Axiom:Lattice Filter Axioms

Definition
Let $\struct {S, \vee, \wedge, \preccurlyeq}$ be a lattice.

Let $F \subseteq S$ be a non-empty subset of $S$.

$F$ is a (lattice) filter of $S$ $F$ satisifes the axioms:

These criteria are called the (lattice) filter axioms.