include "NPlus/defs.ma".
-definition NLE: Nat \to Nat \to Prop \def
- \lambda q,r. \exists p. (p + q == r).
+inductive NLE (q:Nat) (r:Nat): Prop \def
+ | nle_nplus: \forall p. (p + q == r) \to NLE 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.con x y).
+ (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) 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.con
+ (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1)
+ (cic:/matita/RELATIONAL/Nat/defs/Nat.ind#xpointer(1/1/2) x) y).
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "natural 'greater or equal to'" 'geq y x=
+ (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) x y).
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "natural 'greater than'" 'gt y x =
+ (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1)
(cic:/matita/RELATIONAL/Nat/defs/Nat.ind#xpointer(1/1/2) x) y).