--- /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 "ground/lib/bool.ma".
+
+(* CONJUNCTION FOR BOOLEANS *************************************************)
+
+(* Advanced constructions ***************************************************)
+
+lemma commutative_andb:
+ commutative … andb.
+* * // qed.
+
+lemma andb_false_dx (b):
+ (b ∧ Ⓕ) = Ⓕ.
+* // qed.
+
+lemma andb_false_sn (b):
+ (Ⓕ ∧ b) = Ⓕ.
+// qed.
+
+(* Advanced inversions ******************************************************)
+
+lemma andb_inv_true_dx (b1) (b2):
+ (b1 ∧ b2) = Ⓣ → ∧∧ b1 = Ⓣ & b2 = Ⓣ.
+* normalize /2 width=1 by conj/ #b2 #H destruct
+qed-.