(**
  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.

Theorem op_id_uniq : forall x : E, (op_is_id x) -> x = 0.