Section BiKeyOrder.
Variable A: Type.
Variable R1 R2 eqA1 eqA2: relation A.
Definition BiKey := union R1 (intersection eqA1 R2).

Theorem BiKey_StrictTotalOrderViaEquiv:
StrictTotalOrderViaEquiv R1 eqA1 ->
StrictTotalOrderViaEquiv R2 eqA2 ->
StrictTotalOrderViaEquiv BiKey (intersection eqA1 eqA2).