Section Fold.
Variables (A:Type)(eqA:A->A->Prop)(st:Equivalence eqA).
Variables (f:elt->A->A)(Comp:compat_op E.eq eqA f)(Ass:transpose eqA f).
Variables (i:A).
Variables (s s':t)(x:elt).
End Fold.
(** Properties of [cardinal] *)

Lemma union_cardinal:
forall s s', (forall x, mem x s && mem x s'=false) ->
cardinal (union s s')=cardinal s+cardinal s'.