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.

(*L53*)
Lemma share_metric_dif_monotonic: forall s1 s2 n n0,
(s1<=s2)%ba -> n<=n0 ->
height s1 < n ->
height s2 < n ->
(share_metric n s2 - share_metric n s1 <=
share_metric n0 s2 - share_metric n0 s1).