
theorem Th9:
for I,J be closed_interval Subset of REAL, E be Subset of [:RNS_Real,RNS_Real:]
 st E = [:I,J:] holds E is compact
proof
    let I,J be closed_interval Subset of REAL,
    E be Subset of [:RNS_Real,RNS_Real:];
    assume
A1:  E = [:I,J:];
    reconsider A = I, B = J as Subset of RNS_Real;
    A is compact & B is compact by Th7;
    hence thesis by A1,Th8;
end;
