theorem :: LIMFUNC2:62

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