Why does removing the ceiling result in $a + 1$?
I'm reading Introduction to Data Compression by Guy E. Blelloch on page $19$ on Information Theory, here he is proving an upper bound.
$$ \begin{align} 1+\lceil-\log s\rceil &= 1+\lceil-\log_2(\prod_{i=1}^np_i)\rceil\\ &=1+\lceil\sum_{i=1}^n-\log_2p_i\rceil\\ &=1+\lceil\sum_{i=1}^ns_i\rceil\\ &\lt2+\sum_{i=1}^ns_i\\ \end{align} $$
Where $s_i=\log_2\frac{1}{p_i}$. The ceiling was removed and $a + 1$ was added.