Definition:Middle Cancellation Property

Definition

Let $\struct {S, \circ}$ be a semigroup.

Then $\circ$ is said to have the middle cancellation property if and only if:

$\forall a, b, c, d, x \in S: a \circ x \circ b = c \circ x \circ d \implies a \circ b = c \circ d$