theorem Th64: :: LIMFUNC1:64

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