Infinite Sequence Property of Well-Founded Relation/Reverse Implication

Theorem
Let $\struct {S, \RR}$ be a relational structure.

Let $\RR$ be such that there exists no infinite sequence $\sequence {a_n}$ of elements of $S$ such that:
 * $\forall n \in \N: \paren {a_{n + 1} \mathrel \RR a_n} \text { and } \paren {a_{n + 1} \ne a_n}$

Then $\RR$ is a well-founded relation.