
theorem Th11:
  for n be non zero Nat, X be non-empty n-element FinSequence,
      S be SemialgebraFamily of X
  holds for i be Nat st i in Seg n holds X.i in S.i
proof
   let n be non zero Nat, X be non-empty n-element FinSequence,
   S be SemialgebraFamily of X;
   hereby let i be Nat;
    assume i in Seg n; then
    S.i is semialgebra_of_sets of X.i by Def2;
    hence X.i in S.i by SRINGS_3:def 6;
   end;
end;
