proposition: Lemma S_nat_1_plus x : S x ≡ 1 + x.
proof: Proof. reflexivity. Qed.
imports: Coq.Classes.Morphisms Coq.setoid_ring.Ring Coq.Arith.Arith_base Coq.Arith.PeanoNat MathClasses.interfaces.abstract_algebra MathClasses.interfaces.naturals MathClasses.theory.categories MathClasses.interfaces.additional_operations MathClasses.interfaces.orders MathClasses.orders.semirings