by move/ltnW->.
rewrite leq_eqVlt; case/orP; first by move/eqP->.
by move/modp_small; rewrite rpq => h; move: nq0; rewrite h eqxx.
Qed.

Lemma polyXsubC_eqp1 (x : R) : ('X - x%:P %= 1) = false.