proposition: Lemma abs_nonpos (x : R) : x ≤ 0 → abs x = -x.
proof: Proof. intros E. unfold abs, abs_sig. destruct (a x) as [z1 [Ez1 Fz1]]. auto. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.rings