Given (2), we can apply the lemma we proved in section (a). That is:

\[\begin{aligned} p(i,k)&= p(i,j) + |j,k|\\ &\leq t\cdot |i,j| + |j,k| \qquad\text{from (1)}\\ &\leq t\cdot |i,k| \qquad\qquad\text{from (2) & lemma}\end{aligned}\]

and our proof is complete \(\square\).