proposition: Lemma hzeqeisi {i i0 : hz} (e : hzeq i i0) (e' : hzeq i (i0 + 1)) : empty.
proof: Proof. apply nopathstruetofalse. use (pathscomp0 _ (hzbooleqisi i0)). rewrite <- e'. rewrite <- e. apply (! (hzeqbooleqii i)). Qed.
imports: UniMath.Foundations.NaturalNumbers UniMath.MoreFoundations.PartA UniMath.MoreFoundations.NegativePropositions UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.Algebra.RigsAndRings UniMath.NumberSystems.NaturalNumbersAlgebra