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To find a finite subcover, select a finite subcollection $C_1 \subseteq C$ such that the union of the sets in $C_1$ still equals $X$. The chosen sets must come from the original cover $C$.

Conditions: $C_1$ must be a subcollection of $C$.; $C_1$ must be finite.; The union of $C_1$ must equal $X$.

To find a finite subcover, select a finite subcollection $C_1 \subseteq C$ such that the union of the sets in $C_1$ still equals $X$. The chosen sets must come from the original cover $C$.

Conditions: $C_1$ must be a subcollection of $C$.; $C_1$ must be finite.; The union of $C_1$ must equal $X$.