update in ground

[helm.git] / matita / matita / lib / turing / multi_universal / normalTM.ma

diff --git a/matita/matita/lib/turing/multi_universal/normalTM.ma b/matita/matita/lib/turing/multi_universal/normalTM.ma
index 13ef8a66c6e992fcfe9f0c6d8a675555c664967e..28c3920bc576b8f21ca0442fecbfd94b8bf36b7d 100644 (file)
--- a/matita/matita/lib/turing/multi_universal/normalTM.ma
+++ b/matita/matita/lib/turing/multi_universal/normalTM.ma
@@ -12,51 +12,6 @@
 include "turing/multi_universal/alphabet.ma".
 include "turing/mono.ma".
 
-(************************* turning DeqMove into a DeqSet **********************)
-definition move_eq ≝ λm1,m2:move.
-  match m1 with
-  [R ⇒ match m2 with [R ⇒ true | _ ⇒ false]
-  |L ⇒ match m2 with [L ⇒ true | _ ⇒ false]
-  |N ⇒ match m2 with [N ⇒ true | _ ⇒ false]].
-
-lemma move_eq_true:∀m1,m2.
-  move_eq m1 m2 = true ↔ m1 = m2.
-*
-  [* normalize [% #_ % |2,3: % #H destruct ]
-  |* normalize [1,3: % #H destruct |% #_ % ]
-  |* normalize [1,2: % #H destruct |% #_ % ]
-qed.
-
-definition DeqMove ≝ mk_DeqSet move move_eq move_eq_true.
-
-unification hint 0 ≔ ;
-    X ≟ DeqMove
-(* ---------------------------------------- *) ⊢ 
-    move ≡ carr X.
-
-unification hint  0 ≔ m1,m2; 
-    X ≟ DeqMove
-(* ---------------------------------------- *) ⊢ 
-    move_eq m1 m2 ≡ eqb X m1 m2.
-
-
-(************************ turning DeqMove into a FinSet ***********************)
-definition move_enum ≝ [L;R;N].
-
-lemma move_enum_unique: uniqueb ? [L;R;N] = true.
-// qed.
-
-lemma move_enum_complete: ∀x:move. memb ? x [L;R;N] = true.
-* // qed.
-
-definition FinMove ≝ 
-  mk_FinSet DeqMove [L;R;N] move_enum_unique move_enum_complete.
-
-unification hint  0 ≔ ; 
-    X ≟ FinMove
-(* ---------------------------------------- *) ⊢ 
-    move ≡ FinSetcarr X.
-
 (*************************** normal Turing Machines ***************************)
 
 (* A normal turing machine is just an ordinary machine where:
@@ -80,16 +35,34 @@ record normalTM : Type[0] ≝
   nhalt : initN no_states → bool
 }.
 
+lemma decomp_target : ∀n.∀tg: trans_target n. 
+  ∃qout,cout,m. tg = 〈qout,cout,m〉.
+#n * * #q #c #m %{q} %{c} %{m} //
+qed.
+
 (* A normal machine is just a special case of Turing Machine. *)
 
+definition nstart_state ≝ λM.mk_Sig ?? 0 (pos_no_states M).
+
 definition normalTM_to_TM ≝ λM:normalTM.
   mk_TM FinBool (initN (no_states M)) 
-   (ntrans M) (mk_Sig ?? 0 (pos_no_states M)) (nhalt M).
+   (ntrans M) (nstart_state M) (nhalt M).
 
 coercion normalTM_to_TM.
 
 definition nconfig ≝ λn. config FinBool (initN n).
 
+(* A normal machine has a non empty graph *)
+
+definition sample_input: ∀M.trans_source (no_states M).
+#M % [@(nstart_state M) | %]
+qed.
+
+lemma nTM_nog: ∀M. graph_enum ?? (ntrans M) ≠ [ ].
+#M % #H lapply(graph_enum_complete ?? (ntrans M) (sample_input M) ? (refl ??))
+>H normalize #Hd destruct
+qed.
+
 (******************************** tuples **************************************)
 
 (* By general results on FinSets we know that every function f between two 
@@ -187,6 +160,18 @@ definition low_mv ≝ λm.
   | N ⇒ null
   ].
 
+lemma injective_low_char: injective … low_char.
+#c1 #c2 cases c1 cases c2 normalize //
+  [#b1 #H destruct
+  |#b1 #H destruct
+  |#b1 #b2 #H destruct //
+  ]
+qed.   
+
+lemma injective_low_mv: injective … low_mv.
+#m1 #m2 cases m1 cases m2 // normalize #H destruct
+qed.
+   
 (******************************** tuple encoding ******************************)
 definition tuple_type ≝ λn.
  (Nat_to n × (option FinBool)) × (Nat_to n × (option FinBool) × move).