theorem Th9:
  --{f} = {-f}
proof
  let i;
  hereby
    assume i in --{f};
    then consider w such that
A1: i = -w and
A2: w in {f};
    w = f by A2,TARSKI:def 1;
    hence i in {-f} by A1,TARSKI:def 1;
  end;
  assume i in {-f};
  then
A3: i = -f by TARSKI:def 1;
  f in ExtREAL & f in {f} by TARSKI:def 1,XXREAL_0:def 1;
  hence thesis by A3;
end;
