
theorem
  for X being set, F being PartFunc of X,ExtREAL st
  for n being object st n in dom F holds 0. <= F.n holds F is nonnegative
proof
  let X be set, F be PartFunc of X,ExtREAL such that
A1: for n being object st n in dom F holds 0. <= F.n;
  let y be ExtReal;
  assume y in rng F;
  then ex x being object st x in dom F & y = F.x by FUNCT_1:def 3;
  hence thesis by A1;
end;
