Proof with auto.
intros. unfold join in H,H0.
icase c;icase b;icase a1;icase a2;inv H;inv H0;auto.
destruct (ijoin_identity1 _ _ H).
destruct (ijoin_identity1 _ _ H1).
generalize (ijoin_canc _ _ _ _ H1 H).
generalize (join_canc H2 H3); intros.
subst sh2 v2...
generalize (join_canc H2 H3).
generalize (combjoin_canc _ _ _ _ H1 H); intros.
f_equal...
icase sh0; icase sh1.
apply existT_ext...
Qed.

(* Specifications: *)
Lemma combineJ_ex_identities: forall a , {e : combiner &  join e a a}.
Proof with auto.