(*==========================================================  nr IS THE LOWEST PERIOD...  ===========================================================*)
Definition diff_int_aux
(m:fmap)(z:dart)(a b:nat)(t:dart): Prop:=
forall i : nat, (a <= i <= b)%nat ->
Iter (f m) i z <> t.

Lemma diff_int_aux_dec:forall(m:fmap)(z:dart)(a b:nat)(t:dart),
{diff_int_aux m z a b t} + {~diff_int_aux m z a b t}.