theorem Th42: :: MESFUNC9:42

for X being non empty set
for F, G being Functional_Sequence of X,ExtREAL
for n being Nat
for x being Element of X st F is additive & F is with_the_same_dom & G is additive & G is with_the_same_dom & x in (dom (F . 0)) /\ (dom (G . 0)) & ( for k being Nat
for y being Element of X st y in (dom (F . 0)) /\ (dom (G . 0)) holds
(F . k) . y <= (G . k) . y ) holds
((Partial_Sums F) . n) . x <= ((Partial_Sums G) . n) . x