freescale porting

[helm.git] / helm / software / matita / contribs / ng_assembly / num / word32_lemmas.ma

diff --git a/helm/software/matita/contribs/ng_assembly/num/word32_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/word32_lemmas.ma
index d7f6cc5588da9e94803eb6b9deb90ee6742af88a..026086d8f692841003ad4e121cbda6a0ea0dbf63 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/num/word32_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/word32_lemmas.ma
@@ -15,8 +15,8 @@
 (* ********************************************************************** *)
 (*                          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              *)
+(*   Sviluppo: 2008-2010                                                  *)
 (*                                                                        *)
 (* ********************************************************************** *)
 
@@ -143,20 +143,14 @@ nlemma symmetric_plusw32_dc_dc : ∀dw1,dw2,c.plus_w32_dc_dc dw1 dw2 c = plus_w3
  nelim dw2;
  #w3; #w4;
  nchange with (
-  match plus_w16_dc_dc w2 w4 c with
-   [ pair l c ⇒ match plus_w16_dc_dc w1 w3 c with
-    [ pair h c' ⇒ pair … 〈h.l〉 c' ]] =
-  match plus_w16_dc_dc w4 w2 c with
-   [ pair l c ⇒ match plus_w16_dc_dc w3 w1 c with
-    [ pair h c' ⇒ pair … 〈h.l〉 c' ]]);
+  match plus_w16_dc_dc w2 w4 c with [ pair l c ⇒ match plus_w16_dc_dc w1 w3 c with [ pair h c' ⇒ pair … 〈h.l〉 c' ]] =
+  match plus_w16_dc_dc w4 w2 c with [ pair l c ⇒ match plus_w16_dc_dc w3 w1 c with [ pair h c' ⇒ pair … 〈h.l〉 c' ]]);
  nrewrite > (symmetric_plusw16_dc_dc w4 w2 c);
  ncases (plus_w16_dc_dc w2 w4 c);
  #w5; #c1;
  nchange with (
-  match plus_w16_dc_dc w1 w3 c1 with
-   [ pair h c' ⇒ pair … 〈h.w5〉 c' ] =
-  match plus_w16_dc_dc w3 w1 c1 with
-   [ pair h c' ⇒ pair … 〈h.w5〉 c' ]);
+  match plus_w16_dc_dc w1 w3 c1 with [ pair h c' ⇒ pair … 〈h.w5〉 c' ] =
+  match plus_w16_dc_dc w3 w1 c1 with [ pair h c' ⇒ pair … 〈h.w5〉 c' ]);
  nrewrite > (symmetric_plusw16_dc_dc w1 w3 c1);
  napply refl_eq.
 nqed.
@@ -168,10 +162,8 @@ nlemma symmetric_plusw32_dc_d : ∀dw1,dw2,c.plus_w32_dc_d dw1 dw2 c = plus_w32_
  nelim dw2;
  #w3; #w4;
  nchange with (
-  match plus_w16_dc_dc w2 w4 c with
-   [ pair l c ⇒ 〈plus_w16_dc_d w1 w3 c.l〉 ] =
-  match plus_w16_dc_dc w4 w2 c with
-   [ pair l c ⇒ 〈plus_w16_dc_d w3 w1 c.l〉 ]);
+  match plus_w16_dc_dc w2 w4 c with [ pair l c ⇒ 〈plus_w16_dc_d w1 w3 c.l〉 ] =
+  match plus_w16_dc_dc w4 w2 c with [ pair l c ⇒ 〈plus_w16_dc_d w3 w1 c.l〉 ]);
  nrewrite > (symmetric_plusw16_dc_dc w4 w2 c);
  ncases (plus_w16_dc_dc w2 w4 c);
  #w5; #c1;
@@ -201,20 +193,14 @@ nlemma symmetric_plusw32_d_dc : ∀dw1,dw2.plus_w32_d_dc dw1 dw2 = plus_w32_d_dc
  nelim dw2;
  #w3; #w4;
  nchange with (
-  match plus_w16_d_dc w2 w4 with
-   [ pair l c ⇒ match plus_w16_dc_dc w1 w3 c with
-    [ pair h c' ⇒ pair … 〈h.l〉 c' ]] =
-  match plus_w16_d_dc w4 w2 with
-   [ pair l c ⇒ match plus_w16_dc_dc w3 w1 c with
-    [ pair h c' ⇒ pair … 〈h.l〉 c' ]]);
+  match plus_w16_d_dc w2 w4 with [ pair l c ⇒ match plus_w16_dc_dc w1 w3 c with [ pair h c' ⇒ pair … 〈h.l〉 c' ]] =
+  match plus_w16_d_dc w4 w2 with [ pair l c ⇒ match plus_w16_dc_dc w3 w1 c with [ pair h c' ⇒ pair … 〈h.l〉 c' ]]);
  nrewrite > (symmetric_plusw16_d_dc w4 w2);
  ncases (plus_w16_d_dc w2 w4);
  #w5; #c;
  nchange with (
-  match plus_w16_dc_dc w1 w3 c with
-   [ pair h c' ⇒ pair … 〈h.w5〉 c' ] =
-  match plus_w16_dc_dc w3 w1 c with
-   [ pair h c' ⇒ pair … 〈h.w5〉 c' ]);
+  match plus_w16_dc_dc w1 w3 c with [ pair h c' ⇒ pair … 〈h.w5〉 c' ] =
+  match plus_w16_dc_dc w3 w1 c with [ pair h c' ⇒ pair … 〈h.w5〉 c' ]);
  nrewrite > (symmetric_plusw16_dc_dc w1 w3 c);
  napply refl_eq.
 nqed.
@@ -226,10 +212,8 @@ nlemma symmetric_plusw32_d_d : ∀dw1,dw2.plus_w32_d_d dw1 dw2 = plus_w32_d_d dw
  nelim dw2;
  #w3; #w4;
  nchange with (
-  match plus_w16_d_dc w2 w4 with
-   [ pair l c ⇒ 〈plus_w16_dc_d w1 w3 c.l〉 ] =
-  match plus_w16_d_dc w4 w2 with
-   [ pair l c ⇒ 〈plus_w16_dc_d w3 w1 c.l〉 ]);
+  match plus_w16_d_dc w2 w4 with [ pair l c ⇒ 〈plus_w16_dc_d w1 w3 c.l〉 ] =
+  match plus_w16_d_dc w4 w2 with [ pair l c ⇒ 〈plus_w16_dc_d w3 w1 c.l〉 ]);
  nrewrite > (symmetric_plusw16_d_dc w4 w2);
  ncases (plus_w16_d_dc w2 w4);
  #w5; #c;
@@ -325,3 +309,69 @@ nlemma eq_to_eqw32 : ∀dw1,dw2.dw1 = dw2 → eq_w32 dw1 dw2 = true.
  nnormalize;
  napply refl_eq.
 nqed.
+
+nlemma decidable_w32_aux1 : ∀w1,w2,w3,w4.w1 ≠ w3 → 〈w1.w2〉 ≠ 〈w3.w4〉.
+ #w1; #w2; #w3; #w4;
+ nnormalize; #H; #H1;
+ napply (H (word32_destruct_1 … H1)).
+nqed.
+
+nlemma decidable_w32_aux2 : ∀w1,w2,w3,w4.w2 ≠ w4 → 〈w1.w2〉 ≠ 〈w3.w4〉.
+ #w1; #w2; #w3; #w4;
+ nnormalize; #H; #H1;
+ napply (H (word32_destruct_2 … H1)).
+nqed.
+
+nlemma decidable_w32 : ∀x,y:word32.decidable (x = y).
+ #x; nelim x; #w1; #w2;
+ #y; nelim y; #w3; #w4;
+ nnormalize;
+ napply (or2_elim (w1 = w3) (w1 ≠ w3) ? (decidable_w16 w1 w3) …);
+ ##[ ##2: #H; napply (or2_intro2 … (decidable_w32_aux1 w1 w2 w3 w4 H))
+ ##| ##1: #H; napply (or2_elim (w2 = w4) (w2 ≠ w4) ? (decidable_w16 w2 w4) …);
+          ##[ ##2: #H1; napply (or2_intro2 … (decidable_w32_aux2 w1 w2 w3 w4 H1))
+          ##| ##1: #H1; nrewrite > H; nrewrite > H1;
+                        napply (or2_intro1 … (refl_eq ? 〈w3.w4〉))
+          ##]
+ ##]
+nqed.
+
+nlemma neqw32_to_neq : ∀dw1,dw2:word32.(eq_w32 dw1 dw2 = false) → (dw1 ≠ dw2).
+ #dw1; #dw2;
+ nelim dw1;
+ nelim dw2;
+ #w1; #w2; #w3; #w4;
+ nchange with ((((eq_w16 w3 w1) ⊗ (eq_w16 w4 w2)) = false) → ?);
+ #H;
+ napply (or2_elim ((eq_w16 w3 w1) = false) ((eq_w16 w4 w2) = false) ? (andb_false2 … H) …);
+ ##[ ##1: #H1; napply (decidable_w32_aux1 … (neqw16_to_neq … H1))
+ ##| ##2: #H1; napply (decidable_w32_aux2 … (neqw16_to_neq … H1))
+ ##]
+nqed.
+
+nlemma word32_destruct : ∀w1,w2,w3,w4.〈w1.w2〉 ≠ 〈w3.w4〉 → w1 ≠ w3 ∨ w2 ≠ w4.
+ #w1; #w2; #w3; #w4;
+ nnormalize; #H;
+ napply (or2_elim (w1 = w3) (w1 ≠ w3) ? (decidable_w16 w1 w3) …);
+ ##[ ##2: #H1; napply (or2_intro1 … H1)
+ ##| ##1: #H1; napply (or2_elim (w2 = w4) (w2 ≠ w4) ? (decidable_w16 w2 w4) …);
+          ##[ ##2: #H2; napply (or2_intro2 … H2)
+          ##| ##1: #H2; nrewrite > H1 in H:(%);
+                   nrewrite > H2;
+                   #H; nelim (H (refl_eq …))
+          ##]
+ ##]
+nqed.
+
+nlemma neq_to_neqw32 : ∀dw1,dw2.dw1 ≠ dw2 → eq_w32 dw1 dw2 = false.
+ #dw1; #dw2;
+ nelim dw1; #w1; #w2;
+ nelim dw2; #w3; #w4;
+ #H; nchange with (((eq_w16 w1 w3) ⊗ (eq_w16 w2 w4)) = false);
+ napply (or2_elim (w1 ≠ w3) (w2 ≠ w4) ? (word32_destruct … H) …);
+ ##[ ##1: #H1; nrewrite > (neq_to_neqw16 … H1); nnormalize; napply refl_eq
+ ##| ##2: #H1; nrewrite > (neq_to_neqw16 … H1);
+          nrewrite > (symmetric_andbool (eq_w16 w1 w3) false);
+          nnormalize; napply refl_eq
+ ##]
+nqed.