:: deftheorem defines is_left_divergent_to+infty_in LIMFUNC2:def 2 :
for f being PartFunc of REAL,REAL
for x0 being Real holds
( f is_left_divergent_to+infty_in x0 iff ( ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom f ) ) & ( for seq being Real_Sequence st seq is convergent & lim seq = x0 & rng seq c= (dom f) /\ (left_open_halfline x0) holds
f /* seq is divergent_to+infty ) ) );