helm/software/matita/library/Q/q/qinv.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/q/q.ma".
  16 include "Q/ratio/rinv.ma".
  17
  18 definition Qinv : Q → Q ≝
  19  λp.
  20   match p with
  21    [ OQ ⇒ OQ  (* arbitrary value *)
  22    | Qpos r ⇒ Qpos (rinv r)
  23    | Qneg r ⇒ Qneg (rinv r)
  24    ].
  25
  26 theorem Qinv_Qinv: ∀q. Qinv (Qinv q) = q.
  27  intro;
  28  elim q;
  29   [ reflexivity
  30   |*:simplify;
  31     rewrite > rinv_rinv;
  32     reflexivity]
  33 qed.