theorem Th20: :: FDIFF_4:20

for a being Real
for Z being open Subset of REAL
for f1, f2 being PartFunc of REAL,REAL st Z c= dom (f1 + f2) & ( for x being Real st x in Z holds
f1 . x = a ) & f2 = #Z 3 holds
( f1 + f2 is_differentiable_on Z & ( for x being Real st x in Z holds
((f1 + f2) `| Z) . x = 3 * (x |^ 2) ) )