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

theorem Thm34:
  for X being non-empty 1-element FinSequence,
  S being cap-closed-yielding SemiringFamily of X
  holds SemiringProduct(S) is cap-closed semiring_of_sets of product X
  proof
    let X being non-empty 1-element FinSequence,
    S being cap-closed-yielding SemiringFamily of X;
    set S1=the set of all product <*s*> where s is Element of S.1;
    set X1=the set of all <*x*> where x is Element of X.1;
    S1 = SemiringProduct(S) & X1 = product X by Thm21,Thm24;
    hence thesis by Thm33;
  end;
