flase => false :-)

[helm.git] / matita / library / datatypes / bool.ma

diff --git a/matita/library/datatypes/bool.ma b/matita/library/datatypes/bool.ma
index b5abbb35d2b3748630fcc3faee802b9f608e7433..dc397a1b2d978996f32ca319b8b3befe2cad1493 100644 (file)
--- a/matita/library/datatypes/bool.ma
+++ b/matita/library/datatypes/bool.ma
@@ -15,6 +15,7 @@
 set "baseuri" "cic:/matita/datatypes/bool/".
 
 include "logic/equality.ma".
+include "higher_order_defs/functions.ma".
 
 inductive bool : Set \def 
   | true : bool
@@ -36,7 +37,7 @@ unfold Not.intro.
 change with 
 match true with
 [ true \Rightarrow False
-| flase \Rightarrow True].
+| false \Rightarrow True].
 rewrite > H.simplify.exact I.
 qed.
 
@@ -53,6 +54,20 @@ match b with
 intros 2.elim b.exact H. exact H.
 qed.
 
+theorem notb_notb: \forall b:bool. notb (notb b) = b.
+intros.
+elim b;reflexivity.
+qed.
+
+theorem injective_notb: injective bool bool notb.
+unfold injective.
+intros.
+rewrite < notb_notb.
+rewrite < (notb_notb y).
+apply eq_f.
+assumption.
+qed.
+
 (*CSC: the URI must disappear: there is a bug now *)
 interpretation "boolean not" 'not x = (cic:/matita/datatypes/bool/notb.con x).
 
@@ -72,6 +87,18 @@ match b1 with
 intros 3.elim b1.exact H. exact H.
 qed.
 
+theorem and_true: \forall a,b:bool. 
+andb a b =true \to a =true \land b= true.
+intro.elim a
+  [split
+    [reflexivity|assumption]
+  |apply False_ind.
+   apply not_eq_true_false.
+   apply sym_eq.
+   assumption
+  ]
+qed.
+
 theorem andb_true_true: \forall b1,b2. (b1 \land b2) = true \to b1 = true.
 intro. elim b1.
 reflexivity.
@@ -163,11 +190,10 @@ elim A;
     reflexivity.
 qed.
 
-theorem andb_t_t_t: \forall A,B,C:bool.
-A = true \to B = true \to C = true \to (A \land (B \land C)) = true.
+theorem true_to_true_to_andb_true: \forall A,B:bool.
+A = true \to B = true \to (A \land B) = true.
 intros.
 rewrite > H.
 rewrite > H1.
-rewrite > H2.
 reflexivity.
 qed.
\ No newline at end of file