
theorem Th3:
for X be non empty set, f be PartFunc of X,ExtREAL st
 f is without-infty without+infty holds f is PartFunc of X,REAL
proof
   let X be non empty set, f be PartFunc of X,ExtREAL;
   assume f is without-infty without+infty; then
   not -infty in rng f & not +infty in rng f by MESFUNC5:def 3,def 4; then
   rng f c= REAL by XXREAL_0:14;
   hence f is PartFunc of X,REAL by RELSET_1:6;
end;
