
theorem Th32:
for X be set, S be SigmaField of X, M be sigma_Measure of S,
 F be Finite_Sep_Sequence of S
 holds F is Finite_Sep_Sequence of COM(S,M)
proof
    let X be set, S be SigmaField of X, M be sigma_Measure of S,
    F be Finite_Sep_Sequence of S;
    now let y be object;
     assume y in rng F; then
     y is Element of COM(S,M) by Th27;
     hence y in COM(S,M);
    end; then
    rng F c= COM(S,M);
    hence F is Finite_Sep_Sequence of COM(S,M) by FINSEQ_1:def 4;
end;
