+qed.
+
+
+(* some basic properties of and - or*)
+theorem andb_sym: \forall A,B:bool.
+(A \land B) = (B \land A).
+intros.
+elim A;
+ elim B;
+ simplify;
+ reflexivity.
+qed.
+
+theorem andb_assoc: \forall A,B,C:bool.
+(A \land (B \land C)) = ((A \land B) \land C).
+intros.
+elim A;
+ elim B;
+ elim C;
+ simplify;
+ reflexivity.
+qed.
+
+theorem orb_sym: \forall A,B:bool.
+(A \lor B) = (B \lor A).
+intros.
+elim A;
+ elim B;
+ simplify;
+ reflexivity.
+qed.
+
+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.
+reflexivity.
+qed.
\ No newline at end of file