Module Judgement <: DecTypeSig.
Definition t := judgement.
Definition eqb (j1 j2: judgement) :=
match j1, j2 with
| provable, provable
| derivable, derivable
| corable, corable => true
| _, _ => false
end.

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