freescale porting, work in progress

[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 4570f3291f01fc2231110a80cf90085ba1177184..a9c59de32ac9d21f11f2b4fc247d8ec46a5389fd 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/num/word16_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/word16_lemmas.ma
@@ -325,3 +325,69 @@ 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 (or_elim (b1 = b3) (b1 ≠ b3) ? (decidable_b8 b1 b3) …);
+ ##[ ##2: #H; napply (or_intror … (decidable_w16_aux1 b1 b2 b3 b4 H))
+ ##| ##1: #H; napply (or_elim (b2 = b4) (b2 ≠ b4) ? (decidable_b8 b2 b4) …);
+          ##[ ##2: #H1; napply (or_intror … (decidable_w16_aux2 b1 b2 b3 b4 H1))
+          ##| ##1: #H1; nrewrite > H; nrewrite > H1;
+                        napply (or_introl … (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 (or_elim ((eq_b8 b3 b1) = false) ((eq_b8 b4 b2) = false) ? (andb_false … 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 (or_elim (b1 = b3) (b1 ≠ b3) ? (decidable_b8 b1 b3) …);
+ ##[ ##2: #H1; napply (or_introl … H1)
+ ##| ##1: #H1; napply (or_elim (b2 = b4) (b2 ≠ b4) ? (decidable_b8 b2 b4) …);
+          ##[ ##2: #H2; napply (or_intror … 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 (or_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.