theorem
  --(F"") = (--F)""
proof
  let i;
  hereby
    assume i in --F"";
    then -i in F"" by Th2;
    then consider w such that
A1: -i = w" and
A2: w in F;
    (-w)" = -w" & -w in --F by A2,XXREAL_3:99;
    hence i in (--F)"" by A1;
  end;
  assume i in (--F)"";
  then consider w such that
A3: i = w" and
A4: w in --F;
  (-w)" = -w" & -w in F by A4,Th2,XXREAL_3:99;
  then -i in F"" by A3;
  hence thesis by Th2;
end;
