Proof
fun x
=> Monoid.op_neg_def op_monoid x (op_inv_ex x).

(** Proves that negation is one-to-one *)
(** 0 = 0 x + -x = 0 x + -x = y + -y x + -x = y + -x x = y *)
Theorem op_neg_inj
:  is_injective E E op_neg.