diff options
author | glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
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committer | glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
commit | 61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch) | |
tree | 961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Sets/Cpo.v | |
parent | 6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (diff) |
Delete trailing whitespaces in all *.{v,ml*} files
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12337 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Sets/Cpo.v')
-rw-r--r-- | theories/Sets/Cpo.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Sets/Cpo.v b/theories/Sets/Cpo.v index c1e64babc..8c69e6877 100644 --- a/theories/Sets/Cpo.v +++ b/theories/Sets/Cpo.v @@ -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)}. |