Definition:Middle Cancellation Property

Definition
Let $\left({S, \circ}\right)$ be a semigroup.

Then $\circ$ is said to have the middle cancellation property iff:


 * $a \circ x \circ b = c \circ x \circ d \implies a \circ b = c \circ d$

holds for all $a,b,c,d,x \in S$.