Proof Monoid.op_inv_0_l prod_monoid.

(* Specifications: *)
(** Proves that the identity element is its own right inverse. *)
Theorem prod_inv_1_r
:  prod_is_inv_r 1 1.
(** Proves that the identity element is its own inverse. *)
Theorem prod_inv_1
:  prod_is_inv 1 1.
(** Proves that 1 is its own right multiplicative inverse. *)
Theorem recipr_1_r
:  prod_is_inv_r 1 1.