theorem Th19:
  Swap(f, i, i) = f
proof
  reconsider i as Element of NAT by ORDINAL1:def 12;
  per cases;
  suppose
    1 <= i & i <= len f;
    then Swap(f, i, i) = Replace(Replace(f, i, f/.i), i, f/.i) by Def2
      .= Replace(f, i, f/.i) by FUNCT_7:38;
    hence thesis by FUNCT_7:38;
  end;
  suppose
    not (1 <= i & i <= len f);
    hence thesis by Def2;
  end;
end;
