Section PrimeIdealTheory.
Variables (R : comRingType) (I : predPredType R)
(pidealrI : prime_idealr I) (kI : keyed_pred pidealrI).

Lemma prime_idealrM u v : (u * v \in kI) = (u \in kI) || (v \in kI).
End PrimeIdealTheory.