matita/matita/contribs/lambdadelta/ground_2A/lib/bool.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "basics/bool.ma".
  16 include "ground_2A/lib/star.ma".
  17 include "ground_2A/notation/constructors/no_0.ma".
  18 include "ground_2A/notation/constructors/yes_0.ma".
  19
  20 (* BOOLEAN PROPERTIES *******************************************************)
  21
  22 interpretation "boolean false" 'no = false.
  23
  24 interpretation "boolean true" 'yes = true.
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma orb_false_r: ∀b1,b2:bool. (b1 ∨ b2) = false → b1 = false ∧ b2 = false.
  29 * normalize /2 width=1 by conj/ #b2 #H destruct
  30 qed-.
  31
  32 lemma commutative_orb: commutative … orb.
  33 * * // qed.
  34
  35 lemma eq_bool_dec: ∀b1,b2:bool. Decidable (b1 = b2).
  36 * * /2 width=1 by or_introl/
  37 @or_intror #H destruct
  38 qed-.