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

Lemma comp_parts_join: forall L R (HC: Share.comp L = R) a b c, join (Share.glb L a) (Share.glb L b) (Share.glb L c) -> join (Share.glb R a) (Share.glb R b) (Share.glb R c) -> join a b c.