proposition: Lemma nonneg_minus_compat_back (x y z : R) : 0 ≤ z → x ≤ y - z → x ≤ y.
proof: Proof. intros E1 E2. transitivity (y - z); trivial. now apply nonneg_minus_compat. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.semirings