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

theorem :: MEASURE5:21
  q < s & r < s implies not ].r,s.[ c= [.p,q.]
proof
  assume that
A1: q < s and
A2: r < s;
  per cases;
  suppose
A3: r <= q;
    consider t such that
A4: q < t and
A5: t < s by A1,XREAL_1:227;
    take t;
    r < t by A3,A4,XXREAL_0:2;
    hence t in ].r,s.[ by A5,Th4;
    thus thesis by A4,Th1;
  end;
  suppose
A6: q <= r;
    consider t such that
A7: r < t and
A8: t < s by A2,XREAL_1:227;
    take t;
    thus t in ].r,s.[ by A7,A8,Th4;
    q < t by A6,A7,XXREAL_0:2;
    hence thesis by Th1;
  end;
end;
