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/IP2022_pseudo_base.ma".
24 include "common/comp.ma".
25 include "num/bool_lemmas.ma".
27 nlemma eq_to_eqIP2022pseudo : ∀n1,n2.n1 = n2 → eq_IP2022_pseudo n1 n2 = true.
35 nlemma neqIP2022pseudo_to_neq : ∀n1,n2.eq_IP2022_pseudo n1 n2 = false → n1 ≠ n2.
37 napply (not_to_not (n1 = n2) (eq_IP2022_pseudo n1 n2 = true) …);
38 ##[ ##1: napply (eq_to_eqIP2022pseudo n1 n2)
39 ##| ##2: napply (eqfalse_to_neqtrue … H)
43 (* !!! per brevita... *)
44 naxiom eqIP2022pseudo_to_eq : ∀c1,c2.eq_IP2022_pseudo c1 c2 = true → c1 = c2.
46 nlemma neq_to_neqIP2022pseudo : ∀n1,n2.n1 ≠ n2 → eq_IP2022_pseudo n1 n2 = false.
48 napply (neqtrue_to_eqfalse (eq_IP2022_pseudo n1 n2));
49 napply (not_to_not (eq_IP2022_pseudo n1 n2 = true) (n1 = n2) ? H);
50 napply (eqIP2022pseudo_to_eq n1 n2).
53 nlemma decidable_IP2022pseudo : ∀x,y:IP2022_pseudo.decidable (x = y).
55 napply (or2_elim (eq_IP2022_pseudo x y = true) (eq_IP2022_pseudo x y = false) ? (decidable_bexpr ?));
56 ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqIP2022pseudo_to_eq … H))
57 ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqIP2022pseudo_to_neq … H))
61 nlemma symmetric_eqIP2022pseudo : symmetricT IP2022_pseudo bool eq_IP2022_pseudo.
63 napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_IP2022pseudo n1 n2));
64 ##[ ##1: #H; nrewrite > H; napply refl_eq
65 ##| ##2: #H; nrewrite > (neq_to_neqIP2022pseudo n1 n2 H);
66 napply (symmetric_eq ? (eq_IP2022_pseudo n2 n1) false);
67 napply (neq_to_neqIP2022pseudo n2 n1 (symmetric_neq ? n1 n2 H))
71 nlemma IP2022pseudo_is_comparable : comparable.
74 ##| napply forall_IP2022_pseudo
75 ##| napply eq_IP2022_pseudo
76 ##| napply eqIP2022pseudo_to_eq
77 ##| napply eq_to_eqIP2022pseudo
78 ##| napply neqIP2022pseudo_to_neq
79 ##| napply neq_to_neqIP2022pseudo
80 ##| napply decidable_IP2022pseudo
81 ##| napply symmetric_eqIP2022pseudo
85 unification hint 0 ≔ ⊢ carr IP2022pseudo_is_comparable ≡ IP2022_pseudo.