Proof
eq_refl ({-1} # {-1})
|| {-1} # {-1} = a @a by <- prod_n1_x_neg {-1}
|| {-1} # {-1} = a @a by <- neg_n1.

(** Proves that -1 is its own multiplicative inverse. *)
Theorem E_n1_inv
:  prod_is_inv {-1} {-1}.