2 ||M|| This file is part of HELM, an Hypertextual, Electronic
3 ||A|| Library of Mathematics, developed at the Computer Science
4 ||T|| Department of the University of Bologna, Italy.
8 \ / This file is distributed under the terms of the
9 \ / GNU General Public License Version 2
10 V_____________________________________________________________*)
17 include "turing/universal/copy.ma".
18 include "turing/universal/move_tape.ma".
24 if is_true(current) (* current state is final *)
36 if is_marked(current) = false (* match ok *)
49 case bit false: move_tape_l
50 case bit true: move_tape_r
51 case null: adv_to_grid_l; move_l; adv_to_grid_l;
58 definition init_match ≝
60 (seq ? (adv_to_mark_r ? (λc:STape.is_grid (\fst c)))
65 (adv_to_mark_l ? (is_marked ?))))))).
67 definition R_init_match ≝ λt1,t2.
68 ∀ls,l,rs,c,d. no_grids (〈c,false〉::l) → no_marks l →
69 t1 = midtape STape ls 〈c,false〉 (l@〈grid,false〉::〈bar,false〉::〈d,false〉::rs) →
70 t2 = midtape STape ls 〈c,true〉 (l@〈grid,false〉::〈bar,false〉::〈d,true〉::rs).
72 lemma sem_init_match : Realize ? init_match R_init_match.
74 cases (sem_seq ????? (sem_mark ?)
75 (sem_seq ????? (sem_adv_to_mark_r ? (λc:STape.is_grid (\fst c)))
76 (sem_seq ????? (sem_move_r ?)
77 (sem_seq ????? (sem_move_r ?)
78 (sem_seq ????? (sem_mark ?)
79 (sem_seq ????? (sem_move_l ?)
80 (sem_adv_to_mark_l ? (is_marked ?))))))) intape)
81 #k * #outc * #Hloop #HR
82 @(ex_intro ?? k) @(ex_intro ?? outc) % [@Hloop] -Hloop
83 #ls #l #rs #c #d #Hnogrids #Hnomarks #Hintape
85 #ta * whd in ⊢ (%→?); #Hta lapply (Hta … Hintape) -Hta -Hintape #Hta
86 * #tb * whd in ⊢ (%→?); #Htb cases (Htb … Hta) -Htb -Hta
87 [* #Hgridc @False_ind @(absurd … Hgridc) @eqnot_to_noteq
88 @(Hnogrids 〈c,false〉) @memb_hd ]
89 * #Hgrdic #Htb lapply (Htb l 〈grid,false〉 (〈bar,false〉::〈d,false〉::rs) (refl …) (refl …) ?)
90 [#x #membl @Hnogrids @memb_cons @membl] -Htb #Htb
91 * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc -Htb #Htc
92 * #td * whd in ⊢ (%→?); #Htd lapply (Htd … Htc) -Htd -Htc #Htd
93 * #te * whd in ⊢ (%→?); #Hte lapply (Hte … Htd) -Hte -Htd #Hte
94 * #tf * whd in ⊢ (%→?); #Htf lapply (Htf … Hte) -Htf -Hte #Htf
95 whd in ⊢ (%→?); #Htg cases (Htg … Htf) -Htg -Htf
96 [* whd in ⊢ ((??%?)→?); #Habs destruct (Habs)]
97 * #_ #Htg lapply (Htg (〈grid,false〉::reverse ? l) 〈c,true〉 ls (refl …) (refl …) ?)
98 [#x #membl @Hnomarks @daemon] -Htg #Htg >Htg >reverse_cons >reverse_reverse
105 init_current_on_match; (* no marks in current *)
112 definition init_copy ≝
113 seq ? init_current_on_match
115 (seq ? (adv_to_mark_r ? (is_marked ?))
118 definition R_init_copy ≝ λt1,t2.
120 no_marks l1 → no_grids l1 →
121 no_marks l2 → is_grid c = false →
122 t1 = midtape STape (l1@〈c,false〉::〈grid,false〉::ls) 〈grid,false〉 (l2@〈comma,true〉::〈d,false〉::rs) →
123 t2 = midtape STape (〈comma,false〉::(reverse ? l2)@〈grid,false〉::l1@〈c,true〉::〈grid,false〉::ls) 〈d,true〉 rs.
125 lemma list_last: ∀A.∀l:list A.
126 l = [ ] ∨ ∃a,l1. l = l1@[a].
127 #A #l <(reverse_reverse ? l) cases (reverse A l)
129 |#a #l1 %2 @(ex_intro ?? a) @(ex_intro ?? (reverse ? l1)) //
133 lemma sem_init_copy : Realize ? init_copy R_init_copy.
135 cases (sem_seq ????? sem_init_current_on_match
136 (sem_seq ????? (sem_move_r ?)
137 (sem_seq ????? (sem_adv_to_mark_r ? (is_marked ?))
138 (sem_adv_mark_r ?))) intape)
139 #k * #outc * #Hloop #HR
140 @(ex_intro ?? k) @(ex_intro ?? outc) % [@Hloop] -Hloop
141 #l1 #l2 #c #ls #d #rs #Hl1marks #Hl1grids #Hl2marks #Hc #Hintape
143 #ta * whd in ⊢ (%→?); #Hta lapply (Hta … Hl1grids Hc Hintape) -Hta -Hintape #Hta
144 * #tb * whd in ⊢ (%→?); #Htb lapply (Htb … Hta) -Htb -Hta
145 generalize in match Hl1marks; -Hl1marks cases (list_last ? l1)
146 [#eql1 >eql1 #Hl1marks whd in ⊢ ((???%)→?); whd in ⊢ ((???(????%))→?); #Htb
147 * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc -Htb *
148 [* whd in ⊢ ((??%?)→?); #Htemp destruct (Htemp)]
149 * #_ #Htc lapply (Htc … (refl …) (refl …) ?)
150 [#x #membx @Hl2marks @membx]
151 #Htc whd in ⊢ (%→?); #Houtc lapply (Houtc … Htc) -Houtc -Htc #Houtc
153 |* #c1 * #tl #eql1 >eql1 #Hl1marks >reverse_append >reverse_single
154 whd in ⊢ ((???%)→?); whd in ⊢ ((???(????%))→?);
155 >associative_append whd in ⊢ ((???(????%))→?); #Htb
156 * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc -Htb *
157 [* >Hl1marks [#Htemp destruct (Htemp)] @memb_append_l2 @memb_hd]
158 * #_ >append_cons <associative_append #Htc lapply (Htc … (refl …) (refl …) ?)
159 [#x #membx cases (memb_append … membx) -membx #membx
160 [cases (memb_append … membx) -membx #membx
161 [@Hl1marks @memb_append_l1 @daemon
162 |>(memb_single … membx) %
166 #Htc whd in ⊢ (%→?); #Houtc lapply (Houtc … Htc) -Houtc -Htc #Houtc
167 >Houtc >reverse_append >reverse_append >reverse_single
168 >reverse_reverse >associative_append >associative_append
169 >associative_append %
173 definition init_copy ≝
175 (seq ? init_current_on_match
177 (adv_to_mark_r ? (is_marked ?)))).
179 definition R_init_copy ≝ λt1,t2.
181 no_marks l1 → no_grids l1 →
182 no_marks l2 → no_grids l2 → is_grid c = false → is_grid d =false →
183 t1 = midtape STape (l1@〈grid,false〉::l2@〈c,false〉::〈grid,false〉::l3) 〈comma,true〉 (〈d,false〉::rs) →
184 t2 = midtape STape (〈comma,false〉::l1@〈grid,false〉::l2@〈c,true〉::〈grid,false〉::l3) 〈d,true〉 rs.
186 lemma list_last: ∀A.∀l:list A.
187 l = [ ] ∨ ∃a,l1. l = l1@[a].
188 #A #l <(reverse_reverse ? l) cases (reverse A l)
190 |#a #l1 %2 @(ex_intro ?? a) @(ex_intro ?? (reverse ? l1)) //
194 lemma sem_init_copy : Realize ? init_copy R_init_copy.
196 cases (sem_seq ????? (sem_adv_mark_r ?)
197 (sem_seq ????? sem_init_current_on_match
198 (sem_seq ????? (sem_move_r ?)
199 (sem_adv_to_mark_r ? (is_marked ?)))) intape)
200 #k * #outc * #Hloop #HR
201 @(ex_intro ?? k) @(ex_intro ?? outc) % [@Hloop] -Hloop
202 #l1 #l2 #c #l3 #d #rs #Hl1marks #Hl1grids #Hl2marks #Hl2grids #Hc #Hd #Hintape
204 #ta * whd in ⊢ (%→?); #Hta lapply (Hta … Hintape) -Hta -Hintape #Hta
205 * #tb * whd in ⊢ (%→?);
206 >append_cons #Htb lapply (Htb (〈comma,false〉::l1) l2 c … Hta)
208 |#x #membx cases (orb_true_l … membx) -membx #membx
209 [>(\P membx) // | @Hl1grids @membx]
211 * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc -Htb
212 >reverse_append >reverse_cons cases (list_last ? l2)
213 [#Hl2 >Hl2 >associative_append whd in ⊢ ((???(??%%%))→?); #Htc
214 whd in ⊢ (%→?); #Htd cases (Htd … Htc) -Htd -Htc
215 [* whd in ⊢ ((??%?)→?); #Habs destruct (Habs)]
216 * #_ #Htf lapply (Htf … (refl …) (refl …) ?)
217 [#x >reverse_cons #membx cases (memb_append … membx) -membx #membx
218 [@Hl1marks @daemon |>(memb_single … membx) //]
220 |#Htf >Htf >reverse_reverse >associative_append %
222 |* #a * #l21 #Heq >Heq >reverse_append >reverse_single
223 >associative_append >associative_append >associative_append whd in ⊢ ((???(??%%%))→?); #Htc
224 whd in ⊢ (%→?); #Htd cases (Htd … Htc) -Htd -Htc
225 [* >Hl2marks [#Habs destruct (Habs) |>Heq @memb_append_l2 @memb_hd]]
226 * #_ <associative_append <associative_append #Htf lapply (Htf … (refl …) (refl …) ?)
227 [#x >reverse_cons #membx cases (memb_append … membx) -membx #membx
228 [cases (memb_append … membx) -membx #membx
229 [@Hl2marks >Heq @memb_append_l1 @daemon
230 |>(memb_single … membx) //]
231 |cases (memb_append … membx) -membx #membx
232 [@Hl1marks @daemon |>(memb_single … membx) //]
234 | #Htf >Htf >reverse_append >reverse_reverse
235 >reverse_append >reverse_reverse >associative_append
236 >reverse_single >associative_append >associative_append
237 >associative_append %
242 definition exec_move ≝
245 (seq ? (move_r …) move_tape)).
247 definition map_move ≝
248 λc,mv.match c with [ null ⇒ None ? | _ ⇒ Some ? 〈c,false,move_of_unialpha mv〉 ].
250 (* - aggiungere a legal_tape le condizioni
251 only_bits ls, rs; bit_or_null c
252 - ci vuole un lemma che dimostri
253 bit_or_null c1 = true bit_or_null mv = true
254 mv ≠ null → c1 ≠ null
255 dal fatto che c1 e mv sono contenuti nella table
257 definition R_exec_move ≝ λt1,t2.
258 ∀n,curconfig,ls,rs,c0,c1,s0,s1,table1,newconfig,mv,table2.
259 table_TM n (table1@〈comma,false〉::〈s1,false〉::newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2) →
260 no_marks curconfig → only_bits (curconfig@[〈s0,false〉]) →
261 only_bits (〈s1,false〉::newconfig) → bit_or_null c1 = true →
262 |curconfig| = |newconfig| →
263 legal_tape ls 〈c0,false〉 rs →
264 t1 = midtape STape (〈c0,false〉::curconfig@〈s0,false〉::〈grid,false〉::ls) 〈grid,false〉
265 (table1@〈comma,true〉::〈s1,false〉::newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs) →
266 ∀t1'.t1' = lift_tape ls 〈c0,false〉 rs →
268 t2 = midtape STape ls1 〈grid,false〉
269 (〈s1,false〉::newconfig@〈c2,false〉::〈grid,false〉::
270 table1@〈comma,false〉::〈s1,false〉::newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs1) ∧
271 lift_tape ls1 〈c2,false〉 rs1 =
272 tape_move STape t1' (map_move c1 mv) ∧ legal_tape ls1 〈c2,false〉 rs1.
274 (* move the following 2 lemmata to mono.ma *)
275 lemma tape_move_left_eq :
277 tape_move ? t (Some ? 〈c,L〉) =
278 tape_move_left ? (left ? t) c (right ? t).
282 lemma tape_move_right_eq :
284 tape_move ? t (Some ? 〈c,R〉) =
285 tape_move_right ? (left ? t) c (right ? t).
289 lemma lift_tape_not_null :
290 ∀ls,c,bc,rs.c ≠ null → lift_tape ls 〈c,bc〉 rs = midtape ? ls 〈c,bc〉 rs.
291 #ls #c #bc #rs cases c //
292 #Hfalse @False_ind /2/
295 lemma merge_char_not_null :
296 ∀c1,c2.c1 ≠ null → merge_char c1 c2 ≠ null.
297 #c1 #c2 @not_to_not cases c2
298 [ #c1' normalize #Hfalse destruct (Hfalse)
300 | *: normalize #Hfalse destruct (Hfalse)
304 lemma merge_char_null : ∀c.merge_char null c = c.
308 lemma merge_char_cases : ∀c1,c2.merge_char c1 c2 = c1 ∨ merge_char c1 c2 = c2.
315 (* lemma merge_char_c_bit :
316 ∀c1,c2.is_bit c2 = true → merge_char c1 c2 = c2.
319 |*: normalize #Hfalse destruct (Hfalse) ]
322 lemma merge_char_c_bit :
323 ∀c1,c2.is_null c2 = true → merge_char c1 c2 = c1.
326 |*: normalize #Hfalse destruct (Hfalse) ]
331 lemma sem_exec_move : Realize ? exec_move R_exec_move.
333 cases (sem_seq … sem_init_copy
335 (sem_seq … (sem_move_r …) sem_move_tape )) intape)
336 #k * #outc * #Hloop #HR
337 @(ex_intro ?? k) @(ex_intro ?? outc) % [ @Hloop ] -Hloop
338 #n #curconfig #ls #rs #c0 #c1 #s0 #s1 #table1 #newconfig #mv #table2
339 #Htable #Hcurconfig1 #Hcurconfig2 #Hnewconfig #Hc1 #Hlen #Htape #Hintape #t1' #Ht1'
340 cases HR -HR #ta * whd in ⊢ (%→?); #Hta
341 lapply (Hta (〈c0,false〉::curconfig) table1 s0 ls s1
342 (newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs) … Hintape) -Hta
343 [ (*Hcurconfig2*) @daemon
345 | (*bit_or_null c0 = true *) @daemon
346 | (*Hcurconfig1*) @daemon
347 | #Hta * #tb * whd in ⊢ (%→?); #Htb
348 lapply (Htb (〈grid,false〉::ls) s0 s1 c0 c1 (〈mv,false〉::table2@〈grid,false〉::rs) newconfig (〈comma,false〉::reverse ? table1) curconfig Hta ????????) -Htb
349 [9:|*:(* bit_or_null c0,c1; |curconfig| = |newconfig|*) @daemon ]
350 #Htb * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc whd in ⊢(???(??%%%)→?);#Htc
351 whd in ⊢ (%→?); #Houtc whd in Htc:(???%); whd in Htc:(???(??%%%));
353 (〈comma,false〉::〈c1,false〉::reverse ? newconfig@〈s1,false〉::〈comma,false〉::reverse ? table1)
354 mv table2 (merge_char c0 c1) (reverse ? newconfig@[〈s1,false〉]) ls ????????)
355 [3: cases Htape -Htape * * #Hnomarks #Hbits #Hc0 #Hlsrs % [ % [ %
356 [ #x #Hx cases (orb_true_l … Hx) #Hx'
358 | @Hnomarks @memb_cons // ]
360 | cases (merge_char_cases c0 c1) #Hmerge >Hmerge // ]
361 | cases (true_or_false (c0 == null)) #Hc0'
364 [ >(\P Hc0') * #Hfalse @False_ind /2/
367 | % % @merge_char_not_null @(\Pf Hc0') ] ]
368 |4:>Htc @(eq_f3 … (midtape ?))
369 [ @eq_f @eq_f >associative_append >associative_append %
373 || >reverse_cons >reverse_cons >reverse_append >reverse_reverse
374 >reverse_cons >reverse_cons >reverse_reverse
375 >associative_append >associative_append >associative_append
376 >associative_append >associative_append
378 | (* well formedness of table *) @daemon
379 | (* Hnewconfig *) @daemon
380 | (* bit_or_null mv = true (well formedness of table) *) @daemon
381 | -Houtc * #ls1 * #rs1 * #newc * #Hnewtapelegal * #Houtc *
384 @(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc)
387 [ >Houtc -Houtc >reverse_append
388 >reverse_reverse >reverse_single @eq_f
389 >reverse_cons >reverse_cons >reverse_append >reverse_cons
390 >reverse_cons >reverse_reverse >reverse_reverse
391 >associative_append >associative_append
392 >associative_append >associative_append
393 >associative_append >associative_append %
394 | >Hmv >Ht1' >Htapemove
395 (* mv = bit false -→ c1 = bit ? *)
396 cut (∃c1'.c1 = bit c1') [ @daemon ] * #c1' #Hc1
397 >Hc1 >tape_move_left_eq >(legal_tape_left … Htape)
398 >(legal_tape_right … Htape) %
403 @(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc) %
405 [ >Houtc -Houtc >reverse_append
406 >reverse_reverse >reverse_single @eq_f
407 >reverse_cons >reverse_cons >reverse_append >reverse_cons
408 >reverse_cons >reverse_reverse >reverse_reverse
409 >associative_append >associative_append
410 >associative_append >associative_append
411 >associative_append >associative_append %
412 |>Hmv >Ht1' >Htapemove
413 cut (∃c1'.c1 = bit c1') [ @daemon ] * #c1' #Hc1
414 >Hc1 >tape_move_right_eq >(legal_tape_left … Htape)
415 >(legal_tape_right … Htape) %
420 | * * * #Hmv #Hlseq #Hrseq #Hnewc
421 @(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc) %
423 [ >Houtc -Houtc >reverse_append
424 >reverse_reverse >reverse_single @eq_f
425 >reverse_cons >reverse_cons >reverse_append >reverse_cons
426 >reverse_cons >reverse_reverse >reverse_reverse
427 >associative_append >associative_append
428 >associative_append >associative_append
429 >associative_append >associative_append %
430 |>Hmv >Ht1' cases c1 in Hnewc;
431 [ #c1' whd in ⊢ (??%?→?);#Hnewc <Hnewc
432 >Hlseq >Hrseq whd in ⊢ (??%%);
433 >(legal_tape_left … Htape) >(legal_tape_right … Htape) %
434 | whd in ⊢ (??%?→?); #Hnewc >Hnewc >Hlseq >Hrseq %
435 |*: whd in ⊢ (??%?→?);#Hnewc <Hnewc
436 >Hlseq >Hrseq whd in ⊢ (??%%);
437 >(legal_tape_left … Htape) >(legal_tape_right … Htape) %
448 if is_false(current) (* current state is not final *)
451 if is_marked(current) = false (* match ok *)
459 definition uni_step ≝
460 ifTM ? (test_char STape (λc.\fst c == bit false))
461 (single_finalTM ? (seq ? init_match
463 (ifTM ? (test_char ? (λc.¬is_marked ? c))
464 (seq ? exec_move (move_r …))
470 definition R_uni_step_true ≝ λt1,t2.
471 ∀n,table,s0,s1,c0,c1,ls,rs,curconfig,newconfig,mv.
472 0 < |table| → table_TM (S n) table →
473 match_in_table (S n) (〈s0,false〉::curconfig) 〈c0,false〉
474 (〈s1,false〉::newconfig) 〈c1,false〉 〈mv,false〉 table →
475 legal_tape ls 〈c0,false〉 rs →
476 t1 = midtape STape (〈grid,false〉::ls) 〈s0,false〉
477 (curconfig@〈c0,false〉::〈grid,false〉::table@〈grid,false〉::rs) →
478 ∀t1'.t1' = lift_tape ls 〈c0,false〉 rs →
481 (t2 = midtape STape (〈grid,false〉::ls1) 〈s1,false〉
482 (newconfig@〈c2,false〉::〈grid,false〉::table@〈grid,false〉::rs1) ∧
483 lift_tape ls1 〈c2,false〉 rs1 =
484 tape_move STape t1' (map_move c1 mv) ∧ legal_tape ls1 〈c2,false〉 rs1).
486 definition R_uni_step_false ≝ λt1,t2.
487 ∀b. current STape t1 = Some ? 〈bit b,false〉 → b = true ∧ t2 = t1.
489 axiom sem_match_tuple : Realize ? match_tuple R_match_tuple.
492 accRealize ? uni_step (inr … (inl … (inr … start_nop)))
493 R_uni_step_true R_uni_step_false.
494 @(acc_sem_if_app STape … (sem_test_char ? (λc:STape.\fst c == bit false))
495 (sem_seq … sem_init_match
496 (sem_seq … sem_match_tuple
497 (sem_if … (* ????????? (sem_test_char … (λc.¬is_marked FSUnialpha c)) *)
498 (sem_seq … sem_exec_move (sem_move_r …))
504 #ta whd in ⊢ (%→?); #Hta #HR
505 #n #fulltable #s0 #s1 #c0 #c1 #ls #rs #curconfig #newconfig #mv
506 #Htable_len cut (∃t0,table. fulltable =〈bar,false〉::〈t0,false〉::table) [(* 0 < |table| *) @daemon]
507 * #t0 * #table #Hfulltable >Hfulltable -fulltable
508 #Htable #Hmatch #Htape #Hintape #t1' #Ht1'
509 >Hintape in Hta; #Hta cases (Hta ? (refl ??)) -Hta
510 #Hs0 lapply (\P Hs0) -Hs0 #Hs0 #Hta % //
512 #tb * whd in ⊢ (%→?); #Htb
513 lapply (Htb (〈grid,false〉::ls) (curconfig@[〈c0,false〉]) (table@〈grid,false〉::rs) s0 t0 ???)
514 [ >Hta >associative_append %
518 #tc * whd in ⊢ (%→?); #Htc cases (Htc … Htable … Htb) -Htb -Htc
519 [| * #Hcurrent #Hfalse @False_ind
520 (* absurd by Hmatch *) @daemon
522 | (* Htable (con lemma) *) @daemon
523 | (* Hmatch *) @daemon
524 | (* Htable *) @daemon
525 | (* Htable, Hmatch → |config| = n
526 necessaria modifica in R_match_tuple, le dimensioni non corrispondono
529 * #table1 * #newc * #mv1 * #table2 * #Htableeq #Htc *
530 [ * #td * whd in ⊢ (%→?); >Htc -Htc #Htd
531 cases (Htd ? (refl ??)) #_ -Htd
532 cut (newc = 〈s1,false〉::newconfig@[〈c1,false〉]) [@daemon] #Hnewc
533 >Hnewc #Htd cut (mv1 = 〈mv,false〉)
535 * #te * whd in ⊢ (%→?); #Hte
536 cut (td = midtape STape (〈c0,false〉::reverse STape curconfig@〈s0,false〉::〈grid,false〉::ls)
538 ((table1@〈bar,false〉::〈s0,false〉::curconfig@[〈c0,false〉])@〈comma,true〉::〈s1,false〉::
539 newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs))
541 [ >reverse_append >reverse_single %
542 | >associative_append >associative_append normalize
543 >associative_append >associative_append >Hmv1 %
546 -Htd #Htd lapply (Hte … (S n) … Htd … Ht1') -Htd -Hte
548 | (*|curconfig| = |newconfig|*) @daemon
549 | (* Htable → bit_or_null c1 = true *) @daemon
550 | (* only_bits (〈s1,false〉::newconfig) *) @daemon
551 | (* only_bits (curconfig@[〈s0,false〉]) *) @daemon
552 | (* no_marks (reverse ? curconfig) *) @daemon
553 | >Hmv1 in Htableeq; >Hnewc
554 >associative_append >associative_append normalize
555 >associative_append >associative_append
556 #Htableeq <Htableeq // ]
557 * #ls1 * #rs1 * #c2 * * #Hte #Hliftte #Hlegalte
558 whd in ⊢ (%→?); #Houttape lapply (Houttape … Hte) -Houttape #Houttape
559 whd in Houttape:(???%); whd in Houttape:(???(??%%%));
560 @ex_intro [| @(ex_intro ?? rs1) @ex_intro [| % [ %
561 [ >Houttape @eq_f @eq_f @eq_f @eq_f
562 change with ((〈bar,false〉::〈t0,false〉::table)@?) in ⊢ (???%);
563 >Htableeq >associative_append >associative_append
564 >associative_append normalize >associative_append
565 >associative_append normalize >Hnewc <Hmv1
566 >associative_append normalize >associative_append
574 | * #td * whd in ⊢ (%→%→?); >Htc #Htd
575 cases (Htd ? (refl ??)) normalize in ⊢ (%→?);
576 #Hfalse destruct (Hfalse)
579 | #t1 #t2 #t3 whd in ⊢ (%→%→?); #Ht1 #Ht2
580 #b #Hb cases (Ht1 ? Hb) #Hb' #Ht3 >Ht2 % //
581 cases b in Hb'; normalize #H1 //