Definition share_metric (n : nat) (s : canonTree) : nat :=
match n with
| 0 => 0
| S n => match le_dec (height s) n with
| left _ => countBLeafCT n s + 1
| right _ => 0
end
end.

Lemma shareTreeOrd_dec: forall t1 t2 : ShareTree,
{shareTreeOrd t1 t2} + {~shareTreeOrd t1 t2}.