Definition retainer_part (sh: Share.t) := Share.glb Share.Lsh sh.

Lemma left_right_join: forall a b c, join (Share.glb Share.Lsh a) (Share.glb Share.Lsh b) (Share.glb Share.Lsh c) -> join (Share.glb Share.Rsh a) (Share.glb Share.Rsh b) (Share.glb Share.Rsh c) -> join a b c.