(** As noticed by P. Casteran, asking for the general [SetoidList.transpose] here is too restrictive. Think for instance of [f] being [M.add] : in general, [M.add k e (M.add k e' m)] is not equivalent to [M.add k e' (M.add k e m)]. Fortunately, we will never encounter this situation during a real [fold], since the keys received by this [fold] are unique. Hence we can ask the transposition property to hold only for non-equal keys.  This idea could be push slightly further, by asking the transposition property to hold only for (non-equal) keys living in the map given to [fold]. Please contact us if you need such a version.  FSets could also benefit from a restricted [transpose], but for this case the gain is unclear. *)
Definition transpose_neqkey :=
forall k k' e e' a, ~E.eq k k' ->
eqA (f k e (f k' e' a)) (f k' e' (f k e a)).
Hypothesis Tra : transpose_neqkey.

(* Specifications: *)
Lemma fold_commutes : forall i m k e, ~In k m ->
eqA (fold f m (f k e i)) (f k e (fold f m i)).