reserve V, C, x, a, b for set;
reserve A, B for Element of SubstitutionSet (V, C);
reserve C for finite set;
reserve A, B for Element of SubstitutionSet (V, C);
reserve u, v for Element of SubstLatt (V, C);
reserve s, t, a, b for Element of PFuncs (V,C);
reserve K, L for Element of SubstitutionSet (V, C);

theorem Th21:
  for a being Element of PFuncs (V, C) st a is finite for c being
  set st c in Atom(V, C).a holds c = a
proof
  let a be Element of PFuncs (V, C);
  assume a is finite;
  then Atom(V, C).a = { a } by Lm7;
  hence thesis by TARSKI:def 1;
end;
