Proof Ring.sum_inv_0_uniq ring.
(** Represents strongly-specified negation. *)
Definition sum_neg_strong
:  forall x : E, { y | sum_is_inv x y }
:= Ring.sum_neg_strong ring.
(** Represents negation. *)
Definition sum_neg
:  E -> E
:= Ring.sum_neg ring.
Notation "{-}" := (sum_neg) : commutative_ring_scope.
Notation "- x" := (sum_neg x) : commutative_ring_scope.
(** Asserts that the negation returns the inverse of its argument. *)
Definition sum_neg_def
:  forall x : E, sum_is_inv x (- x)
:= Ring.sum_neg_def ring.

(** Proves that negation is one-to-one *)
Theorem sum_neg_inj
:  is_injective E E sum_neg.