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

theorem :: MEASURE6:37
  p <> +infty implies [.+infty,p.] = {}
proof
  assume
A1: p <> +infty;
  not ex x being object st x in [.+infty,p.]
  proof
    given x being object such that
A2: x in [.+infty,p.];
    reconsider s = x as ExtReal by A2;
A3: +infty <= s by A2,Th1;
    s <= p by A2,Th1;
    hence contradiction by A1,A3,XXREAL_0:2,4;
  end;
  hence thesis;
end;
