theorem Th10: :: ORDEQ_01:10

for X being non empty closed_interval Subset of REAL
for Y being RealNormSpace
for f, g, h being VECTOR of (R_VectorSpace_of_ContinuousFunctions (X,Y))
for f9, g9, h9 being continuous PartFunc of REAL,Y st f9 = f & g9 = g & h9 = h & dom f9 = X & dom g9 = X & dom h9 = X holds
( h = f + g iff for x being Element of X holds h9 /. x = (f9 /. x) + (g9 /. x) )