theorem Th45: :: LIMFUNC2:45

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_left_convergent_in x0 & f2 is_left_convergent_in x0 & ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom (f1 + f2) ) ) holds
( f1 + f2 is_left_convergent_in x0 & lim_left ((f1 + f2),x0) = (lim_left (f1,x0)) + (lim_left (f2,x0)) )