= Finitely generated incline is well-quasi-ordered by reverse absorption
{title2=$x\preceq y\iff x+y=x$}
Expand every term in finitely many generators as a finite nonempty sum of <monomials>, and associate its exponent support with the upward-closed <subset> of $\mathbb N^r$ that it generates. The <reverse-inclusion well-quasi-ordering of monomial ideals> supplies an earlier support upset containing a later one. Every later <monomial> is then a multiple of an earlier <monomial>, hence is absorbed by it under $a+ab=a$. The earlier sum absorbs the later sum. Thus every infinite term <sequence> has an earlier element preceding a later one in the reverse natural order. Reflexivity, antisymmetry and transitivity follow directly from commutative idempotent addition.
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