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
ex h being PartFunc of REAL,REAL st
( h = f +* g & ( for x being Real st x in dom h holds
h is_continuous_in x ) )