blob: 28cc6a5f691b3c2f28a5305acb143818050296ec (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
|
(****************************************************************************)
(* *)
(* Naive Set Theory in Coq *)
(* *)
(* INRIA INRIA *)
(* Rocquencourt Sophia-Antipolis *)
(* *)
(* Coq V6.1 *)
(* *)
(* Gilles Kahn *)
(* Gerard Huet *)
(* *)
(* *)
(* *)
(* Acknowledgments: This work was started in July 1993 by F. Prost. Thanks *)
(* to the Newton Institute for providing an exceptional work environment *)
(* in Summer 1995. Several developments by E. Ledinot were an inspiration. *)
(****************************************************************************)
(* $Id$ *)
Require Export Relations_1.
Section Relations_2.
Variable U: Type.
Variable R: (Relation U).
Inductive Rstar : (Relation U) :=
Rstar_0: (x: U) (Rstar x x)
| Rstar_n: (x, y, z: U) (R x y) -> (Rstar y z) -> (Rstar x z).
Inductive Rstar1 : (Relation U) :=
Rstar1_0: (x: U) (Rstar1 x x)
| Rstar1_1: (x: U) (y: U) (R x y) -> (Rstar1 x y)
| Rstar1_n: (x, y, z: U) (Rstar1 x y) -> (Rstar1 y z) -> (Rstar1 x z).
Inductive Rplus : (Relation U) :=
Rplus_0: (x, y: U) (R x y) -> (Rplus x y)
| Rplus_n: (x, y, z: U) (R x y) -> (Rplus y z) -> (Rplus x z).
Definition Strongly_confluent : Prop :=
(x, a, b: U) (R x a) -> (R x b) -> (exT U [z: U] (R a z) /\ (R b z)).
End Relations_2.
Hints Resolve Rstar_0 : sets v62.
Hints Resolve Rstar1_0 : sets v62.
Hints Resolve Rstar1_1 : sets v62.
Hints Resolve Rplus_0 : sets v62.
|