Proof with auto.
intros. unfold join in H|-*.
icase a; icase b.
icase c; red in H; red; destruct H;
split...
apply ijoin_com...
apply join_comm...
Qed.

Lemma combineJ_canc {C1: Canc_alg T1}: forall a1 a2 b c : combiner,
join a1 b c -> join a2 b c -> a1=a2.