Axiom:Auxiliary Relation Axioms

Definition
Let $L = \struct {S, \vee, \preceq}$ be a bounded below join semilattice.

Let $\RR \subseteq S \times S$ be a relation on $S$.

$\RR$ satisfies the auxiliary relation axioms $\RR$ satisifes the axioms:

where $\bot$ denotes the bottom and $\land$ denotes conjunction.