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Definition adhDa (D:R -> Prop) (a:R) : Prop :=
  forall alp:R, alp > 0 ->  exists x : R, D x /\ Rdist x a < alp.

Lemma single_limit : forall (f:R -> R) (D:R -> Prop) (l l' x0:R), adhDa D x0 -> limit1_in f D l x0 -> limit1_in f D l' x0 -> l = l'.