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

Lemma join_parts: forall L R (HC: Share.comp L = R) sh1 sh2 sh, join sh1 sh2 (Share.glb L sh) -> Share.glb L sh1 = sh1 /\ Share.glb R sh1 = Share.bot /\ Share.glb L sh2 = sh2 /\ Share.glb R sh2 = Share.bot.