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