Is the lifting of an ordering $≤$ to the a relation on the powerset $X⊑Y:=∀x∈X,y∈Y. x ≤ y$ a known construction?

Question

Let $(A, ≤)$ be a poset. We can define a relation on $\mathcal{P}(A)$: $X⊑Y:=∀x∈X,y∈Y. x ≤ y$. My question is: Is this a known derived ordering? It's clearly not the lexicographical, since $∀X. X⊑∅$ (but $∅$ is also a bottom element).