From 75bf98d7d7a16ff8ce2c530e718809e2bc331568 Mon Sep 17 00:00:00 2001
From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Fri, 25 May 2012 08:59:21 +0000
Subject: [PATCH] Porting to the new defintion of finset

---
 matita/matita/lib/turing/if_machine.ma        |   4 +-
 matita/matita/lib/turing/mono.ma              |   6 +-
 .../matita/lib/turing/universal/alphabet.ma   |  12 +-
 matita/matita/lib/turing/universal/marks.ma   | 117 ++++++++++--------
 matita/matita/lib/turing/universal/tests.ma   |  40 +++---
 matita/matita/lib/turing/universal/tuples.ma  |  27 ++++
 6 files changed, 133 insertions(+), 73 deletions(-)

diff --git a/matita/matita/lib/turing/if_machine.ma b/matita/matita/lib/turing/if_machine.ma
index 03d49d4b6..3d6675d02 100644
--- a/matita/matita/lib/turing/if_machine.ma
+++ b/matita/matita/lib/turing/if_machine.ma
@@ -77,7 +77,7 @@ axiom acc_sem_if: ∀sig,M1,M2,M3,Rtrue,Rfalse,R2,R3,acc.
   accRealize sig M1 acc Rtrue Rfalse → Realize sig M2 R2 → Realize sig M3 R3 → 
     accRealize sig 
      (ifTM sig M1 (single_finalTM … M2) M3 acc) 
-     (inr … (inl … (inr … 0)))
+     (inr … (inl … (inr … start_nop)))
      (Rtrue ∘ R2) 
      (Rfalse ∘ R3).
      
@@ -87,7 +87,7 @@ lemma acc_sem_if_app: ∀sig,M1,M2,M3,Rtrue,Rfalse,R2,R3,R4,R5,acc.
     (∀t1,t2,t3. Rfalse t1 t3 → R3 t3 t2 → R5 t1 t2) → 
     accRealize sig 
      (ifTM sig M1 (single_finalTM … M2) M3 acc) 
-     (inr … (inl … (inr … 0)))
+     (inr … (inl … (inr … start_nop)))
      R4 R5.    
 #sig #M1 #M2 #M3 #Rtrue #Rfalse #R2 #R3 #R4 #R5 #acc
 #HRacc #HRtrue #HRfalse #Hsub1 #Hsub2 
diff --git a/matita/matita/lib/turing/mono.ma b/matita/matita/lib/turing/mono.ma
index e89d710c9..7d6bad37f 100644
--- a/matita/matita/lib/turing/mono.ma
+++ b/matita/matita/lib/turing/mono.ma
@@ -290,17 +290,19 @@ definition accRealize ≝ λsig.λM:TM sig.λacc:states sig M.λRtrue,Rfalse:rel
   *)
   
 definition nop_states ≝ initN 1.
+definition start_nop : initN 1 ≝ mk_Sig ?? 0 (le_n … (S 0)).
 
 definition nop ≝ 
   λalpha:FinSet.mk_TM alpha nop_states
   (λp.let 〈q,a〉 ≝ p in 〈q,None ?〉)
-  O (λ_.true).
+  start_nop (λ_.true).
   
 definition R_nop ≝ λalpha.λt1,t2:tape alpha.t2 = t1.
 
 lemma sem_nop :
   ∀alpha.Realize alpha (nop alpha) (R_nop alpha).
-#alpha #intape @(ex_intro ?? 1) @ex_intro [| % normalize % ]
+#alpha #intape @(ex_intro ?? 1) 
+@(ex_intro … (mk_config ?? start_nop intape)) % % 
 qed.
 
 (* Compositions *)
diff --git a/matita/matita/lib/turing/universal/alphabet.ma b/matita/matita/lib/turing/universal/alphabet.ma
index 04701aeec..bf2484f29 100644
--- a/matita/matita/lib/turing/universal/alphabet.ma
+++ b/matita/matita/lib/turing/universal/alphabet.ma
@@ -39,10 +39,18 @@ definition DeqUnialpha ≝ mk_DeqSet unialpha unialpha_eq ?.
   |*: * [1,6,11,16: #y ] normalize % #H1 destruct % ]
 qed.
 
-axiom unialpha_unique : uniqueb DeqUnialpha [bit true;bit false;comma;bar;grid] = true.
+lemma unialpha_unique : 
+  uniqueb DeqUnialpha [bit true;bit false;null;comma;bar;grid] = true.
+// qed.
+
+lemma unialpha_complete :∀x:DeqUnialpha. 
+  memb ? x [bit true;bit false;null;comma;bar;grid] = true.
+* // * //
+qed.
 
 definition FSUnialpha ≝ 
-  mk_FinSet DeqUnialpha [bit true;bit false;null;comma;bar;grid] unialpha_unique.
+  mk_FinSet DeqUnialpha [bit true;bit false;null;comma;bar;grid] 
+  unialpha_unique unialpha_complete.
 
 definition is_bit ≝ λc.match c with [ bit _ ⇒ true | _ ⇒ false ].
 
diff --git a/matita/matita/lib/turing/universal/marks.ma b/matita/matita/lib/turing/universal/marks.ma
index 17992f95f..70000e399 100644
--- a/matita/matita/lib/turing/universal/marks.ma
+++ b/matita/matita/lib/turing/universal/marks.ma
@@ -30,17 +30,21 @@ include "turing/universal/tests.ma".
 
 definition atm_states ≝ initN 3.
 
+definition atm0 : atm_states ≝ mk_Sig ?? 0 (leb_true_to_le 1 3 (refl …)).
+definition atm1 : atm_states ≝ mk_Sig ?? 1 (leb_true_to_le 2 3 (refl …)).
+definition atm2 : atm_states ≝ mk_Sig ?? 2 (leb_true_to_le 3 3 (refl …)).
+
 definition atmr_step ≝ 
   λalpha:FinSet.λtest:alpha→bool.
   mk_TM alpha atm_states
   (λp.let 〈q,a〉 ≝ p in
    match a with
-   [ None ⇒ 〈1, None ?〉
+   [ None ⇒ 〈atm1, None ?〉
    | Some a' ⇒ 
      match test a' with
-     [ true ⇒ 〈1,None ?〉
-     | false ⇒ 〈2,Some ? 〈a',R〉〉 ]])
-  O (λx.notb (x == 0)).
+     [ true ⇒ 〈atm1,None ?〉
+     | false ⇒ 〈atm2,Some ? 〈a',R〉〉 ]])
+  atm0 (λx.notb (x == atm0)).
 
 definition Ratmr_step_true ≝ 
   λalpha,test,t1,t2.
@@ -57,43 +61,45 @@ definition Ratmr_step_false ≝
 lemma atmr_q0_q1 :
   ∀alpha,test,ls,a0,rs. test a0 = true → 
   step alpha (atmr_step alpha test)
-    (mk_config ?? 0 (midtape … ls a0 rs)) =
-  mk_config alpha (states ? (atmr_step alpha test)) 1
+    (mk_config ?? atm0 (midtape … ls a0 rs)) =
+  mk_config alpha (states ? (atmr_step alpha test)) atm1
     (midtape … ls a0 rs).
-#alpha #test #ls #a0 #ts #Htest normalize >Htest %
+#alpha #test #ls #a0 #ts #Htest whd in ⊢ (??%?);
+whd in match (trans … 〈?,?〉); >Htest %
 qed.
      
 lemma atmr_q0_q2 :
   ∀alpha,test,ls,a0,rs. test a0 = false → 
   step alpha (atmr_step alpha test)
-    (mk_config ?? 0 (midtape … ls a0 rs)) =
-  mk_config alpha (states ? (atmr_step alpha test)) 2
+    (mk_config ?? atm0 (midtape … ls a0 rs)) =
+  mk_config alpha (states ? (atmr_step alpha test)) atm2
     (mk_tape … (a0::ls) (option_hd ? rs) (tail ? rs)).
-#alpha #test #ls #a0 #ts #Htest normalize >Htest cases ts //
+#alpha #test #ls #a0 #ts #Htest whd in ⊢ (??%?);
+whd in match (trans … 〈?,?〉); >Htest cases ts //
 qed.
 
 lemma sem_atmr_step :
   ∀alpha,test.
   accRealize alpha (atmr_step alpha test) 
-    2 (Ratmr_step_true alpha test) (Ratmr_step_false alpha test).
+    atm2 (Ratmr_step_true alpha test) (Ratmr_step_false alpha test).
 #alpha #test *
 [ @(ex_intro ?? 2)
-  @(ex_intro ?? (mk_config ?? 1 (niltape ?))) %
-  [ % // #Hfalse destruct | #_ % // % % ]
-| #a #al @(ex_intro ?? 2) @(ex_intro ?? (mk_config ?? 1 (leftof ? a al)))
-  % [ % // #Hfalse destruct | #_ % // % % ]
-| #a #al @(ex_intro ?? 2) @(ex_intro ?? (mk_config ?? 1 (rightof ? a al)))
-  % [ % // #Hfalse destruct | #_ % // % % ]
+  @(ex_intro ?? (mk_config ?? atm1 (niltape ?))) %
+  [ % // whd in ⊢ ((??%%)→?); #Hfalse destruct | #_ % // % % ]
+| #a #al @(ex_intro ?? 2) @(ex_intro ?? (mk_config ?? atm1 (leftof ? a al)))
+  % [ % // whd in ⊢ ((??%%)→?); #Hfalse destruct | #_ % // % % ]
+| #a #al @(ex_intro ?? 2) @(ex_intro ?? (mk_config ?? atm1 (rightof ? a al)))
+  % [ % // whd in ⊢ ((??%%)→?); #Hfalse destruct | #_ % // % % ]
 | #ls #c #rs @(ex_intro ?? 2)
   cases (true_or_false (test c)) #Htest
-  [ @(ex_intro ?? (mk_config ?? 1 ?))
+  [ @(ex_intro ?? (mk_config ?? atm1 ?))
     [| % 
       [ % 
         [ whd in ⊢ (??%?); >atmr_q0_q1 //
-        | #Hfalse destruct ]
+        | whd in ⊢ ((??%%)→?); #Hfalse destruct ]
       | #_ % // %2 @(ex_intro ?? c) % // ]
     ]
-  | @(ex_intro ?? (mk_config ?? 2 (mk_tape ? (c::ls) (option_hd ? rs) (tail ? rs))))
+  | @(ex_intro ?? (mk_config ?? atm2 (mk_tape ? (c::ls) (option_hd ? rs) (tail ? rs))))
     % 
     [ %
       [ whd in ⊢ (??%?); >atmr_q0_q2 //
@@ -116,7 +122,7 @@ definition R_adv_to_mark_r ≝ λalpha,test,t1,t2.
      t2 = midtape ? (reverse ? rs1@c::ls) b rs2))).
      
 definition adv_to_mark_r ≝ 
-  λalpha,test.whileTM alpha (atmr_step alpha test) 2.
+  λalpha,test.whileTM alpha (atmr_step alpha test) atm2.
 
 lemma wsem_adv_to_mark_r :
   ∀alpha,test.
@@ -188,15 +194,18 @@ qed.
  
 definition mark_states ≝ initN 2.
 
+definition ms0 : mark_states ≝ mk_Sig ?? 0 (leb_true_to_le 1 2 (refl …)).
+definition ms1 : mark_states ≝ mk_Sig ?? 1 (leb_true_to_le 2 2 (refl …)).
+
 definition mark ≝ 
   λalpha:FinSet.mk_TM (FinProd … alpha FinBool) mark_states
   (λp.let 〈q,a〉 ≝ p in
     match a with
-    [ None ⇒ 〈1,None ?〉
-    | Some a' ⇒ match q with
-      [ O ⇒ let 〈a'',b〉 ≝ a' in 〈1,Some ? 〈〈a'',true〉,N〉〉
-      | S q ⇒ 〈1,None ?〉 ] ])
-  O (λq.q == 1).
+    [ None ⇒ 〈ms1,None ?〉
+    | Some a' ⇒ match (pi1 … q) with
+      [ O ⇒ let 〈a'',b〉 ≝ a' in 〈ms1,Some ? 〈〈a'',true〉,N〉〉
+      | S q ⇒ 〈ms1,None ?〉 ] ])
+  ms0 (λq.q == ms1).
   
 definition R_mark ≝ λalpha,t1,t2.
   ∀ls,c,b,rs.
@@ -223,16 +232,18 @@ qed.
 *)
 
 definition move_states ≝ initN 2.
+definition move0 : move_states ≝ mk_Sig ?? 0 (leb_true_to_le 1 2 (refl …)).
+definition move1 : move_states ≝ mk_Sig ?? 1 (leb_true_to_le 2 2 (refl …)).
 
 definition move_r ≝ 
   λalpha:FinSet.mk_TM alpha move_states
   (λp.let 〈q,a〉 ≝ p in
     match a with
-    [ None ⇒ 〈1,None ?〉
-    | Some a' ⇒ match q with
-      [ O ⇒ 〈1,Some ? 〈a',R〉〉
-      | S q ⇒ 〈1,None ?〉 ] ])
-  O (λq.q == 1).
+    [ None ⇒ 〈move1,None ?〉
+    | Some a' ⇒ match (pi1 … q) with
+      [ O ⇒ 〈move1,Some ? 〈a',R〉〉
+      | S q ⇒ 〈move1,None ?〉 ] ])
+  move0 (λq.q == move1).
   
 definition R_move_r ≝ λalpha,t1,t2.
   ∀ls,c,rs.
@@ -263,11 +274,11 @@ definition move_l ≝
   λalpha:FinSet.mk_TM alpha move_states
   (λp.let 〈q,a〉 ≝ p in
     match a with
-    [ None ⇒ 〈1,None ?〉
-    | Some a' ⇒ match q with
-      [ O ⇒ 〈1,Some ? 〈a',L〉〉
-      | S q ⇒ 〈1,None ?〉 ] ])
-  O (λq.q == 1).
+    [ None ⇒ 〈move1,None ?〉
+    | Some a' ⇒ match pi1 … q with
+      [ O ⇒ 〈move1,Some ? 〈a',L〉〉
+      | S q ⇒ 〈move1,None ?〉 ] ])
+  move0 (λq.q == move1).
   
 definition R_move_l ≝ λalpha,t1,t2.
   ∀ls,c,rs.
@@ -297,18 +308,22 @@ qed.
  
 definition mrm_states ≝ initN 3.
 
+definition mrm0 : mrm_states ≝ mk_Sig ?? 0 (leb_true_to_le 1 3 (refl …)).
+definition mrm1 : mrm_states ≝ mk_Sig ?? 1 (leb_true_to_le 2 3 (refl …)).
+definition mrm2 : mrm_states ≝ mk_Sig ?? 2 (leb_true_to_le 3 3 (refl …)).
+
 definition move_right_and_mark ≝ 
   λalpha:FinSet.mk_TM (FinProd … alpha FinBool) mrm_states
   (λp.let 〈q,a〉 ≝ p in
     match a with
-    [ None ⇒ 〈2,None ?〉
-    | Some a' ⇒ match q with
-      [ O ⇒ 〈1,Some ? 〈a',R〉〉
+    [ None ⇒ 〈mrm2,None ?〉
+    | Some a' ⇒ match pi1 … q with
+      [ O ⇒ 〈mrm1,Some ? 〈a',R〉〉
       | S q ⇒ match q with
         [ O ⇒ let 〈a'',b〉 ≝ a' in
-              〈2,Some ? 〈〈a'',true〉,N〉〉
-        | S _ ⇒ 〈2,None ?〉 ] ] ])
-  O (λq.q == 2).
+              〈mrm2,Some ? 〈〈a'',true〉,N〉〉
+        | S _ ⇒ 〈mrm2,None ?〉 ] ] ])
+  mrm0 (λq.q == mrm2).
   
 definition R_move_right_and_mark ≝ λalpha,t1,t2.
   ∀ls,c,d,b,rs.
@@ -337,15 +352,19 @@ qed.
  
 definition clear_mark_states ≝ initN 3.
 
+definition clear0 : clear_mark_states ≝ mk_Sig ?? 0 (leb_true_to_le 1 3 (refl …)).
+definition clear1 : clear_mark_states ≝ mk_Sig ?? 1 (leb_true_to_le 2 3 (refl …)).
+definition claer2 : clear_mark_states ≝ mk_Sig ?? 2 (leb_true_to_le 3 3 (refl …)).
+
 definition clear_mark ≝ 
   λalpha:FinSet.mk_TM (FinProd … alpha FinBool) clear_mark_states
   (λp.let 〈q,a〉 ≝ p in
     match a with
-    [ None ⇒ 〈1,None ?〉
-    | Some a' ⇒ match q with
-      [ O ⇒ let 〈a'',b〉 ≝ a' in 〈1,Some ? 〈〈a'',false〉,N〉〉
-      | S q ⇒ 〈1,None ?〉 ] ])
-  O (λq.q == 1).
+    [ None ⇒ 〈clear1,None ?〉
+    | Some a' ⇒ match pi1 … q with
+      [ O ⇒ let 〈a'',b〉 ≝ a' in 〈clear1,Some ? 〈〈a'',false〉,N〉〉
+      | S q ⇒ 〈clear1,None ?〉 ] ])
+  clear0 (λq.q == clear1).
   
 definition R_clear_mark ≝ λalpha,t1,t2.
   ∀ls,c,b,rs.
@@ -704,7 +723,7 @@ definition R_comp_step_false ≝
    is_marked ? c = false ∧ t2 = t1.
    
 lemma sem_comp_step : 
-  accRealize ? comp_step (inr … (inl … (inr … 0))) 
+  accRealize ? comp_step (inr … (inl … (inr … start_nop))) 
     R_comp_step_true R_comp_step_false.
 #intape
 cases (acc_sem_if … (sem_test_char ? (is_marked ?))
@@ -769,7 +788,7 @@ cases (acc_sem_if … (sem_test_char ? (is_marked ?))
 qed.
 
 definition compare ≝ 
-  whileTM ? comp_step (inr … (inl … (inr … 0))).
+  whileTM ? comp_step (inr … (inl … (inr … start_nop))).
 
 (*
 definition R_compare :=
diff --git a/matita/matita/lib/turing/universal/tests.ma b/matita/matita/lib/turing/universal/tests.ma
index 24a486bc1..2e7092b95 100644
--- a/matita/matita/lib/turing/universal/tests.ma
+++ b/matita/matita/lib/turing/universal/tests.ma
@@ -22,19 +22,21 @@ include "turing/if_machine.ma".
 
 definition tc_states ≝ initN 3.
 
-definition tc_true ≝ 1.
+definition tc_start : tc_states ≝ mk_Sig ?? 0 (leb_true_to_le 1 3 (refl …)).
+definition tc_true : tc_states ≝ mk_Sig ?? 1 (leb_true_to_le 2 3 (refl …)).
+definition tc_false : tc_states ≝ mk_Sig ?? 2 (leb_true_to_le 3 3 (refl …)).
 
 definition test_char ≝ 
   λalpha:FinSet.λtest:alpha→bool.
   mk_TM alpha tc_states
   (λp.let 〈q,a〉 ≝ p in
    match a with
-   [ None ⇒ 〈1, None ?〉
+   [ None ⇒ 〈tc_true, None ?〉
    | Some a' ⇒ 
      match test a' with
-     [ true ⇒ 〈1,None ?〉
-     | false ⇒ 〈2,None ?〉 ]])
-  O (λx.notb (x == 0)).
+     [ true ⇒ 〈tc_true,None ?〉
+     | false ⇒ 〈tc_false,None ?〉 ]])
+  tc_start (λx.notb (x == tc_start)).
 
 definition Rtc_true ≝ 
   λalpha,test,t1,t2.
@@ -49,47 +51,49 @@ definition Rtc_false ≝
 lemma tc_q0_q1 :
   ∀alpha,test,ls,a0,rs. test a0 = true → 
   step alpha (test_char alpha test)
-    (mk_config ?? 0 (midtape … ls a0 rs)) =
-  mk_config alpha (states ? (test_char alpha test)) 1
+    (mk_config ?? tc_start (midtape … ls a0 rs)) =
+  mk_config alpha (states ? (test_char alpha test)) tc_true
     (midtape … ls a0 rs).
-#alpha #test #ls #a0 #ts #Htest normalize >Htest %
+#alpha #test #ls #a0 #ts #Htest whd in ⊢ (??%?); 
+whd in match (trans … 〈?,?〉); >Htest %
 qed.
      
 lemma tc_q0_q2 :
   ∀alpha,test,ls,a0,rs. test a0 = false → 
   step alpha (test_char alpha test)
-    (mk_config ?? 0 (midtape … ls a0 rs)) =
-  mk_config alpha (states ? (test_char alpha test)) 2
+    (mk_config ?? tc_start (midtape … ls a0 rs)) =
+  mk_config alpha (states ? (test_char alpha test)) tc_false
     (midtape … ls a0 rs).
-#alpha #test #ls #a0 #ts #Htest normalize >Htest %
+#alpha #test #ls #a0 #ts #Htest whd in ⊢ (??%?); 
+whd in match (trans … 〈?,?〉); >Htest %
 qed.
 
 lemma sem_test_char :
   ∀alpha,test.
   accRealize alpha (test_char alpha test) 
-    1 (Rtc_true alpha test) (Rtc_false alpha test).
+    tc_true (Rtc_true alpha test) (Rtc_false alpha test).
 #alpha #test *
 [ @(ex_intro ?? 2)
-  @(ex_intro ?? (mk_config ?? 1 (niltape ?))) %
+  @(ex_intro ?? (mk_config ?? tc_true (niltape ?))) %
   [ % // #_ #c normalize #Hfalse destruct | #_ #c normalize #Hfalse destruct (Hfalse) ]
-| #a #al @(ex_intro ?? 2) @(ex_intro ?? (mk_config ?? 1 (leftof ? a al)))
+| #a #al @(ex_intro ?? 2) @(ex_intro ?? (mk_config ?? tc_true (leftof ? a al)))
   % [ % // #_ #c normalize #Hfalse destruct | #_ #c normalize #Hfalse destruct (Hfalse) ]
-| #a #al @(ex_intro ?? 2) @(ex_intro ?? (mk_config ?? 1 (rightof ? a al)))
+| #a #al @(ex_intro ?? 2) @(ex_intro ?? (mk_config ?? tc_true (rightof ? a al)))
   % [ % // #_ #c normalize #Hfalse destruct | #_ #c normalize #Hfalse destruct (Hfalse) ]
 | #ls #c #rs @(ex_intro ?? 2)
   cases (true_or_false (test c)) #Htest
-  [ @(ex_intro ?? (mk_config ?? 1 ?))
+  [ @(ex_intro ?? (mk_config ?? tc_true ?))
     [| % 
       [ % 
         [ whd in ⊢ (??%?); >tc_q0_q1 //
         | #_ #c0 #Hc0 % // normalize in Hc0; destruct // ]
       | * #Hfalse @False_ind @Hfalse % ]
     ]
-  | @(ex_intro ?? (mk_config ?? 2 (midtape ? ls c rs)))
+  | @(ex_intro ?? (mk_config ?? tc_false (midtape ? ls c rs)))
     % 
     [ %
       [ whd in ⊢ (??%?); >tc_q0_q2 //
-      | #Hfalse destruct (Hfalse) ]
+      | whd in ⊢ ((??%%)→?); #Hfalse destruct (Hfalse) ]
     | #_ #c0 #Hc0 % // normalize in Hc0; destruct (Hc0) //
     ]
   ]
diff --git a/matita/matita/lib/turing/universal/tuples.ma b/matita/matita/lib/turing/universal/tuples.ma
index 909c817e2..f13e1dd73 100644
--- a/matita/matita/lib/turing/universal/tuples.ma
+++ b/matita/matita/lib/turing/universal/tuples.ma
@@ -51,7 +51,33 @@ qed.
 
 definition mk_tuple ≝ λqin,cin,qout,cout,mv.
   qin @ cin :: 〈comma,false〉:: qout @ cout :: 〈comma,false〉 :: [mv].
+
+axiom num_of_state : ∀state:FinSet. state → list (unialpha × bool).
+
+definition tuple_of_pair ≝ λstates: FinSet.
+  λhalt:states →bool. 
+  λp: (states × (option FinBool)) × (states × (option (FinBool × move))).
+  let 〈inp,outp〉 ≝ p in
+  let 〈q,a〉 ≝ inp in
+  let cin ≝ match a with [ None ⇒ null | Some b ⇒ bit b ] in
+  let 〈qn,action〉 ≝ outp in
+  let 〈cout,mv〉 ≝ 
+    match action with 
+    [ None ⇒ 〈null,null〉
+    | Some act ⇒ let 〈na,m〉 ≝ act in 
+      match m with 
+      [ R ⇒ 〈bit na,bit true〉
+      | L ⇒ 〈bit na,bit false〉
+      | N ⇒ 〈bit na,null〉]
+    ] in
+  let qin ≝ num_of_state states q in
+  let qout ≝ num_of_state states qn in
+  mk_tuple qin 〈cin,false〉 qout 〈cout,false〉 〈mv,false〉.
+
+
   
+  
+
 (* by definition, a tuple is not marked *)
 definition tuple_TM : nat → list STape → Prop ≝ 
  λn,t.∃qin,cin,qout,cout,mv.
@@ -487,6 +513,7 @@ generalize in match Hc; generalize in match Hl2; cases l2
    ]
 qed.
 *)
+
 definition init_current ≝ 
   seq ? (adv_to_mark_l ? (is_marked ?))
     (seq ? (clear_mark ?)
-- 
2.39.2