
theorem Th72:
  for A be Interval holds B-Meas.A = diameter A
proof
    let A be Interval;
A1: A in Family_of_Intervals by MEASUR10:def 1;
A2: Family_of_Intervals c= Field_generated_by Family_of_Intervals
      by SRINGS_3:21;
A3: Field_generated_by Family_of_Intervals c= Borel_Sets
      by PROB_1:def 9,MEASUR10:6;
A4: Field_generated_by Family_of_Intervals
      c= sigma_Field C_Meas J-Meas by MEASURE8:20;
    B-Meas.A = (sigma_Meas(C_Meas J-Meas)).A by A3,A2,A1,FUNCT_1:49
     .= (C_Meas J-Meas).A by A4,A2,A1,MEASURE4:def 3
     .= J-Meas.A by A2,A1,MEASURE8:18;
    hence B-Meas.A = diameter A by Th71;
end;
