We claim that ci ≥ i-2 for each i with 2≤i≤d: Just before yi was made a child of x, y1,...,yi−1 were already children of x, and so x had degree at least i−1 at that time.
Mi tvrdimo da ci ≥ i-2 za svaki i sa 2≤i≤d: stačno pre yi je postao dete od x,y1,...,yi−1 su već bili deca od x, i tako x je imao stepen najmanje i−1 u tom trenutku.