Definition:Multiplicative Relation

Definition

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

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

Then $\RR$ is multiplicative (relation) if and only if

$\forall a, x, y \in S: \paren {\tuple {a, x}, \tuple {a, y} \in \RR \implies \tuple {a, x \wedge y} \in \RR}$

Sources

• Mizar article WAYBEL_7:def 7