
theorem Th33:
for F be sequence of bool REAL, G be sequence of Funcs(NAT,bool REAL) st
 (for n be Element of NAT holds G.n is Open_Interval_Covering of F.n)
 holds G is Open_Interval_Covering of F
proof
    let F be sequence of bool REAL, G be sequence of Funcs(NAT,bool REAL);
    assume
A1:  for n be Element of NAT holds G.n is Open_Interval_Covering of F.n; then
    for n be Element of NAT holds G.n is Interval_Covering of F.n; then
    G is Interval_Covering of F by MEASURE7:def 3;
    hence thesis by A1,Def6;
end;
