theorem Th8: :: RSSPACE4:8

for X being non empty set
for Y being RealNormSpace
for f, g, h being VECTOR of (R_VectorSpace_of_BoundedFunctions (X,Y))
for f9, g9, h9 being bounded Function of X, the carrier of Y st f9 = f & g9 = g & h9 = h holds
( h = f + g iff for x being Element of X holds h9 . x = (f9 . x) + (g9 . x) )