freescale porting, work in progress

[helm.git] / helm / software / matita / contribs / ng_assembly / common / nat.ma

diff --git a/helm/software/matita/contribs/ng_assembly/common/nat.ma b/helm/software/matita/contribs/ng_assembly/common/nat.ma
index 874ab7d8c4d0ed53ffd1ccf006cdb80f3bc32862..7e9ec23e436463bdc3b09b4bb7da2e5d7a4a2b85 100755 (executable)
--- a/helm/software/matita/contribs/ng_assembly/common/nat.ma
+++ b/helm/software/matita/contribs/ng_assembly/common/nat.ma
@@ -49,6 +49,20 @@ nlet rec le_nat n m ≝
    [ O ⇒ false | (S q) ⇒ le_nat p q ]
   ].
 
+interpretation "natural 'less or equal to'" 'leq x y = (le_nat x y).
+
+ndefinition lt_nat ≝ λn1,n2:nat.(le_nat n1 n2) ⊗ (⊖ (eq_nat n1 n2)).
+
+interpretation "natural 'less than'" 'lt x y = (lt_nat x y).
+
+ndefinition ge_nat ≝ λn1,n2:nat.(⊖ (le_nat n1 n2)) ⊕ (eq_nat n1 n2).
+
+interpretation "natural 'greater or equal to'" 'geq x y = (ge_nat x y).
+
+ndefinition gt_nat ≝ λn1,n2:nat.⊖ (le_nat n1 n2).
+
+interpretation "natural 'greater than'" 'gt x y = (gt_nat x y).
+
 nlet rec plus (n1,n2:nat) on n1 ≝ 
  match n1 with
   [ O ⇒ n2