Complement of Top/Bounded Lattice

Theorem
Let $\struct {S, \vee, \wedge, \preceq}$ be a bounded lattice.

Then the top $\top$ has a unique complement, namely $\bot$, bottom.

Proof
By Dual Pairs (Order Theory), $\top$ is dual to $\bot$.

The result follows from the Duality Principle and Complement of Bottom.

Also see

 * Complement of Bottom