theorem :: LIMFUNC2:10

for x0 being Real
for f being PartFunc of REAL,REAL holds
( f is_right_convergent_in x0 iff ( ( for r being Real st x0 < r holds
ex g being Real st
( g < r & x0 < g & g in dom f ) ) & ex g being Real st
for g1 being Real st 0 < g1 holds
ex r being Real st
( x0 < r & ( for r1 being Real st r1 < r & x0 < r1 & r1 in dom f holds
|.((f . r1) - g).| < g1 ) ) ) )