step (almost) done

[helm.git] / matita / matita / lib / turing / multi_to_mono / exec_moves.ma

diff --git a/matita/matita/lib/turing/multi_to_mono/exec_moves.ma b/matita/matita/lib/turing/multi_to_mono/exec_moves.ma
index dae4aa6afd585ff7b3bee662e75fa1d06795f6ee..9f6cb718b9e7db3b8f71763a3f0e97153599b554 100644 (file)
--- a/matita/matita/lib/turing/multi_to_mono/exec_moves.ma
+++ b/matita/matita/lib/turing/multi_to_mono/exec_moves.ma
@@ -2,75 +2,6 @@
 
 include "turing/multi_to_mono/exec_trace_move.ma".
 (* include "turing/turing.ma". *)
-
-(**************************** Vector Operations *******************************)
-
-let rec resize A (l:list A) i d on i ≝
-  match i with 
-  [ O ⇒ [ ]
-  | S j ⇒ (hd ? l d)::resize A (tail ? l) j d
-  ].
-
-lemma length_resize : ∀A,l,i,d. |resize A l i d| = i.
-#A #l #i lapply l -l elim i 
-  [#l #d % 
-  |#m #Hind #l cases l 
-    [#d normalize @eq_f @Hind
-    |#a #tl #d normalize @eq_f @Hind
-    ]
-  ]
-qed.
-
-lemma resize_id : ∀A,n,l,d. |l| = n → 
-  resize A l n d = l.
-#A #n elim n 
-  [#l #d #H >(lenght_to_nil … H) //
-  |#m #Hind * #d normalize 
-    [#H destruct |#a #tl #H @eq_f @Hind @injective_S // ]
-  ]
-qed.
-
-definition resize_vec :∀A,n.Vector A n → ∀i.A→Vector A i.
-#A #n #a #i #d @(mk_Vector A i (resize A a i d) ) @length_resize
-qed.
-
-axiom nth_resize_vec :∀A,n.∀v:Vector A n.∀d,i,j. i < j →i < n →
-  nth i ? (resize_vec A n v j d) d = nth i ? v d.
-  
-lemma resize_vec_id : ∀A,n.∀v:Vector A n.∀d. 
-  resize_vec A n v n d = v.
-#A #n #v #d @(eq_vec … d) #i #ltin @nth_resize_vec //
-qed.
-
-definition vec_single: ∀A,a. Vector A 1 ≝ λA,a.
-  mk_Vector A 1 [a] (refl ??).
-  
-definition vec_cons_right : ∀A.∀a:A.∀n. Vector A n → Vector A (S n).
-#A #a #n #v >(plus_n_O n) >plus_n_Sm @(vec_append … v (vec_single A a))
->length_append >(len A n v) //
-qed.
-
-lemma eq_cons_right : ∀A,a1,a2.∀n.∀v1,v2:Vector A n.
-  a1 = a2 → v1 = v2 → vec_cons_right A a1 n v1 = vec_cons_right A a2 n v2.
-// qed.
-
-axiom nth_cons_right: ∀A.∀a:A.∀n.∀v:Vector A n.∀d. 
-  nth n ? (vec_cons_right A a n v) d = a.
-(*
-#A #a #n elim n 
-  [#v #d >(vector_nil … v) //
-  |#m #Hind #v #d >(vec_expand … v) whd in ⊢ (??%?);    
-   whd in match (vec_cons_right ????);  
-*)
-
-lemma get_moves_cons_right: ∀Q,sig,n,q,moves,a.
-  get_moves Q sig (S n)
-    (vec_cons_right ? (Some ? (inl ?? 〈q,moves〉)) (S n) a) = moves.
-#Q #sig #n #q #moves #a whd in ⊢(??%?); >nth_cons_right //
-qed.
-    
-axiom resize_cons_right: ∀A.∀a:A.∀n.∀v:Vector A n.∀d. 
-  resize_vec ? (S n) (vec_cons_right A a n v) n d = v.
   
 let rec exec_moves Q sig n i on i : TM (MTA (HC Q n) sig (S n)) ≝
   match i with 
@@ -131,15 +62,18 @@ definition R_exec_moves ≝ λQ,sig,n,i,t1,t2.
   ∃ls1,a1,rs1. 
    t2 = midtape (MTA (HC Q n) sig (S n)) ls1 a1 rs1 ∧
    (∀i.regular_trace (TA (HC Q n) sig) (S n) a1 ls1 rs1 i) ∧
-   readback ? (S n) ls1 (vec … a1) rs1 i = 
-     tape_moves ?? (readback ? (S n) ls (vec … a) rs i) (vec_moves Q sig n a i) ∧
-   (∀j. i ≤ j → j ≤ n →  
+   (∀j. j < i → j ≤ n →
+    rb_trace_i ? (S n) ls1 (vec … a1) rs1 j =
+     tape_move ? (rb_trace_i ? (S n) ls (vec … a) rs j) (get_move Q sig n a j)) ∧
+    (* tape_moves ?? (readback ? (S n) ls (vec … a) rs i) (vec_moves Q sig n a i) ∧ *)
+   (∀j. i ≤ j → j ≤ n → 
     rb_trace_i ? (S n) ls1 (vec … a1) rs1 j = 
       rb_trace_i ? (S n) ls (vec … a) rs j).
      
 (* alias id "Realize_to_Realize" = 
   "cic:/matita/turing/mono/Realize_to_Realize.def(13)". *)
 
+(*
 lemma nth_readback: ∀sig,n,ls,a,rs,j,i. i < j →
  nth i ? (readback sig n ls a rs j) (niltape ?) = 
    rb_trace_i sig n ls a rs (j - S i).
@@ -150,14 +84,14 @@ lemma nth_readback: ∀sig,n,ls,a,rs,j,i. i < j →
     |#m #Hmj >minus_S_S @Hind @le_S_S_to_le //
     ]
   ]
-qed.
+qed. *)
 
 lemma sem_exec_moves: ∀Q,sig,n,i. i ≤ n → 
   exec_moves Q sig n i ⊨ R_exec_moves Q sig n i.
 #Q #sig #n #i elim i 
   [#_ @(Realize_to_Realize … (sem_nop …))
    #t1 #t2 #H #a #ls #rs #Ht1 #Hreg #H1 #H2 #H3 
-   %{ls} %{a} %{rs} %[% >H [%[@Ht1|@Hreg]| %]|//]
+   %{ls} %{a} %{rs} %[% >H [%[@Ht1|@Hreg]| #j #ltjO @False_ind /2/]|//]
   |#j #Hind #lttj lapply (lt_to_le … lttj) #ltj
    @(sem_seq_app … (Hind ltj) (sem_exec_move_i … lttj)) -Hind
    #int #outt * #t1 * #H1 #H2
@@ -173,13 +107,10 @@ lemma sem_exec_moves: ∀Q,sig,n,i. i ≤ n →
    cut (∀i. get_move Q sig n a i = get_move Q sig n a1 i)
      [@daemon] #aa1
    %[%[%[@Houtt|@Hregout]
-      |whd in ⊢ (??%?); @Vector_eq >(vec_moves_cons … lttj)
-       >tape_moves_def >pmap_vec_cons @eq_f2
-        [<H10 [>aa1 @Hrboutt |@ltj |@le_n]
-        |<tape_moves_def <H9 (* mitico *) @eq_f 
-         @(eq_vec … (niltape ?)) #i #ltij 
-         >(nth_readback … ltij) >(nth_readback … ltij) @Hrbid 
-          [@(transitive_le … ltj) // |@lt_to_not_eq @lt_plus_to_minus //]
+      |#k #ltk cases (le_to_or_lt_eq … ltk) #Hk #lekn
+        [>(Hrbid … lekn) [2:@lt_to_not_eq @le_S_S_to_le @Hk]
+         @(H9 k ? lekn) @le_S_S_to_le @Hk
+        |destruct (Hk) <H10 // @Hrboutt
         ]
       ]
     |#a #Hja #Han >(Hrbid … Han)