freescale porting, work in progress

[helm.git] / helm / software / matita / contribs / ng_assembly / freescale / opcode_base_lemmas1.ma

diff --git a/helm/software/matita/contribs/ng_assembly/freescale/opcode_base_lemmas1.ma b/helm/software/matita/contribs/ng_assembly/freescale/opcode_base_lemmas1.ma
new file mode 100755 (executable)
index 0000000..ba63e60
--- /dev/null
+++ b/helm/software/matita/contribs/ng_assembly/freescale/opcode_base_lemmas1.ma
@@ -0,0 +1,126 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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: Cosimo Oliboni, oliboni@cs.unibo.it                   *)
+(*     Cosimo Oliboni, oliboni@cs.unibo.it                                *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "freescale/opcode_base_lemmas_opcode2.ma".
+include "freescale/opcode_base_lemmas_instrmode2.ma".
+include "num/word16_lemmas.ma".
+
+(* ********************************************** *)
+(* MATTONI BASE PER DEFINIRE LE TABELLE DELLE MCU *)
+(* ********************************************** *)
+
+nlemma anyop_destruct : ∀m.∀x1,x2:opcode.anyOP m x1 = anyOP m x2 → x1 = x2.
+ #m; #x1; #x2; #H;
+ nchange with (match anyOP m x2 with [ anyOP a ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma symmetric_eqanyop : ∀m.∀op1,op2:any_opcode m.eq_anyop m op1 op2 = eq_anyop m op2 op1.
+ #m;
+ ncases m;
+ #op1; #op2;
+ ncases op1;
+ #x1;
+ ncases op2;
+ #x2;
+ nchange with (eq_op x1 x2 = eq_op x2 x1);
+ nrewrite > (symmetric_eqop x1 x2);
+ napply refl_eq.
+nqed.
+
+nlemma eqanyop_to_eq : ∀m.∀op1,op2:any_opcode m.eq_anyop m op1 op2 = true → op1 = op2.
+ #m;
+ ncases m;
+ #op1; #op2;
+ ncases op1;
+ #x1;
+ ncases op2;
+ #x2;
+ nchange with ((eq_op x1 x2 = true) → ?);
+ #H;
+ nrewrite > (eqop_to_eq … H);
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqanyop : ∀m.∀op1,op2:any_opcode m.op1 = op2 → eq_anyop m op1 op2 = true.
+ #m;
+ ncases m;
+ #op1; #op2;
+ ncases op1;
+ #p1;
+ ncases op2;
+ #p2; #H;
+ nrewrite > (anyop_destruct … H);
+ nchange with (eq_op p2 p2 = true);
+ nrewrite > (eq_to_eqop p2 p2 (refl_eq opcode p2));
+ napply refl_eq.
+nqed.
+
+nlemma b8w16_destruct_b8_b8 : ∀x1,x2.Byte x1 = Byte x2 → x1 = x2.
+ #x1; #x2; #H;
+ nchange with (match Byte x2 with [ Byte a ⇒ x1 = a | Word _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma b8w16_destruct_w16_w16 : ∀x1,x2.Word x1 = Word x2 → x1 = x2.
+ #x1; #x2; #H;
+ nchange with (match Word x2 with [ Word a ⇒ x1 = a | Byte _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma b8w16_destruct_b8_w16 : ∀x1,x2.Byte x1 = Word x2 → False.
+ #x1; #x2; #H;
+ nchange with (match Byte x1 with [ Word _ ⇒ True | Byte a ⇒ False ]);
+ nrewrite > H;
+ nnormalize;
+ napply I.
+nqed.
+
+nlemma b8w16_destruct_w16_b8 : ∀x1,x2.Word x1 = Byte x2 → False.
+ #x1; #x2; #H;
+ nchange with (match Word x1 with [ Word a ⇒ False | Byte _ ⇒ True ]);
+ nrewrite > H;
+ nnormalize;
+ napply I.
+nqed.
+
+nlemma symmetric_eqb8w16 : ∀bw1,bw2.eq_b8w16 bw1 bw2 = eq_b8w16 bw2 bw1.
+ #bw1; #bw2;
+ ncases bw1;
+ #x1;
+ ncases bw2;
+ #x2;
+ ##[ ##1: nchange with (eq_b8 x1 x2 = eq_b8 x2 x1);
+          nrewrite > (symmetric_eqb8 x1 x2);
+          napply refl_eq
+ ##| ##2,3: nnormalize; napply refl_eq
+ ##| ##4: nchange with (eq_w16 x1 x2 = eq_w16 x2 x1);
+          nrewrite > (symmetric_eqw16 x1 x2);
+          napply refl_eq
+ ##]
+nqed.