Section Fix_X.
Variable (X:Type).
Context {intX : registered X}.
Fixpoint inb eqb (x:X) (A: list X) :=
match A with
nil => false
| a::A' => orb (eqb a x) (inb eqb x A')
end.
Variable X_eqb : X -> X -> bool.
Hypothesis X_eqb_spec : (forall (x y:X), Bool.reflect (x=y) (X_eqb x y)).

Lemma inb_spec: forall x A, Bool.reflect (In x A) (inb X_eqb x A).