diff options
Diffstat (limited to 'theories/Sets/Partial_Order.v')
| -rw-r--r-- | theories/Sets/Partial_Order.v | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/theories/Sets/Partial_Order.v b/theories/Sets/Partial_Order.v index 6210913c..4fe8f4f6 100644 --- a/theories/Sets/Partial_Order.v +++ b/theories/Sets/Partial_Order.v @@ -24,27 +24,27 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Partial_Order.v 9245 2006-10-17 12:53:34Z notin $ i*) +(*i $Id$ i*) Require Export Ensembles. Require Export Relations_1. Section Partial_orders. Variable U : Type. - + Definition Carrier := Ensemble U. - + Definition Rel := Relation U. - + Record PO : Type := Definition_of_PO { Carrier_of : Ensemble U; Rel_of : Relation U; PO_cond1 : Inhabited U Carrier_of; PO_cond2 : Order U Rel_of }. Variable p : PO. - + Definition Strict_Rel_of : Rel := fun x y:U => Rel_of p x y /\ x <> y. - + Inductive covers (y x:U) : Prop := Definition_of_covers : Strict_Rel_of x y -> @@ -60,7 +60,7 @@ Hint Resolve Definition_of_covers: sets v62. Section Partial_order_facts. Variable U : Type. Variable D : PO U. - + Lemma Strict_Rel_Transitive_with_Rel : forall x y z:U, Strict_Rel_of U D x y -> Rel_of U D y z -> Strict_Rel_of U D x z. |