for S, T being RealNormSpace
for f being PartFunc of S,T
for x0 being Point of S st f is_differentiable_in x0 holds
for z being Point of S
for h being non-zero 0 -convergent Real_Sequence
for c being constant sequence of S st rng c = {x0} & rng ((h * z) + c) c= dom f holds
( (h ") (#) ((f /* ((h * z) + c)) - (f /* c)) is convergent & (diff (f,x0)) . z = lim ((h ") (#) ((f /* ((h * z) + c)) - (f /* c))) )