set "baseuri" "cic:/matita/RELATIONAL/NLE/defs".
-include "logic/equality.ma".
+include "NPlus/defs.ma".
-include "Nat/defs.ma".
-
-inductive NLE: Nat \to Nat \to Prop \def
- | NLE_zero: \forall q. NLE zero q
- | NLE_succ: \forall p,q. NLE p q \to NLE (succ p) (succ q)
-.
+definition NLE: Nat \to Nat \to Prop \def
+ \lambda q,r. \exists p. (p + q == r).
(*CSC: the URI must disappear: there is a bug now *)
-interpretation "natural 'less or equal to'" 'leq x y =
- (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) x y).
+interpretation "natural 'less or equal to'" 'leq x y =
+ (cic:/matita/RELATIONAL/NLE/defs/NLE.con x y).
(*CSC: the URI must disappear: there is a bug now *)
interpretation "natural 'less than'" 'lt x y =
- (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1)
+ (cic:/matita/RELATIONAL/NLE/defs/NLE.con
(cic:/matita/RELATIONAL/Nat/defs/Nat.ind#xpointer(1/1/2) x) y).