helm/software/matita/library/Q/ratio/ratio.ma

   1 (**************************************************************************)
   2 (*       ___                                                                *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
   8 (*      ||A||       E.Tassi, S.Zacchiroli                                 *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU Lesser General Public License Version 2.1         *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "Q/fraction/fraction.ma".
  16
  17 inductive ratio : Set \def
  18       one :  ratio
  19     | frac : fraction \to ratio.
  20
  21 definition unfrac \def \lambda f.
  22 match f with
  23   [one \Rightarrow pp O
  24   |frac f \Rightarrow f
  25   ]
  26 .
  27
  28 lemma injective_frac: injective fraction ratio frac.
  29 unfold.intros.
  30 change with ((unfrac (frac x)) = (unfrac (frac y))).
  31 rewrite < H.reflexivity.
  32 qed.