proposition: Lemma int_abs_nat n : int_abs Z N (f n) = n.
proof: Proof. apply (injective f). destruct (int_abs_spec (f n)) as [[? E]|[? E]]; intuition. apply naturals.negate_to_ring. now rewrite E, involutive. 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