
theorem
for m,n be non zero Nat, X be non-empty m-element FinSequence,
 S be sigmaFieldFamily of X st n <= m holds
  S.n is SigmaField of ElmFin(X,n)
proof
    let m,n be non zero Nat, X be non-empty m-element FinSequence,
    S be sigmaFieldFamily of X;
    assume
A1:  n <= m; then
A2: ElmFin(X,n) = X.n by Def1;
    1 <= n by NAT_1:14; then
    n in Seg m by A1;
    hence S.n is SigmaField of ElmFin(X,n) by A2,Def2;
end;
