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 *)
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15 (* This file was automatically generated: do not edit *********************)
19 (*#**********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
25 (* \VV/ *************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#**********************************************************************)
33 include "Num/Axioms.ma".
35 include "Num/AddProps.ma".
37 include "Num/NeqProps.ma".
39 (*#* This file contains basic properties of the less than relation *)
41 inline procedural "cic:/Coq/Num/LtProps/lt_anti_sym.con" as lemma.
44 Hints Resolve lt_anti_refl : num.
47 inline procedural "cic:/Coq/Num/LtProps/eq_not_lt.con" as lemma.
50 Hints Resolve eq_not_lt : num.
53 inline procedural "cic:/Coq/Num/LtProps/lt_0_1.con" as lemma.
56 Hints Resolve lt_0_1 : num.
59 inline procedural "cic:/Coq/Num/LtProps/eq_lt_x_Sy.con" as lemma.
62 Hints Resolve eq_lt_x_Sy : num.
65 inline procedural "cic:/Coq/Num/LtProps/lt_lt_x_Sy.con" as lemma.
68 Hints Immediate lt_lt_x_Sy : num.
71 inline procedural "cic:/Coq/Num/LtProps/lt_Sx_y_lt.con" as lemma.
74 Hints Immediate lt_Sx_y_lt : num.
77 (*#* Relating [<] and [=] *)
79 inline procedural "cic:/Coq/Num/LtProps/lt_neq.con" as lemma.
82 Hints Immediate lt_neq : num.
85 inline procedural "cic:/Coq/Num/LtProps/lt_neq_sym.con" as lemma.
88 Hints Immediate lt_neq_sym : num.
91 (*#* Application to inequalities properties *)
93 inline procedural "cic:/Coq/Num/LtProps/neq_x_Sx.con" as lemma.
96 Hints Resolve neq_x_Sx : num.
99 inline procedural "cic:/Coq/Num/LtProps/neq_0_1.con" as lemma.
102 Hints Resolve neq_0_1 : num.
105 (*#* Relating [<] and [+] *)
107 inline procedural "cic:/Coq/Num/LtProps/lt_add_compat_r.con" as lemma.
110 Hints Resolve lt_add_compat_r : num.
113 inline procedural "cic:/Coq/Num/LtProps/lt_add_compat.con" as lemma.
116 Hints Immediate lt_add_compat : num.