theorem Th4: :: L_HOSPIT:4

for f being PartFunc of REAL,REAL
for x0 being Real st ex N being Neighbourhood of x0 st N \ {x0} c= dom f holds
for r1, r2 being Real st r1 < x0 & x0 < r2 holds
ex g1, g2 being Real st
( r1 < g1 & g1 < x0 & g1 in dom f & g2 < r2 & x0 < g2 & g2 in dom f )