1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
17 include "NPlus/defs.ma".
19 inductive NLE: Nat \to Nat \to Prop \def
20 | nle_zero_1: \forall q. NLE zero q
21 | nle_succ_succ: \forall p,q. NLE p q \to NLE (succ p) (succ q)
24 (*CSC: the URI must disappear: there is a bug now *)
25 interpretation "natural 'greater or equal to'" 'geq y x=
26 (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) x y).
28 (*CSC: the URI must disappear: there is a bug now *)
29 interpretation "natural 'greater than'" 'gt y x =
30 (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1)
31 (cic:/matita/RELATIONAL/datatypes/Nat/Nat.ind#xpointer(1/1/2) x) y).
33 (*CSC: the URI must disappear: there is a bug now *)
34 interpretation "natural 'less or equal to'" 'leq x y =
35 (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) x y).
37 (*CSC: the URI must disappear: there is a bug now *)
38 interpretation "natural 'less than'" 'lt x y =
39 (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1)
40 (cic:/matita/RELATIONAL/datatypes/Nat/Nat.ind#xpointer(1/1/2) x) y).