matita/matita/contribs/lambda/preamble.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "arithmetics/nat.ma".
  16
  17 include "xoa_notation.ma".
  18 include "xoa.ma".
  19
  20 (* Note: For some reason this cannot be in the standard library *)
  21 interpretation "logical false" 'false = False.
  22
  23 notation "⊥"
  24   non associative with precedence 90
  25   for @{'false}.
  26
  27 lemma lt_refl_false: ∀n. n < n → ⊥.
  28 #n #H elim (lt_to_not_eq … H) -H /2 width=1/
  29 qed-.
  30
  31 lemma lt_zero_false: ∀n. n < 0 → ⊥.
  32 #n #H elim (lt_to_not_le … H) -H /2 width=1/
  33 qed-.