Max Operation Yields Supremum of Parameters/General Case

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

Let $x_1, x_2, \dots ,x_n \in S$ for some $n \in \N_{>0}$.

Then:
 * $\max \set {x_1, x_2, \dots ,x_n} = \sup \set {x_1, x_2, \dots ,x_n}$

where:
 * $\max$ denotes the max operation
 * $\sup$ denotes the supremum.

Proof
Supremum of Singleton