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___,, * 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: Rstar.v,v 1.8.2.1 2004/07/16 19:31:16 herbelin Exp $ i*)
35 (*#* Properties of a binary relation [R] on type [A] *)
42 cic:/Coq/Relations/Rstar/Rstar/A.var
46 cic:/Coq/Relations/Rstar/Rstar/R.var
49 (*#* Definition of the reflexive-transitive closure [R*] of [R] *)
51 (*#* Smallest reflexive [P] containing [R o P] *)
53 inline procedural "cic:/Coq/Relations/Rstar/Rstar.con" as definition.
55 inline procedural "cic:/Coq/Relations/Rstar/Rstar_reflexive.con" as theorem.
57 inline procedural "cic:/Coq/Relations/Rstar/Rstar_R.con" as theorem.
59 (*#* We conclude with transitivity of [Rstar] : *)
61 inline procedural "cic:/Coq/Relations/Rstar/Rstar_transitive.con" as theorem.
63 (*#* Another characterization of [R*] *)
65 (*#* Smallest reflexive [P] containing [R o R*] *)
67 inline procedural "cic:/Coq/Relations/Rstar/Rstar'.con" as definition.
69 inline procedural "cic:/Coq/Relations/Rstar/Rstar'_reflexive.con" as theorem.
71 inline procedural "cic:/Coq/Relations/Rstar/Rstar'_R.con" as theorem.
73 (*#* Equivalence of the two definitions: *)
75 inline procedural "cic:/Coq/Relations/Rstar/Rstar'_Rstar.con" as theorem.
77 inline procedural "cic:/Coq/Relations/Rstar/Rstar_Rstar'.con" as theorem.
79 (*#* Property of Commutativity of two relations *)
81 inline procedural "cic:/Coq/Relations/Rstar/commut.con" as definition.