theorem Th26: :: INTEGRA4:26

for a being Real
for A being non empty closed_interval Subset of REAL
for f, g, h being Function of A,REAL st f | A is bounded & g | A is bounded & a >= 0 & ( for x, y being Real st x in A & y in A holds
|.((h . x) - (h . y)).| <= a * (|.((f . x) - (f . y)).| + |.((g . x) - (g . y)).|) ) holds
(upper_bound (rng h)) - (lower_bound (rng h)) <= a * (((upper_bound (rng f)) - (lower_bound (rng f))) + ((upper_bound (rng g)) - (lower_bound (rng g))))