[ None ⇒ 〈null,false〉
| Some c0 ⇒ c0 ].
-definition mk_tuple ≝ λc,newc,mv.
- c @ 〈comma,false〉:: newc @ 〈comma,false〉 :: [〈mv,false〉].
-
-inductive match_in_table (c,newc:list STape) (mv:unialpha) : list STape → Prop ≝
-| mit_hd :
- ∀tb.
- match_in_table c newc mv (mk_tuple c newc mv@〈bar,false〉::tb)
-| mit_tl :
- ∀c0,newc0,mv0,tb.
- match_in_table c newc mv tb →
- match_in_table c newc mv (mk_tuple c0 newc0 mv0@〈bar,false〉::tb).
definition move_of_unialpha ≝
λc.match c with
definition R_move_tape_l_abstract ≝ λt1,t2.
∀rs,n,table,curc,curconfig,ls.
- bit_or_null curc = true → only_bits_or_nulls curconfig → table_TM n (reverse ? table) →
+ is_bit curc = true → only_bits_or_nulls curconfig → table_TM n (reverse ? table) →
t1 = midtape STape (table@〈grid,false〉::〈curc,false〉::curconfig@〈grid,false〉::ls)
〈grid,false〉 rs →
- no_nulls ls → no_marks ls →
legal_tape ls 〈curc,false〉 rs →
∀t1'.t1' = lift_tape ls 〈curc,false〉 rs →
∃ls1,rs1,newc.
∀t1,t2.R_move_tape_l t1 t2 → R_move_tape_l_abstract t1 t2.
#t1 #t2 whd in ⊢(%→?); #Hconcrete
#rs #n #table #curc #curconfig #ls #Hcurc #Hcurconfig #Htable #Ht1
-#Hlsnonulls #Hlsnomarks #Htape #t1' #Ht1'
+* * * #Hnomarks #Hbits #Hcurc #Hlegal #t1' #Ht1'
cases (Hconcrete … Htable Ht1) //
[ * #Hls #Ht2
@(ex_intro ?? [])
[ %
[ >Ht2 %
| >Hls % ]
- | % % % ]
-| * * #l0 #bl0 * #ls0 * #Hls
- cut (bl0 = false) [@(Hlsnomarks 〈l0,bl0〉) >Hls @memb_hd]
+ | % [ % [ %
+ [ #x #Hx cases (orb_true_l … Hx) #Hx'
+ [ >(\P Hx') %
+ | @Hnomarks >Hls @Hx' ]
+ | #x #Hx cases (orb_true_l … Hx) #Hx'
+ [ >(\P Hx') //
+ | @Hbits >Hls @Hx' ]]
+ | % ]
+ | % %2 % ]
+ ]
+| * * #l0 #bl0 * #ls0 * #Hls
+ cut (bl0 = false)
+ [ @(Hnomarks 〈l0,bl0〉) @memb_cons @memb_append_l1 >Hls @memb_hd]
#Hbl0 >Hbl0 in Hls; #Hls #Ht2
- @(ex_intro ?? ls0)
- @(ex_intro ?? (〈curc,false〉::rs))
+ @(ex_intro ?? ls0) @(ex_intro ?? (〈curc,false〉::rs))
@(ex_intro ?? l0) %
[ %
[ >Ht2 %
| >Hls >lift_tape_not_null
[ %
- | @(Hlsnonulls 〈l0,false〉) >Hls @memb_hd ] ]
- | @legal_tape_conditions % % % #Hl0 >Hl0 in Hls; #Hls
- lapply (Hlsnonulls 〈null,false〉 ?)
- [ >Hls @memb_hd | normalize #H destruct (H) ]
- ]
-qed.
-
+ | @bit_not_null @(Hbits 〈l0,false〉) >Hls @memb_append_l1 @memb_hd ] ]
+ | % [ % [ %
+ [ #x #Hx cases (orb_true_l … Hx) #Hx'
+ [ >(\P Hx') %
+ | cases (memb_append … Hx') #Hx'' @Hnomarks
+ [ >Hls @memb_cons @memb_cons @(memb_append_l1 … Hx'')
+ | cases (orb_true_l … Hx'') #Hx'''
+ [ >(\P Hx''') @memb_hd
+ | @memb_cons @(memb_append_l2 … Hx''')]
+ ]
+ ]
+ | whd in ⊢ (?%); #x #Hx cases (memb_append … Hx) #Hx'
+ [ @Hbits >Hls @memb_cons @(memb_append_l1 … Hx')
+ | cases (orb_true_l … Hx') #Hx''
+ [ >(\P Hx'') //
+ | @Hbits @(memb_append_l2 … Hx'')
+ ]]]
+ | whd in ⊢ (??%?); >(Hbits 〈l0,false〉) //
+ @memb_append_l1 >Hls @memb_hd ]
+ | % % % #Hl0 lapply (Hbits 〈l0,false〉?)
+ [ @memb_append_l1 >Hls @memb_hd
+ | >Hl0 normalize #Hfalse destruct (Hfalse)
+ ] ] ] ]
+qed.
+
lemma Realize_to_Realize :
∀alpha,M,R1,R2.(∀t1,t2.R1 t1 t2 → R2 t1 t2) → Realize alpha M R1 → Realize alpha M R2.
#alpha #M #R1 #R2 #Himpl #HR1 #intape
tc_true) tc_true.
definition R_move_tape ≝ λt1,t2.
- ∀rs,n,table1,c,table2,curc,curconfig,ls.
- bit_or_null curc = true → bit_or_null c = true → only_bits_or_nulls curconfig →
- table_TM n (reverse ? table1@〈c,false〉::table2) →
+ ∀rs,n,table1,mv,table2,curc,curconfig,ls.
+ bit_or_null mv = true → only_bits_or_nulls curconfig →
+ (is_bit mv = true → is_bit curc = true) →
+ table_TM n (reverse ? table1@〈mv,false〉::table2) →
t1 = midtape STape (table1@〈grid,false〉::〈curc,false〉::curconfig@〈grid,false〉::ls)
- 〈c,false〉 (table2@〈grid,false〉::rs) →
- no_nulls ls → no_nulls rs → no_marks ls → no_marks rs →
+ 〈mv,false〉 (table2@〈grid,false〉::rs) →
legal_tape ls 〈curc,false〉 rs →
∀t1'.t1' = lift_tape ls 〈curc,false〉 rs →
∃ls1,rs1,newc.
legal_tape ls1 〈newc,false〉 rs1 ∧
(t2 = midtape STape ls1 〈grid,false〉 (reverse ? curconfig@〈newc,false〉::
- 〈grid,false〉::reverse ? table1@〈c,false〉::table2@〈grid,false〉::rs1) ∧
- ((c = bit false ∧ lift_tape ls1 〈newc,false〉 rs1 = tape_move_left STape ls 〈curc,false〉 rs) ∨
- (c = bit true ∧ lift_tape ls1 〈newc,false〉 rs1 = tape_move_right STape ls 〈curc,false〉 rs) ∨
- (c = null ∧ ls1 = ls ∧ rs1 = rs ∧ curc = newc))).
+ 〈grid,false〉::reverse ? table1@〈mv,false〉::table2@〈grid,false〉::rs1) ∧
+ ((mv = bit false ∧ lift_tape ls1 〈newc,false〉 rs1 = tape_move_left STape ls 〈curc,false〉 rs) ∨
+ (mv = bit true ∧ lift_tape ls1 〈newc,false〉 rs1 = tape_move_right STape ls 〈curc,false〉 rs) ∨
+ (mv = null ∧ ls1 = ls ∧ rs1 = rs ∧ curc = newc))).
lemma sem_move_tape : Realize ? move_tape R_move_tape.
#intape
(sem_seq … (sem_move_l …) (sem_adv_to_mark_l ? (λc:STape.is_grid (\fst c)))))) intape)
#k * #outc * #Hloop #HR
@(ex_intro ?? k) @(ex_intro ?? outc) % [@Hloop] -Hloop
-#rs #n #table1 #c #table2 #curc #curconfig #ls
-#Hcurc #Hc #Hcurconfig #Htable #Hintape #Hls #Hrs #Hls1 #Hrs1 #Htape #t1' #Ht1'
+#rs #n #table1 #mv #table2 #curc #curconfig #ls
+#Hmv #Hcurconfig #Hmvcurc #Htable #Hintape #Htape #t1' #Ht1'
generalize in match HR; -HR *
-[ * #ta * whd in ⊢ (%→?); #Hta cases (Hta 〈c,false〉 ?)
+[ * #ta * whd in ⊢ (%→?); #Hta cases (Hta 〈mv,false〉 ?)
[| >Hintape % ] -Hta #Hceq #Hta lapply (\P Hceq) -Hceq #Hceq destruct (Hta Hceq)
* #tb * whd in ⊢ (%→?); #Htb cases (Htb … Hintape) -Htb -Hintape
[ * normalize in ⊢ (%→?); #Hfalse destruct (Hfalse) ]
* #_ #Htb lapply (Htb … (refl ??) (refl ??) ?)
[ @daemon ] -Htb >append_cons <associative_append #Htb
whd in ⊢ (%→?); #Houtc lapply (Houtc … Htb … Ht1') //
- [ >reverse_append >reverse_append >reverse_reverse @Htable |]
+ [ >reverse_append >reverse_append >reverse_reverse @Htable
+ | /2/
+ ||]
-Houtc -Htb * #ls1 * #rs1 * #newc * * #Houtc #Hnewtape #Hnewtapelegal
@(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc) %
[ //
>associative_append >associative_append %
| % % % // ]
]
-| * #ta * whd in ⊢ (%→?); #Hta cases (Hta 〈c,false〉 ?)
- [| >Hintape % ] -Hta #Hcneq cut (c ≠ bit false)
+| * #ta * whd in ⊢ (%→?); #Hta cases (Hta 〈mv,false〉 ?)
+ [| >Hintape % ] -Hta #Hcneq cut (mv ≠ bit false)
[ lapply (\Pf Hcneq) @not_to_not #Heq >Heq % ] -Hcneq #Hcneq #Hta destruct (Hta)
*
- [ * #tb * whd in ⊢ (%→?);#Htb cases (Htb 〈c,false〉 ?)
+ [ * #tb * whd in ⊢ (%→?);#Htb cases (Htb 〈mv,false〉 ?)
[| >Hintape % ] -Htb #Hceq #Htb lapply (\P Hceq) -Hceq #Hceq destruct (Htb Hceq)
* #tc * whd in ⊢ (%→?); #Htc cases (Htc … Hintape) -Htc -Hintape
[ * normalize in ⊢ (%→?); #Hfalse destruct (Hfalse) ]
* #_ #Htc lapply (Htc … (refl ??) (refl ??) ?)
[ @daemon ] -Htc >append_cons <associative_append #Htc
whd in ⊢ (%→?); #Houtc lapply (Houtc … Htc … Ht1') //
- [ >reverse_append >reverse_append >reverse_reverse @Htable |]
+ [ >reverse_append >reverse_append >reverse_reverse @Htable
+ | /2/ |]
-Houtc -Htc * #ls1 * #rs1 * #newc * * #Houtc #Hnewtape #Hnewtapelegal
@(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc) %
[ //
>associative_append >associative_append %
| % %2 % // ]
]
- | * #tb * whd in ⊢ (%→?); #Htb cases (Htb 〈c,false〉 ?)
- [| >Hintape % ] -Htb #Hcneq' cut (c ≠ bit true)
+ | * #tb * whd in ⊢ (%→?); #Htb cases (Htb 〈mv,false〉 ?)
+ [| >Hintape % ] -Htb #Hcneq' cut (mv ≠ bit true)
[ lapply (\Pf Hcneq') @not_to_not #Heq >Heq % ] -Hcneq' #Hcneq' #Htb destruct (Htb)
* #tc * whd in ⊢ (%→?); #Htc cases (Htc … Hintape)
- [ * >(bit_or_null_not_grid … Hc) #Hfalse destruct (Hfalse) ] -Htc
+ [ * >(bit_or_null_not_grid … Hmv) #Hfalse destruct (Hfalse) ] -Htc
* #_ #Htc lapply (Htc … (refl ??) (refl ??) ?) [@daemon] -Htc #Htc
* #td * whd in ⊢ (%→?); #Htd lapply (Htd … Htc) -Htd -Htc
whd in ⊢ (???%→?); #Htd whd in ⊢ (%→?); #Houtc lapply (Houtc … Htd) -Houtc *
- [ * >(bit_or_null_not_grid … Hcurc) #Hfalse destruct (Hfalse) ]
+ [ * cases Htape * * #_ #_ #Hcurc #_
+ >(bit_or_null_not_grid … Hcurc) #Hfalse destruct (Hfalse) ]
* #_ #Houtc lapply (Houtc … (refl ??) (refl ??) ?) [@daemon] -Houtc #Houtc
@(ex_intro ?? ls) @(ex_intro ?? rs) @(ex_intro ?? curc) %
[ //
[ @Houtc
| %2 % // % // % //
generalize in match Hcneq; generalize in match Hcneq';
- cases c in Hc; normalize //
+ cases mv in Hmv; normalize //
[ * #_ normalize [ #Hfalse @False_ind cases Hfalse /2/ | #_ #Hfalse @False_ind cases Hfalse /2/ ]
|*: #Hfalse destruct (Hfalse) ]
]
* // normalize #H destruct
qed.
+definition mk_tuple ≝ λqin,cin,qout,cout,mv.
+ qin @ cin :: 〈comma,false〉:: qout @ cout :: 〈comma,false〉 :: [mv].
+
(* by definition, a tuple is not marked *)
definition tuple_TM : nat → list STape → Prop ≝
- λn,t.∃qin,qout,mv.
- no_marks t ∧
- only_bits_or_nulls qin ∧ only_bits_or_nulls qout ∧ bit_or_null mv = true ∧
- |qin| = n ∧ |qout| = n (* ∧ |mv| = ? *) ∧
- t = qin@〈comma,false〉::qout@〈comma,false〉::[〈mv,false〉].
+ λn,t.∃qin,cin,qout,cout,mv.
+ no_marks qin ∧ no_marks qout ∧
+ only_bits qin ∧ only_bits qout ∧
+ bit_or_null cin = true ∧ bit_or_null cout = true ∧ bit_or_null mv = true ∧
+ (cout = null → mv = null) ∧
+ |qin| = n ∧ |qout| = n ∧
+ t = mk_tuple qin 〈cin,false〉 qout 〈cout,false〉 〈mv,false〉.
-inductive table_TM : nat → list STape → Prop ≝
-| ttm_nil : ∀n.table_TM n []
-| ttm_cons : ∀n,t1,T.tuple_TM n t1 → table_TM n T → table_TM n (t1@〈bar,false〉::T).
+inductive table_TM (n:nat) : list STape → Prop ≝
+| ttm_nil : table_TM n []
+| ttm_cons : ∀t1,T.tuple_TM n t1 → table_TM n T → table_TM n (t1@〈bar,false〉::T).
+
+inductive match_in_table (qin:list STape) (cin: STape)
+ (qout:list STape) (cout:STape) (mv:STape)
+: list STape → Prop ≝
+| mit_hd :
+ ∀tb.
+ match_in_table qin cin qout cout mv
+ (mk_tuple qin cin qout cout mv @〈bar,false〉::tb)
+| mit_tl :
+ ∀qin0,cin0,qout0,cout0,mv0,tb.
+ match_in_table qin cin qout cout mv tb →
+ match_in_table qin cin qout cout mv
+ (mk_tuple qin0 cin0 qout0 cout0 mv0@〈bar,false〉::tb).
+
+axiom append_l1_injective :
+ ∀A.∀l1,l2,l3,l4:list A. |l1| = |l2| → l1@l3 = l2@l4 → l1 = l2.
+axiom append_l2_injective :
+ ∀A.∀l1,l2,l3,l4:list A. |l1| = |l2| → l1@l3 = l2@l4 → l3 = l4.
+
+
+lemma generic_match_to_match_in_table :
+ ∀n,T.table_TM n T →
+ ∀qin,cin,qout,cout,mv.|qin| = n → |qout| = n →
+ ∀t1,t2.
+ T = t1@qin@cin::〈comma,false〉::qout@cout::〈comma,false〉::mv::t2 →
+ match_in_table qin cin qout cout mv T.
+#n #T #Htable #qin #cin #qout #cout #mv #Hlenqin #Hlenqout
+elim Htable
+[ #t1 #t2 <associative_append cases (t1@qin) normalize
+ [ #Hfalse destruct (Hfalse) | #c0 #t0 #Hfalse destruct (Hfalse) ]
+| #tuple #T0 * #qin0 * #cin0 * #qout0 * #cout0 * #mv0
+ * * * * * * * * * *
+ #Hqin0marks #Hqout0marks #Hqinbits #Hqoutbits #Hcin0 #Hcout0 #Hmv0 #Hcout0mv0
+ #Hlenqin0 #Hlenqout0 #Htuple #Htable0 #IH #t1 #t2 #HT
+ cases t1 in HT;
+ [ >Htuple normalize in ⊢ (??%%→?);
+ >associative_append #HT
+ cut (qin0 = qin ∧ (〈cin0,false〉 = cin ∧ (qout0 = qout ∧
+ (〈cout0,false〉 = cout ∧ (〈mv0,false〉 = mv ∧ 〈bar,false〉::T0 = t2)))))
+ [ lapply (append_l1_injective … HT) [ >Hlenqin @Hlenqin0 ]
+ #Hqin % [ @Hqin ] -Hqin
+ lapply (append_l2_injective … HT) [ >Hlenqin @Hlenqin0 ] -HT #HT
+ destruct (HT)
+
lemma no_grids_in_table: ∀n.∀l.table_TM n l → no_grids l.
#n #l #t elim t
definition R_exec_move ≝ λt1,t2.
∀n,curconfig,ls,rs,c0,c1,s0,s1,table1,newconfig,mv,table2.
table_TM n (table1@〈comma,false〉::〈s1,false〉::newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2) →
- no_marks curconfig → only_bits (curconfig@[〈s0,false〉]) → only_bits (〈s1,false〉::newconfig) →
+ no_marks curconfig → only_bits (curconfig@[〈s0,false〉]) →
+ only_bits (〈s1,false〉::newconfig) → bit_or_null c1 = true →
|curconfig| = |newconfig| →
- no_nulls ls → no_nulls rs → no_marks ls → no_marks rs →
legal_tape ls 〈c0,false〉 rs →
t1 = midtape STape (〈c0,false〉::curconfig@〈s0,false〉::〈grid,false〉::ls) 〈grid,false〉
(table1@〈comma,true〉::〈s1,false〉::newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs) →
]
qed.
+lemma merge_char_null : ∀c.merge_char null c = c.
+* //
+qed.
+
+lemma merge_char_cases : ∀c1,c2.merge_char c1 c2 = c1 ∨ merge_char c1 c2 = c2.
+#c1 *
+[ #c1' %2 %
+| % %
+| *: %2 % ]
+qed.
+
+(* lemma merge_char_c_bit :
+ ∀c1,c2.is_bit c2 = true → merge_char c1 c2 = c2.
+#c1 *
+[ #c2' #_ %
+|*: normalize #Hfalse destruct (Hfalse) ]
+qed.
+
+lemma merge_char_c_bit :
+ ∀c1,c2.is_null c2 = true → merge_char c1 c2 = c1.
+#c1 *
+[ #c2' #_ %
+|*: normalize #Hfalse destruct (Hfalse) ]
+qed.
+
+*)
+
lemma sem_exec_move : Realize ? exec_move R_exec_move.
#intape
cases (sem_seq … sem_init_copy
#k * #outc * #Hloop #HR
@(ex_intro ?? k) @(ex_intro ?? outc) % [ @Hloop ] -Hloop
#n #curconfig #ls #rs #c0 #c1 #s0 #s1 #table1 #newconfig #mv #table2
-#Htable #Hcurconfig1 #Hcurconfig2 #Hnewconfig #Hlen #Hls #Hrs #Hls1 #Hrs1 #Htape #Hintape #t1' #Ht1'
+#Htable #Hcurconfig1 #Hcurconfig2 #Hnewconfig #Hc1 #Hlen #Htape #Hintape #t1' #Ht1'
cases HR -HR #ta * whd in ⊢ (%→?); #Hta
lapply (Hta (〈c0,false〉::curconfig) table1 s0 ls s1
(newconfig@〈c1,false〉::〈comma,false〉::〈mv,false〉::table2@〈grid,false〉::rs) … Hintape) -Hta
whd in ⊢ (%→?); #Houtc whd in Htc:(???%); whd in Htc:(???(??%%%));
lapply (Houtc rs n
(〈comma,false〉::〈c1,false〉::reverse ? newconfig@〈s1,false〉::〈comma,false〉::reverse ? table1)
- mv table2 (merge_char c0 c1) (reverse ? newconfig@[〈s1,false〉]) ls ?????
- Hls Hrs Hls1 Hrs1 ???)
- [3: cases (true_or_false (c0 == null)) #Hc0
- [ >(\P Hc0) in Htape; #Htape cases (legal_tape_cases … Htape)
- [ * #Hfalse @False_ind /2/
- | * #_ *
- [ #Hlsnil @legal_tape_conditions % %2 //
- | #Hrsnil @legal_tape_conditions %2 //
- ]
- ]
- | @legal_tape_conditions % % @merge_char_not_null @(\Pf Hc0) ]
+ mv table2 (merge_char c0 c1) (reverse ? newconfig@[〈s1,false〉]) ls ????????)
+ [3: cases Htape -Htape * * #Hnomarks #Hbits #Hc0 #Hlsrs % [ % [ %
+ [ #x #Hx cases (orb_true_l … Hx) #Hx'
+ [ >(\P Hx') %
+ | @Hnomarks @memb_cons // ]
+ | @Hbits ]
+ | cases (merge_char_cases c0 c1) #Hmerge >Hmerge // ]
+ | cases (true_or_false (c0 == null)) #Hc0'
+ [ cases Hlsrs -Hlsrs
+ [ *
+ [ >(\P Hc0') * #Hfalse @False_ind /2/
+ | #Hlsnil % %2 // ]
+ | #Hrsnil %2 // ]
+ | % % @merge_char_not_null @(\Pf Hc0') ] ]
|4:>Htc @(eq_f3 … (midtape ?))
[ @eq_f @eq_f >associative_append >associative_append %
| %
>associative_append >associative_append >associative_append
>associative_append >associative_append
@Htable
+ | (* well formedness of table *) @daemon
| (* Hnewconfig *) @daemon
- | (* bit_or_null mv = true *) @daemon
- | (* bit_or_null c1,c2 → bit_or_null (merge_char c1 c2) *) @daemon
+ | (* bit_or_null mv = true (well formedness of table) *) @daemon
| -Houtc * #ls1 * #rs1 * #newc * #Hnewtapelegal * #Houtc *
[ *
[ * #Hmv #Htapemove
| >Hmv >Ht1' >Htapemove
(* mv = bit false -→ c1 = bit ? *)
cut (∃c1'.c1 = bit c1') [ @daemon ] * #c1' #Hc1
- >Hc1 >tape_move_left_eq cases (legal_tape_cases … Htape)
- [ #Hc0 >lift_tape_not_null /2/
- | * #Hc0 *
- [ #Hls >Hc0 >Hls whd in ⊢ (??%%); cases rs;
- [%| #r0 #rs0 %]
- | #Hrs >Hc0 >Hrs cases ls; [%| #l0 #ls0 %]
- ]
- ]
+ >Hc1 >tape_move_left_eq >(legal_tape_left … Htape)
+ >(legal_tape_right … Htape) %
]
| //
]
>associative_append >associative_append %
|>Hmv >Ht1' >Htapemove
cut (∃c1'.c1 = bit c1') [ @daemon ] * #c1' #Hc1
- >Hc1 >tape_move_right_eq cases (legal_tape_cases … Htape)
- [ #Hc0 >lift_tape_not_null /2/
- | * #Hc0 *
- [ #Hls >Hc0 >Hls whd in ⊢ (??%%); cases rs;
- [%| #r0 #rs0 %]
- | #Hrs >Hc0 >Hrs cases ls; [%| #l0 #ls0 %]
- ]
+ >Hc1 >tape_move_right_eq >(legal_tape_left … Htape)
+ >(legal_tape_right … Htape) %
]
+ | //
]
- | //
]
- ]
- | * * * #Hmv #Hlseq #Hrseq #Hnewc
- @(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc) %
- [ %
- [ >Houtc -Houtc >reverse_append
- >reverse_reverse >reverse_single @eq_f
- >reverse_cons >reverse_cons >reverse_append >reverse_cons
- >reverse_cons >reverse_reverse >reverse_reverse
- >associative_append >associative_append
- >associative_append >associative_append
- >associative_append >associative_append %
- |>Hmv >Ht1' cases c1 in Hnewc;
- [ #c1' whd in ⊢ (??%?→?);#Hnewc <Hnewc
- >Hlseq >Hrseq cases Htape * #Hleft #Hright #_
- whd in ⊢ (??%%); >Hleft >Hright %
- | whd in ⊢ (??%?→?); #Hnewc >Hnewc >Hlseq >Hrseq %
- |*: whd in ⊢ (??%?→?);#Hnewc <Hnewc
- >Hlseq >Hrseq cases Htape * #Hleft #Hright #_
- whd in ⊢ (??%%); >Hleft >Hright % ]
+ | * * * #Hmv #Hlseq #Hrseq #Hnewc
+ @(ex_intro ?? ls1) @(ex_intro ?? rs1) @(ex_intro ?? newc) %
+ [ %
+ [ >Houtc -Houtc >reverse_append
+ >reverse_reverse >reverse_single @eq_f
+ >reverse_cons >reverse_cons >reverse_append >reverse_cons
+ >reverse_cons >reverse_reverse >reverse_reverse
+ >associative_append >associative_append
+ >associative_append >associative_append
+ >associative_append >associative_append %
+ |>Hmv >Ht1' cases c1 in Hnewc;
+ [ #c1' whd in ⊢ (??%?→?);#Hnewc <Hnewc
+ >Hlseq >Hrseq whd in ⊢ (??%%);
+ >(legal_tape_left … Htape) >(legal_tape_right … Htape) %
+ | whd in ⊢ (??%?→?); #Hnewc >Hnewc >Hlseq >Hrseq %
+ |*: whd in ⊢ (??%?→?);#Hnewc <Hnewc
+ >Hlseq >Hrseq whd in ⊢ (??%%);
+ >(legal_tape_left … Htape) >(legal_tape_right … Htape) %
+ ]
+ ]
+ | //
]
- | //
]
]
]
cut (mv1 = 〈\fst mv1,false〉)
[ >(eq_pair_fst_snd … mv1) @eq_f (*Htable, Htableeq*) @daemon ] #Hmv1
* #te * whd in ⊢ (%→?); #Hte
- (* mv1 ha tipo lista ma dovrebbe avere tipo unialpha *)
cut (td = midtape STape (〈c0,false〉::reverse STape curconfig@〈s0,false〉::〈grid,false〉::ls)
〈grid,false〉
((table1@〈s0,false〉::curconfig@[〈c0,false〉])@〈comma,true〉::〈s1,false〉::
]
-Htd #Htd lapply (Hte … (S n) … Htd … Ht1') -Htd -Hte
[ //
- |2,3,4,5: (* dovrebbe scomparire (lo metteremo nel legal_tape) *) @daemon
| (*|curconfig| = |newconfig|*) @daemon
+ | (* Htable → bit_or_null c1 = true *) @daemon
| (* only_bits (〈s1,false〉::newconfig) *) @daemon
| (* only_bits (curconfig@[〈s0,false〉]) *) @daemon
| (* no_marks (reverse ? curconfig) *) @daemon
projects / helm.git / commitdiff