
theorem
  for A being free Universal_Algebra for o being OperSymbol of A
  for p being FinSequence st p in dom Den(o,A)
  for n being Nat st Den(o,A).p in (Generators A)|^(n+1)
  holds rng p c= (Generators A)|^n
proof
  let A be free Universal_Algebra;
  set G = Generators A;
  let o be OperSymbol of A;
  now
    let o9 be OperSymbol of A, p be FinSequence;
    reconsider op = Den(o9,A) as Element of Operations A;
    assume p in dom Den(o9,A);
    then op.p in rng op by FUNCT_1:3;
    hence Den(o9,A).p in G implies o9 <> o by Th26;
  end;
  hence thesis by Th39;
end;
