Definition union_spec : In x (union s s') <-> In x s \/ In x s'
   := @MF.union_iff s s' x.Definition inter_spec : In x (inter s s') <-> In x s /\ In x s'
   := @MF.inter_iff s s' x.Definition diff_spec : In x (diff s s') <-> In x s /\ ~In x s'
   := @MF.diff_iff s s' x.Definition fold_spec : forall (A : Type) (i : A) (f : elt -> A -> A),
   fold f s i = fold_left (flip f) (elements s) i
   := @M.fold_1 s.Definition cardinal_spec : cardinal s = length (elements s)
   := @M.cardinal_1 s.

Lemma elements_spec1 : InA E.eq x (elements s) <-> In x s.