X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Fturing%2Funiversal%2Falphabet.ma;h=4d87907d23130f1a6937a99ccd0d3df371bc9b31;hb=7d466423e4696ab52cca1068611ceb86c16136b8;hp=04701aeec180b8b868e7388f186cb173900bb2ef;hpb=67948c54e4e20ef530d2d2115c9a056275360012;p=helm.git

diff --git a/matita/matita/lib/turing/universal/alphabet.ma b/matita/matita/lib/turing/universal/alphabet.ma
index 04701aeec..4d87907d2 100644
--- a/matita/matita/lib/turing/universal/alphabet.ma
+++ b/matita/matita/lib/turing/universal/alphabet.ma
@@ -39,11 +39,20 @@ 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.
 
+(*************************** testing characters *******************************)
 definition is_bit ≝ λc.match c with [ bit _ ⇒ true | _ ⇒ false ].
 
 definition is_null ≝ λc.match c with [ null ⇒ true | _ ⇒ false ].
@@ -55,3 +64,42 @@ definition is_bar ≝ λc.match c with [ bar ⇒ true | _ ⇒ false ].
 definition is_comma ≝ λc.match c with [ comma ⇒ true | _ ⇒ false ].
 
 definition bit_or_null ≝ λc.is_bit c ∨ is_null c.
+
+lemma bit_not_grid: ∀d. is_bit d = true → is_grid d = false.
+* // normalize #H destruct
+qed.
+
+lemma bit_or_null_not_grid: ∀d. bit_or_null d = true → is_grid d = false.
+* // normalize #H destruct
+qed.
+
+lemma bit_not_bar: ∀d. is_bit d = true → is_bar d = false.
+* // normalize #H destruct
+qed.
+
+lemma bit_or_null_not_bar: ∀d. bit_or_null d = true → is_bar d = false.
+* // normalize #H destruct
+qed.
+(**************************** testing strings *********************************)
+definition is_marked ≝ λalpha.λp:FinProd … alpha FinBool.
+  let 〈x,b〉 ≝ p in b.
+
+definition STape ≝ FinProd … FSUnialpha FinBool.
+
+definition only_bits ≝ λl.
+  ∀c.memb STape c l = true → is_bit (\fst c) = true.
+
+definition only_bits_or_nulls ≝ λl.
+  ∀c.memb STape c l = true → bit_or_null (\fst c) = true.
+  
+definition no_grids ≝ λl.
+  ∀c.memb STape c l = true → is_grid (\fst c) = false.
+
+definition no_bars ≝ λl.
+  ∀c.memb STape c l = true → is_bar (\fst c) = false.
+
+definition no_marks ≝ λl.
+  ∀c.memb STape c l = true → is_marked ? c = false.
+
+definition bar_or_grid ≝ λc:STape.is_bar (\fst c) ∨ is_grid (\fst c).
+