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;
reserve X for set, f for Function;
reserve U1,U2 for non empty set;

theorem x in D*\{{}} iff (x is D-valued FinSequence & x is non empty)
proof
(x is D-valued FinSequence & x is non empty) iff
(x is non empty FinSequence of D) by Lm1; hence thesis by Th5;
end;
