Proof
fun x
=> sum_inv_uniq x (- x) (x # {-1})
(sum_neg_def x)
(prod_x_n1_inv x).

(** Accepts one element, x, and proves that -1 x equals the additive negation of x. *)
Theorem prod_n1_x_neg
:  forall x : E, {-1} # x = - x.