theorem Th14: :: INTEGRA3:15

for x being Real
for A being non empty closed_interval Subset of REAL
for D1, D2 being Division of A
for f being Function of A,REAL st x in divset (D1,(len D1)) & vol A <> 0 & D1 <= D2 & rng D2 = (rng D1) \/ {x} & f | A is bounded & x > lower_bound A holds
(Sum (upper_volume (f,D1))) - (Sum (upper_volume (f,D2))) <= ((upper_bound (rng f)) - (lower_bound (rng f))) * (delta D1)