On positive theories of semigroup varieties and pseudovarieties

Let $\mathcal P$ be a positive language, $\mathcal L\subseteq\mathcal P$, then $\mathcal L\mathfrak X=\mathcal L\mathfrak X\cap\mathfrak F$, where $\mathfrak X$ is a nonperiodic semigroup variety and $\mathfrak X\cap\mathfrak F$ is a finite trace of the variety $\mathfrak X$.