freescale porting

[helm.git] / helm / software / matita / contribs / ng_assembly / num / word16_lemmas.ma

diff --git a/helm/software/matita/contribs/ng_assembly/num/word16_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/word16_lemmas.ma
index 3e53841ae0ab0c16b547ce5eeb0b4f9ded73fe5b..2e38a06fcba8fd5084b03bc854175ba3bc70543c 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/num/word16_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/word16_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_plusw16_dc_dc : ∀w1,w2,c.plus_w16_dc_dc w1 w2 c = plus_w16_dc
  nelim w2;
  #b3; #b4;
  nchange with (
-  match plus_b8_dc_dc b2 b4 c with
-   [ pair l c ⇒ match plus_b8_dc_dc b1 b3 c with
-    [ pair h c' ⇒ pair … 〈h:l〉 c' ]] =
-  match plus_b8_dc_dc b4 b2 c with
-   [ pair l c ⇒ match plus_b8_dc_dc b3 b1 c with
-    [ pair h c' ⇒ pair … 〈h:l〉 c' ]]);
+  match plus_b8_dc_dc b2 b4 c with [ pair l c ⇒ match plus_b8_dc_dc b1 b3 c with [ pair h c' ⇒ pair … 〈h:l〉 c' ]] =
+  match plus_b8_dc_dc b4 b2 c with [ pair l c ⇒ match plus_b8_dc_dc b3 b1 c with [ pair h c' ⇒ pair … 〈h:l〉 c' ]]);
  nrewrite > (symmetric_plusb8_dc_dc b4 b2 c);
  ncases (plus_b8_dc_dc b2 b4 c);
  #b5; #c1;
  nchange with (
-  match plus_b8_dc_dc b1 b3 c1 with
-   [ pair h c' ⇒ pair … 〈h:b5〉 c' ] =
-  match plus_b8_dc_dc b3 b1 c1 with
-   [ pair h c' ⇒ pair … 〈h:b5〉 c' ]);
+  match plus_b8_dc_dc b1 b3 c1 with [ pair h c' ⇒ pair … 〈h:b5〉 c' ] =
+  match plus_b8_dc_dc b3 b1 c1 with [ pair h c' ⇒ pair … 〈h:b5〉 c' ]);
  nrewrite > (symmetric_plusb8_dc_dc b1 b3 c1);
  napply refl_eq.
 nqed.
@@ -168,10 +162,8 @@ nlemma symmetric_plusw16_dc_d : ∀w1,w2,c.plus_w16_dc_d w1 w2 c = plus_w16_dc_d
  nelim w2;
  #b3; #b4;
  nchange with (
-  match plus_b8_dc_dc b2 b4 c with
-   [ pair l c ⇒ 〈plus_b8_dc_d b1 b3 c:l〉 ] =
-  match plus_b8_dc_dc b4 b2 c with
-   [ pair l c ⇒ 〈plus_b8_dc_d b3 b1 c:l〉 ]);
+  match plus_b8_dc_dc b2 b4 c with [ pair l c ⇒ 〈plus_b8_dc_d b1 b3 c:l〉 ] =
+  match plus_b8_dc_dc b4 b2 c with [ pair l c ⇒ 〈plus_b8_dc_d b3 b1 c:l〉 ]);
  nrewrite > (symmetric_plusb8_dc_dc b4 b2 c);
  ncases (plus_b8_dc_dc b2 b4 c);
  #b5; #c1;
@@ -201,20 +193,14 @@ nlemma symmetric_plusw16_d_dc : ∀w1,w2.plus_w16_d_dc w1 w2 = plus_w16_d_dc w2
  nelim w2;
  #b3; #b4;
  nchange with (
-  match plus_b8_d_dc b2 b4 with
-   [ pair l c ⇒ match plus_b8_dc_dc b1 b3 c with
-    [ pair h c' ⇒ pair … 〈h:l〉 c' ]] =
-  match plus_b8_d_dc b4 b2 with
-   [ pair l c ⇒ match plus_b8_dc_dc b3 b1 c with
-    [ pair h c' ⇒ pair … 〈h:l〉 c' ]]);
+  match plus_b8_d_dc b2 b4 with [ pair l c ⇒ match plus_b8_dc_dc b1 b3 c with [ pair h c' ⇒ pair … 〈h:l〉 c' ]] =
+  match plus_b8_d_dc b4 b2 with [ pair l c ⇒ match plus_b8_dc_dc b3 b1 c with [ pair h c' ⇒ pair … 〈h:l〉 c' ]]);
  nrewrite > (symmetric_plusb8_d_dc b4 b2);
  ncases (plus_b8_d_dc b2 b4);
  #b5; #c;
  nchange with (
-  match plus_b8_dc_dc b1 b3 c with
-   [ pair h c' ⇒ pair … 〈h:b5〉 c' ] =
-  match plus_b8_dc_dc b3 b1 c with
-   [ pair h c' ⇒ pair … 〈h:b5〉 c' ]);
+  match plus_b8_dc_dc b1 b3 c with [ pair h c' ⇒ pair … 〈h:b5〉 c' ] =
+  match plus_b8_dc_dc b3 b1 c with [ pair h c' ⇒ pair … 〈h:b5〉 c' ]);
  nrewrite > (symmetric_plusb8_dc_dc b1 b3 c);
  napply refl_eq.
 nqed.
@@ -226,10 +212,8 @@ nlemma symmetric_plusw16_d_d : ∀w1,w2.plus_w16_d_d w1 w2 = plus_w16_d_d w2 w1.
  nelim w2;
  #b3; #b4;
  nchange with (
-  match plus_b8_d_dc b2 b4 with
-   [ pair l c ⇒ 〈plus_b8_dc_d b1 b3 c:l〉 ] =
-  match plus_b8_d_dc b4 b2 with
-   [ pair l c ⇒ 〈plus_b8_dc_d b3 b1 c:l〉 ]);
+  match plus_b8_d_dc b2 b4 with [ pair l c ⇒ 〈plus_b8_dc_d b1 b3 c:l〉 ] =
+  match plus_b8_d_dc b4 b2 with [ pair l c ⇒ 〈plus_b8_dc_d b3 b1 c:l〉 ]);
  nrewrite > (symmetric_plusb8_d_dc b4 b2);
  ncases (plus_b8_d_dc b2 b4);
  #b5; #c;
@@ -325,3 +309,69 @@ nlemma eq_to_eqw16 : ∀w1,w2.w1 = w2 → eq_w16 w1 w2 = true.
  nnormalize;
  napply refl_eq.
 nqed.
+
+nlemma decidable_w16_aux1 : ∀b1,b2,b3,b4.b1 ≠ b3 → 〈b1:b2〉 ≠ 〈b3:b4〉.
+ #b1; #b2; #b3; #b4;
+ nnormalize; #H; #H1;
+ napply (H (word16_destruct_1 … H1)).
+nqed.
+
+nlemma decidable_w16_aux2 : ∀b1,b2,b3,b4.b2 ≠ b4 → 〈b1:b2〉 ≠ 〈b3:b4〉.
+ #b1; #b2; #b3; #b4;
+ nnormalize; #H; #H1;
+ napply (H (word16_destruct_2 … H1)).
+nqed.
+
+nlemma decidable_w16 : ∀x,y:word16.decidable (x = y).
+ #x; nelim x; #b1; #b2;
+ #y; nelim y; #b3; #b4;
+ nnormalize;
+ napply (or2_elim (b1 = b3) (b1 ≠ b3) ? (decidable_b8 b1 b3) …);
+ ##[ ##2: #H; napply (or2_intro2 … (decidable_w16_aux1 b1 b2 b3 b4 H))
+ ##| ##1: #H; napply (or2_elim (b2 = b4) (b2 ≠ b4) ? (decidable_b8 b2 b4) …);
+          ##[ ##2: #H1; napply (or2_intro2 … (decidable_w16_aux2 b1 b2 b3 b4 H1))
+          ##| ##1: #H1; nrewrite > H; nrewrite > H1;
+                        napply (or2_intro1 … (refl_eq ? 〈b3:b4〉))
+          ##]
+ ##]
+nqed.
+
+nlemma neqw16_to_neq : ∀w1,w2:word16.(eq_w16 w1 w2 = false) → (w1 ≠ w2).
+ #w1; #w2;
+ nelim w1;
+ nelim w2;
+ #b1; #b2; #b3; #b4;
+ nchange with ((((eq_b8 b3 b1) ⊗ (eq_b8 b4 b2)) = false) → ?);
+ #H;
+ napply (or2_elim ((eq_b8 b3 b1) = false) ((eq_b8 b4 b2) = false) ? (andb_false2 … H) …);
+ ##[ ##1: #H1; napply (decidable_w16_aux1 … (neqb8_to_neq … H1))
+ ##| ##2: #H1; napply (decidable_w16_aux2 … (neqb8_to_neq … H1))
+ ##]
+nqed.
+
+nlemma word16_destruct : ∀b1,b2,b3,b4.〈b1:b2〉 ≠ 〈b3:b4〉 → b1 ≠ b3 ∨ b2 ≠ b4.
+ #b1; #b2; #b3; #b4;
+ nnormalize; #H;
+ napply (or2_elim (b1 = b3) (b1 ≠ b3) ? (decidable_b8 b1 b3) …);
+ ##[ ##2: #H1; napply (or2_intro1 … H1)
+ ##| ##1: #H1; napply (or2_elim (b2 = b4) (b2 ≠ b4) ? (decidable_b8 b2 b4) …);
+          ##[ ##2: #H2; napply (or2_intro2 … H2)
+          ##| ##1: #H2; nrewrite > H1 in H:(%);
+                   nrewrite > H2;
+                   #H; nelim (H (refl_eq …))
+          ##]
+ ##]
+nqed.
+
+nlemma neq_to_neqw16 : ∀w1,w2.w1 ≠ w2 → eq_w16 w1 w2 = false.
+ #w1; #w2;
+ nelim w1; #b1; #b2;
+ nelim w2; #b3; #b4;
+ #H; nchange with (((eq_b8 b1 b3) ⊗ (eq_b8 b2 b4)) = false);
+ napply (or2_elim (b1 ≠ b3) (b2 ≠ b4) ? (word16_destruct … H) …);
+ ##[ ##1: #H1; nrewrite > (neq_to_neqb8 … H1); nnormalize; napply refl_eq
+ ##| ##2: #H1; nrewrite > (neq_to_neqb8 … H1);
+          nrewrite > (symmetric_andbool (eq_b8 b1 b3) false);
+          nnormalize; napply refl_eq
+ ##]
+nqed.