Remark lem_redln_cons_gen :
 forall (aP R Q : list (poly A0 eqA ltM)) (a b : poly A0 eqA ltM),
 In a aP ->
 In b aP ->
 redIn a b aP Q R ->
 forall (c : poly A0 eqA ltM) (Q1 : list (poly A0 eqA ltM)),
 incl
   (addEnd A A0 eqA n ltM
      (nf A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM ltM_dec
         os c aP) aP) R ->
 Q = c :: Q1 ->
 redIn a 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 c aP) aP) Q1 R.

Theorem OBuch_Inv : forall aP R Q : list (poly A0 eqA ltM), OBuch aP Q R -> (forall a b : poly A0 eqA ltM, In a aP -> In b aP -> redIn a b aP Q R) -> forall a b : poly A0 eqA ltM, In a R -> In b R -> reds a b R.