proposition: Lemma int_abs_nonpos x : x ≤ 0 -> f (int_abs Z N x) = -x.
proof: Proof. intros E. rewrite <-int_abs_negate, int_abs_nonneg; auto. apply flip_nonpos_negate. 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