Proof Monoid.op_id op_monoid.
(** Accepts two group elements, x and y, and asserts that y is x's left inverse. *)
Definition op_is_inv_l := Monoid.op_is_inv_l op_monoid.
(** Accepts two group elements, x and y, and asserts that y is x's right inverse. *)
Definition op_is_inv_r := Monoid.op_is_inv_r op_monoid.

(** Proves that the left identity element is unique. *)
Theorem op_id_l_uniq
:  forall x : E, (op_is_id_l x) -> x = 0.