for X being set
for F1 being FinSequence of bool X
for A1 being SetSequence of X st ( for k being Nat st k in dom F1 holds
A1 . k = F1 . k ) & ( for k being Nat st not k in dom F1 holds
A1 . k = {} ) holds
( A1 . 0 = {} & Union A1 = Union F1 )