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[helm.git] / matitaB / matita / library / Q / ratio / rinv.ma

diff --git a/matitaB/matita/library/Q/ratio/rinv.ma b/matitaB/matita/library/Q/ratio/rinv.ma
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+(**************************************************************************)
+(*       ___                                                               *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
+(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU Lesser General Public License Version 2.1         *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "Q/ratio/ratio.ma".
+include "Q/fraction/finv.ma".
+
+definition rinv : ratio \to ratio \def
+\lambda r:ratio.
+  match r with
+  [one \Rightarrow one
+  | (frac f) \Rightarrow frac (finv f)].
+
+theorem rinv_rinv: ∀r. rinv (rinv r) = r.
+ intro;
+ elim r;
+  [ reflexivity
+  | simplify;
+    rewrite > finv_finv;
+    reflexivity]
+qed.