quality:corruption, information:extraction
Indexed subfamily

An indexed family (B i) i ∈ J {\displaystyle \left(B_{i}\right)_{i\in J}} is a subfamily of an indexed family (A i) i ∈ I, {\displaystyle \left(A_{i}\right)_{i\in I},} if and only if J {\displaystyle J} is a subset of I {\displaystyle I} and B i = A i {\displaystyle B_{i}=A_{i}} holds for all i ∈ J. {\displaystyle i\in J.}