Proof with try tauto;try omega.
intros. icase n.
apply tree_avg_avg2round in H.
destruct H.
destruct (le_dec (height s) (S n))...
rewrite tree_round_left_None in H...
inv H.
Qed.

Lemma decompose_Lsh: forall sh,
unrel Lsh sh = fst (decompose sh).