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. apply nonneg_minus_compat;trivial. apply reflexivity. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.rings HoTT.Classes.orders.semirings