The admissible-monomial prediction for the maps $\Phi$

Let $P_n=\mathbb F_2[x_1,\ldots,x_n]$ be the polynomial algebra, let $B_n(\omega)$ denote the admissible monomials in $P_n$ of weight vector $\omega$, and let $\Phi$ be the union of the maps $\phi_{(i;I)}$ defined from admissible monomials in $P_{n-1}$ to $P_n$.

Admissible-monomial prediction. If $\omega$ is a weight vector, then

$$\Phi(B_{n-1}(\omega))\subset B_n(\omega).$$

This predicts a weight-preserving relation between admissible monomials in successive polynomial algebras and is presented as the paper's prediction; no resolution is supplied in the given text.