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.
End Equivalence.

Lemma equivalence_partition_pblock P D :
partition P D -> equivalence_partition (fun x y => y \in pblock P x) D = P.