induction  B as [| a B HrecB].
auto.
simpl in |- *.
elim (Aeq_dec x a).
intro.
unfold not in |- *.
unfold not in HrecB.
intro.
apply HrecB; auto.
intro.
unfold not in |- *.
unfold not in HrecB.
simpl in |- *.
intro.
elim H.
intro.
cut (a = x /\ a <> x).
intro.
auto.
split.
auto.
auto.
auto.
Qed.

(* Specifications: *)
Lemma set_In_dec : forall (a : A) (x : set), {set_In a x} + {~ set_In a x}.
unfold set_In in |- *.