proposition: Lemma NType_succ_1_plus x : succ x = 1 + x.
proof: Proof. unfold_equiv. rewrite spec_succ, rings.preserves_plus, rings.preserves_1. now rewrite commutativity. Qed.
imports: Coq.Setoids.Setoid Bignums.SpecViaZ.NSig Bignums.SpecViaZ.NSigNAxioms Coq.NArith.NArith Coq.ZArith.ZArith Coq.Program.Program Coq.Classes.Morphisms MathClasses.interfaces.abstract_algebra MathClasses.interfaces.naturals MathClasses.interfaces.integers MathClasses.interfaces.orders MathClasses.interfaces.additional_operations