diff options
Diffstat (limited to 'theories/Sets/Cpo.v')
| -rw-r--r-- | theories/Sets/Cpo.v | 12 |
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)}. |