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

Lemma beq_correct: forall x y, beq x y = true -> eq x y.
Definition ge (x y: t) : Prop :=
match x, y with
| None, _ => True
| _, None => False
| Some x1, Some y1 => L.ge x1 y1
end.