blob: 7b427aa5f0b02c52eb593c3c5cc51aa0cf4842f0 (
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
50
51
52
53
54
55
56
57
|
(****************************************************************************)
(* *)
(* 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. *)
(****************************************************************************)
Require Export Relations_1.
Require Export Relations_2.
Section Relations_3.
Variable U: Type.
Variable R: (Relation U).
Definition coherent : U -> U -> Prop :=
[x,y: U] (EXT z | (Rstar U R x z) /\ (Rstar U R y z)).
Definition locally_confluent : U -> Prop :=
[x: U] (y,z: U) (R x y) -> (R x z) -> (coherent y z).
Definition Locally_confluent : Prop := (x: U) (locally_confluent x).
Definition confluent : U -> Prop :=
[x: U] (y,z: U) (Rstar U R x y) -> (Rstar U R x z) -> (coherent y z).
Definition Confluent : Prop := (x: U) (confluent x).
Inductive noetherian : U -> Prop :=
definition_of_noetherian:
(x: U) ((y: U) (R x y) -> (noetherian y)) -> (noetherian x).
Definition Noetherian : Prop := (x: U) (noetherian x).
End Relations_3.
Hints Unfold coherent : sets v62.
Hints Unfold locally_confluent : sets v62.
Hints Unfold confluent : sets v62.
Hints Unfold Confluent : sets v62.
Hints Resolve definition_of_noetherian : sets v62.
Hints Unfold Noetherian : sets v62.
(* $Id$ *)
|