proposition: Lemma int_abs_negate x : int_abs Z N (-x) = int_abs Z N x.
proof: Proof. destruct (int_abs_spec x) as [[_ E]|[_ E]]. rewrite <-E at 1. now apply int_abs_negate_nat. rewrite <-E at 1. now apply int_abs_nat. 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