matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_minus.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground_2/relocation/rtmap_tl.ma".
  16
  17 (* RELOCATION MAP ***********************************************************)
  18
  19 let rec minus (f:rtmap) (n:nat) on n: rtmap ≝ match n with
  20 [ O ⇒ f | S m ⇒ ↓(minus f m) ].
  21
  22 interpretation "minus (rtmap)" 'minus f n = (minus f n).
  23
  24 (* Basic properties *********************************************************)
  25
  26 lemma minus_rew_O: ∀f. f = f - 0.
  27 // qed.
  28
  29 lemma minus_rew_S: ∀f,n. ↓(f - n) = f - ⫯n.
  30 // qed.
  31
  32 lemma minus_eq_repl: ∀n. eq_repl (λf1,f2. f1 - n ≗ f2 - n).
  33 #n elim n -n /3 width=1 by tl_eq_repl/
  34 qed.
  35
  36 (* Advancedd properties *****************************************************)
  37
  38 lemma minus_xn: ∀n,f. (↓f) - n = f - ⫯n.
  39 #n elim n -n //
  40 qed.