(** From a [StrictOrder] to the corresponding [PartialOrder]: [le = lt \/ eq]. If the order is total, we could also say [ge = ~lt]. *)

Lemma StrictOrder_PreOrder
`(Equivalence A eqA, StrictOrder A R, Proper _ (eqA==>eqA==>iffT) R) :
PreOrder (relation_disjunction R eqA).