Right Operation is Left Distributive over All Operations

Theorem
Let $\left({S, \circ, \rightarrow}\right)$ be an algebraic structure where:
 * $\rightarrow$ is the right operation
 * $\circ$ is any arbitrary binary operation.

Then $\rightarrow$ is left distributive over $\circ$.

Proof
By definition of the right operation:

The result follows by definition of left distributivity.