theorem Th5: :: BHSP_6:5

for X being RealUnitarySpace st the addF of X is commutative & the addF of X is associative & the addF of X is having_a_unity holds

for S being finite Subset of X st not S is empty holds

for L being linear-Functional of X holds L . (setsum S) = setopfunc (S, the carrier of X,REAL,L,addreal)

for S being finite Subset of X st not S is empty holds

for L being linear-Functional of X holds L . (setsum S) = setopfunc (S, the carrier of X,REAL,L,addreal)