Definition opppT : polyF -> polyF := map (GRing.Mul (- 1%T)%T).

Lemma rgcdp_loopP (k : polyF -> fF) : (forall p e, qf_eval e (k p) = qf_eval e (k (lift (eval_poly e p)))) -> forall n p q e, qf_eval e (rgcdp_loopT n p q k) = qf_eval e (k (lift (rgcdp_loop n (eval_poly e p) (eval_poly e q)))).