Proportion is Equivalence Relation

Theorem
Proportion is an equivalence relation.

Proof

 * Proportion is Reflexive: $\forall x \in \R: x \propto x$
 * Proportion is Symmetric: $\forall x, y \in \R: x \propto y \implies y \propto x$
 * Proportion is Transitive: $\forall x, y, z \in \R: x \propto y \land y \propto z \implies x \propto z$

The result follows from the definition of an equivalence relation.