
theorem Th71:
  for A be Interval holds J-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;
    reconsider F = <*A*>
     as disjoint_valued FinSequence of Family_of_Intervals by A1,FINSEQ_1:74;
    rng F = {A} by FINSEQ_1:38; then
    union rng F = A; then
    A = Union F by CARD_3:def 4; then
    J-Meas.A = Sum(pre-Meas*F) by A2,A1,Def9; then
    J-Meas.A = Sum(<*pre-Meas.A*>) by Th62; then
    J-Meas.A = pre-Meas.A by EXTREAL1:8;
    hence J-Meas.A = diameter A by Th59;
end;
