theorem FTh42A: :: ORDEQ_02:8

for Y being RealNormSpace
for I being Function of REAL,(REAL-NS 1)
for x0 being Point of (REAL-NS 1)
for y0 being Element of REAL
for g being PartFunc of REAL,Y
for f being PartFunc of (REAL-NS 1),Y st I = (proj (1,1)) " & x0 in dom f & y0 in dom g & x0 = <*y0*> & f * I = g & f is_differentiable_in x0 holds
||.(diff (g,y0)).|| = ||.(diff (f,x0)).||