Proof fun x => sum_inv_uniq 1 {-1} x E_n1_def.

(** Proves that -1 * x equals the multiplicative inverse of x.  -1 x + x = 0 -1 x + 1 x = 0 (-1 + 1) x = 0 0 x = 0 0 = 0 *)
Theorem prod_n1_x_inv_l
:  forall x : E, sum_is_inv_l x ({-1} # x).