proposition: Lemma flip_nonneg_minus (x y : R) : 0 ≤ y - x ↔ x ≤ y.
proof: Proof. setoid_replace x with (0 + x) at 2 by ring. now apply flip_le_minus_r. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.semirings