
theorem
for a,b be Real st a > b
  holds B-Meas.([.a,b.]) = 0 & B-Meas.([.a,b.[) = 0
      & B-Meas.(].a,b.]) = 0 & B-Meas.(].a,b.[) = 0
      & L-Meas.([.a,b.]) = 0 & L-Meas.([.a,b.[) = 0
      & L-Meas.(].a,b.]) = 0 & L-Meas.(].a,b.[) = 0
proof
    let a,b be Real;
    assume
A1:  a > b;
    reconsider a1=a, b1=b as R_eal by XXREAL_0:def 1;
    B-Meas.([.a,b.]) = diameter [.a1,b1.]
  & B-Meas.([.a,b.[) = diameter [.a1,b1.[
  & B-Meas.(].a,b.]) = diameter ].a1,b1.]
  & B-Meas.(].a,b.[) = diameter ].a1,b1.[
  & L-Meas.([.a,b.]) = diameter [.a1,b1.]
  & L-Meas.([.a,b.[) = diameter [.a1,b1.[
  & L-Meas.(].a,b.]) = diameter ].a1,b1.]
  & L-Meas.(].a,b.[) = diameter ].a1,b1.[ by MEASUR12:71,76;
    hence thesis by A1,MEASURE5:5,6,7,8;
end;
