Definition Lsh  : t := fst (split top).
Definition Rsh  : t := snd (split top).
Definition splice (a b: t) : t := lub (rel Lsh a) (rel Rsh b).

Axiom unrel_lub: forall a b1 b2, unrel a (lub b1 b2) = lub (unrel a b1) (unrel a b2).