
theorem Th9:
  for X being non empty set, x being Element of X holds (UnitBag x)
  .x = 1 & for y being Element of X st x <> y holds (UnitBag x).y = 0
proof
  let X be non empty set, x be Element of X;
A1: dom (X -->0) = X;
  thus (UnitBag x).x = ((X --> 0)+*(x, 1)).x by PBOOLE:def 3
    .= 1 by A1,FUNCT_7:31;
  let y be Element of X;
  assume x <> y;
  hence (UnitBag x).y = (EmptyBag X).y by FUNCT_7:32
    .= 0 by PBOOLE:5;
end;
