reserve x, x1, x2, y, z, X9 for set,
  X, Y for finite set,
  n, k, m for Nat,
  f for Function;
reserve F,Ch for Function;
reserve Fy for finite-yielding Function;

theorem Th38:
  dom Fy is finite implies union rng Fy is finite
proof
  assume dom Fy is finite;
  then rng Fy is finite by FINSET_1:8;
  hence thesis;
end;
