proposition: Theorem CombLinear_reduceplus : forall (Q : list (poly A0 eqA ltM)) (p q : list (Term A n)), reduceplus A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q p q -> canonical A0 eqA ltM p -> CombLinear Q q -> CombLinear Q p.
proof: Proof. Proof using os cs. intros Q p q H'0; elim H'0; auto. intros x y H' H'1 H'2. apply CombLinear_comp with (p := y); auto. apply (eqp_sym _ _ _ _ _ _ _ _ _ cs n); auto. intros x y z H' H'1 H'2 H'3 H'4. apply CombLinear_reduce with (q := y); auto. apply H'2; auto. apply canonical_reduce with (1 := cs) (3 := H'); auto. Qed.