Infinite Sequence Property of Strictly 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:
 * $\forall n \in \N: a_{n + 1} \mathrel \RR a_n$

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