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;
reserve s for Element of D*;
reserve m,n for Nat,
  s,w for FinSequence of NAT;

theorem
  for A being set, i being Nat holds i-tuples_on A c= A*
proof
  let A be set, i be Nat, x be object;
  assume x in i-tuples_on A;
  then x is FinSequence of A by Def3;
  hence thesis by FINSEQ_1:def 11;
end;
