Definition genPcPf0 :
  forall (i : poly A0 eqA ltM) (aP R : list (poly A0 eqA ltM)),
  {Q : list (poly A0 eqA ltM) | genPcP i aP R Q}.Definition genPcPf :
  poly A0 eqA ltM ->
  list (poly A0 eqA ltM) -> list (poly A0 eqA ltM) -> list (poly A0 eqA ltM).

Theorem Cb_genPcPf : forall (b : poly A0 eqA ltM) (P Q R : list (poly A0 eqA ltM)), Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec b R -> (forall a : poly A0 eqA ltM, In a P -> Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec a R) -> (forall a : poly A0 eqA ltM, In a Q -> Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec a R) -> forall a : poly A0 eqA ltM, In a (genPcPf b P Q) -> Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec a R.