(* 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.