304 |
[ |
305 |
(Asm_simp_tac 1), |
|
306 |
(simp_tac (!simpset addsimps dnat_rews) 1) |
|
307 |
]); |
|
1274 | 308 |
|
309 |
val dnat_take = temp::dnat_take; |
|
310 |
||
311 |
val temp = prove_goalw Dnat.thy [dnat_take_def] |
|
312 |
"dnat_take (Suc n)`(dsucc`xs)=dsucc`(dnat_take n ` xs)" |
|
313 |
(fn prems => |
|
1461 | 314 |
[ |
1675 | 315 |
(case_tac "xs=UU" 1), |
1461 | 316 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
317 |
(Asm_simp_tac 1), |
|
318 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
319 |
(res_inst_tac [("n","n")] natE 1), |
|
320 |
(Asm_simp_tac 1), |
|
321 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
322 |
(Asm_simp_tac 1), |
|
323 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
324 |
(Asm_simp_tac 1), |
|
325 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1) |
|
326 |
]); |
|
1274 | 327 |
|
328 |
val dnat_take = temp::dnat_take; |
|
329 |
||
330 |
val dnat_rews = dnat_take @ dnat_rews; |
|
331 |
||
332 |
||
333 |
(* ------------------------------------------------------------------------*) |
|
334 |
(* take lemma for dnats *) |
|
335 |
(* ------------------------------------------------------------------------*) |
|
336 |
||
337 |
fun prover reach defs thm = prove_goalw Dnat.thy defs thm |
|
338 |
(fn prems => |
|
1461 | 339 |
[ |
340 |
(res_inst_tac [("t","s1")] (reach RS subst) 1), |
|
341 |
(res_inst_tac [("t","s2")] (reach RS subst) 1), |
|
2033 | 342 |
(stac fix_def2 1), |
343 |
(stac contlub_cfun_fun 1), |
|
1461 | 344 |
(rtac is_chain_iterate 1), |
2033 | 345 |
(stac contlub_cfun_fun 1), |
1461 | 346 |
(rtac is_chain_iterate 1), |
347 |
(rtac lub_equal 1), |
|
348 |
(rtac (is_chain_iterate RS ch2ch_fappL) 1), |
|
349 |
(rtac (is_chain_iterate RS ch2ch_fappL) 1), |
|
350 |
(rtac allI 1), |
|
351 |
(resolve_tac prems 1) |
|
352 |
]); |
|
1274 | 353 |
|
354 |
val dnat_take_lemma = prover dnat_reach [dnat_take_def] |
|
1461 | 355 |
"(!!n.dnat_take n`s1 = dnat_take n`s2) ==> s1=s2"; |
1274 | 356 |
|
357 |
||
358 |
(* ------------------------------------------------------------------------*) |
|
359 |
(* Co -induction for dnats *) |
|
360 |
(* ------------------------------------------------------------------------*) |
|
361 |
||
362 |
qed_goalw "dnat_coind_lemma" Dnat.thy [dnat_bisim_def] |
|
363 |
"dnat_bisim R ==> ! p q. R p q --> dnat_take n`p = dnat_take n`q" |
|
364 |
(fn prems => |
|
1461 | 365 |
[ |
366 |
(cut_facts_tac prems 1), |
|
367 |
(nat_ind_tac "n" 1), |
|
368 |
(simp_tac (!simpset addsimps dnat_take) 1), |
|
369 |
(strip_tac 1), |
|
370 |
((etac allE 1) THEN (etac allE 1) THEN (etac (mp RS disjE) 1)), |
|
371 |
(atac 1), |
|
372 |
(asm_simp_tac (!simpset addsimps dnat_take) 1), |
|
373 |
(etac disjE 1), |
|
374 |
(asm_simp_tac (!simpset addsimps dnat_take) 1), |
|
375 |
(etac exE 1), |
|
376 |
(etac exE 1), |
|
377 |
(asm_simp_tac (!simpset addsimps dnat_take) 1), |
|
378 |
(REPEAT (etac conjE 1)), |
|
379 |
(rtac cfun_arg_cong 1), |
|
380 |
(fast_tac HOL_cs 1) |
|
381 |
]); |
|
1274 | 382 |
|
383 |
qed_goal "dnat_coind" Dnat.thy "[|dnat_bisim R;R p q|] ==> p = q" |
|
384 |
(fn prems => |
|
1461 | 385 |
[ |
386 |
(rtac dnat_take_lemma 1), |
|
387 |
(rtac (dnat_coind_lemma RS spec RS spec RS mp) 1), |
|
388 |
(resolve_tac prems 1), |
|
389 |
(resolve_tac prems 1) |
|
390 |
]); |
|
1274 | 391 |
|
392 |
||
393 |
(* ------------------------------------------------------------------------*) |
|
394 |
(* structural induction for admissible predicates *) |
|
395 |
(* ------------------------------------------------------------------------*) |
|
396 |
||
397 |
(* not needed any longer |
|
398 |
qed_goal "dnat_ind" Dnat.thy |
|
399 |
"[| adm(P);\ |
|
400 |
\ P(UU);\ |
|
401 |
\ P(dzero);\ |
|
402 |
\ !! s1.[|s1~=UU ; P(s1)|] ==> P(dsucc`s1)|] ==> P(s)" |
|
403 |
(fn prems => |
|
1461 | 404 |
[ |
405 |
(rtac (dnat_reach RS subst) 1), |
|
406 |
(res_inst_tac [("x","s")] spec 1), |
|
407 |
(rtac fix_ind 1), |
|
408 |
(rtac adm_all2 1), |
|
409 |
(rtac adm_subst 1), |
|
410 |
(cont_tacR 1), |
|
411 |
(resolve_tac prems 1), |
|
412 |
(Simp_tac 1), |
|
413 |
(resolve_tac prems 1), |
|
414 |
(strip_tac 1), |
|
415 |
(res_inst_tac [("n","xa")] dnatE 1), |
|
416 |
(asm_simp_tac (!simpset addsimps dnat_copy) 1), |
|
417 |
(resolve_tac prems 1), |
|
418 |
(asm_simp_tac (!simpset addsimps dnat_copy) 1), |
|
419 |
(resolve_tac prems 1), |
|
420 |
(asm_simp_tac (!simpset addsimps dnat_copy) 1), |
|
1675 | 421 |
(case_tac "x`xb=UU" 1), |
1461 | 422 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
423 |
(resolve_tac prems 1), |
|
424 |
(eresolve_tac prems 1), |
|
425 |
(etac spec 1) |
|
426 |
]); |
|
1274 | 427 |
*) |
428 |
||
429 |
qed_goal "dnat_finite_ind" Dnat.thy |
|
430 |
"[|P(UU);P(dzero);\ |
|
431 |
\ !! s1.[|s1~=UU;P(s1)|] ==> P(dsucc`s1)\ |
|
432 |
\ |] ==> !s.P(dnat_take n`s)" |
|
433 |
(fn prems => |
|
1461 | 434 |
[ |
435 |
(nat_ind_tac "n" 1), |
|
436 |
(simp_tac (!simpset addsimps dnat_rews) 1), |
|
437 |
(resolve_tac prems 1), |
|
438 |
(rtac allI 1), |
|
439 |
(res_inst_tac [("n","s")] dnatE 1), |
|
440 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
441 |
(resolve_tac prems 1), |
|
442 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
443 |
(resolve_tac prems 1), |
|
444 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
1675 | 445 |
(case_tac "dnat_take n1`x=UU" 1), |
1461 | 446 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
447 |
(resolve_tac prems 1), |
|
448 |
(resolve_tac prems 1), |
|
449 |
(atac 1), |
|
450 |
(etac spec 1) |
|
451 |
]); |
|
1274 | 452 |
|
453 |
qed_goal "dnat_all_finite_lemma1" Dnat.thy |
|
454 |
"!s.dnat_take n`s=UU |dnat_take n`s=s" |
|
455 |
(fn prems => |
|
1461 | 456 |
[ |
457 |
(nat_ind_tac "n" 1), |
|
458 |
(simp_tac (!simpset addsimps dnat_rews) 1), |
|
459 |
(rtac allI 1), |
|
460 |
(res_inst_tac [("n","s")] dnatE 1), |
|
461 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
462 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
463 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
464 |
(eres_inst_tac [("x","x")] allE 1), |
|
465 |
(etac disjE 1), |
|
466 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
467 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1) |
|
468 |
]); |
|
1274 | 469 |
|
470 |
qed_goal "dnat_all_finite_lemma2" Dnat.thy "? n.dnat_take n`s=s" |
|
471 |
(fn prems => |
|
1461 | 472 |
[ |
1675 | 473 |
(case_tac "s=UU" 1), |
1461 | 474 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
475 |
(subgoal_tac "(!n.dnat_take(n)`s=UU) |(? n.dnat_take(n)`s=s)" 1), |
|
476 |
(etac disjE 1), |
|
477 |
(eres_inst_tac [("P","s=UU")] notE 1), |
|
478 |
(rtac dnat_take_lemma 1), |
|
479 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
480 |
(atac 1), |
|
481 |
(subgoal_tac "!n.!s.dnat_take(n)`s=UU |dnat_take(n)`s=s" 1), |
|
482 |
(fast_tac HOL_cs 1), |
|
483 |
(rtac allI 1), |
|
484 |
(rtac dnat_all_finite_lemma1 1) |
|
485 |
]); |
|
1274 | 486 |
|
487 |
||
488 |
qed_goal "dnat_ind" Dnat.thy |
|
489 |
"[|P(UU);P(dzero);\ |
|
490 |
\ !! s1.[|s1~=UU;P(s1)|] ==> P(dsucc`s1)\ |
|
491 |
\ |] ==> P(s)" |
|
492 |
(fn prems => |
|
1461 | 493 |
[ |
494 |
(rtac (dnat_all_finite_lemma2 RS exE) 1), |
|
495 |
(etac subst 1), |
|
496 |
(rtac (dnat_finite_ind RS spec) 1), |
|
497 |
(REPEAT (resolve_tac prems 1)), |
|
498 |
(REPEAT (atac 1)) |
|
499 |
]); |
|
1274 | 500 |
|
501 |
||
2277
9174de6c7143
moved Lift*.* to Up*.*, renaming of all constans and theorems concerned,
oheimb
parents:
2033
diff
changeset
|
502 |
qed_goalw "dnat_flat" Dnat.thy [flat_def] "flat(dzero)" |
1274 | 503 |
(fn prems => |
1461 | 504 |
[ |
505 |
(rtac allI 1), |
|
506 |
(res_inst_tac [("s","x")] dnat_ind 1), |
|
507 |
(fast_tac HOL_cs 1), |
|
508 |
(rtac allI 1), |
|
509 |
(res_inst_tac [("n","y")] dnatE 1), |
|
510 |
(fast_tac (HOL_cs addSIs [UU_I]) 1), |
|
511 |
(Asm_simp_tac 1), |
|
512 |
(asm_simp_tac (!simpset addsimps dnat_dist_less) 1), |
|
513 |
(rtac allI 1), |
|
514 |
(res_inst_tac [("n","y")] dnatE 1), |
|
515 |
(fast_tac (HOL_cs addSIs [UU_I]) 1), |
|
516 |
(asm_simp_tac (!simpset addsimps dnat_dist_less) 1), |
|
517 |
(asm_simp_tac (!simpset addsimps dnat_rews) 1), |
|
518 |
(strip_tac 1), |
|
519 |
(subgoal_tac "s1<<xa" 1), |
|
520 |
(etac allE 1), |
|
521 |
(dtac mp 1), |
|
522 |
(atac 1), |
|
523 |
(etac disjE 1), |
|
524 |
(contr_tac 1), |
|
525 |
(Asm_simp_tac 1), |
|
526 |
(resolve_tac dnat_invert 1), |
|
527 |
(REPEAT (atac 1)) |
|
528 |
]); |
|
1274 | 529 |
|
530 |
||
531 |
||
532 |
||
533 |
||
534 |