\begin{definition}[Definition:Partial Subtraction]
'''Partial subtraction''' is the operation $\dot - : \N \times \N \to \N$ defined on the set of natural numbers $\N$ as follows:
:$\forall a, b \in \N: a \mathop {\dot -} b = \begin{cases}
0 & : a < b \\
a - b & : a \ge b
\end{cases}$
where $a - b$ denotes natural number subtraction.
\end{definition}