Lemma join_splice2_aux: forall a1 a2 a3 b1 b2 b3, Share.lub (Share.rel Share.Lsh (Share.lub a1 a2)) (Share.rel Share.Rsh (Share.lub b1 b2)) = Share.lub (Share.rel Share.Lsh a3) (Share.rel Share.Rsh b3) -> Share.lub a1 a2 = a3 /\ Share.lub b1 b2 = b3.