proposition: Theorem eqp_pluspf_com : forall p q r t, canonical A0 eqA ltM p -> canonical A0 eqA ltM q -> canonical A0 eqA ltM r -> canonical A0 eqA ltM t -> eqP A eqA n p r -> eqP A eqA n q t -> eqP A eqA n (pluspf p q) (pluspf r t).
proof: Proof. Proof using os multA minusA invA divA cs A1. intros p q r t H' H'0 H'1 H'2 H'3 H'4. apply (eqp_trans _ _ _ _ _ _ _ _ _ cs n) with (y := pluspf r q); auto. apply eqp_pluspf_com_l; auto. apply eqp_pluspf_com_r; auto. Qed.
imports: Coq(Arith) Buchberger(LetP)