:: deftheorem defines is_left_convergent_in LIMFUNC2:def 1 :
for f being PartFunc of REAL,REAL
for x0 being Real holds
( f is_left_convergent_in x0 iff ( ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom f ) ) & ex g being Real st
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 convergent & lim (f /* seq) = g ) ) );