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 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
25 (* \VV/ **************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (*i $Id: Between.v,v 1.12.2.1 2004/07/16 19:30:59 herbelin Exp $ i*)
35 include "Arith/Le.ma".
37 include "Arith/Lt.ma".
40 Open Local Scope nat_scope.
44 Implicit Types k l p q r : nat.
52 cic:/Coq/Arith/Between/Between/P.var
56 cic:/Coq/Arith/Between/Between/Q.var
59 inline procedural "cic:/Coq/Arith/Between/between.ind".
62 Hint Constructors between: arith v62.
65 inline procedural "cic:/Coq/Arith/Between/bet_eq.con" as lemma.
68 Hint Resolve bet_eq: arith v62.
71 inline procedural "cic:/Coq/Arith/Between/between_le.con" as lemma.
74 Hint Immediate between_le: arith v62.
77 inline procedural "cic:/Coq/Arith/Between/between_Sk_l.con" as lemma.
80 Hint Resolve between_Sk_l: arith v62.
83 inline procedural "cic:/Coq/Arith/Between/between_restr.con" as lemma.
85 inline procedural "cic:/Coq/Arith/Between/exists_between.ind".
88 Hint Constructors exists_between: arith v62.
91 inline procedural "cic:/Coq/Arith/Between/exists_le_S.con" as lemma.
93 inline procedural "cic:/Coq/Arith/Between/exists_lt.con" as lemma.
96 Hint Immediate exists_le_S exists_lt: arith v62.
99 inline procedural "cic:/Coq/Arith/Between/exists_S_le.con" as lemma.
102 Hint Immediate exists_S_le: arith v62.
105 inline procedural "cic:/Coq/Arith/Between/in_int.con" as definition.
107 inline procedural "cic:/Coq/Arith/Between/in_int_intro.con" as lemma.
110 Hint Resolve in_int_intro: arith v62.
113 inline procedural "cic:/Coq/Arith/Between/in_int_lt.con" as lemma.
115 inline procedural "cic:/Coq/Arith/Between/in_int_p_Sq.con" as lemma.
117 inline procedural "cic:/Coq/Arith/Between/in_int_S.con" as lemma.
120 Hint Resolve in_int_S: arith v62.
123 inline procedural "cic:/Coq/Arith/Between/in_int_Sp_q.con" as lemma.
126 Hint Immediate in_int_Sp_q: arith v62.
129 inline procedural "cic:/Coq/Arith/Between/between_in_int.con" as lemma.
131 inline procedural "cic:/Coq/Arith/Between/in_int_between.con" as lemma.
133 inline procedural "cic:/Coq/Arith/Between/exists_in_int.con" as lemma.
135 inline procedural "cic:/Coq/Arith/Between/in_int_exists.con" as lemma.
137 inline procedural "cic:/Coq/Arith/Between/between_or_exists.con" as lemma.
139 inline procedural "cic:/Coq/Arith/Between/between_not_exists.con" as lemma.
141 inline procedural "cic:/Coq/Arith/Between/P_nth.ind".
143 inline procedural "cic:/Coq/Arith/Between/nth_le.con" as lemma.
145 inline procedural "cic:/Coq/Arith/Between/eventually.con" as definition.
147 inline procedural "cic:/Coq/Arith/Between/event_O.con" as lemma.
154 Hint Resolve nth_O bet_S bet_emp bet_eq between_Sk_l exists_S exists_le
155 in_int_S in_int_intro: arith v62.
159 Hint Immediate in_int_Sp_q exists_le_S exists_S_le: arith v62.