reserve f, g, h for Function;
reserve x, y, z, u, X for set,
  A for non empty set,
  n for Element of NAT,
  f for Function of X, X;
reserve f for c=-monotone Function of bool X, bool X,
  S for Subset of X;
reserve X, Y for non empty set,
  f for Function of X, Y,
  g for Function of Y, X;

theorem
  f is one-to-one & g is one-to-one implies X,Y are_equipotent
proof
  assume f is one-to-one & g is one-to-one;
  then ex h being Function of X,Y st h is bijective by Th10;
  hence thesis by Th11;
end;
