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

theorem Th91:
  (-1)*x = -x
proof
  per cases by XXREAL_0:14;
  suppose
    x in REAL;
    then reconsider x, y=-1 as Real;
    y*x = -x;
    hence thesis;
  end;
  suppose
A1: x = -infty;
    hence (-1)*x = +infty by Def5
      .= -x by A1,Def3;
  end;
  suppose
A2: x = +infty;
    hence (-1)*x = -infty by Def5
      .= -x by A2,Def3;
  end;
end;
