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

Lemma add_cardinal_2:
forall s x, mem x s=false -> cardinal (add x s)=S (cardinal s).