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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.

(* Specifications: *)
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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'.
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Lemma limit_comp :
forall (f g:R -> R) (Df Dg:R -> Prop) (l l' x0:R),
limit1_in f Df l x0 ->
limit1_in g Dg l' l -> limit1_in (fun x:R => g (f x)) (Dgf Df Dg f) l' x0.