proposition: Lemma int_to_nat_le_r x y : x ≤ y → x ≤ f (int_to_nat Z N y).
proof: Proof. intros E1. destruct (int_to_nat_spec y) as [[? E2]|[? E2]]. now rewrite E2. rewrite E2, preserves_0. now transitivity y. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.naturals MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.nat_int MathClasses.theory.integers MathClasses.theory.rings MathClasses.orders.rings