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(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(*i $Id $ i*)
(*s
Axiomatisation of a numerical set
It will be instantiated by Z and R later on
We choose to introduce many operation to allow flexibility in definition
([S] is primitive in the definition of [nat] while [add] and [one]
are primitive in the definition
*)
Parameter N:Type.
Parameter zero:N.
Parameter one:N.
Parameter add:N->N->N.
Parameter S:N->N.
(*s Relations *)
Parameter eq,lt,le,gt,ge:N->N->Prop.
Definition neq [x,y:N] := (eq x y)->False.
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