proposition: Lemma int_abs_nonneg_plus x y : 0 ≤ x -> 0 ≤ y -> int_abs Z N (x + y) = int_abs Z N x + int_abs Z N y.
proof: Proof. intros. apply (injective f). rewrite (preserves_plus (f:=f)), !int_abs_nonneg;auto. apply nonneg_plus_compat;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