ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Collection of sets
Set union
Set cover
Definition D75
Set subcover
Formulation 0
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)