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]];trivial. apply naturals.negate_to_ring. rewrite E, involutive. trivial. Qed.
imports: HoTT.Classes.interfaces.naturals HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.orders.nat_int HoTT.Classes.theory.integers HoTT.Classes.theory.rings HoTT.Classes.theory.groups HoTT.Classes.orders.rings