theorem Th54: :: LIMFUNC2:54

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