The sum of the depths is at most two-thirds of what it was before.
Each tree is about two-thirds as deep as it was before.
The remainder of the estimation is largely as before with B replaced by C.
Most of the theorems presented here have never been published before.
Note that P comes before Q along the arc l.
We may require that the point P lie in one of the trees constructed before or during the ith stage of the induction.