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.

(*L50*)
Lemma share_metric_height_monotonic : forall s n1 n2,
n1<=n2 ->
share_metric n1 s <= share_metric n2 s.