theorem :: LIMFUNC1:63

for f being PartFunc of REAL,REAL st ex r being Real st
( f | (right_open_halfline r) is increasing & not f | (right_open_halfline r) is bounded_above ) & ( for r being Real ex g being Real st
( r < g & g in dom f ) ) holds
f is divergent_in+infty_to+infty by Th62;