for n being Element of NAT
for a, b, c, d being Real
for f being PartFunc of REAL,(REAL n) st a <= c & c <= d & d <= b & f is_integrable_on ['a,b'] & f | ['a,b'] is bounded & ['a,b'] c= dom f holds
( f is_integrable_on ['c,d'] & f | ['c,d'] is bounded )