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

theorem :: MEASURE5:32
  r < p & r < s implies not ].r,s.] c= ].p,q.[
proof
  assume that
A1: r < p and
A2: r < s;
  per cases;
  suppose
A3: s <= p;
    consider t such that
A4: r < t and
A5: t < s by A2,XREAL_1:227;
    take t;
    thus t in ].r,s.] by A4,A5,Th2;
    t < p by A3,A5,XXREAL_0:2;
    hence thesis by Th4;
  end;
  suppose
A6: p <= s;
    consider t such that
A7: r < t and
A8: t < p by A1,XREAL_1:227;
    take t;
    t <= s by A6,A8,XXREAL_0:2;
    hence t in ].r,s.] by A7,Th2;
    thus thesis by A8,Th4;
  end;
end;
