reserve w, w1, w2 for Element of ExtREAL;
reserve c, c1, c2 for Complex;
reserve A, B, C, D for complex-membered set;
reserve F, G, H, I for ext-real-membered set;
reserve a, b, s, t, z for Complex;
reserve f, g, h, i, j for ExtReal;
reserve r for Real;
reserve e for set;

theorem Th5:
  -- (F \/ G) = (--F) \/ (--G)
proof
  let i;
  hereby
    assume i in --(F\/G);
    then -i in F \/ G by Th2;
    then -i in F or -i in G by XBOOLE_0:def 3;
    then i in --F or i in --G by Th2;
    hence i in --F \/ --G by XBOOLE_0:def 3;
  end;
  assume i in --F \/ --G;
  then i in --F or i in --G by XBOOLE_0:def 3;
  then -i in F or -i in G by Th2;
  then -i in F \/ G by XBOOLE_0:def 3;
  hence thesis by Th2;
end;
