helm/software/matita/contribs/ng_assembly/emulator/opcodes/RS08_instr_mode_lemmas.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 (* ********************************************************************** *)
  16 (*                          Progetto FreeScale                            *)
  17 (*                                                                        *)
  18 (*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
  19 (*   Sviluppo: 2008-2010                                                  *)
  20 (*                                                                        *)
  21 (* ********************************************************************** *)
  22
  23 include "num/bool_lemmas.ma".
  24 include "emulator/opcodes/RS08_instr_mode.ma".
  25 include "num/oct_lemmas.ma".
  26 include "num/exadecim_lemmas.ma".
  27 include "num/bitrigesim_lemmas.ma".
  28
  29 nlemma eq_to_eqRS08im : ∀n1,n2.n1 = n2 → eq_RS08_im n1 n2 = true.
  30  #n1; #n2; #H;
  31  nrewrite > H;
  32  nelim n2;
  33  ##[ ##11,12: #o; nrewrite > (eq_to_eqoct … (refl_eq …))
  34  ##| ##13: #e; nrewrite > (eq_to_eqex … (refl_eq …))
  35  ##| ##14: #t; nrewrite > (eq_to_eqbit … (refl_eq …)) ##]
  36  nnormalize;
  37  napply refl_eq.
  38 nqed.
  39
  40 nlemma neqRS08im_to_neq : ∀n1,n2.eq_RS08_im n1 n2 = false → n1 ≠ n2.
  41  #n1; #n2; #H;
  42  napply (not_to_not (n1 = n2) (eq_RS08_im n1 n2 = true) …);
  43  ##[ ##1: napply (eq_to_eqRS08im n1 n2)
  44  ##| ##2: napply (eqfalse_to_neqtrue … H)
  45  ##]
  46 nqed.
  47
  48 (* !!! per brevita... *)
  49 naxiom eqRS08im_to_eq : ∀c1,c2.eq_RS08_im c1 c2 = true → c1 = c2.
  50
  51 nlemma neq_to_neqRS08im : ∀n1,n2.n1 ≠ n2 → eq_RS08_im n1 n2 = false.
  52  #n1; #n2; #H;
  53  napply (neqtrue_to_eqfalse (eq_RS08_im n1 n2));
  54  napply (not_to_not (eq_RS08_im n1 n2 = true) (n1 = n2) ? H);
  55  napply (eqRS08im_to_eq n1 n2).
  56 nqed.
  57
  58 nlemma decidable_RS08im : ∀x,y:RS08_instr_mode.decidable (x = y).
  59  #x; #y; nnormalize;
  60  napply (or2_elim (eq_RS08_im x y = true) (eq_RS08_im x y = false) ? (decidable_bexpr ?));
  61  ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqRS08im_to_eq … H))
  62  ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqRS08im_to_neq … H))
  63  ##]
  64 nqed.
  65
  66 nlemma symmetric_eqRS08im : symmetricT RS08_instr_mode bool eq_RS08_im.
  67  #n1; #n2;
  68  napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_RS08im n1 n2));
  69  ##[ ##1: #H; nrewrite > H; napply refl_eq
  70  ##| ##2: #H; nrewrite > (neq_to_neqRS08im n1 n2 H);
  71           napply (symmetric_eq ? (eq_RS08_im n2 n1) false);
  72           napply (neq_to_neqRS08im n2 n1 (symmetric_neq ? n1 n2 H))
  73  ##]
  74 nqed.