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                nr IS THE LOWEST PERIOD... 

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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}.