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.

(*L51*)
Lemma share_metric_lub : forall s s' n,
~(s'<=s)%ba->
0 < share_metric n s ->
0 < share_metric n (lub s s') ->
(share_metric n s<share_metric n (lub s s')).