Section StrictTotalOrderViaEquiv.
Variable A: Type.
Variables R eqA: relation A.
Variable Order: StrictTotalOrderViaEquiv R eqA.
Instance ProperViaEquiv: Proper (eqA ==> eqA ==> iff) R.
End StrictTotalOrderViaEquiv.

Theorem StrictTotalOrder_is_StrictTotalOrderViaEquiv:
forall {A} (R: relation A), StrictTotalOrder R <-> StrictTotalOrderViaEquiv R eq.