reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem Th39:
  for X being set holds X--> 0 is bag of X
proof
  let X be set;
  set f = X --> 0;
  support f = {}
  proof
    assume not thesis;
    then consider x being object such that
A2: x in support f by XBOOLE_0:def 1;
    f.x = 0;
    hence contradiction by A2,Def7;
  end;
  hence thesis by Def8;
end;
