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[helm.git] / matitaB / matita / contribs / ng_assembly / emulator / opcodes / Freescale_pseudo_lemmas.ma

diff --git a/matitaB/matita/contribs/ng_assembly/emulator/opcodes/Freescale_pseudo_lemmas.ma b/matitaB/matita/contribs/ng_assembly/emulator/opcodes/Freescale_pseudo_lemmas.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(*                          Progetto FreeScale                            *)
+(*                                                                        *)
+(*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
+(*   Sviluppo: 2008-2010                                                  *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "num/bool_lemmas.ma".
+include "emulator/opcodes/Freescale_pseudo.ma".
+
+nlemma eq_to_eqFreescalepseudo : ∀n1,n2.n1 = n2 → eq_Freescale_pseudo n1 n2 = true.
+ #n1; #n2; #H;
+ nrewrite > H;
+ nelim n2;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma neqFreescalepseudo_to_neq : ∀n1,n2.eq_Freescale_pseudo n1 n2 = false → n1 ≠ n2.
+ #n1; #n2; #H;
+ napply (not_to_not (n1 = n2) (eq_Freescale_pseudo n1 n2 = true) …);
+ ##[ ##1: napply (eq_to_eqFreescalepseudo n1 n2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
+ ##]
+nqed.
+
+(* !!! per brevita... *)
+naxiom eqFreescalepseudo_to_eq : ∀c1,c2.eq_Freescale_pseudo c1 c2 = true → c1 = c2.
+
+nlemma neq_to_neqFreescalepseudo : ∀n1,n2.n1 ≠ n2 → eq_Freescale_pseudo n1 n2 = false.
+ #n1; #n2; #H;
+ napply (neqtrue_to_eqfalse (eq_Freescale_pseudo n1 n2));
+ napply (not_to_not (eq_Freescale_pseudo n1 n2 = true) (n1 = n2) ? H);
+ napply (eqFreescalepseudo_to_eq n1 n2).
+nqed.
+
+nlemma decidable_Freescalepseudo : ∀x,y:Freescale_pseudo.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_Freescale_pseudo x y = true) (eq_Freescale_pseudo x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqFreescalepseudo_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqFreescalepseudo_to_neq … H))
+ ##]
+nqed.
+
+nlemma symmetric_eqFreescalepseudo : symmetricT Freescale_pseudo bool eq_Freescale_pseudo.
+ #n1; #n2;
+ napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_Freescalepseudo n1 n2));
+ ##[ ##1: #H; nrewrite > H; napply refl_eq
+ ##| ##2: #H; nrewrite > (neq_to_neqFreescalepseudo n1 n2 H);
+          napply (symmetric_eq ? (eq_Freescale_pseudo n2 n1) false);
+          napply (neq_to_neqFreescalepseudo n2 n1 (symmetric_neq ? n1 n2 H))
+ ##]
+nqed.