theorem :: LIMFUNC1:59

for f being PartFunc of REAL,REAL
for r being Real holds
( ( f is divergent_in-infty_to+infty & r > 0 implies r (#) f is divergent_in-infty_to+infty ) & ( f is divergent_in-infty_to+infty & r < 0 implies r (#) f is divergent_in-infty_to-infty ) & ( f is divergent_in-infty_to-infty & r > 0 implies r (#) f is divergent_in-infty_to-infty ) & ( f is divergent_in-infty_to-infty & r < 0 implies r (#) f is divergent_in-infty_to+infty ) )