Strict_Ordering_Preserved_under_Product_with_Cancellable_Element

Let $\left({S, \circ, \preceq}\right)$ be an ordered semigroup. Let $x, y, z \in S$ be such that $(1): \quad z$ is cancellable for $\circ$ $(2): \quad x \prec y$ Then $x \circ z \prec y \circ z$ $z \circ x \prec z \circ y$