
theorem Th38:
for A,B be Subset of REAL, F be Open_Interval_Covering of A st B c= A holds
 F is Open_Interval_Covering of B
proof
    let A,B be Subset of REAL, F be Open_Interval_Covering of A;
    assume B c= A; then
A1: F is Interval_Covering of B by Th37;
    for n be Element of NAT holds F.n is open_interval;
    hence F is Open_Interval_Covering of B by A1,Def5;
end;
