
theorem Th4:
for I,J,K be Interval holds
  [:[:I,J:],K:] is Subset of [:[:RNS_Real,RNS_Real:],RNS_Real:]
& [:[:I,J:],K:] in sigma measurable_rectangles(
    sigma measurable_rectangles(L-Field,L-Field),L-Field)
proof
    let I,J,K be Interval;
    set S = sigma measurable_rectangles(L-Field,L-Field);
A1: [:I,J:] in S by MESFUN16:11;
    K in L-Field by MEASUR10:5,MEASUR12:75; then
A2: [:[:I,J:],K:] in measurable_rectangles(S,L-Field) by A1;
    measurable_rectangles(S,L-Field) c= sigma measurable_rectangles(S,L-Field)
      by PROB_1:def 9;
    hence thesis by A2;
end;
