Section Equivalence.
Variables (R : rel T) (D : {set T}).
Let Px x := [set y in D | R x y].
Definition equivalence_partition := [set Px x | x in D].
Local Notation P := equivalence_partition.
Hypothesis eqiR : {in D & &, equivalence_rel R}.
Let Pxx x : x \in D -> x \in Px x.

Lemma pblock_equivalence_partition :
{in D &, forall x y, (y \in pblock P x) = R x y}.