proposition: Lemma abs_nonpos_plus (x y : R) : x ≤ 0 → y ≤ 0 → abs (x + y) = abs x + abs y.
proof: Proof. intros Ex Ey. rewrite ?abs_nonpos; trivial. ring. now apply nonpos_plus_compat. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.rings