I would like to give some definiton is that ; Let $S$ be a dominating subset of $[\mathbb{N}]^{\infty}$ and $S=\{s_{\alpha} : \alpha<\mathfrak{d}\}$ is called $\mathfrak{d}$-scale if for every $\alpha<\beta<\mathfrak{d}$ $s_{\beta}\nleq^{*} s_{\alpha}$.

In the paper from Tsaban, there is a lemma which is , 'every $\mathfrak{d}-scale$ is $\mathfrak{d}-concentrated$ on $[\mathbb{N}]^{<\infty}$.

for this lemma, how can we start? it is obvious that every $scale$ is $\mathfrak{d}-concentrated$ on $[\mathbb{N}]^{<\infty}$, but $\mathfrak{d}-scales$ any help will be appreciated. thank you in advance.