In general, elements of the universal enveloping algebra are linear combinations of products of the generators in all possible orders. Using the defining relations of the universal enveloping algebra, we can always re-order those products in a particular order, say with all the factors of formula_29 first, then factors of formula_30, etc. For example, whenever we have a term that contains formula_31 (in the "wrong" order), we can use the relations to rewrite this as formula_32 plus a linear combination of the formula_33's. Doing this sort of thing repeatedly eventually converts any element into a linear combination of terms in ascending order. Thus, elements of the form