Proof
fun x y
=> conj
(op_neg_distrib_inv_l x y)
(op_neg_distrib_inv_r x y).

(** Proves that negation is distributive: i.e. -(x + y) = -y + -x. *)
Theorem op_neg_distrib
:  forall x y : E, - (x + y) = - y + - x.