
theorem Th58:
  for I be Element of Family_of_Intervals holds pre-Meas.I = diameter I
proof
    let I be Element of Family_of_Intervals;
    I in the set of all J where J is Interval by MEASUR10:def 1; then
A1: ex J be Interval st I = J;
    pre-Meas.I = OS_Meas.I by FUNCT_1:49;
    hence pre-Meas.I = diameter I by A1,Th57;
end;
