Lemma join_splice2_aux1: forall a1 a2 b1 b2, Share.lub (Share.rel Share.Lsh (Share.glb a1 a2)) (Share.rel Share.Rsh (Share.glb b1 b2)) = Share.bot -> Share.glb a1 a2 = Share.bot /\ Share.glb b1 b2 = Share.bot.