Proof
fun x H
=> proj2_sig (op_neg_strong x H).

(* Specifications: *)
(** Proves that, forall x and H, where H is a proof that x has an inverse, x is the inverse of `- x H`.  Note: this lemma is an immediate consequence of the symmetry of the inverse predicate. *)
Theorem op_neg_inv
:  forall (x : M) (H : has_inv x), op_is_inv ({-} x H) x.