
theorem
  for X be non empty set,
      f be without-infty without+infty Function of X,ExtREAL holds
    f is Function of X,REAL
proof
   let X be non empty set,
       f be without-infty without+infty Function of X,ExtREAL;
A1:dom f = X by FUNCT_2:def 1;
   now let x be object;
    assume x in X; then
    f.x in ExtREAL & f.x > -infty & f.x < +infty
       by FUNCT_2:5,MESFUNC5:def 5,def 6;
    hence f.x in REAL by XXREAL_0:14;
   end;
   hence thesis by A1,FUNCT_2:3;
end;
