Does $|P'| - |P|$ mean the order of partition $P'$ minus the order of partition $P$?

Question

I am currently proving a theorem which states: 'If $P'$ is a refinement of $P$ then $U(f,P') \leq U(f,P)$ and $L(f,P') \geq L(f,P)$.

The book I am using states to prove it via induction on $m = |P'|-|P|$.

I am simply wondering whether $|P'|$ and $|P|$ means take the order of the partitions $P'$ and $P$ where a partition is a set $\{x_0,...,x_n\}$ on the interval $[a,b]$?