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 Th32:
  (A \/ B)"" = (A"") \/ (B"")
proof
  let a;
  hereby
    assume a in (A\/B)"";
    then a" in A\/B by Th29;
    then a" in A or a" in B by XBOOLE_0:def 3;
    then a in A"" or a in B"" by Th29;
    hence a in A"" \/ B"" by XBOOLE_0:def 3;
  end;
  assume a in A"" \/ B"";
  then a in A"" or a in B"" by XBOOLE_0:def 3;
  then a" in A or a" in B by Th29;
  then a" in A\/B by XBOOLE_0:def 3;
  hence thesis by Th29;
end;
