
theorem
  for X1,X2 be set, F1 be Field_Subset of X1, F2 be Field_Subset of X2
  holds the set of all [:A,B:] where A is Element of F1, B is Element of F2
   is semialgebra_of_sets of [:X1,X2:]
proof
   let X1,X2 be set, F1 be Field_Subset of X1, F2 be Field_Subset of X2;
   set S = the set of all [:A,B:] where A is Element of F1, B is Element of F2;
   F1 is semialgebra_of_sets of X1 & F2 is semialgebra_of_sets of X2
     by SRINGS_3:20;
   hence thesis by Th09;
end;
