theorem Th15: :: FCONT_2:15

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
for r being Real st r in [.(f . p),(f . g).] \/ [.(f . g),(f . p).] holds
ex s being Real st
( s in [.p,g.] & r = f . s )