intro H; apply H; clear H.
assert (Share.glb Share.Rsh
(fst (Share.split Share.Lsh)) = Share.bot); [ | rewrite H; auto].
apply sub_glb_bot with Share.Lsh.
destruct (Share.split Share.Lsh) eqn:H.
apply Share.split_together in H.
simpl.
rewrite <- H.
apply leq_join_sub.
apply Share.lub_upper1.
apply glb_Rsh_Lsh.
Qed.

Lemma perm_of_res_op2:
forall r,
perm_order'' (perm_of_res' r) (perm_of_res_lock r).