
theorem Th37:
for A,B be Subset of REAL, F be Interval_Covering of A st B c= A holds
 F is Interval_Covering of B
proof
    let A,B be Subset of REAL, F be Interval_Covering of A;
    assume
A1:  B c= A;
A2: A c= union rng F & for n be Element of NAT holds F.n is Interval
      by MEASURE7:def 2; then
    B c= union rng F by A1;
    hence F is Interval_Covering of B by A2,MEASURE7:def 2;
end;
