intros Q x y z H'; elim H'; auto.
intros x0 y0 H'0 H'1 H'2.
apply reduceplus_eqp_com with (p := y0) (q := z); auto.
apply eqp_imp_canonical with (1 := cs) (p := x0); auto.
apply (eqp_sym _ _ _ _ _ _ _ _ _ cs n); auto.
intros x0 y0 z0 H'0 H'1 H'2 H'3 H'4.
apply Rstar_n with (y := y0); auto.
apply H'2; auto.
apply canonical_reduce with (1 := cs) (3 := H'0); auto.
Qed.

(* Specifications: *)
Theorem canonical_reduceplus :
forall (Q : list (poly A0 eqA ltM)) (p q : list (Term A n)),
reduceplus Q p q -> canonical A0 eqA ltM p -> canonical A0 eqA ltM q.