Proportion is Symmetric

Theorem
Proportion is a symmetric relation.

That is:


 * $\forall x, y \in \R: x \propto y \implies y \propto x$

Proof
Let $x, y$ be arbitrary.

Let $x$ be proportional to $y$:


 * $x \propto y$

Then by definition:

The result follows from the definition of symmetry and proportion.