Ltac pfullshare_join :=
elimtype False;
solve [ eapply pshare_join_full_false1; eauto
| eapply pshare_join_full_false2; eauto
| eapply pshare_join_full_false3; eauto
| eapply pshare_join_full_false4; eauto
| eapply pshare_pjoin_full_false3; eauto
| eapply pshare_pjoin_full_false4; eauto
].
Program Definition split_pshare (sh: pshare) : pshare * pshare :=
(mk_lifted (fst (Share.split sh)) _, mk_lifted (snd (Share.split sh)) _).
Next Obligation.
Next Obligation.

(* Specifications: *)
Lemma psplit_split: forall psh psha pshb,
(split_pshare psh = (psha, pshb)) =
(Share.split (lifted_obj psh) = (lifted_obj psha, lifted_obj pshb)).
Lemma psplit_pjoin: forall psh psha pshb,
split_pshare psh = (psha, pshb) ->
join psha pshb psh.
Lemma pshare_split_neq1: forall psh psh1 psh2, split_pshare psh = (psh1, psh2) -> psh1 <> psh.
Lemma pshare_split_neq2: forall psh psh1 psh2, split_pshare psh = (psh1, psh2) -> psh2 <> psh.
Definition pLhalf : pshare := fst (split_pshare pfullshare).