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).

Lemma remove_fold_1:
mem x s=true -> eqA (f x (fold f (remove x s) i)) (fold f s i).