Proof
fun x H
=> (proj1 (op_inv_sym x ({-} x H))) (op_neg_def x H).

(** Proves that, forall x and H, where H is a proof that x has an inverse, `- x H` has an inverse.  Note: this lemma is a weakening of `op_neg_inv` and is used to apply the lemmas and theorems in this section to expressions involving `op_neg`. *)
Theorem op_neg_inv_ex
:  forall (x : M) (H : has_inv x), has_inv ({-} x H).