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

theorem Th10: :: MEMBER_1:3
  -f = -g implies f = g
proof
  assume
A1: -f = -g;
  per cases by XXREAL_0:14;
  suppose
A2: f in REAL;
    now
      assume not g in REAL;
      then g = +infty or g = -infty by XXREAL_0:14;
      hence contradiction by A1,A2,Def3;
    end;
    then
A3: ex a being Complex st g = a & -g = -a by Def3;
    ex a being Complex st f = a & -f = -a by A2,Def3;
    hence thesis by A1,A3;
  end;
  suppose
    f = +infty;
    hence thesis by A1,Th5;
  end;
  suppose
    f = -infty;
    then - -g = -infty by A1;
    hence thesis by A1;
  end;
end;
