Let $G$ be any CFG Grammar. There exists number $K$ dependent to $G$ so that for each $w\in L(G)$ with length bigger or equal than $K$, we can be write $w=uvxyz$ such that $uv^nxy^nz \in L(G)\; \forall\,n\geq 0$ and $|vy|\geq 1$.
My question is that this statement does not include the case of $|vxy|\leq K$. Should it be included for the theorem completeness, or is it redundant and it is indeed a special case (my professor did not include it e.g. but on Wikipedia and other books I always see that they include it)?