(* Merging two equivalence classes *)
Section IDENTIFY.
Variable uf: t.
Variables a b: elt.
Hypothesis a_canon: M.get a uf.(m) = None.
Hypothesis not_same_class: repr uf b <> a.

Lemma identify_order:
forall x y,
order (M.set a b uf.(m)) y x <->
order uf.(m) y x \/ (x = a /\ y = b).