reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem
  for f being sequence of D st q = f|(Seg i) holds len q = i
proof
  let f be sequence of D;
  reconsider i as Element of NAT by ORDINAL1:def 12;
  dom(f|(Seg i)) = Seg i by FUNCT_2:def 1;
  hence thesis by FINSEQ_1:def 3;
end;
