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.

(*L52*)
Lemma share_metric_glb : forall s s' n,
~(s<=s')%ba->
0 < share_metric n s ->
0 < share_metric n (glb s s') ->
(share_metric n (glb s s') < share_metric n s)%nat.