helm/software/matita/contribs/ng_assembly2/emulator/opcodes/IP2022_instr_mode.ma

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   3 (*      ||M||                                                             *)
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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 "emulator/opcodes/IP2022_instr_mode_base.ma".
  24
  25 nlemma eq_to_eqIP2022im : ∀n1,n2.n1 = n2 → eq_IP2022_im n1 n2 = true.
  26  #n1; #n2; #H;
  27  nrewrite > H;
  28  nelim n2;
  29  ##[ ##4,11,12: #o; nrewrite > (eq_to_eqoct … (refl_eq …))
  30  ##| ##6: #t; nrewrite > (eq_to_eqbit … (refl_eq …)) ##]
  31  nnormalize;
  32  napply refl_eq.
  33 nqed.
  34
  35 nlemma neqIP2022im_to_neq : ∀n1,n2.eq_IP2022_im n1 n2 = false → n1 ≠ n2.
  36  #n1; #n2; #H;
  37  napply (not_to_not (n1 = n2) (eq_IP2022_im n1 n2 = true) …);
  38  ##[ ##1: napply (eq_to_eqIP2022im n1 n2)
  39  ##| ##2: napply (eqfalse_to_neqtrue … H)
  40  ##]
  41 nqed.
  42
  43 (* !!! per brevita... *)
  44 naxiom eqIP2022im_to_eq : ∀c1,c2.eq_IP2022_im c1 c2 = true → c1 = c2.
  45
  46 nlemma neq_to_neqIP2022im : ∀n1,n2.n1 ≠ n2 → eq_IP2022_im n1 n2 = false.
  47  #n1; #n2; #H;
  48  napply (neqtrue_to_eqfalse (eq_IP2022_im n1 n2));
  49  napply (not_to_not (eq_IP2022_im n1 n2 = true) (n1 = n2) ? H);
  50  napply (eqIP2022im_to_eq n1 n2).
  51 nqed.
  52
  53 nlemma decidable_IP2022im : ∀x,y:IP2022_instr_mode.decidable (x = y).
  54  #x; #y; nnormalize;
  55  napply (or2_elim (eq_IP2022_im x y = true) (eq_IP2022_im x y = false) ? (decidable_bexpr ?));
  56  ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqIP2022im_to_eq … H))
  57  ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqIP2022im_to_neq … H))
  58  ##]
  59 nqed.
  60
  61 nlemma symmetric_eqIP2022im : symmetricT IP2022_instr_mode bool eq_IP2022_im.
  62  #n1; #n2;
  63  napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_IP2022im n1 n2));
  64  ##[ ##1: #H; nrewrite > H; napply refl_eq
  65  ##| ##2: #H; nrewrite > (neq_to_neqIP2022im n1 n2 H);
  66           napply (symmetric_eq ? (eq_IP2022_im n2 n1) false);
  67           napply (neq_to_neqIP2022im n2 n1 (symmetric_neq ? n1 n2 H))
  68  ##]
  69 nqed.
  70
  71 nlemma IP2022im_is_comparable : comparable.
  72  @ IP2022_instr_mode
  73   ##[ napply MODE_INH
  74   ##| napply forall_IP2022_im
  75   ##| napply eq_IP2022_im
  76   ##| napply eqIP2022im_to_eq
  77   ##| napply eq_to_eqIP2022im
  78   ##| napply neqIP2022im_to_neq
  79   ##| napply neq_to_neqIP2022im
  80   ##| napply decidable_IP2022im
  81   ##| napply symmetric_eqIP2022im
  82   ##]
  83 nqed.
  84
  85 unification hint 0 ≔ ⊢ carr IP2022im_is_comparable ≡ IP2022_instr_mode.