End StrictTotalOrderViaEquiv.
Section Operators.
Variable A: Type.
Variable R1 R2 eqA: relation A.

Lemma union_IrreflViaEquiv: IrreflViaEquiv R1 eqA -> IrreflViaEquiv R2 eqA -> IrreflViaEquiv (union R1 R2) eqA.