proposition: Lemma between_nonneg (x : R) : 0 ≤ x → -x ≤ x.
proof: Proof. intros E. transitivity 0; trivial. now apply flip_nonneg_negate. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.semirings