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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
(*i $Id$ i*)
Require Export NZAxioms.
Set Implicit Arguments.
Module Type Opp (Import T:Typ).
Parameter Inline opp : t -> t.
End Opp.
Module Type OppNotation (T:Typ)(Import O : Opp T).
Notation "- x" := (opp x) (at level 35, right associativity).
End OppNotation.
Module Type Opp' (T:Typ) := Opp T <+ OppNotation T.
(** We obtain integers by postulating that every number has a predecessor. *)
Module Type IsOpp (Import Z : NZAxiomsSig')(Import O : Opp' Z).
Declare Instance opp_wd : Proper (eq==>eq) opp.
Axiom succ_pred : forall n, S (P n) == n.
Axiom opp_0 : - 0 == 0.
Axiom opp_succ : forall n, - (S n) == P (- n).
End IsOpp.
Module Type ZAxiomsSig := NZOrdAxiomsSig <+ Opp <+ IsOpp.
Module Type ZAxiomsSig' := NZOrdAxiomsSig' <+ Opp' <+ IsOpp.
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