helm/software/matita/contribs/ng_assembly/emulator/opcodes/IP2022_instr_mode_lemmas.ma

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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/IP2022_instr_mode.ma".
  25 include "num/oct_lemmas.ma".
  26 include "num/bitrigesim_lemmas.ma".
  27
  28 nlemma eq_to_eqIP2022im : ∀n1,n2.n1 = n2 → eq_IP2022_im n1 n2 = true.
  29  #n1; #n2; #H;
  30  nrewrite > H;
  31  nelim n2;
  32  ##[ ##4,11,12: #o; nrewrite > (eq_to_eqoct … (refl_eq …))
  33  ##| ##6: #t; nrewrite > (eq_to_eqbit … (refl_eq …)) ##]
  34  nnormalize;
  35  napply refl_eq.
  36 nqed.
  37
  38 nlemma neqIP2022im_to_neq : ∀n1,n2.eq_IP2022_im n1 n2 = false → n1 ≠ n2.
  39  #n1; #n2; #H;
  40  napply (not_to_not (n1 = n2) (eq_IP2022_im n1 n2 = true) …);
  41  ##[ ##1: napply (eq_to_eqIP2022im n1 n2)
  42  ##| ##2: napply (eqfalse_to_neqtrue … H)
  43  ##]
  44 nqed.
  45
  46 (* !!! per brevita... *)
  47 naxiom eqIP2022im_to_eq : ∀c1,c2.eq_IP2022_im c1 c2 = true → c1 = c2.
  48
  49 nlemma neq_to_neqIP2022im : ∀n1,n2.n1 ≠ n2 → eq_IP2022_im n1 n2 = false.
  50  #n1; #n2; #H;
  51  napply (neqtrue_to_eqfalse (eq_IP2022_im n1 n2));
  52  napply (not_to_not (eq_IP2022_im n1 n2 = true) (n1 = n2) ? H);
  53  napply (eqIP2022im_to_eq n1 n2).
  54 nqed.
  55
  56 nlemma decidable_IP2022im : ∀x,y:IP2022_instr_mode.decidable (x = y).
  57  #x; #y; nnormalize;
  58  napply (or2_elim (eq_IP2022_im x y = true) (eq_IP2022_im x y = false) ? (decidable_bexpr ?));
  59  ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqIP2022im_to_eq … H))
  60  ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqIP2022im_to_neq … H))
  61  ##]
  62 nqed.
  63
  64 nlemma symmetric_eqIP2022im : symmetricT IP2022_instr_mode bool eq_IP2022_im.
  65  #n1; #n2;
  66  napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_IP2022im n1 n2));
  67  ##[ ##1: #H; nrewrite > H; napply refl_eq
  68  ##| ##2: #H; nrewrite > (neq_to_neqIP2022im n1 n2 H);
  69           napply (symmetric_eq ? (eq_IP2022_im n2 n1) false);
  70           napply (neq_to_neqIP2022im n2 n1 (symmetric_neq ? n1 n2 H))
  71  ##]
  72 nqed.