theorem :: FUZNUM_1:28

for a, b being Real
for f, g being PartFunc of REAL,REAL st g is continuous & not g is empty & f = (AffineMap (0,0)) | (REAL \ ].a,b.[) & dom g = [.a,b.] & g . a = 0 & g . b = 0 holds
f +* g is continuous