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, p being FinSequence of
  A holds p in i-tuples_on A iff len p = i
proof
  let A be set, i be Nat, p be FinSequence of A;
  rng p c= A by RELAT_1:def 19;
  hence thesis by Th130;
end;
