--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basics/bool.ma".
+include "ground_2/notation/constructors/no_0.ma".
+include "ground_2/notation/constructors/yes_0.ma".
+
+(* BOOLEAN PROPERTIES *******************************************************)
+
+interpretation "boolean false" 'no = false.
+
+interpretation "boolean true" 'yes = true.
+
+lemma orb_false_r: ∀b1,b2:bool. (b1 ∨ b2) = false → b1 = false ∧ b2 = false.
+* normalize /2 width=1 by conj/ #b2 #H destruct
+qed-.
+
+lemma commutative_orb: commutative … orb.
+* * // qed.