Proof with auto.
intros.
icase a; icase a'; icase b; icase c.
unfold ijoin in *.
apply existT_ext.
eapply join_canc; eauto.
Qed.

Lemma ijoin_identity1 {A}  {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{CA: Disj_alg A}: forall a b,
ijoin a b b ->
False.