theorem Th2: :: FDIFF_3:2

for f being PartFunc of REAL,REAL
for x0 being Real st ex r being Real st
( r > 0 & [.x0,(x0 + r).] c= dom f ) holds
ex h being non-zero 0 -convergent Real_Sequence ex c being constant Real_Sequence st
( rng c = {x0} & rng (h + c) c= dom f & ( for n being Nat holds h . n > 0 ) )