reserve A,B,C,Y,x,y,z for set, U, D for non empty set,
X for non empty Subset of D, d,d1,d2 for Element of D;
reserve P,Q,R for Relation, g for Function, p,q for FinSequence;
reserve f for BinOp of D, i,m,n for Nat;

theorem Th16: for p being FinSequence st p is Y-valued & p is m-element holds
p in m-tuples_on Y
proof
reconsider mm=m as Element of NAT by ORDINAL1:def 12;
let p be FinSequence; assume p is Y-valued & p is m-element; then
rng p c= Y & len p = mm by  CARD_1:def 7;
hence thesis by FINSEQ_2:132;
end;
