Section Preim.
Variables (rT : eqType) (f : T -> rT).
Definition preim_partition := equivalence_partition (fun x y => f x == f y).

(* Specifications: *)
Lemma preim_partitionP D : partition (preim_partition D) D.
Lemma transversalP P D : partition P D -> is_transversal (transversal P D) P D.
Section Transversals.