freescale porting, work in progress

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

diff --git a/helm/software/matita/contribs/ng_assembly/num/exadecim_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/exadecim_lemmas.ma
index ccfbdd73c0437f3daa1c86d01907dfc7e3ba009e..47847434eb909921c312e8f7c383433cfa530972 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/num/exadecim_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/exadecim_lemmas.ma
@@ -461,3 +461,33 @@ nlemma eq_to_eqex : ∀e1,e2.e1 = e2 → eq_ex e1 e2 = true.
  ##| ##*: #H; napply (exadecim_destruct … H)
  ##]
 nqed.
+
+nlemma decidable_ex : ∀x,y:exadecim.decidable (x = y).
+ #x; #y;
+ nnormalize;
+ nelim x;
+ nelim y;
+ ##[ ##1,18,35,52,69,86,103,120,137,154,171,188,205,222,239,256: napply (or_introl (? = ?) (? ≠ ?) …); napply refl_eq
+ ##| ##*: napply (or_intror (? = ?) (? ≠ ?) …); nnormalize; #H; napply False_ind; napply (exadecim_destruct … H)
+ ##]
+nqed.
+
+nlemma neqex_to_neq : ∀e1,e2:exadecim.(eq_ex e1 e2 = false) → (e1 ≠ e2).
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,18,35,52,69,86,103,120,137,154,171,188,205,222,239,256: #H; napply (bool_destruct … H)
+ ##| ##*: #H; #H1; napply (exadecim_destruct … H1)
+ ##]
+nqed.
+
+nlemma neq_to_neqex : ∀e1,e2.e1 ≠ e2 → eq_ex e1 e2 = false.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,18,35,52,69,86,103,120,137,154,171,188,205,222,239,256: #H; nelim (H (refl_eq …))
+ ##| ##*: #H; napply refl_eq
+ ##]
+nqed.