intros aP R Q a b c H' H'0 H'1 H'2.
apply lem_redln_cons_gen with (Q := c :: Q); auto.
Qed.
Hint Resolve redln_cons_gen.

Theorem red_gen_in :
forall (a : poly A0 eqA ltM) (aP R Q : list (poly A0 eqA ltM)),
~
BuchAux.zerop A A0 eqA n ltM
(nf A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM ltM_dec os a
aP) ->
OBuch
(addEnd A A0 eqA n ltM
(nf A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM ltM_dec
os a aP) aP)
(genPcPf
(nf A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM ltM_dec
os a aP) aP Q) R ->
(forall b c : poly A0 eqA ltM, In b aP -> In c aP -> redIn b c aP (a :: Q) R) ->
forall b : poly A0 eqA ltM,
In b aP ->
~ BuchAux.zerop A A0 eqA n ltM b ->
redIn
(nf A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM ltM_dec os a
aP) b
(addEnd A A0 eqA n ltM
(nf A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM ltM_dec
os a aP) aP)
(genPcPf
(nf A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM ltM_dec
os a aP) aP Q) R.