helm/software/matita/contribs/ng_assembly/freescale/multivm_lemmas.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 (* ********************************************************************** *)
  16 (*                          Progetto FreeScale                            *)
  17 (*                                                                        *)
  18 (*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
  19 (*   Ultima modifica: 05/08/2009                                          *)
  20 (*                                                                        *)
  21 (* ********************************************************************** *)
  22
  23 include "freescale/multivm.ma".
  24 include "common/nat_lemmas.ma".
  25
  26 nlemma breakpoint_err : ∀m,t,s,err,n.execute m t (TickERR ? s err) n = TickERR ? s err.
  27  #m; #t; #s; #err; #n;
  28  ncases n;
  29  ##[ ##2: #n1; ##]
  30  nnormalize;
  31  napply refl_eq.
  32 nqed.
  33
  34 nlemma breakpoint_susp : ∀m,t,s,susp,n.execute m t (TickSUSP ? s susp) n = TickSUSP ? s susp.
  35  #m; #t; #s; #susp; #n;
  36  ncases n;
  37  ##[ ##2: #n1; ##]
  38  nnormalize;
  39  napply refl_eq.
  40 nqed.
  41
  42 nlemma breakpoint :
  43  ∀m,t,n1,n2,s. execute m t s (n1 + n2) = execute m t (execute m t s n1) n2.
  44  #m; #t; #n1;
  45  nelim n1;
  46  ##[ ##1: nnormalize; #n2; #s; ncases s; nnormalize; ##[ ##1,2: #x ##] #y; napply refl_eq
  47  ##| ##2: #n3; #H; #n2; #s; ncases s;
  48           ##[ ##1: #x; #y; nnormalize; nrewrite > (breakpoint_err m t x y n2); napply refl_eq
  49           ##| ##2: #x; #y; nnormalize; nrewrite > (breakpoint_susp m t x y n2); napply refl_eq
  50           ##| ##3: #x; nrewrite > (Sn_p_n_to_S_npn n3 n2);
  51                    nchange with ((execute m t (tick m t x) (n3+n2)) =
  52                                  (execute m t (execute m t (tick m t x) n3) n2));
  53                    nrewrite > (H n2 (tick m t x));
  54                    napply refl_eq
  55           ##]
  56  ##]
  57 nqed.