Complement (Lattice)

An element $y$ is the complement of an element $x$ in a bound lattice $(A,\bigsqcup ,\sqcap ,\perp ,\top )$ iff

$$x\bigsqcup y=\top x\sqcap y=\perp$$

Equivalently:

$$\frac{x\le zy\le z}{z=\top }\frac{z\le xz\le y}{z=\perp }$$