reserve
  x for object, X for set,
  i, n, m for Nat,
  r, s for Real,
  c, c1, c2, d for Complex,
  f, g for complex-valued Function,
  g1 for n-element complex-valued FinSequence,
  f1 for n-element real-valued FinSequence,
  T for non empty TopSpace,
  p for Element of TOP-REAL n;

theorem
  for X being trivial set, Y being set st X,Y are_equipotent holds Y is trivial
  proof
    let X be trivial set, Y be set such that
A1: X,Y are_equipotent;
A2: card X < 2 by NAT_D:60;
A3: Y is finite by A1,CARD_1:38;
    card X = card Y by A1,CARD_1:5;
    hence thesis by A2,A3,NAT_D:60;
  end;
