Proof
fun x H
=> proj2 (sum_neg_def x)
|| x + a = 0 @a by <- H
|| a = 0     @a by <- sum_id_r x.

(** Prove that 0 is the only element whose additive inverse (negation) equals 0. *)
Theorem sum_neg_0_uniq
:  unique (fun x => - x = 0) 0.