(* DIFFERENCE IN AN INTERVAL *)
Definition diff_int
(m:fmap)(z:dart)(a b:nat): Prop:=
forall i j : nat, (a <= i /\ i < j /\ j <= b)%nat ->
Iter (f m) i z <> Iter (f m) j z.

Lemma diff_int_le:forall(m:fmap)(z:dart)(a b:nat),
(b <= a)%nat -> diff_int m z a b.