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 LeftProperViaEquiv: forall x x0 y, eqA x x0 -> R x y -> R x0 y.