theorem Th11: :: ORDEQ_01:11

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