Fixpoint rgdcop_recT n (q : polyF) (p : polyF) :=
if n is m.+1 then
'let g <- rgcdpT p q; 'let sg <- sizeT g;
if sg == 1%N then ret p
else 'let r <- rdivpT p g;
rgdcop_recT m q r
else 'let b <- isnull q; ret [::b%:R%T].

Lemma rgdcop_recTP (k : polyF -> fF) :
(forall p e, qf_eval e (k p) = qf_eval e (k (lift (eval_poly e p))))
-> forall p q n e, qf_eval e (rgdcop_recT n p q k)
= qf_eval e (k (lift (rgdcop_rec (eval_poly e p) (eval_poly e q) n))).