End RelationDef.
Arguments union {A} R1 R2 x y /.
Arguments intersection {A} R1 R2 x y /.
Module StrictTotalOrderViaEquiv.
Section StrictTotalOrderViaEquiv.
Variable A: Type.
Variables R eqA: relation A.
Variable Order: StrictTotalOrderViaEquiv R eqA.

Lemma RightProperViaEquiv: forall x y y0, eqA y0 y -> R x y -> R x y0.
Instance ProperViaEquiv: Proper (eqA ==> eqA ==> iff) R.