Section option_eqb.
Variable X : Type.
Variable eqb : X -> X -> bool.
Variable spec : forall x y, reflect (x = y) (eqb x y).
Definition option_eqb (A B : option X) :=
match A,B with
| None,None => true
| Some x, Some y => eqb x y
| _,_ => false
end.

Lemma option_eqb_spec A B : reflect (A = B) (option_eqb A B).