Definition ex_elim_seq (ps : seq polyF) (q : polyF) : fF :=
('let g <- rgcdpTs ps; 'let d <- rgdcopT q g;
'let n <- sizeT d; ret (n != 1%N)) GRing.Bool.

(* Specifications: *)
Lemma ex_elim_seqP (ps : seq polyF) (q : polyF) (e : seq F) :
let gp := (\big[@rgcdp _/0%:P]_(p <- ps)(eval_poly e p)) in
qf_eval e (ex_elim_seq ps q) = (size (rgdcop (eval_poly e q) gp) != 1%N).
Lemma ex_elim_seq_qf  (ps : seq polyF) (q : polyF) :
all rpoly ps -> rpoly q -> qf (ex_elim_seq ps q).