(**************************************************************************)
(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
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(* This file was automatically generated: do not edit *********************)

include "Coq.ma".

(*s Instantiating [eqN] with Leibniz equality *)

include "Num/NSyntax.ma".

inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/eqN.con" as definition.

(* UNEXPORTED
Hints Unfold eqN : num.
*)

(* NOTATION
Grammar constr constr1 :=
eq_impl [ constr0($c) "=" constr0($c2) ] -> [ (eqN $c $c2) ].
*)

(* NOTATION
Syntax constr
  level 1:
    equal [ (eqN $t1 $t2) ] -> [ [<hov 0> $t1:E [0 1]  "=" $t2:E ] ].
*)

(*s Lemmas for [eqN] *)

inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/eq_refl.con" as lemma.

inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/eq_sym.con" as lemma.

inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/eq_trans.con" as lemma.

(* UNEXPORTED
Hints Resolve eq_refl eq_trans : num.
*)

(* UNEXPORTED
Hints Immediate eq_sym : num.
*)

(*s Compatibility lemmas for [S], [add], [lt] *)

inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/S_eq_compat.con" as lemma.

(* UNEXPORTED
Hints Resolve S_eq_compat : nat.
*)

inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/add_eq_compat.con" as lemma.

(* UNEXPORTED
Hints Resolve add_eq_compat : nat.
*)

inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/lt_eq_compat.con" as lemma.

(* UNEXPORTED
Hints Resolve add_eq_compat S_eq_compat lt_eq_compat : num.
*)