proposition: Lemma abs_nonneg_plus (x y : R) : 0 ≤ x → 0 ≤ y → abs (x + y) = abs x + abs y.
proof: Proof. intros Ex Ey. rewrite ?abs_nonneg; try easy. now apply nonneg_plus_compat. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.rings