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

theorem Th81:
  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
    x = -infty or x = +infty;
    hence thesis by Def5;
  end;
end;
