proposition: Lemma negate_to_ring x y : -f x = f y → f x = f y.
proof: Proof. intros E. destruct (to_ring_zero_sum x y E) as [E2 E3]. now rewrite E2, E3. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.implementations.peano_naturals MathClasses.theory.rings Coq.Arith.PeanoNat MathClasses.categories.varieties MathClasses.theory.ua_transference MathClasses.interfaces.naturals