reserve x for set,
  p,q,r,s,t,u for ExtReal,
  g for Real,
  a for Element of ExtREAL;

theorem
  [.-infty,+infty.] = ExtREAL
proof
  let r;
  thus r in [.-infty,+infty.] implies r in ExtREAL by XXREAL_0:def 1;
  assume r in ExtREAL;
A1: -infty <= r by XXREAL_0:5;
  r <= +infty by XXREAL_0:3;
  hence thesis by A1,Th1;
end;
