Assume two hypotheses classes $H_A\subset H_B$ defined over the same instance space $\delta$. Assume also $VC(H_A)=d$, does this mean $VC(H_B)\geq d$ ? where $VC$ is the VC dimension.
We can use the same set of instances shattered $H_A$ to shatter $H_B$. Seems obvious to me but is it true? is there a reference for this?