reserve x,y,z,w for ExtReal,
  r for Real;
reserve f,g for ExtReal;
reserve t for ExtReal;

theorem :: MEMBER_1:1
  (-f)" = -f"
proof
  per cases by XXREAL_0:14;
  suppose
A1: f in REAL;
    then reconsider g = f as Real;
A2: -f = -g;
    consider a being Complex such that
A3: f = a and
A4: f" = a" by A1,Def6;
A5: (-a)" = -a" by XCMPLX_1:222;
    ex m being Complex st -f = m & -f" = m"
    proof
      take -a;
      thus -f = -a by A3,A2;
      thus thesis by A4,A5,A2,Def3;
    end;
    hence thesis by A2,Def6;
  end;
  suppose
A6: f = +infty;
    hence (-f)" = (-infty)" by Def3
      .= -f" by A6;
  end;
  suppose
A7: f = -infty;
    hence (-f)" = (+infty)" by Def3
      .= -f" by A7;
  end;
end;
