update in ground

[helm.git] / matita / matita / lib / turing / inject.ma

diff --git a/matita/matita/lib/turing/inject.ma b/matita/matita/lib/turing/inject.ma
index e00f3a36d5ba6000b3d4bdf0ecabc8900bbe0bf0..ed0ecaea85db4965cd1467747af3a704c897125d 100644 (file)
--- a/matita/matita/lib/turing/inject.ma
+++ b/matita/matita/lib/turing/inject.ma
@@ -10,8 +10,10 @@
       V_____________________________________________________________*)
 
 include "turing/turing.ma".
+(* include "turing/basic_machines.ma". *)
 
 (******************* inject a mono machine into a multi tape one **********************)
+
 definition inject_trans ≝ λsig,states:FinSet.λn,i:nat.
   λtrans:states × (option sig) → states  × (option sig × move).
   λp:states × (Vector (option sig) (S n)).
@@ -30,28 +32,38 @@ lapply (trans sig M)  #trans #x lapply (trans x) * *
 #s #a #m % [ @s | % [ @a | @m ] ]
 qed.
 
-axiom current_chars_change_vec: ∀sig,n,v,a,i. i < S n →
+lemma current_chars_change_vec: ∀sig,n,v,a,i. i < S n →
    current_chars sig ? (change_vec ? (S n) v a i) =
    change_vec ? (S n)(current_chars ?? v) (current ? a) i.
+#sig #n #v #a #i #Hi @(eq_vec … (None ?)) #i0 #Hi0
+change with (vec_map ?????) in match (current_chars ???);
+<(nth_vec_map … (niltape ?))
+cases (decidable_eq_nat i i0) #Hii0
+[ >Hii0 >nth_change_vec // >nth_change_vec //
+| >nth_change_vec_neq // >nth_change_vec_neq // @nth_vec_map ]
+qed.
 
 lemma inject_trans_def :∀sig:FinSet.∀n,i:nat.i < S n → 
   ∀M,v,s,a,sn,an,mn.
   trans sig M 〈s,a〉 = 〈sn,an,mn〉 → 
-  cic:/matita/turing/turing/trans.fix(0,2,9) sig n (inject_TM sig M n i) 〈s,change_vec ? (S n) v a i〉 = 
+  cic:/matita/turing/turing/trans#fix:0:2:9 sig n (inject_TM sig M n i) 〈s,change_vec ? (S n) v a i〉 = 
     〈sn,change_vec ? (S n) (null_action ? n) 〈an,mn〉 i〉.
 #sig #n #i #Hlt #M #v #s #a #sn #an #mn #Htrans
 whd in ⊢ (??%?); >nth_change_vec // >Htrans //
 qed.
 
+lemma inj_ter: ∀A,B,C.∀p:A×B×C. 
+  p = 〈\fst (\fst p), \snd (\fst p), \snd p〉.
+// qed.
 
-axiom inject_step : ∀sig,n,M,i,q,t,nq,nt,v. i < S n →
+lemma inject_step : ∀sig,n,M,i,q,t,nq,nt,v. i < S n →
   step sig M (mk_config ?? q t) = mk_config ?? nq nt → 
-  cic:/matita/turing/turing/step.def(11) sig n (inject_TM sig M n i) 
+  cic:/matita/turing/turing/step#def:12 sig n (inject_TM sig M n i) 
     (mk_mconfig ?? n q (change_vec ? (S n) v t i)) 
   = mk_mconfig ?? n nq (change_vec ? (S n) v nt i).
-(*#sig #n #M #i #q #t #nq #nt #v #lein whd in ⊢ (??%?→?);
+#sig #n #M #i #q #t #nq #nt #v #lein whd in ⊢ (??%?→?);
 whd in match (step ????); >(current_chars_change_vec … lein)
->(eq_pair_fst_snd … (trans sig M ?)) whd in ⊢ (??%?→?); #H
+>(inj_ter … (trans sig M ?)) whd in ⊢ (??%?→?); #H
 >(inject_trans_def sig n i lein M …) 
 [|>(eq_pair_fst_snd ?? (trans sig M 〈q,current sig t〉))
   >(eq_pair_fst_snd ?? (\fst (trans sig M 〈q,current sig t〉))) %
@@ -59,14 +71,14 @@ whd in match (step ????); >(current_chars_change_vec … lein)
 whd in ⊢ (??%?); @eq_f2 [destruct (H) // ]
 @(eq_vec … (niltape ?)) #i0 #lei0n
 cases (decidable_eq_nat … i i0) #Hii0
-[ >Hii0 >nth_change_vec // >pmap_change >nth_change_vec // destruct (H) //
-| >nth_change_vec_neq // >pmap_change >nth_change_vec_neq 
-  >tape_move_null_action //
+[ >Hii0 >nth_change_vec // >tape_move_multi_def >pmap_change >nth_change_vec // destruct (H) //
+| >nth_change_vec_neq // >tape_move_multi_def  >pmap_change >nth_change_vec_neq //
+  <tape_move_multi_def >tape_move_null_action //
 ]
-qed. *)
+qed. 
 
 lemma halt_inject: ∀sig,n,M,i,x.
-  cic:/matita/turing/turing/halt.fix(0,2,9) sig n (inject_TM sig M n i) x
+  cic:/matita/turing/turing/halt#fix:0:2:9 sig n (inject_TM sig M n i) x
    = halt sig M x.
 // qed.
 
@@ -76,7 +88,7 @@ qed.
 
 lemma loop_inject: ∀sig,n,M,i,k,ins,int,outs,outt,vt.i < S n → 
  loopM sig M k (mk_config ?? ins int) = Some ? (mk_config ?? outs outt) → 
- cic:/matita/turing/turing/loopM.def(12) sig n (inject_TM sig M n i) k (mk_mconfig ?? n ins (change_vec ?? vt int i))
+ cic:/matita/turing/turing/loopM#def:13 sig n (inject_TM sig M n i) k (mk_mconfig ?? n ins (change_vec ?? vt int i))
   =Some ? (mk_mconfig sig ? n outs (change_vec ?? vt outt i)).
 #sig #n #M #i #k elim k -k
   [#ins #int #outs #outt #vt #Hin normalize in ⊢ (%→?); #H destruct
@@ -100,35 +112,11 @@ lemma loop_inject: ∀sig,n,M,i,k,ins,int,outs,outt,vt.i < S n →
   ]
 qed.
 
-(*
-lemma cstate_inject: ∀sig,n,M,i,x. *)
-
 definition inject_R ≝ λsig.λR:relation (tape sig).λn,i:nat.
   λv1,v2: (Vector (tape sig) (S n)).
   R (nth i ? v1 (niltape ?)) (nth i ? v2 (niltape ?)) ∧
   ∀j. i ≠ j → nth j ? v1 (niltape ?) = nth j ? v2 (niltape ?). 
 
-(*
-lemma nth_make : ∀A,i,n,j,a,d. i < n → nth i ? (make_veci A a n j) d = a (j+i).
-#A #i elim i
-  [#n #j #a #d #ltOn @(lt_O_n_elim … ltOn) <plus_n_O //
-  |#m #Hind #n #j #a #d #Hlt lapply Hlt @(lt_O_n_elim … (ltn_to_ltO … Hlt)) 
-   #p <plus_n_Sm #ltmp @Hind @le_S_S_to_le //  
-  ]
-qed. *)
-
-(*
-lemma mk_config_eq_s: ∀S,sig,s1,s2,t1,t2. 
-  mk_config S sig s1 t1 = mk_config S sig s2 t2 → s1=s2.
-#S #sig #s1 #s2 #t1 #t2 #H destruct //
-qed.
-
-lemma mk_config_eq_t: ∀S,sig,s1,s2,t1,t2. 
-  mk_config S sig s1 t1 = mk_config S sig s2 t2 → s1=s2.
-#S #sig #s1 #s2 #t1 #t2 #H destruct //
-qed.
-*)
-
 theorem sem_inject: ∀sig.∀M:TM sig.∀R.∀n,i.
  i≤n → M ⊨ R → inject_TM sig M n i ⊨ inject_R sig R n i. 
 #sig #M #R #n #i #lein #HR #vt cases (HR (nth i ? vt (niltape ?)))