
theorem Th13:
  for X be non-empty 1-element FinSequence, S be SemialgebraFamily of X
    holds SemiringProduct(S) is semialgebra_of_sets of product X
proof
   let X be non-empty 1-element FinSequence, S be SemialgebraFamily 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 SRINGS_4:23,25;
   hence thesis by Th12;
end;
