
theorem Th4:
for X1,X2 be set, F1 be SetSequence of X1, F2 be SetSequence of X2, n be Nat
  st F1 is non-descending & F2 is non-descending
  holds [:F1.n,F2.n:] c= [:F1.(n+1),F2.(n+1):]
proof
   let X1,X2 be set, F1 be SetSequence of X1, F2 be SetSequence of X2,
   n be Nat;
   assume F1 is non-descending & F2 is non-descending; then
   F1.n c= F1.(n+1) & F2.n c= F2.(n+1) by PROB_1:def 5,NAT_1:11;
   hence [:F1.n,F2.n:] c= [:F1.(n+1),F2.(n+1):] by ZFMISC_1:96;
end;
