for X being non empty set
for F being Functional_Sequence of X,ExtREAL
for n being Nat
for x being Element of X
for D being set st F is additive & F is with_the_same_dom & D c= dom (F . 0) & x in D holds
(Partial_Sums (F # x)) . n = ((Partial_Sums F) # x) . n