theorem :: LIMFUNC2:61

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_left_convergent_in x0 & lim_left (f1,x0) = 0 & ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom (f1 (#) f2) ) ) & ex r being Real st
( 0 < r & f2 | ].(x0 - r),x0.[ is bounded ) holds
( f1 (#) f2 is_left_convergent_in x0 & lim_left ((f1 (#) f2),x0) = 0 )