Proof sum_neg_rev 1 {-1} neg_1.

(** Proves that -1 * -1 = 1.  -1 * -1 = -1 * -1 -1 * -1 = prod -1 -1 -1 * -1 = - -1 -1 * -1 = 1 *)
Theorem prod_n1_n1
:  {-1} # {-1} = 1.