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.

Lemma ex_elim_seq_qf  (ps : seq polyF) (q : polyF) :
all rpoly ps -> rpoly q -> qf (ex_elim_seq ps q).