reserve X1,X2,X3,X4 for set;
reserve n for non zero Nat;
reserve X for non-empty n-element FinSequence;

theorem Thm17:
  for S being SemiringFamily of X holds
  for i be Nat st i in Seg n holds union (S.i) c= X.i
  proof
    let S be SemiringFamily of X;
    let i be Nat;
    assume i in Seg n;
    then S.i is semiring_of_sets of X.i by Def2;
    then union (S.i) c= union bool (X.i) by ZFMISC_1:77;
    hence union (S.i) c= X.i by ZFMISC_1:81;
  end;
