theorem Th12: :: INTEGR25:12

for f1, f2 being PartFunc of REAL,REAL st f1 is divergent_in+infty_to-infty & ( for r being Real ex g being Real st
( r < g & g in dom (f1 + f2) ) ) & ex r being Real st f2 | (right_open_halfline r) is bounded_above holds
f1 + f2 is divergent_in+infty_to-infty