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".
19 include "turing/universal/match_machines.ma".
25 if is_true(current) (* current state is final *)
37 if is_marked(current) = false (* match ok *)
50 case bit false: move_tape_l
51 case bit true: move_tape_r
52 case null: adv_to_grid_l; move_l; adv_to_grid_l;
59 definition init_match ≝
60 mark ? · adv_to_mark_r ? (λc:STape.is_grid (\fst c)) · move_r ? ·
61 move_r ? · mark ? · move_l ? · adv_to_mark_l ? (is_marked ?).
63 definition R_init_match ≝ λt1,t2.
64 ∀ls,l,rs,c,d. no_grids (〈c,false〉::l) → no_marks l →
65 t1 = midtape STape ls 〈c,false〉 (l@〈grid,false〉::〈bar,false〉::〈d,false〉::rs) →
66 t2 = midtape STape ls 〈c,true〉 (l@〈grid,false〉::〈bar,false〉::〈d,true〉::rs).
68 lemma sem_init_match : Realize ? init_match R_init_match.
70 cases (sem_seq ????? (sem_mark ?)
71 (sem_seq ????? (sem_adv_to_mark_r ? (λc:STape.is_grid (\fst c)))
72 (sem_seq ????? (sem_move_r ?)
73 (sem_seq ????? (sem_move_r ?)
74 (sem_seq ????? (sem_mark ?)
75 (sem_seq ????? (sem_move_l ?)
76 (sem_adv_to_mark_l ? (is_marked ?))))))) intape)
77 #k * #outc * #Hloop #HR
78 @(ex_intro ?? k) @(ex_intro ?? outc) % [@Hloop] -Hloop
79 #ls #l #rs #c #d #Hnogrids #Hnomarks #Hintape
81 #ta * whd in ⊢ (%→?); #Hta lapply (Hta … Hintape) -Hta -Hintape #Hta
82 * #tb * whd in ⊢ (%→?); #Htb cases (Htb … Hta) -Htb -Hta
83 [* #Hgridc @False_ind @(absurd … Hgridc) @eqnot_to_noteq
84 @(Hnogrids 〈c,false〉) @memb_hd ]
85 * #Hgrdic #Htb lapply (Htb l 〈grid,false〉 (〈bar,false〉::〈d,false〉::rs) (refl …) (refl …) ?)
86 [#x #membl @Hnogrids @memb_cons @membl] -Htb #Htb
87 * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc -Htb #Htc
88 * #td * whd in ⊢ (%→?); #Htd lapply (Htd … Htc) -Htd -Htc #Htd
89 * #te * whd in ⊢ (%→?); #Hte lapply (Hte … Htd) -Hte -Htd #Hte
90 * #tf * whd in ⊢ (%→?); #Htf lapply (Htf … Hte) -Htf -Hte #Htf
91 whd in ⊢ (%→?); #Htg cases (Htg … Htf) -Htg -Htf
92 [* whd in ⊢ ((??%?)→?); #Habs destruct (Habs)]
93 * #_ #Htg lapply (Htg (〈grid,false〉::reverse ? l) 〈c,true〉 ls (refl …) (refl …) ?)
94 [#x #membl @Hnomarks @daemon] -Htg #Htg >Htg >reverse_cons >reverse_reverse
100 init_current_on_match; (* no marks in current *)
107 definition init_copy ≝
108 init_current_on_match · move_r ? ·
109 adv_to_mark_r ? (is_marked ?) · adv_mark_r ?.
111 definition R_init_copy ≝ λt1,t2.
113 no_marks l1 → no_grids l1 →
114 no_marks l2 → is_grid c = false →
115 t1 = midtape STape (l1@〈c,false〉::〈grid,false〉::ls) 〈grid,false〉 (l2@〈comma,true〉::〈d,false〉::rs) →
116 t2 = midtape STape (〈comma,false〉::(reverse ? l2)@〈grid,false〉::l1@〈c,true〉::〈grid,false〉::ls) 〈d,true〉 rs.
118 lemma list_last: ∀A.∀l:list A.
119 l = [ ] ∨ ∃a,l1. l = l1@[a].
120 #A #l <(reverse_reverse ? l) cases (reverse A l)
122 |#a #l1 %2 @(ex_intro ?? a) @(ex_intro ?? (reverse ? l1)) //
126 lemma sem_init_copy : Realize ? init_copy R_init_copy.
128 cases (sem_seq ????? sem_init_current_on_match
129 (sem_seq ????? (sem_move_r ?)
130 (sem_seq ????? (sem_adv_to_mark_r ? (is_marked ?))
131 (sem_adv_mark_r ?))) intape)
132 #k * #outc * #Hloop #HR
133 @(ex_intro ?? k) @(ex_intro ?? outc) % [@Hloop] -Hloop
134 #l1 #l2 #c #ls #d #rs #Hl1marks #Hl1grids #Hl2marks #Hc #Hintape
136 #ta * whd in ⊢ (%→?); #Hta lapply (Hta … Hl1grids Hc Hintape) -Hta -Hintape #Hta
137 * #tb * whd in ⊢ (%→?); #Htb lapply (Htb … Hta) -Htb -Hta
138 generalize in match Hl1marks; -Hl1marks cases (list_last ? l1)
139 [#eql1 >eql1 #Hl1marks whd in ⊢ ((???%)→?); whd in ⊢ ((???(????%))→?); #Htb
140 * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc -Htb *
141 [* whd in ⊢ ((??%?)→?); #Htemp destruct (Htemp)]
142 * #_ #Htc lapply (Htc … (refl …) (refl …) ?)
143 [#x #membx @Hl2marks @membx]
144 #Htc whd in ⊢ (%→?); #Houtc lapply (Houtc … Htc) -Houtc -Htc #Houtc
146 |* #c1 * #tl #eql1 >eql1 #Hl1marks >reverse_append >reverse_single
147 whd in ⊢ ((???%)→?); whd in ⊢ ((???(????%))→?);
148 >associative_append whd in ⊢ ((???(????%))→?); #Htb
149 * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc -Htb *
150 [* >Hl1marks [#Htemp destruct (Htemp)] @memb_append_l2 @memb_hd]
151 * #_ >append_cons <associative_append #Htc lapply (Htc … (refl …) (refl …) ?)
152 [#x #membx cases (memb_append … membx) -membx #membx
153 [cases (memb_append … membx) -membx #membx
154 [@Hl1marks @memb_append_l1 @daemon
155 |>(memb_single … membx) %
159 #Htc whd in ⊢ (%→?); #Houtc lapply (Houtc … Htc) -Houtc -Htc #Houtc
160 >Houtc >reverse_append >reverse_append >reverse_single
161 >reverse_reverse >associative_append >associative_append
162 >associative_append %
166 definition init_copy ≝
168 (seq ? init_current_on_match
170 (adv_to_mark_r ? (is_marked ?)))).
172 definition R_init_copy ≝ λt1,t2.
174 no_marks l1 → no_grids l1 →
175 no_marks l2 → no_grids l2 → is_grid c = false → is_grid d =false →
176 t1 = midtape STape (l1@〈grid,false〉::l2@〈c,false〉::〈grid,false〉::l3) 〈comma,true〉 (〈d,false〉::rs) →
177 t2 = midtape STape (〈comma,false〉::l1@〈grid,false〉::l2@〈c,true〉::〈grid,false〉::l3) 〈d,true〉 rs.
179 lemma list_last: ∀A.∀l:list A.
180 l = [ ] ∨ ∃a,l1. l = l1@[a].
181 #A #l <(reverse_reverse ? l) cases (reverse A l)
183 |#a #l1 %2 @(ex_intro ?? a) @(ex_intro ?? (reverse ? l1)) //
187 lemma sem_init_copy : Realize ? init_copy R_init_copy.
189 cases (sem_seq ????? (sem_adv_mark_r ?)
190 (sem_seq ????? sem_init_current_on_match
191 (sem_seq ????? (sem_move_r ?)
192 (sem_adv_to_mark_r ? (is_marked ?)))) intape)
193 #k * #outc * #Hloop #HR
194 @(ex_intro ?? k) @(ex_intro ?? outc) % [@Hloop] -Hloop
195 #l1 #l2 #c #l3 #d #rs #Hl1marks #Hl1grids #Hl2marks #Hl2grids #Hc #Hd #Hintape
197 #ta * whd in ⊢ (%→?); #Hta lapply (Hta … Hintape) -Hta -Hintape #Hta
198 * #tb * whd in ⊢ (%→?);
199 >append_cons #Htb lapply (Htb (〈comma,false〉::l1) l2 c … Hta)
201 |#x #membx cases (orb_true_l … membx) -membx #membx
202 [>(\P membx) // | @Hl1grids @membx]
204 * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc -Htb
205 >reverse_append >reverse_cons cases (list_last ? l2)
206 [#Hl2 >Hl2 >associative_append whd in ⊢ ((???(??%%%))→?); #Htc
207 whd in ⊢ (%→?); #Htd cases (Htd … Htc) -Htd -Htc
208 [* whd in ⊢ ((??%?)→?); #Habs destruct (Habs)]
209 * #_ #Htf lapply (Htf … (refl …) (refl …) ?)
210 [#x >reverse_cons #membx cases (memb_append … membx) -membx #membx
211 [@Hl1marks @daemon |>(memb_single … membx) //]
213 |#Htf >Htf >reverse_reverse >associative_append %
215 |* #a * #l21 #Heq >Heq >reverse_append >reverse_single
216 >associative_append >associative_append >associative_append whd in ⊢ ((???(??%%%))→?); #Htc
217 whd in ⊢ (%→?); #Htd cases (Htd … Htc) -Htd -Htc
218 [* >Hl2marks [#Habs destruct (Habs) |>Heq @memb_append_l2 @memb_hd]]
219 * #_ <associative_append <associative_append #Htf lapply (Htf … (refl …) (refl …) ?)
220 [#x >reverse_cons #membx cases (memb_append … membx) -membx #membx
221 [cases (memb_append … membx) -membx #membx
222 [@Hl2marks >Heq @memb_append_l1 @daemon
223 |>(memb_single … membx) //]
224 |cases (memb_append … membx) -membx #membx
225 [@Hl1marks @daemon |>(memb_single … membx) //]
227 | #Htf >Htf >reverse_append >reverse_reverse
228 >reverse_append >reverse_reverse >associative_append
229 >reverse_single >associative_append >associative_append
230 >associative_append %
235 definition exec_action ≝
236 init_copy · copy · move_r … · move_tape.
238 definition map_move ≝
239 λc,mv.match c with [ null ⇒ None ? | _ ⇒ Some ? 〈c,false,move_of_unialpha mv〉 ].
241 (* - aggiungere a legal_tape le condizioni
242 only_bits ls, rs; bit_or_null c
243 - ci vuole un lemma che dimostri
244 bit_or_null c1 = true bit_or_null mv = true
245 mv ≠ null → c1 ≠ null
246 dal fatto che c1 e mv sono contenuti nella table
248 definition R_exec_action ≝ λt1,t2.
249 ∀n,curconfig,ls,rs,c0,c1,s0,s1,table1,newconfig,mv,table2.
250 table_TM n (table1@〈comma,false〉::〈s1,false〉::newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2) →
251 no_marks curconfig → only_bits (curconfig@[〈s0,false〉]) →
252 only_bits (〈s1,false〉::newconfig) → bit_or_null c1 = true →
253 |curconfig| = |newconfig| →
254 legal_tape ls 〈c0,false〉 rs →
255 t1 = midtape STape (〈c0,false〉::curconfig@〈s0,false〉::〈grid,false〉::ls) 〈grid,false〉
256 (table1@〈comma,true〉::〈s1,false〉::newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs) →
257 ∀t1'.t1' = lift_tape ls 〈c0,false〉 rs →
259 t2 = midtape STape ls1 〈grid,false〉
260 (〈s1,false〉::newconfig@〈c2,false〉::〈grid,false〉::
261 table1@〈comma,false〉::〈s1,false〉::newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs1) ∧
262 lift_tape ls1 〈c2,false〉 rs1 =
263 tape_move STape t1' (map_move c1 mv) ∧ legal_tape ls1 〈c2,false〉 rs1.
265 (* move the following 2 lemmata to mono.ma *)
266 lemma tape_move_left_eq :
268 tape_move ? t (Some ? 〈c,L〉) =
269 tape_move_left ? (left ? t) c (right ? t).
273 lemma tape_move_right_eq :
275 tape_move ? t (Some ? 〈c,R〉) =
276 tape_move_right ? (left ? t) c (right ? t).
280 lemma lift_tape_not_null :
281 ∀ls,c,bc,rs.c ≠ null → lift_tape ls 〈c,bc〉 rs = midtape ? ls 〈c,bc〉 rs.
282 #ls #c #bc #rs cases c //
283 #Hfalse @False_ind /2/
286 lemma merge_char_not_null :
287 ∀c1,c2.c1 ≠ null → merge_char c1 c2 ≠ null.
288 #c1 #c2 @not_to_not cases c2
289 [ #c1' normalize #Hfalse destruct (Hfalse)
291 | *: normalize #Hfalse destruct (Hfalse)
295 lemma merge_char_null : ∀c.merge_char null c = c.
299 lemma merge_char_cases : ∀c1,c2.merge_char c1 c2 = c1 ∨ merge_char c1 c2 = c2.
306 (* lemma merge_char_c_bit :
307 ∀c1,c2.is_bit c2 = true → merge_char c1 c2 = c2.
310 |*: normalize #Hfalse destruct (Hfalse) ]
313 lemma merge_char_c_bit :
314 ∀c1,c2.is_null c2 = true → merge_char c1 c2 = c1.
317 |*: normalize #Hfalse destruct (Hfalse) ]
322 lemma sem_exec_action : Realize ? exec_action R_exec_action.
324 cases (sem_seq … sem_init_copy
326 (sem_seq … (sem_move_r …) sem_move_tape )) intape)
327 #k * #outc * #Hloop #HR
328 @(ex_intro ?? k) @(ex_intro ?? outc) % [ @Hloop ] -Hloop
329 #n #curconfig #ls #rs #c0 #c1 #s0 #s1 #table1 #newconfig #mv #table2
330 #Htable #Hcurconfig1 #Hcurconfig2 #Hnewconfig #Hc1 #Hlen #Htape #Hintape #t1' #Ht1'
331 cases HR -HR #ta * whd in ⊢ (%→?); #Hta
332 lapply (Hta (〈c0,false〉::curconfig) table1 s0 ls s1
333 (newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs) … Hintape) -Hta
334 [ (*Hcurconfig2*) @daemon
336 | (*bit_or_null c0 = true *) @daemon
337 | (*Hcurconfig1*) @daemon
338 | #Hta * #tb * whd in ⊢ (%→?); #Htb
339 lapply (Htb (〈grid,false〉::ls) s0 s1 c0 c1 (〈mv,false〉::table2@〈grid,false〉::rs) newconfig (〈comma,false〉::reverse ? table1) curconfig Hta ????????) -Htb
340 [9:|*:(* bit_or_null c0,c1; |curconfig| = |newconfig|*) @daemon ]
341 #Htb * #tc * whd in ⊢ (%→?); #Htc lapply (Htc … Htb) -Htc whd in ⊢(???(??%%%)→?);#Htc
342 whd in ⊢ (%→?); #Houtc whd in Htc:(???%); whd in Htc:(???(??%%%));
344 (〈comma,false〉::〈c1,false〉::reverse ? newconfig@〈s1,false〉::〈comma,false〉::reverse ? table1)
345 mv table2 (merge_char c0 c1) (reverse ? newconfig@[〈s1,false〉]) ls ????????)
346 [3: cases Htape -Htape * * #Hnomarks #Hbits #Hc0 #Hlsrs % [ % [ %
347 [ #x #Hx cases (orb_true_l … Hx) #Hx'
349 | @Hnomarks @memb_cons // ]
351 | cases (merge_char_cases c0 c1) #Hmerge >Hmerge // ]
352 | cases (true_or_false (c0 == null)) #Hc0'
355 [ >(\P Hc0') * #Hfalse @False_ind /2/
358 | % % @merge_char_not_null @(\Pf Hc0') ] ]
359 |4:>Htc @(eq_f3 … (midtape ?))
360 [ @eq_f @eq_f >associative_append >associative_append %
364 || >reverse_cons >reverse_cons >reverse_append >reverse_reverse
365 >reverse_cons >reverse_cons >reverse_reverse
366 >associative_append >associative_append >associative_append
367 >associative_append >associative_append
369 | (* well formedness of table *) @daemon
370 | (* Hnewconfig *) @daemon
371 | (* bit_or_null mv = true (well formedness of table) *) @daemon
372 | -Houtc * #ls1 * #rs1 * #newc * #Hnewtapelegal * #Houtc *
375 @(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc)
378 [ >Houtc -Houtc >reverse_append
379 >reverse_reverse >reverse_single @eq_f
380 >reverse_cons >reverse_cons >reverse_append >reverse_cons
381 >reverse_cons >reverse_reverse >reverse_reverse
382 >associative_append >associative_append
383 >associative_append >associative_append
384 >associative_append >associative_append %
385 | >Hmv >Ht1' >Htapemove
386 (* mv = bit false -→ c1 = bit ? *)
387 cut (∃c1'.c1 = bit c1') [ @daemon ] * #c1' #Hc1
388 >Hc1 >tape_move_left_eq >(legal_tape_left … Htape)
389 >(legal_tape_right … Htape) %
394 @(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc) %
396 [ >Houtc -Houtc >reverse_append
397 >reverse_reverse >reverse_single @eq_f
398 >reverse_cons >reverse_cons >reverse_append >reverse_cons
399 >reverse_cons >reverse_reverse >reverse_reverse
400 >associative_append >associative_append
401 >associative_append >associative_append
402 >associative_append >associative_append %
403 |>Hmv >Ht1' >Htapemove
404 cut (∃c1'.c1 = bit c1') [ @daemon ] * #c1' #Hc1
405 >Hc1 >tape_move_right_eq >(legal_tape_left … Htape)
406 >(legal_tape_right … Htape) %
411 | * * * #Hmv #Hlseq #Hrseq #Hnewc
412 @(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc) %
414 [ >Houtc -Houtc >reverse_append
415 >reverse_reverse >reverse_single @eq_f
416 >reverse_cons >reverse_cons >reverse_append >reverse_cons
417 >reverse_cons >reverse_reverse >reverse_reverse
418 >associative_append >associative_append
419 >associative_append >associative_append
420 >associative_append >associative_append %
421 |>Hmv >Ht1' cases c1 in Hnewc;
422 [ #c1' whd in ⊢ (??%?→?);#Hnewc <Hnewc
423 >Hlseq >Hrseq whd in ⊢ (??%%);
424 >(legal_tape_left … Htape) >(legal_tape_right … Htape) %
425 | whd in ⊢ (??%?→?); #Hnewc >Hnewc >Hlseq >Hrseq %
426 |*: whd in ⊢ (??%?→?);#Hnewc <Hnewc
427 >Hlseq >Hrseq whd in ⊢ (??%%);
428 >(legal_tape_left … Htape) >(legal_tape_right … Htape) %
439 if is_false(current) (* current state is not final *)
442 if is_marked(current) = false (* match ok *)
450 definition uni_step ≝
451 ifTM ? (test_char STape (λc.\fst c == bit false))
453 (init_match · match_tuple ·
454 (ifTM ? (test_char ? (λc.¬is_marked ? c))
455 (exec_action · move_r …)
459 definition R_uni_step_true ≝ λt1,t2.
460 ∀n,table,s0,s1,c0,c1,ls,rs,curconfig,newconfig,mv.
461 0 < |table| → table_TM (S n) table →
462 match_in_table (S n) (〈s0,false〉::curconfig) 〈c0,false〉
463 (〈s1,false〉::newconfig) 〈c1,false〉 〈mv,false〉 table →
464 legal_tape ls 〈c0,false〉 rs →
465 t1 = midtape STape (〈grid,false〉::ls) 〈s0,false〉
466 (curconfig@〈c0,false〉::〈grid,false〉::table@〈grid,false〉::rs) →
467 ∀t1'.t1' = lift_tape ls 〈c0,false〉 rs →
470 (t2 = midtape STape (〈grid,false〉::ls1) 〈s1,false〉
471 (newconfig@〈c2,false〉::〈grid,false〉::table@〈grid,false〉::rs1) ∧
472 lift_tape ls1 〈c2,false〉 rs1 =
473 tape_move STape t1' (map_move c1 mv) ∧ legal_tape ls1 〈c2,false〉 rs1).
475 definition R_uni_step_false ≝ λt1,t2.
476 ∀b. current STape t1 = Some ? 〈bit b,false〉 → b = true ∧ t2 = t1.
478 axiom sem_match_tuple : Realize ? match_tuple R_match_tuple.
480 definition us_acc : states ? uni_step ≝ (inr … (inl … (inr … start_nop))).
483 accRealize ? uni_step us_acc
484 R_uni_step_true R_uni_step_false.
485 @(acc_sem_if_app STape … (sem_test_char ? (λc:STape.\fst c == bit false))
486 (sem_seq … sem_init_match
487 (sem_seq … sem_match_tuple
488 (sem_if … (* ????????? (sem_test_char … (λc.¬is_marked FSUnialpha c)) *)
489 (sem_seq … sem_exec_action (sem_move_r …))
495 #ta whd in ⊢ (%→?); #Hta #HR
496 #n #fulltable #s0 #s1 #c0 #c1 #ls #rs #curconfig #newconfig #mv
497 #Htable_len cut (∃t0,table. fulltable =〈bar,false〉::〈t0,false〉::table) [(* 0 < |table| *) @daemon]
498 * #t0 * #table #Hfulltable >Hfulltable -fulltable
499 #Htable #Hmatch #Htape #Hintape #t1' #Ht1'
500 >Hintape in Hta; #Hta cases (Hta ? (refl ??)) -Hta
501 #Hs0 lapply (\P Hs0) -Hs0 #Hs0 #Hta % //
503 #tb * whd in ⊢ (%→?); #Htb
504 lapply (Htb (〈grid,false〉::ls) (curconfig@[〈c0,false〉]) (table@〈grid,false〉::rs) s0 t0 ???)
505 [ >Hta >associative_append %
509 #tc * whd in ⊢ (%→?); #Htc cases (Htc … Htable … Htb) -Htb -Htc
510 [| * #Hcurrent #Hfalse @False_ind
511 (* absurd by Hmatch *) @daemon
513 | (* Htable (con lemma) *) @daemon
514 | (* Hmatch *) @daemon
515 | (* Htable *) @daemon
516 | (* Htable, Hmatch → |config| = n
517 necessaria modifica in R_match_tuple, le dimensioni non corrispondono
520 * #table1 * #newc * #mv1 * #table2 * #Htableeq #Htc *
521 [ * #td * whd in ⊢ (%→?); >Htc -Htc #Htd
522 cases (Htd ? (refl ??)) #_ -Htd
523 cut (newc = 〈s1,false〉::newconfig@[〈c1,false〉]) [@daemon] #Hnewc
524 >Hnewc #Htd cut (mv1 = 〈mv,false〉)
526 * #te * whd in ⊢ (%→?); #Hte
527 cut (td = midtape STape (〈c0,false〉::reverse STape curconfig@〈s0,false〉::〈grid,false〉::ls)
529 ((table1@〈bar,false〉::〈s0,false〉::curconfig@[〈c0,false〉])@〈comma,true〉::〈s1,false〉::
530 newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs))
532 [ >reverse_append >reverse_single %
533 | >associative_append >associative_append normalize
534 >associative_append >associative_append >Hmv1 %
537 -Htd #Htd lapply (Hte … (S n) … Htd … Ht1') -Htd -Hte
539 | (*|curconfig| = |newconfig|*) @daemon
540 | (* Htable → bit_or_null c1 = true *) @daemon
541 | (* only_bits (〈s1,false〉::newconfig) *) @daemon
542 | (* only_bits (curconfig@[〈s0,false〉]) *) @daemon
543 | (* no_marks (reverse ? curconfig) *) @daemon
544 | >Hmv1 in Htableeq; >Hnewc
545 >associative_append >associative_append normalize
546 >associative_append >associative_append
547 #Htableeq <Htableeq // ]
548 * #ls1 * #rs1 * #c2 * * #Hte #Hliftte #Hlegalte
549 whd in ⊢ (%→?); #Houttape lapply (Houttape … Hte) -Houttape #Houttape
550 whd in Houttape:(???%); whd in Houttape:(???(??%%%));
551 @ex_intro [| @(ex_intro ?? rs1) @ex_intro [| % [ %
552 [ >Houttape @eq_f @eq_f @eq_f @eq_f
553 change with ((〈bar,false〉::〈t0,false〉::table)@?) in ⊢ (???%);
554 >Htableeq >associative_append >associative_append
555 >associative_append normalize >associative_append
556 >associative_append normalize >Hnewc <Hmv1
557 >associative_append normalize >associative_append
565 | * #td * whd in ⊢ (%→%→?); >Htc #Htd
566 cases (Htd ? (refl ??)) normalize in ⊢ (%→?);
567 #Hfalse destruct (Hfalse)
570 | #t1 #t2 #t3 whd in ⊢ (%→%→?); #Ht1 #Ht2
571 #b #Hb cases (Ht1 ? Hb) #Hb' #Ht3 >Ht2 % //
572 cases b in Hb'; normalize #H1 //