proposition: Lemma to_ring_zero_sum x y : -f x = f y -> x = 0 /\ y = 0.
proof: Proof. intros E. apply zero_sum, (injective f). rewrite rings.preserves_0, rings.preserves_plus, <-E. apply plus_negate_r. Qed.
imports: HoTT.Basics.Decidable HoTT.Classes.interfaces.orders HoTT.Classes.implementations.peano_naturals HoTT.Classes.theory.rings HoTT.Classes.isomorphisms.rings HoTT.Classes.interfaces.naturals