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 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
19 (*s Instantiating [eqN] with Leibniz equality *)
21 include "Num/NSyntax.ma".
23 inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/eqN.con" as definition.
26 Hints Unfold eqN : num.
30 Grammar constr constr1 :=
31 eq_impl [ constr0($c) "=" constr0($c2) ] -> [ (eqN $c $c2) ].
37 equal [ (eqN $t1 $t2) ] -> [ [<hov 0> $t1:E [0 1] "=" $t2:E ] ].
40 (*s Lemmas for [eqN] *)
42 inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/eq_refl.con" as lemma.
44 inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/eq_sym.con" as lemma.
46 inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/eq_trans.con" as lemma.
49 Hints Resolve eq_refl eq_trans : num.
53 Hints Immediate eq_sym : num.
56 (*s Compatibility lemmas for [S], [add], [lt] *)
58 inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/S_eq_compat.con" as lemma.
61 Hints Resolve S_eq_compat : nat.
64 inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/add_eq_compat.con" as lemma.
67 Hints Resolve add_eq_compat : nat.
70 inline procedural "cic:/Coq/Num/Leibniz/EqAxioms/lt_eq_compat.con" as lemma.
73 Hints Resolve add_eq_compat S_eq_compat lt_eq_compat : num.