theorem Th6: :: BHSP_7:6

for X being RealHilbertSpace 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 OrthonormalFamily of X
for H being Functional of X st S c= dom H & ( for x being Point of X st x in S holds
H . x = x .|. x ) holds
( S is summable_set iff S is_summable_set_by H )