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 Th6:
  -- (F /\ G) = (--F) /\ (--G)
proof
  let i;
  hereby
    assume i in --(F/\G);
    then
A1: -i in F /\ G by Th2;
    then -i in G by XBOOLE_0:def 4;
    then
A2: i in --G by Th2;
    -i in F by A1,XBOOLE_0:def 4;
    then i in --F by Th2;
    hence i in (--F) /\ --G by A2,XBOOLE_0:def 4;
  end;
  assume
A3: i in (--F) /\ --G;
  then i in --G by XBOOLE_0:def 4;
  then
A4: -i in G by Th2;
  i in --F by A3,XBOOLE_0:def 4;
  then -i in F by Th2;
  then -i in F /\ G by A4,XBOOLE_0:def 4;
  hence thesis by Th2;
end;
