for F being RealNormSpace
for x0 being Real
for f1, f2 being PartFunc of REAL, the carrier of F st f1 is_differentiable_in x0 & f2 is_differentiable_in x0 holds
( f1 - f2 is_differentiable_in x0 & diff ((f1 - f2),x0) = (diff (f1,x0)) - (diff (f2,x0)) )