End IdealDef.
Module Quotient.
Section ZmodQuotient.
Variables (R : zmodType) (I : predPredType R)
(zmodI : zmodPred I) (kI : keyed_pred zmodI).
Definition equiv (x y : R) := (x - y) \in kI.

Lemma equivE x y : (equiv x y) = (x - y \in kI). Proof. by []. Qed.