Definition foreigner : poly A0 eqA ltM -> poly A0 eqA ltM -> Prop.Definition foreigner_dec :
  forall a b : poly A0 eqA ltM, {foreigner a b} + {~ foreigner a b}.

Theorem foreigner_red : forall (a b : poly A0 eqA ltM) (P : list (poly A0 eqA ltM)), foreigner a b -> In a P -> In b P -> red (spolyp a b) P.