for Y being RealNormSpace
for I being Function of REAL,(REAL-NS 1)
for x0 being Point of (REAL-NS 1)
for y0 being 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 holds
( f is_differentiable_in x0 iff g is_differentiable_in y0 )