theorem Th3: :: ROLLE:3

for p, g being Real st p < g holds
for f being PartFunc of REAL,REAL st [.p,g.] c= dom f & f | [.p,g.] is continuous & f is_differentiable_on ].p,g.[ holds
ex x0 being Real st
( x0 in ].p,g.[ & diff (f,x0) = ((f . g) - (f . p)) / (g - p) )