diff options
Diffstat (limited to 'theories/Classes')
| -rw-r--r-- | theories/Classes/CMorphisms.v | 8 | ||||
| -rw-r--r-- | theories/Classes/RelationClasses.v | 5 |
2 files changed, 9 insertions, 4 deletions
diff --git a/theories/Classes/CMorphisms.v b/theories/Classes/CMorphisms.v index 048faa91..fdedbf67 100644 --- a/theories/Classes/CMorphisms.v +++ b/theories/Classes/CMorphisms.v @@ -266,11 +266,12 @@ Section GenericInstances. transitivity (y x0)... Qed. - (** The complement of a crelation conserves its proper elements. *) + Unset Strict Universe Declaration. - Program Definition complement_proper + (** The complement of a crelation conserves its proper elements. *) + Program Definition complement_proper (A : Type@{k}) (RA : crelation A) `(mR : Proper (A -> A -> Prop) (RA ==> RA ==> iff) R) : - Proper (RA ==> RA ==> iff) (complement R) := _. + Proper (RA ==> RA ==> iff) (complement@{i j Prop} R) := _. Next Obligation. Proof. @@ -280,7 +281,6 @@ Section GenericInstances. Qed. (** The [flip] too, actually the [flip] instance is a bit more general. *) - Program Definition flip_proper `(mor : Proper (A -> B -> C) (RA ==> RB ==> RC) f) : Proper (RB ==> RA ==> RC) (flip f) := _. diff --git a/theories/Classes/RelationClasses.v b/theories/Classes/RelationClasses.v index 1a40e5d5..15cb02d3 100644 --- a/theories/Classes/RelationClasses.v +++ b/theories/Classes/RelationClasses.v @@ -89,6 +89,11 @@ Section Defs. Global Instance Equivalence_PER {R} `(E:Equivalence R) : PER R | 10 := { }. + (** An Equivalence is a PreOrder plus symmetry. *) + + Global Instance Equivalence_PreOrder {R} `(E:Equivalence R) : PreOrder R | 10 := + { }. + (** We can now define antisymmetry w.r.t. an equivalence relation on the carrier. *) Class Antisymmetric eqA `{equ : Equivalence eqA} (R : relation A) := |