for a being Real
for A being non empty set
for f, g being Function of A,REAL st rng f is bounded_below & rng g is bounded_below & ( for x being set st x in A holds
|.((f . x) - (g . x)).| <= a ) holds
( (lower_bound (rng f)) - (lower_bound (rng g)) <= a & (lower_bound (rng g)) - (lower_bound (rng f)) <= a )