Top is Prime Element

Theorem
Let $L = \struct {S, \wedge, \preceq}$ be a bounded above meet semilattice.

Then $\top$ is a prime element

where $\top$ denotes the greatest element of $L$.

Proof
Let $x, y \in S$ such that
 * $x \wedge y \preceq \top$

Thus by definition of greatest element:
 * $x \preceq \top$ or $y \preceq \top$