by rewrite -(eqp_dvdr _ eqr) dvdp_gcdl (eqp_dvdr _ eqr) dvdp_gcdl.
Qed.

(* Specifications: *)
Lemma eqp_gcd p1 p2 q1 q2 : p1 %= p2 -> q1 %= q2 -> gcdp p1 q1 %= gcdp p2 q2.
Lemma eqp_rgcd_gcd p q : rgcdp p q %= gcdp p q.
Lemma gcdp_modr m n : gcdp m (n %% m) %= gcdp m n.
Lemma gcdp_modl m n : gcdp (m %% n) n %= gcdp m n.
Lemma gcdp_def d m n :
d %| m -> d %| n -> (forall d', d' %| m -> d' %| n -> d' %| d) ->
gcdp m n %= d.