1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* ********************************************************************** *)
16 (* Progetto FreeScale *)
18 (* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
19 (* Sviluppo: 2008-2010 *)
21 (* ********************************************************************** *)
23 include "emulator/opcodes/Freescale_instr_mode_base.ma".
24 include "common/comp.ma".
25 include "num/bool_lemmas.ma".
27 nlemma eq_to_eqFreescaleim :
28 ∀n1,n2.n1 = n2 → eq_Freescale_im n1 n2 = true.
32 ##[ ##31,32: #o; nrewrite > (eq_to_eqc … (refl_eq …))
33 ##| ##33: #e; nrewrite > (eq_to_eqc … (refl_eq …))
34 ##| ##34: #t; nrewrite > (eq_to_eqc … (refl_eq …)) ##]
38 nlemma neqFreescaleim_to_neq : ∀n1,n2.eq_Freescale_im n1 n2 = false → n1 ≠ n2.
40 napply (not_to_not (n1 = n2) (eq_Freescale_im n1 n2 = true) …);
41 ##[ ##1: napply (eq_to_eqFreescaleim n1 n2)
42 ##| ##2: napply (eqfalse_to_neqtrue … H)
46 (* !!! per brevita... *)
47 naxiom eqFreescaleim_to_eq : ∀c1,c2.eq_Freescale_im c1 c2 = true → c1 = c2.
49 nlemma neq_to_neqFreescaleim : ∀n1,n2.n1 ≠ n2 → eq_Freescale_im n1 n2 = false.
51 napply (neqtrue_to_eqfalse (eq_Freescale_im n1 n2));
52 napply (not_to_not (eq_Freescale_im n1 n2 = true) (n1 = n2) ? H);
53 napply (eqFreescaleim_to_eq n1 n2).
56 nlemma decidable_Freescaleim : ∀x,y:Freescale_instr_mode.decidable (x = y).
58 napply (or2_elim (eq_Freescale_im x y = true) (eq_Freescale_im x y = false) ? (decidable_bexpr ?));
59 ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqFreescaleim_to_eq … H))
60 ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqFreescaleim_to_neq … H))
64 nlemma symmetric_eqFreescaleim : symmetricT Freescale_instr_mode bool eq_Freescale_im.
66 napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_Freescaleim n1 n2));
67 ##[ ##1: #H; nrewrite > H; napply refl_eq
68 ##| ##2: #H; nrewrite > (neq_to_neqFreescaleim n1 n2 H);
69 napply (symmetric_eq ? (eq_Freescale_im n2 n1) false);
70 napply (neq_to_neqFreescaleim n2 n1 (symmetric_neq ? n1 n2 H))
74 nlemma Freescaleim_is_comparable : comparable.
75 @ Freescale_instr_mode
77 ##| napply forall_Freescale_im
78 ##| napply eq_Freescale_im
79 ##| napply eqFreescaleim_to_eq
80 ##| napply eq_to_eqFreescaleim
81 ##| napply neqFreescaleim_to_neq
82 ##| napply neq_to_neqFreescaleim
83 ##| napply decidable_Freescaleim
84 ##| napply symmetric_eqFreescaleim
88 unification hint 0 ≔ ⊢ carr Freescaleim_is_comparable ≡ Freescale_instr_mode.