propagating the arithmetics library, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / lib / bool_and.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/bool_and.ma b/matita/matita/contribs/lambdadelta/ground/lib/bool_and.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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-.