Module JudgementClass.
Definition t := judgement_class.
Definition eqb (jc1 jc2: judgement_class) :=
match jc1, jc2 with
| Provable, Provable => true
| Derivable, Derivable => true
| _, _ => false
end.

Lemma eqb_spec: forall x y, Bool.reflect (x = y) (eqb x y).