theorem Th19: :: FCONT_2:19

for g, p being Real
for f being PartFunc of REAL,REAL st p <= g & [.p,g.] c= dom f & f | [.p,g.] is continuous holds
f .: [.p,g.] = [.(lower_bound (f .: [.p,g.])),(upper_bound (f .: [.p,g.])).]