theorem Th5: :: LIMFUNC3:5

for r2, x0 being Real
for f being PartFunc of REAL,REAL st 0 < r2 & ].(x0 - r2),x0.[ \/ ].x0,(x0 + r2).[ 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 )