intros until sh2; intros H H0.
destruct (dec_share_identity sh2).
generalize (split_nontrivial' _ _ _ H0); intro.
spec H1...
destruct (eq_dec sh1 sh)...
subst sh1.
generalize (split_join _ _ _ H0); intro.
apply join_comm in H1.
apply unit_identity in H1...
Qed.

Lemma nonemp_split_neq2: forall sh sh1 sh2, nonidentity sh -> split sh = (sh1, sh2) -> sh2 <> sh.
Proof with auto.