Infinite Sequence Property of Well-Founded Relation

Theorem
Let $\struct {S, \preceq}$ be an ordered set.

Then $\struct {S, \preceq}$ is well-founded there is no infinite sequence $\sequence {a_n}$ of elements of $S$ such that:
 * $\forall n \in \N: a_{n + 1} \prec a_n$

That is, there is no infinite sequence $\sequence {a_n}$ such that $a_0 \succ a_1 \succ a_2 \succ \cdots$.