Many changes

[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 722f4fda98cffe44bbcd7b488edd0e69a66c00f4..d7851d85f938ba480045bd170c5e6c2f1a1af493 100644 (file)
--- a/matita/matita/lib/turing/inject.ma
+++ b/matita/matita/lib/turing/inject.ma
@@ -125,36 +125,29 @@ 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 ?)))
 #k * * #outs #outt * #Hloop #HRout @(ex_intro ?? k) 
-@(ex_intro ?? (mk_mconfig ?? n outs (change_vec ? (S n) vt outt i))) % 
-  [elim k in Hloop;
-    [normalize in ⊢ (%\to ?); #H destruct
-    |#k0 #Hind whd in ⊢ (??%?→??%?);
-     >halt_inject whd in match (cstate ????);
-     whd in match (cstate sig (states sig M)
-       (initc sig M (nth i (tape sig) vt (niltape sig)))); 
-     cases (true_or_false (halt sig M (start sig M))) #Hhalt >Hhalt 
-     whd in ⊢ (??%?→??%?);
-      [#H @eq_f whd in ⊢ (??%?); lapply (de_option ??? H) -H 
-       whd  in ⊢ (??%?→?); #H @eq_f2  
-        [whd in ⊢ (??%?); destruct (H) //
-        |@(eq_vec … (niltape ?)) #j #lejn
-         cases (true_or_false (eqb i j)) #eqij
-          [>(eqb_true_to_eq … eqij) >nth_change_vec //
-           <(eqb_true_to_eq … eqij) destruct (H) //
-          |>nth_change_vec_neq // @(eqb_false_to_not_eq … eqij)
-          ]
-        ]
-      |#H <Hind STOP
-        [(* whd in ⊢ (???(?????%)); >loop_inject // *)
-        | <H whd in ⊢ (??%?);
+@(ex_intro ?? (mk_mconfig ?? n outs (change_vec ? (S n) vt outt i))) %
+  [whd in ⊢ (??(?????%)?); <(change_vec_same ?? vt i (niltape ?)) in ⊢ (??%?);
+   @loop_inject /2 by refl, trans_eq, le_S_S/
   |%[>nth_change_vec // @le_S_S //
     |#j #i >nth_change_vec_neq //
     ]
   ]
-          
-  
-  
-
-  
-
+qed.
 
+theorem acc_sem_inject: ∀sig.∀M:TM sig.∀Rtrue,Rfalse,acc.∀n,i.
+ i≤n → M ⊨ [ acc : Rtrue, Rfalse ] → 
+ inject_TM sig M n i ⊨ [ acc : inject_R sig Rtrue n i, inject_R sig Rfalse n i ]. 
+#sig #M #Rtrue #Rfalse #acc #n #i #lein #HR #vt cases (HR (nth i ? vt (niltape ?)))
+#k * * #outs #outt * * #Hloop #HRtrue #HRfalse @(ex_intro ?? k) 
+@(ex_intro ?? (mk_mconfig ?? n outs (change_vec ? (S n) vt outt i))) % [ %
+  [whd in ⊢ (??(?????%)?); <(change_vec_same ?? vt i (niltape ?)) in ⊢ (??%?);
+   @loop_inject /2 by refl, trans_eq, le_S_S/
+  |#Hqtrue %
+    [>nth_change_vec /2 by le_S_S/
+    |#j #Hneq >nth_change_vec_neq //
+    ] ]
+  |#Hqfalse %
+    [>nth_change_vec /2 by le_S_S/ @HRfalse @Hqfalse
+    |#j #Hneq >nth_change_vec_neq //
+    ] ]
+qed.
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