\begin{definition}[Definition:Left Cancellable Operation]
Let $\struct {S, \circ}$ be an algebraic structure.
The operation $\circ$ in $\struct {S, \circ}$ is '''left cancellable''' {{iff}}:
:$\forall a, b, c \in S: a \circ b = a \circ c \implies b = c$
That is, {{iff}} all elements of $\struct {S, \circ}$ are left cancellable.
\end{definition}