Definition BiKey := union R1 (intersection eqA1 R2).

(* Specifications: *)
Theorem BiKey_StrictTotalOrderViaEquiv: StrictTotalOrderViaEquiv R1 eqA1 -> StrictTotalOrderViaEquiv R2 eqA2 -> StrictTotalOrderViaEquiv BiKey (intersection eqA1 eqA2).
Lemma BiKey_StrictTotalOrder: StrictTotalOrderViaEquiv R1 eqA1 -> StrictTotalOrder R2 -> StrictTotalOrder BiKey.