
theorem Th15:
  for X be non empty set, r be Real,
      f be without-infty without+infty Function of X,ExtREAL holds
    r(#)f is without-infty without+infty
proof
   let X be non empty set, r be Real,
   f be without-infty without+infty Function of X,ExtREAL;
   per cases;
   suppose r >= 0;
    hence r(#)f is without-infty without+infty;
   end;
   suppose r < 0;
    hence r(#)f is without-infty without+infty;
   end;
end;
