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
index 7deed371672ed12fd9c9256e891de68149ac59bd..78a284c30224a49246ee638633eb3bf76d543e1e 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/freescale/opcode_base_lemmas1.ma
+++ b/helm/software/matita/contribs/ng_assembly/freescale/opcode_base_lemmas1.ma
@@ -15,14 +15,14 @@
 (* ********************************************************************** *)
 (*                          Progetto FreeScale                            *)
 (*                                                                        *)
-(*   Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it                   *)
-(*     Cosimo Oliboni, oliboni@cs.unibo.it                                *)
+(*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
+(*   Ultima modifica: 05/08/2009                                          *)
 (*                                                                        *)
 (* ********************************************************************** *)
 
-include "freescale/opcode_base_lemmas_opcode2.ma".
-include "freescale/opcode_base_lemmas_instrmode2.ma".
-include "freescale/word16_lemmas.ma".
+include "freescale/opcode_base_lemmas_opcode.ma".
+include "freescale/opcode_base_lemmas_instrmode.ma".
+include "num/word16_lemmas.ma".
 
 (* ********************************************** *)
 (* MATTONI BASE PER DEFINIRE LE TABELLE DELLE MCU *)
@@ -33,7 +33,7 @@ nlemma anyop_destruct : ∀m.∀x1,x2:opcode.anyOP m x1 = anyOP m x2 → x1 = x2
  nchange with (match anyOP m x2 with [ anyOP a ⇒ x1 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma symmetric_eqanyop : ∀m.∀op1,op2:any_opcode m.eq_anyop m op1 op2 = eq_anyop m op2 op1.
@@ -46,7 +46,7 @@ nlemma symmetric_eqanyop : ∀m.∀op1,op2:any_opcode m.eq_anyop m op1 op2 = eq_
  #x2;
  nchange with (eq_op x1 x2 = eq_op x2 x1);
  nrewrite > (symmetric_eqop x1 x2);
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma eqanyop_to_eq : ∀m.∀op1,op2:any_opcode m.eq_anyop m op1 op2 = true → op1 = op2.
@@ -59,8 +59,8 @@ nlemma eqanyop_to_eq : ∀m.∀op1,op2:any_opcode m.eq_anyop m op1 op2 = true 
  #x2;
  nchange with ((eq_op x1 x2 = true) → ?);
  #H;
- nrewrite > (eqop_to_eq ?? H);
- napply (refl_eq ??).
+ 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.
@@ -71,10 +71,39 @@ nlemma eq_to_eqanyop : ∀m.∀op1,op2:any_opcode m.op1 = op2 → eq_anyop m op1
  #p1;
  ncases op2;
  #p2; #H;
- nrewrite > (anyop_destruct ??? 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 ??).
+ napply refl_eq.
+nqed.
+
+nlemma decidable_anyop : ∀m.∀x,y:any_opcode m.decidable (x = y).
+ #m; #x; nelim x; #e1; #y; nelim y; #e2;
+ nnormalize;
+ napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_op e1 e2) …);
+ ##[ ##2: #H; napply (or2_intro2 (? = ?) (? ≠ ?) … ); nnormalize; #H1; napply (H (anyop_destruct m … H1))
+ ##| ##1: #H; nrewrite > H; napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …))
+ ##]
+nqed.
+
+nlemma neqanyop_to_neq : ∀m.∀op1,op2:any_opcode m.(eq_anyop m op1 op2 = false) → (op1 ≠ op2).
+ #m; #op1; nelim op1; #e1; #op2; nelim op2; #e2;
+ nchange with (((eq_op e1 e2) = false) → ?);
+ #H;
+ nnormalize;
+ #H1;
+ napply (neqop_to_neq … H);
+ napply (anyop_destruct m … H1).
+nqed.
+
+nlemma neq_to_neqanyop : ∀m.∀op1,op2:any_opcode m.op1 ≠ op2 → eq_anyop m op1 op2 = false.
+ #m; #op1; nelim op1; #e1; #op2; nelim op2; #e2;
+ #H; nchange with ((eq_op e1 e2) = false);
+ napply (neq_to_neqop e1 e2 ?);
+ nnormalize;
+ #H1;
+ nrewrite > H1 in H:(%); #H;
+ napply (H (refl_eq …)).
 nqed.
 
 nlemma b8w16_destruct_b8_b8 : ∀x1,x2.Byte x1 = Byte x2 → x1 = x2.
@@ -82,7 +111,7 @@ nlemma b8w16_destruct_b8_b8 : ∀x1,x2.Byte x1 = Byte x2 → x1 = x2.
  nchange with (match Byte x2 with [ Byte a ⇒ x1 = a | Word _ ⇒ False ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma b8w16_destruct_w16_w16 : ∀x1,x2.Word x1 = Word x2 → x1 = x2.
@@ -90,7 +119,7 @@ nlemma b8w16_destruct_w16_w16 : ∀x1,x2.Word x1 = Word x2 → x1 = x2.
  nchange with (match Word x2 with [ Word a ⇒ x1 = a | Byte _ ⇒ False ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma b8w16_destruct_b8_w16 : ∀x1,x2.Byte x1 = Word x2 → False.
@@ -117,10 +146,63 @@ nlemma symmetric_eqb8w16 : ∀bw1,bw2.eq_b8w16 bw1 bw2 = eq_b8w16 bw2 bw1.
  #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 ??)
+          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 ??)
+          napply refl_eq
+ ##]
+nqed.
+
+nlemma eqb8w16_to_eq : ∀bw1,bw2.eq_b8w16 bw1 bw2 = true → bw1 = bw2.
+ #bw1; #bw2;
+ ncases bw1; #e1; ncases bw2; #e2;
+ ##[ ##1: nchange with ((eq_b8 e1 e2 = true) → ?); #H; nrewrite > (eqb8_to_eq … H); napply refl_eq
+ ##| ##2,3: nnormalize; #H; napply (bool_destruct … H)
+ ##| ##4: nchange with ((eq_w16 e1 e2 = true) → ?); #H; nrewrite > (eqw16_to_eq … H); napply refl_eq
+ ##]
+nqed.
+
+nlemma eq_to_eqb8w16 : ∀bw1,bw2.bw1 = bw2 → eq_b8w16 bw1 bw2 = true.
+ #bw1; #bw2;
+ ncases bw1; #e1; ncases bw2; #e2;
+ ##[ ##1: #H; nrewrite > (b8w16_destruct_b8_b8 … H);
+          nchange with (eq_b8 e2 e2 = true);
+          nrewrite > (eq_to_eqb8 e2 e2 (refl_eq …));
+          napply refl_eq
+ ##| ##2: #H; nelim (b8w16_destruct_b8_w16 … H)
+ ##| ##3: #H; nelim (b8w16_destruct_w16_b8 … H);
+ ##| ##4: #H; nrewrite > (b8w16_destruct_w16_w16 … H);
+          nchange with (eq_w16 e2 e2 = true);
+          nrewrite > (eq_to_eqw16 e2 e2 (refl_eq …));
+          napply refl_eq
+ ##]
+nqed.
+
+nlemma decidable_b8w16 : ∀x,y:byte8_or_word16.decidable (x = y).
+ #x; nelim x; #e1; #y; nelim y; #e2;
+ nnormalize;
+ ##[ ##1: napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 e1 e2) …);
+          ##[ ##2: #H; napply (or2_intro2 (? = ?) (? ≠ ?) … ); nnormalize; #H1; napply (H (b8w16_destruct_b8_b8 … H1))
+          ##| ##1: #H; nrewrite > H; napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …))
+          ##]
+ ##| ##2: napply (or2_intro2 (? = ?) (? ≠ ?) …); nnormalize; #H; napply (b8w16_destruct_b8_w16 … H)
+ ##| ##3: napply (or2_intro2 (? = ?) (? ≠ ?) …); nnormalize; #H; napply (b8w16_destruct_w16_b8 … H)
+ ##| ##4: napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 e1 e2) …);
+          ##[ ##2: #H; napply (or2_intro2 (? = ?) (? ≠ ?) … ); nnormalize; #H1; napply (H (b8w16_destruct_w16_w16 … H1))
+          ##| ##1: #H; nrewrite > H; napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …))
+          ##]
+ ##]
+nqed.
+
+nlemma neqb8w16_to_neq : ∀bw1,bw2.eq_b8w16 bw1 bw2 = false → bw1 ≠ bw2.
+ #bw1; #bw2;
+ ncases bw1; #e1; ncases bw2; #e2;
+ ##[ ##1: nchange with ((eq_b8 e1 e2 = false) → ?); #H;
+          nnormalize; #H1; napply (neqb8_to_neq … H); napply (b8w16_destruct_b8_b8 … H1)
+ ##| ##2: nnormalize; #H; #H1; napply (b8w16_destruct_b8_w16 … H1)
+ ##| ##3: nnormalize; #H; #H1; napply (b8w16_destruct_w16_b8 … H1)
+ ##| ##4: nchange with ((eq_w16 e1 e2 = false) → ?); #H;
+          nnormalize; #H1; napply (neqw16_to_neq … H); napply (b8w16_destruct_w16_w16 … H1)
  ##]
 nqed.