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 (m+1)-tuples_on Y c= Y*\{{}} ::#Th9
proof
reconsider k=m, K=m+1 as Element of NAT by ORDINAL1:def 12;
A1: 0-tuples_on Y misses K-tuples_on Y by Lm5;
K-tuples_on Y c= Y*\ (0-tuples_on Y) by FINSEQ_2:134, XBOOLE_1:86, A1;
hence thesis by Lm6;
end;
