
theorem Th19:
for m,n be non zero Nat, X be non-empty m-element FinSequence,
 S be sigmaFieldFamily of X st n <= m holds
  (ProdSigmaFldFinSeq S).n is SigmaField of (ProdFinSeq 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;
    1 <= n by NAT_1:14; then
    n in Seg m by A1;
    hence thesis by Def2;
end;
