helm/software/matita/library/Q/ratio/rinv.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/ratio/ratio.ma".
  16 include "Q/fraction/finv.ma".
  17
  18 definition rinv : ratio \to ratio \def
  19 \lambda r:ratio.
  20   match r with
  21   [one \Rightarrow one
  22   | (frac f) \Rightarrow frac (finv f)].
  23
  24 theorem rinv_rinv: ∀r. rinv (rinv r) = r.
  25  intro;
  26  elim r;
  27   [ reflexivity
  28   | simplify;
  29     rewrite > finv_finv;
  30     reflexivity]
  31 qed.