freescale porting, work in progress

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

diff --git a/helm/software/matita/contribs/ng_assembly/num/quatern_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/quatern_lemmas.ma
index 8d3bdf5d3d685efa6f03f236f4957585fbac4e0f..d32aa0f3e83321a3f3ca587424a15c1782f1a51a 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/num/quatern_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/quatern_lemmas.ma
@@ -93,3 +93,33 @@ nlemma eq_to_eqqu : ∀n1,n2.n1 = n2 → eq_qu n1 n2 = true.
  ##| ##*: #H; napply (quatern_destruct … H)
  ##]
 nqed.
+
+nlemma decidable_qu : ∀x,y:quatern.decidable (x = y).
+ #x; #y;
+ nnormalize;
+ nelim x;
+ nelim y;
+ ##[ ##1,6,11,16: napply (or_introl (? = ?) (? ≠ ?) …); napply refl_eq
+ ##| ##*: napply (or_intror (? = ?) (? ≠ ?) …); nnormalize; #H; napply False_ind; napply (quatern_destruct … H)
+ ##]
+nqed.
+
+nlemma neqqu_to_neq : ∀n1,n2.eq_qu n1 n2 = false → n1 ≠ n2.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,6,11,16: #H; napply (bool_destruct … H)
+ ##| ##*: #H; #H1; napply (quatern_destruct … H1)
+ ##]
+nqed.
+
+nlemma neq_to_neqqu : ∀n1,n2.n1 ≠ n2 → eq_qu n1 n2 = false.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,6,11,16: #H; nelim (H (refl_eq …))
+ ##| ##*: #H; napply refl_eq
+ ##]
+nqed.