| le_n : le n n
| le_S : \forall m:nat. le n m \to le n (S m).
+(*CSC: the URI must disappear: there is a bug now *)
interpretation "natural 'less or equal to'" 'leq x y = (cic:/matita/nat/orders/le.ind#xpointer(1/1) x y).
-alias symbol "leq" (instance 0) = "natural 'less or equal to'".
definition lt: nat \to nat \to Prop \def
\lambda n,m:nat.(S n) \leq m.
+(*CSC: the URI must disappear: there is a bug now *)
interpretation "natural 'less than'" 'lt x y = (cic:/matita/nat/orders/lt.con x y).
definition ge: nat \to nat \to Prop \def
\lambda n,m:nat.m \leq n.
+(*CSC: the URI must disappear: there is a bug now *)
interpretation "natural 'greater or equal to'" 'geq x y = (cic:/matita/nat/orders/ge.con x y).
definition gt: nat \to nat \to Prop \def
\lambda n,m:nat.m<n.
+(*CSC: the URI must disappear: there is a bug now *)
interpretation "natural 'greater than'" 'gt x y = (cic:/matita/nat/orders/gt.con x y).
theorem transitive_le : transitive nat le.