auto.
Qed.
Inductive reds :
poly A0 eqA ltM -> poly A0 eqA ltM -> list (poly A0 eqA ltM) -> Prop :=
| reds0 :
forall (P : list (poly A0 eqA ltM)) (a b : poly A0 eqA ltM),
red A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec
(spolyp A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM
ltM_dec os a b) P -> reds a b P
| reds1 :
forall (P : list (poly A0 eqA ltM)) (a b c : poly A0 eqA ltM),
In c P ->
reds a c P ->
reds c b P ->
divp A A0 eqA multA divA n ltM
(ppcp A A0 A1 eqA plusA invA minusA multA divA cs n ltM a b) c ->
reds a b P.

Theorem reds_com :
forall (P : list (poly A0 eqA ltM)) (a b : poly A0 eqA ltM),
reds a b P -> reds b a P.