\begin{definition}[Definition:Decreasing/Sequence]
Let $\struct {S, \preceq}$ be a totally ordered set.
Then a sequence $\sequence {a_k}_{k \mathop \in A}$ of terms of $S$ is '''decreasing''' {{iff}}:
:$\forall j, k \in A: j < k \implies a_k \preceq a_j$
\end{definition}