intros t1 t2 u0 t0 u1.
generalize u0; clear u0.
elim u1; clear u1 t0 t1.
trivial.
intros t0 t1 in_t1 t3 suc_t3_t1 ih suc_t2_t3.
apply (successor_trans t0 t1 in_t1 t2).
apply ih; assumption.
Qed.

Lemma succs_refl : forall t : Tree, Successor t t.
intros.