\begin{definition}[Definition:Middle Cancellation Property]
Let $\struct {S, \circ}$ be a semigroup.
Then $\circ$ is said to have the '''middle cancellation property''' {{iff}}:
:$\forall a, b, c, d, x \in S: a \circ x \circ b = c \circ x \circ d \implies a \circ b = c \circ d$
Category:Definitions/Cancellability
Category:Definitions/Semigroups
\end{definition}