helm/software/matita/contribs/ng_assembly/emulator/opcodes/HC08_instr_mode_lemmas.ma

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  16 (*                          Progetto FreeScale                            *)
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  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/HC08_instr_mode.ma".
  25 include "num/oct_lemmas.ma".
  26
  27 nlemma eq_to_eqHC08im : ∀n1,n2.n1 = n2 → eq_HC08_im n1 n2 = true.
  28  #n1; #n2; #H;
  29  nrewrite > H;
  30  nelim n2;
  31  ##[ ##31,32: #o; nrewrite > (eq_to_eqoct … (refl_eq …)) ##]
  32  nnormalize;
  33  napply refl_eq.
  34 nqed.
  35
  36 nlemma neqHC08im_to_neq : ∀n1,n2.eq_HC08_im n1 n2 = false → n1 ≠ n2.
  37  #n1; #n2; #H;
  38  napply (not_to_not (n1 = n2) (eq_HC08_im n1 n2 = true) …);
  39  ##[ ##1: napply (eq_to_eqHC08im n1 n2)
  40  ##| ##2: napply (eqfalse_to_neqtrue … H)
  41  ##]
  42 nqed.
  43
  44 (* !!! per brevita... *)
  45 naxiom eqHC08im_to_eq : ∀c1,c2.eq_HC08_im c1 c2 = true → c1 = c2.
  46
  47 nlemma neq_to_neqHC08im : ∀n1,n2.n1 ≠ n2 → eq_HC08_im n1 n2 = false.
  48  #n1; #n2; #H;
  49  napply (neqtrue_to_eqfalse (eq_HC08_im n1 n2));
  50  napply (not_to_not (eq_HC08_im n1 n2 = true) (n1 = n2) ? H);
  51  napply (eqHC08im_to_eq n1 n2).
  52 nqed.
  53
  54 nlemma decidable_HC08im : ∀x,y:HC08_instr_mode.decidable (x = y).
  55  #x; #y; nnormalize;
  56  napply (or2_elim (eq_HC08_im x y = true) (eq_HC08_im x y = false) ? (decidable_bexpr ?));
  57  ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqHC08im_to_eq … H))
  58  ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqHC08im_to_neq … H))
  59  ##]
  60 nqed.
  61
  62 nlemma symmetric_eqHC08im : symmetricT HC08_instr_mode bool eq_HC08_im.
  63  #n1; #n2;
  64  napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_HC08im n1 n2));
  65  ##[ ##1: #H; nrewrite > H; napply refl_eq
  66  ##| ##2: #H; nrewrite > (neq_to_neqHC08im n1 n2 H);
  67           napply (symmetric_eq ? (eq_HC08_im n2 n1) false);
  68           napply (neq_to_neqHC08im n2 n1 (symmetric_neq ? n1 n2 H))
  69  ##]
  70 nqed.