Infinite Sequence Property of Well-Founded Relation/Reverse Implication

Theorem
Let $\left({S, \preceq}\right)$ be an ordered set.

Suppose that there is no infinite sequence $\left \langle {a_n}\right \rangle$ of elements of $S$ such that $\forall n \in \N: a_{n+1} \prec a_n$.

Then $\left({S, \preceq}\right)$ is well-founded.