proposition: Lemma le_iff_lt_S x y : x ≤ y ↔ x < 1 + y.
proof: Proof. rewrite commutativity. now apply le_iff_lt_plus_1. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.naturals MathClasses.interfaces.orders MathClasses.theory.naturals MathClasses.theory.rings MathClasses.implementations.peano_naturals MathClasses.orders.semirings