Section FoldOpt.
Variables (A:Type)(eqA:A->A->Prop)(st:Equivalence eqA).
Variables (f:elt->A->A)(Comp:Proper (E.eq==>eqA==>eqA) f).
End FoldOpt.
(** An alternative version of [choose_3] *)

Lemma choose_equal : forall s s', Equal s s' ->
match choose s, choose s' with
| Some x, Some x' => E.eq x x'
| None, None => True
| _, _ => False
end.