summaryrefslogtreecommitdiff
path: root/theories/Sets/Cpo.v
diff options
context:
space:
mode:
Diffstat (limited to 'theories/Sets/Cpo.v')
-rw-r--r--theories/Sets/Cpo.v12
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Sets/Cpo.v b/theories/Sets/Cpo.v
index 1e1b70d5..8c69e687 100644
--- a/theories/Sets/Cpo.v
+++ b/theories/Sets/Cpo.v
@@ -24,7 +24,7 @@
(* in Summer 1995. Several developments by E. Ledinot were an inspiration. *)
(****************************************************************************)
-(*i $Id: Cpo.v 9245 2006-10-17 12:53:34Z notin $ i*)
+(*i $Id$ i*)
Require Export Ensembles.
Require Export Relations_1.
@@ -35,7 +35,7 @@ Section Bounds.
Variable D : PO U.
Let C := Carrier_of U D.
-
+
Let R := Rel_of U D.
Inductive Upper_Bound (B:Ensemble U) (x:U) : Prop :=
@@ -45,7 +45,7 @@ Section Bounds.
Inductive Lower_Bound (B:Ensemble U) (x:U) : Prop :=
Lower_Bound_definition :
In U C x -> (forall y:U, In U B y -> R x y) -> Lower_Bound B x.
-
+
Inductive Lub (B:Ensemble U) (x:U) : Prop :=
Lub_definition :
Upper_Bound B x -> (forall y:U, Upper_Bound B y -> R x y) -> Lub B x.
@@ -57,7 +57,7 @@ Section Bounds.
Inductive Bottom (bot:U) : Prop :=
Bottom_definition :
In U C bot -> (forall y:U, In U C y -> R bot y) -> Bottom bot.
-
+
Inductive Totally_ordered (B:Ensemble U) : Prop :=
Totally_ordered_definition :
(Included U B C ->
@@ -77,7 +77,7 @@ Section Bounds.
Included U (Couple U x1 x2) X ->
exists x3 : _, In U X x3 /\ Upper_Bound (Couple U x1 x2) x3) ->
Directed X.
-
+
Inductive Complete : Prop :=
Definition_of_Complete :
(exists bot : _, Bottom bot) ->
@@ -102,7 +102,7 @@ Section Specific_orders.
Record Cpo : Type := Definition_of_cpo
{PO_of_cpo : PO U; Cpo_cond : Complete U PO_of_cpo}.
-
+
Record Chain : Type := Definition_of_chain
{PO_of_chain : PO U;
Chain_cond : Totally_ordered U PO_of_chain (Carrier_of U PO_of_chain)}.