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

theorem Th29:  :: MEASURE5:12
  p < q implies [.q,p.] = {}
proof
  assume
A1: p < q;
  assume [.q,p.] <> {};
  then consider r such that
A2: r in [.q,p.];
A3: q <= r by A2,Th1;
  r <= p by A2,Th1;
  hence contradiction by A1,A3,XXREAL_0:2;
end;
