Let $X$ be a D11: Set.
Let $\mathcal{C}$ be a D74: Set cover for $X$.
A D11: Set $\mathcal{S}$ is a subcover of $\mathcal{C}$ for $X$ if and only if

(1)	$X \subseteq \cup \mathcal{S}$ (D74: Set cover)
(2)	$\mathcal{S} \subseteq \mathcal{C}$ (D78: Subset)