Definition ge (x y: t) : Prop := x = y \/ x = true.

Lemma eq_trans: forall x y z, eq x y -> eq y z -> eq x z.
Definition beq (x y: t) : bool :=
match x, y with
| None, None => true
| Some x1, Some y1 => L.beq x1 y1
| _, _ => false
end.