by move=> ?; apply/idP/idP; apply: Hmn; rewrite // eqp_sym.
by rewrite /eqp; case/andP=> dd' d'd dp; apply: (dvdp_trans d'd).
Qed.

(* Specifications: *)
Lemma dvdp_scaler c m n : c != 0 -> m %| c *: n = (m %| n).
Lemma eqp_mulr q p r : (p %= q) -> (p * r %= q * r).
Lemma polyC_eqp1 (c : R) : (c%:P %= 1) = (c != 0).
Lemma dvdUp d p: d %= 1 -> d %| p.
Lemma eqp_root p q : p %= q -> root p =1 root q.
Lemma eqp_rmod_mod p q : rmodp p q %= modp p q.
Lemma eqp_rdiv_div p q : rdivp p q %= divp p q.
Lemma dvd_eqp_divl d p q (dvd_dp : d %| q) (eq_pq : p %= q) :
p %/ d %= q %/ d.