Section Quotient.
Variable A:Type.
Variable R:relation A.
Hypothesis equivR:equivalence R.
Definition equiv_class (x:A) : Ensemble A :=
[ y:A | R x y ].
Definition equiv_classes : Ensemble (Ensemble A) :=
Im Full_set equiv_class.
Definition quotient : Type :=
{ S:Ensemble A | In equiv_classes S }.

Lemma equiv_class_in_quotient: forall x:A,
In equiv_classes (equiv_class x).