helm/software/matita/library/Q/fraction/finv.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 "Z/plus.ma".
  16 include "Q/fraction/fraction.ma".
  17
  18 let rec finv f ≝
  19   match f with
  20   [ pp n ⇒ nn n
  21   | nn n ⇒ pp n
  22   | cons x g ⇒ cons (Zopp x) (finv g)].
  23
  24 theorem finv_finv: ∀f. finv (finv f) = f.
  25  intro;
  26  elim f;
  27   [1,2: reflexivity
  28   | simplify;
  29     rewrite > H;
  30     rewrite > Zopp_Zopp;
  31     reflexivity
  32   ]
  33 qed.